Hi this thread is actually devoted to Prince James and how we may be able to paradox the paradox so to speak.:)

It is best described by asking two comparative questions:
1]
How many infintesimally thin planes can be fitted into the volume of a 12 inch brick?
2]
How many zero thick planes can be fitted into the volume of a 12 inch brick?


Now by using the words infinitely thin we are granting according to Prince James an ultimately smallest thickness in that infinitely can not reduce to zero. So there fore at it's smallest point it must have thickness.
So therfore more zero thick planes by an infinite amount will fit into the volume of the 12 inch brick than planes that have thickness even if infinitely thin.
So therefore zero is the only value that can be legitimately used infinitely with in a given volume where as infinitely small can not be granted the same priviledge as the use becomes irrational or illogical.

The point being that the use of infinitey in these ways ends up always paradoxical.
My main arguement to Prince james is that infinitey is an absolute notion and cannot be in any way limited to a given stop point or finish point as in his time segmented arguement using zenos paradox as it's founding.

So if used commonly and in my opinoin incorrectly an infinite number of infinitely thin planes should fit into our 12 inch bricks volume.

And the same would apply to zero think planes but I would bet that zero thick planes would be a better use of infinity than infinitely thin. [ because no matter how thin you go an infinitely thin plane will always have thickness where as a zero thick plane does not. Thus infinity poses a paradox when qualified using words like "thin" or "small" or "slow"]

And thus it is worth debating I think to clarify this issue.
Care to discuss?
Could be fun!

I'll post the stuff I wrote in the other thread on this here, then ask you a question:

I do not ascribe to the reality of anything less than 3 spatial dimensions. But theoretically speaking, yes.

The difference, however, would be that infinitesimally small planes could produce a substantial plane which is non-infinitesimal together. A zero-dimensional plane in the 3rd dimension (a two dimensional plane) could never do so.

One would be "1 + 1" the other would be "0 + 0".

Now my question:

What is 0 * x, where x is any integer?

Now by using the words infinitely thin we are granting according to Prince James an ultimately smallest thickness in that infinitely can not reduce to zero.

Clearly this is a question of existence in the mathematical/Platonic sense versus existence in the physical sense, and so it is somewhat akin to arguing about angels on the heads of pins, or whether anyone can actually draw a "perfect circle". The point is, an infinitely thin plane exists in principle, and we can do thought experiments with it, and we can derive equations. The problem is that when we go into the lab to try and BUILD an infinitely thin plane, and do experiments on it, our equations are off by a bit. The bit that they're off by lets us know how good of an approximation we made in getting there.

James is correct because everything has a physical dimension, because it must be built out of atoms, which have some effective radius (if only due to the fact that they have some charge). So in some sense, there is no such thing as an infinitely thin plane. However, this does not preclude one from considering ideal solids or massless strings---this is what a physicist does, to avoid having to work with complicated equations.

Another example is to think in four dimensions. When you take a picture, you have a three dimensional slice of the four dimensions we live in. If the picture is infinitely good (i.e. corresponding to an infinite shutter speed in your camera, or something), you have an infinitely thin three dimensional slice of our universe.

Sorry to be boring, but this is akin to the question "how many real numbers are in the interval [0,1]"? We know that this interval is finite, but we also know it contains infinitely many real numbers.

This is an issue which crops up repeatedly on discussion fora - the confusion between the notion of an infinite number of elements in a finite interval, and the notion of an interval of infinite extension, say (-\infty, \infty).

A classic example is the frequent claim that \pi is infinite. True, it has, as far as one knows, an infinitely non-recurring decimal expansion. But it is most surely an element in the finite real open interval (3,4), and is therefore finite.

P.S As I have had a couple of beers, let me say this. There is a school of thought, which I discussed with D H in another thread, that says something like this; you say that \pi exists, but then, say I, unless you can write it out explicitly, digit by digit, then I am not obliged to accept that it exists.

This is, of course, a characterture of what is known as the "constructivist" view of mathematics. D H finds it repellent; I feel some sympathy with it it - but only some.....

P.S As I have had a couple of beers, let me say this. There is a school of thought, which I discussed with D H in another thread, that says something like this; you say that \pi exists, but then, say I, unless you can write it out explicitly, digit by digit, then I am not obliged to accept that it exists.

This is, of course, a characterture of what is known as the "constructivist" view of mathematics. D H finds it repellent; I feel some sympathy with it it - but only some.....
The problem I have with this view is that the same thing can pretty much be said for any infinite structure in mathematics. Considering, say, 1 as a real, you cannot "write it out explicitly, digit by digit" any more than you can with \pi - even though you have a recurrent pattern, there's no reason that one such recurrent pattern should count as real, and another not. Hell, even for finite structures, most of them will be so incomprehensively cumbersome in their naïve representations that the same impossibility of "writing out" applies.

Actually thinking on pi for the moment.
Pi is an infinite resolution to an equation. yes?

In other words pi is simply providing an infinite clarity to a given problem.
A perfect example of infinite reductionalism....ha IMO
a bit like comparing a 2 megpix image with a infinite megpix image that happen to have the same dimensions [ height X width ]

The problem that I see is that once you subscribe a value to the thiness of a plane that plane can not longer be used infinitely to fill a given volume.

So the process fails to work in reverse thus the supposed paradox.

ie.
We have a 12 inch long rectangular brick.
We decide that we can construct an infinitely thin plane.
How ever the question begs:
How many infinitely thin planes can fit into a 12 inch brick.

The answer IMO must be less that infinity.
So infinity in one direction fails in the other.
logically the only plane that can fit infinitely into the volume of a 12 inch brick must be zero thick. As soon as you subscribe thickness you no longer can use infinity as infinity is now limited.

re pi:
an interesting thought:

A given figure say 8.125 could be said to be absolutely resolved where as pi can not be said to be absolutely resolved.
Yet it must be... hmmmmm.......

so is pi a finite resolution afterall....? hmmmmm

Clearly this is a question of existence in the mathematical/Platonic sense versus existence in the physical sense, and so it is somewhat akin to arguing about angels on the heads of pins, or whether anyone can actually draw a "perfect circle". The point is, an infinitely thin plane exists in principle, and we can do thought experiments with it, and we can derive equations. The problem is that when we go into the lab to try and BUILD an infinitely thin plane, and do experiments on it, our equations are off by a bit. The bit that they're off by lets us know how good of an approximation we made in getting there.

James is correct because everything has a physical dimension, because it must be built out of atoms, which have some effective radius (if only due to the fact that they have some charge). So in some sense, there is no such thing as an infinitely thin plane. However, this does not preclude one from considering ideal solids or massless strings---this is what a physicist does, to avoid having to work with complicated equations.

Another example is to think in four dimensions. When you take a picture, you have a three dimensional slice of the four dimensions we live in. If the picture is infinitely good (i.e. corresponding to an infinite shutter speed in your camera, or something), you have an infinitely thin three dimensional slice of our universe.
I disagree as I tend to think that infinity is an imaginary concept and far from real. So the requirement that it be "physical" is not necessarilly true.

Sorry to be boring, but this is akin to the question "how many real numbers are in the interval [0,1]"? We know that this interval is finite, but we also know it contains infinitely many real numbers.

This is an issue which crops up repeatedly on discussion fora - the confusion between the notion of an infinite number of elements in a finite interval, and the notion of an interval of infinite extension, say (-\infty, \infty).

A classic example is the frequent claim that \pi is infinite. True, it has, as far as one knows, an infinitely non-recurring decimal expansion. But it is most surely an element in the finite real open interval (3,4), and is therefore finite.

P.S As I have had a couple of beers, let me say this. There is a school of thought, which I discussed with D H in another thread, that says something like this; you say that \pi exists, but then, say I, unless you can write it out explicitly, digit by digit, then I am not obliged to accept that it exists.

This is, of course, a characterture of what is known as the "constructivist" view of mathematics. D H finds it repellent; I feel some sympathy with it it - but only some.....

so maybe this sort of discussion has a sort of pi resolution in that it is infinitely unresolvable?!:)
actually all jokes aside I think this has been, will be and is the case...IMO

QH:


The answer IMO must be less that infinity.
So infinity in one direction fails in the other.
logically the only plane that can fit infinitely into the volume of a 12 inch brick must be zero thick. As soon as you subscribe thickness you no longer can use infinity as infinity is now limited.

Zero thick would never fit into the brick. 0 * 0 = 0.

Divide the brick infinitely and you will "eventually" get to infinitely small.

QH:



Zero thick would never fit into the brick. 0 * 0 = 0.

Divide the brick infinitely and you will "eventually" get to infinitely small.
The whole point with infinity is that you can never get to infinitely small because it is an infinite progression without time to an impossible to reach destination. IMO
it just keeps on getting smaller infinitely

Quantum Heraclitus:


The whole point with infinity is that you can never get to infinitely small because it is and infinite progression without time to an impossible to reach destination.

It is an ideal which can be referenced coherently. Furthermore, we know the answer from analytic means.

Quantum Heraclitus:



It is an ideal which can be referenced coherently. Furthermore, we know the answer from analytic means.
Exactly because infinity is an irrational notion. And once you apply a finite boundary or limitation which is excatly what you are doing it is no longer infinity but a finite infinity.

Quantum Heraclitus:


exactly because infinity is an irrational notion.

If it is coherent it is not irrational. Furthermore, it is not irrational in any other way - what about it do you find it irrational?


And once you apply a finite boundary or limitation which is excatly what you are doing it is no longer infinity but a finite infinity.

I am not giving a "finite limitation". An infinitesimal is beneath every number. Any given number is infinitely far from the infinitesimal.

try:
How big is an infinitely large sphere?
How deep is an infinitely deep ocean?
and apply the same logic to the infintely small and if not why not?

Quantum Heraclitus:


How big is an infinitely large sphere?

Infinitely large.


How deep is an infinitely deep ocean?

Infinite deep.


and apply the same logic to the infintely small and if not why not?

Infinitely small.

Quantum Heraclitus:



I am not giving a "finite limitation". An infinitesimal is beneath every number. Any given number is infinitely far from the infinitesimal.
Correction:
An infinitesimal is INFINITELY beneath every number.
imo

your infinitesimal segment can be divided infinitely again and again ad-infinitum as thsi is what infinity is...infinite:)
why stop at any given size?

you have a number say
.0000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000000000000000 and so on and it finishes with a number one at some point. This is still a finite number no matter how many decimal places we talk about.
an infinite progression cannot finish as that is why it is called an infinte progression

Quantum Heraclitus:


your infinitesimal segment can be divided infinitely again and again ad-infinitum as thsi is what infinity is...infinite
why stop at any given size?

No it cannot. It is the product of an infinite series of divisions (ideal). It has no size except "infinitely small".

To ape Wittgenstein: What is North of the North Pole? What is smaller than the infinitely small?


.0000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000000000000000 and so on and it finishes with a number one at some point. This is still a finite number no matter how many decimal places we talk about.

It is beneath all of those.

lim f(x)=1/x as x approaches infinity = 0
lim g(x)=x as x approaches infinity = infinity
lim f(x)*g(x) as x approaches infnity= 1

Apply to Ben's camera example:
x=Frames per second of camera
f(x)=exposure time of a single frame
g(x)=number of frames (assuming one shot immediatly after the other, think video camera) captured in a 1 second interval
f(x)*g(x)=temporal periode represented by these frames

Thus, as you can see, as we increase the rate of the shutter, we are still able to capture the entire periode of time even when the camera is so perfect so as to allow no exposure time whatsoever (an infinite number of frames per second.)

Contrarily, if I have a bunch of sheets, of thickness 0, the limit of the sum of all n=0 (thickness of each sheet) for i=0 to i=x (counting each sheet) as x approaches infinity, will always = 0. (That is, gathering more sheets will never give me a volume.)

You know, this question sounds like: "What's 0/0 ?"
I could argue that lim x/x as x approaches 0 = 1, and hence, 0/0=1
Or I could argue that lim 0/x as x approaches 0 = 0, and hence, 0/0=0. etc...

The answer of course to 0/0 is indeterminant: you need the context of the problem that the term appears in. Hence: perfect video cameras can make movies, but perfectly thin sheets can never form a brick.
Though, I could slice a brick into an infinite number of infnitly thin sheets which would have a volume equal to that of the original brick! (see the first set of equations, where x is the number of cuts, and go from there.)

But, back to what Ben originaly said, there is no such thing (physcialy) as a perfectly thin sheet, nor a perfect camera, etc... In physics and engineering, one compromises a certain degree of accuracy for simplicity. No need to drag the gamma factor into play if your measuring the length of time of a car ride, despite the fact that Newtonian mechanics are truly only valid when the speed is 0. In this case, we have said "The car is going so slow, that it's speed might as well be 0 for the purpose of computing gamma."

-Andrew

Quantum Heraclitus:



No it cannot. It is the product of an infinite series of divisions (ideal). It has no size except "infinitely small".

To ape Wittgenstein: What is North of the North Pole? What is smaller than the infinitely small?



It is beneath all of those.
the north pole is a finite resolution is it not, so nothing is beyond the finite resolution.

why limit infinity PJ?
as you are determining an impossible to determine value?

lim f(x)=1/x as x approaches infinity = 0
lim g(x)=x as x approaches infinity = infinity
lim f(x)*g(x) as x approaches infnity= 1

Apply to Ben's camera example:
x=Frames per second of camera
f(x)=exposure time of a single frame
g(x)=number of frames (assuming one shot immediatly after the other, think video camera) captured in a 1 second interval
f(x)*g(x)=temporal periode represented by these frames

Thus, as you can see, as we increase the rate of the shutter, we are still able to capture the entire periode of time even when the camera is so perfect so as to allow no exposure time whatsoever (an infinite number of frames per second.)

Contrarily, if I have a bunch of sheets, of thickness 0, the limit of the sum of all n=0 (thickness of each sheet) for i=0 to i=x (counting each sheet) as x approaches infinity, will always = 0. (That is, gathering more sheets will never give me a volume.)

You know, this question sounds like: "What's 0/0 ?"
I could argue that lim x/x as x approaches 0 = 1, and hence, 0/0=1
Or I could argue that lim 0/x as x approaches 0 = 0, and hence, 0/0=0. etc...

The answer of course to 0/0 is indeterminant: you need the context of the problem that the term appears in. Hence: perfect video cameras can make movies, but perfectly thin sheets can never form a brick.
Though, I could slice a brick into an infinite number of infnitly thin sheets which would have a volume equal to that of the original brick! (see the first set of equations, where x is the number of cuts, and go from there.)

But, back to what Ben originaly said, there is no such thing (physcialy) as a perfectly thin sheet, nor a perfect camera, etc... In physics and engineering, one compromises a certain degree of accuracy for simplicity. No need to drag the gamma factor into play if your measuring the length of time of a car ride, despite the fact that Newtonian mechanics are truly only valid when the speed is 0. In this case, we have said "The car is going so slow, that it's speed might as well be 0 for the purpose of computing gamma."

-Andrew
so the use of the notion infinity is always paradoxical. damned if you do and damned if you don't sort of thingo...

PJ,
What makes something finite in the contrext of our discussion?
How is finite different from infinite?

Quantum Heraclitus:


the north pole is a finite resolution is it not, so nothing is beyond the finite resolution.

The analogue to the infinitely small still stands. To ask "what is smaller than that which is smallest?" is irrational when the answer to "the smallest" is "infinitely small".


why limit infinity PJ?
as you are determining an impossible to determine value?

I've given a value: More than nothing, less than any (other) number. The product of infinite division.


What makes something finite in the contrext of our discussion?
How is finite different from infinite

Any finite number is countable given finite time.

Any infinite number is not countable given finite time.

Though, I could slice a brick into an infinite number of infnitly thin sheets which would have a volume equal to that of the original brick! (see the first set of equations, where x is the number of cuts, and go from there.)
You will notice by rereading the OP that I am not asking how many slices make a brick. I am asking how many slices can fit into the volume of a brick.

This is a big difference.
If you give a slice a given thinness then a finite number of slices will fit into the volume of the brick? yes?
If you quantify infinity to a given thinness then this is what you are doing applying a finite value to and infinite value. Therefore PJ's infitesimal smallest segment [slice] will not fit within the volume infinitely as the segment [slice] is no longer infinitely small as he has clearly stated that it is the smallest one can go. Therfore it is finite and not infinite.

If you give a slice zero thickness then there is no doubt that an infinite number of slices would fit into the volume of a brick.

An infinitely small slice will fit infinitely also as long as it is never quantified as being the smallest.

Is this arguement logical?
Is it rational?

If not why not?

The relevance to Zeno's metaphor IMO is that the hare may never overtake the tourtise but he has to keep trying to do so. A soon as he stops trying the paradox fails. And the solution becomes finite.

In philosophy this is why perfection can never be achieved or a perfect circle can never be drawn but the trying to do so is what counts.

Quantum Heraclitus:


If you give a slice zero thickness then there is no doubt that an infinite number of slices would fit into the volume of a brick.

Actually, you'd never reach the thickness of the brick: 0 * 0...


The relevance to Zeno's metaphor IMO is that the hare may never overtake the tourtise but he has to keep trying to do so. A soon as he stops trying the paradox fails. And the solution becomes finite.

If he stop trying, then he fails.

Quantum Heraclitus:



Actually, you'd never reach the thickness of the brick: 0 * 0...



If he stop trying, then he fails.
re- read post 27
not interested in making a brick...just how many slices can fit into the volume of a brick

Quantum Heraclitus:


If you quantify infinity to a given thinness then this is what you are doing applying a finite value to and infinite value. Therefore PJ's infitesimal smallest segment [slice] will not fit within the volume infinitely as the segment [slice] is no longer infinitely small as he has clearly stated that it is the smallest one can go. Therfore it is finite and not infinite.

It is infinitely small: It is smallest than any number, but larger than zero. Any number/infinity = infinitely small. As such, you're wrong that there'd be a finite amount within any finite segment. No, there'd be an infinite amount of these slices.


An infinitely small slice will fit infinitely also as long as it is never quantified as being the smallest

That is absurd: It would have to be smallest in order to be infinitely small.

I think I'll have another beer.

What brand?

rather a malt whiskey my self....but beer is good

So in the year 2100 are we still going to be debating this issue?
If yes then this is good and helps prove infinity. If no then the hare has given up....:D
yeah I know we should be both dead and buried and that is exactly my point...

So in the year 2100 are we still going to be debating this issue?
If yes then this is good and helps prove infinity. If no then the hare has given up....

BA DUM DUM PSHHHHHHHHHH! *Rimshots.*

back in 6 hours for more....uhm....fun:)

Alright, the problem is, that you have ill-defined the problem.

Prince James is talking about slices of 0 thickness, while Quantum Quack is talking about slices of infinite thinness. There is a difference.
Slices of 0 thickness always have 0 volume, no matter how many you have, because they have been defined in 2-dimensional space
While slices of infinite thinness have a non-zero volume, as the number of sheet's approaches infinity, because they have been defined in three dimensional space.

The former is a single limit, the latter is a 2-limit problem for multivariable calculus.

Try creating a more meaningfull situation.
-Andrew

I would like to introduce Information Theory, and the definition of the clear and defineable difference between data and information.

In this stuation we seek to garner knowledge on how many slices of immesurably small size will fit into a measurably hefty 12" brick. Conversely, given that we at all wish to come to a helpful number, however mindblowingly large, that the brick must, by the end of the thought experiment, be divided. Such is this a criteria for finding information from the given data, and that unless we dont care whether we find the answer, that the size of the slice must conform and equal x>0 and hence a foreseeable answer will arise...

BUT if in fact we dont actually care and that one (1) is in fact indefinite (say 1.000... recurring to the nth and utterly unhelpful degree) then even if one were to ask how many inches are there along a 12" brick we must answer "I dont care.". Seeing as this makes total sense, most teenagers are actually the universal equivalent to God, who clearly does not care the slightest whether a brick has any decisive power over its fate... which IMO is highly maleveolent.

Seeing this my heart felt a twang and i wanted to care about the 12" brick and so thought, if 1=1 in any sense that x=x then 1 [x] must be a defineable answer. And given so, maintaining clear reasoning and the will to live... we MUST have an answer.

For if not the poor little brick doesnt actually exist. And nor do we.

...

I'm going to go smoke some opium now, Benjimania.

possibly the issue could be better led to a conclusion this way.

we have two knifes, both with infinitely sharp edges on one length
we butt the two infinitely sharp edges together so that they touch like so ><

Now is the space between them zero or infinitely small?

By using this thought experiment we can define that zero = < infinity
However if there is infinitesimal space between our knives we have just proved that zero doesn't exist.

You could do the same using an alternating frequency.
Where by the signal must pass though zero to change polarity. + 0 - 0 + 0 - 0 +

Quantum Quack:


Now is the space between them zero or infinitely small?

If they are touching there is no space between them.

By using this thought experiment we can define that zero = < infinity
However if there is infinitesimal space between our knives we have just proved that zero doesn't exist.No, you would demonstrate nothing.

Mathematically, 0 exists. It's a well defined concept. All groups, rings, fields, modules and vector fields have an element analogous to zero. The Reals are an example of a field.

All of your results in your thought experiment would rest on mathematical results, you cannot use it to prove the results it relies on.

For instance, how close can the edges of your knives be? Well you're asking "Is there a smallest positive Real", call it A, such that the distance from the points of the blades cannot be smaller than A.

The answer is no. The Reals are a field. Therefore for real x and y, (x+yB)/2 is a Real. The Reals are also orderable, so you end up, assuming x<y with x<(x+y)/2 < y. Basically the average of two different numbers is between them. So let x=0 and y=A and you get that 0 < A/2 < A. Pretty obvious stuff, but it's not true in general for things which are not fields, since if you're working over the integers (a group under addition) then if x=0 and y=1, 1/2 isn't an integer.

This also leads you to 0.9r=1, because if they aren't equal then there's a number between them, since by 0.9r<1 you have that 0.9r<(0.9r+1)/2 < 1. You can see from decimal expansions that no such number exists.

Quantum Quack:



If they are touching there is no space between them.


So if we have two of your infinitesimal time segments and consider them to be analoguous with the knives would you agree that nothing or zero separates those time segments?

The next question is if both knives are infinitely sharp and we agree that if they are touching and the separating distance is zero then what is there to prevent us from claiming them to be one object [knife] instead of two objects?
If zero is separating them then they are one are they not?
Yet we definitely have two knives yes?


Proposition:
The only thing keeping them as two objects instead of one is our pre-conceptions and therefore our imaginations.

[re: body/mind problem. dualism in reflection - how far are the mirrors apart sort of issue]
The the light cone diagram below
I ask :

Are the two cones touching in the center as with the knives gendanken.
Is your answer the same?
That if they are touching the separation is zero?

http://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/481px-World_line.svg.png

So what is the time duration of the imaginary point between past and future?
[given your answer to the two knives gendanken.]

"Can you have a past without a future?
Can you have a future with out a past?
Are the cones really demonstrating mathematicaly an event horizon of potentiality at their center?
Are they one or are they two?"

As an aside:
Is not the mind/body problem/solution in philosophy exactly the same?
The being or entity only has potential if both the mind and body are present as one yet retain their separation.
Using the diagram:
label the observer as "entity"
label the future cone as "mind" - motivation
label the past cone as "body" -temporal and passive

No, you would demonstrate nothing.

Mathematically, 0 exists. It's a well defined concept. All groups, rings, fields, modules and vector fields have an element analogous to zero. The Reals are an example of a field.

All of your results in your thought experiment would rest on mathematical results, you cannot use it to prove the results it relies on.

For instance, how close can the edges of your knives be? Well you're asking "Is there a smallest positive Real", call it A, such that the distance from the points of the blades cannot be smaller than A.

The answer is no. The Reals are a field. Therefore for real x and y, (x+yB)/2 is a Real. The Reals are also orderable, so you end up, assuming x<y with x<(x+y)/2 < y. Basically the average of two different numbers is between them. So let x=0 and y=A and you get that 0 < A/2 < A. Pretty obvious stuff, but it's not true in general for things which are not fields, since if you're working over the integers (a group under addition) then if x=0 and y=1, 1/2 isn't an integer.

This also leads you to 0.9r=1, because if they aren't equal then there's a number between them, since by 0.9r<1 you have that 0.9r<(0.9r+1)/2 < 1. You can see from decimal expansions that no such number exists.
I am sorry Alpha but my math skills fall way too short to fully appreciate your description. I do though believe it to be articulate. In summary though what are you saying?

You cannot apply physical constraints to a mathematical system. There are no infinitesimals in physics.

An example of your 'infinitely sharp knife' would be f(x) = |x|. No matter how much you zoom into x=0 you find it's a perfect wedge. So what about the two functions f(x) = |x| and g(x) = -|x|. They touch at one and only one point, (0,0).

And your comments about the mind and body are completely unsupported. Nothing in the maths relates to that, you are attempting to justify an unjustified claim by giving it superficial trappings of mathematical rigour, when it has none. Put bluntly, you'd 'doing a Reiku'.

You cannot apply physical constraints to a mathematical system. There are no infinitesimals in physics.

An example of your 'infinitely sharp knife' would be f(x) = |x|. No matter how much you zoom into x=0 you find it's a perfect wedge. So what about the two functions f(x) = |x| and g(x) = -|x|. They touch at one and only one point, (0,0).

And your comments about the mind and body are completely unsupported. Nothing in the maths relates to that, you are attempting to justify an unjustified claim by giving it superficial trappings of mathematical rigour, when it has none. Put bluntly, you'd 'doing a Reiku'.

Actually I agree in a way that I am, however I am not using mathematics as a proof but merely as a metaphor or analogue.
As mathematics already is.

In philosophy there are many similarities for example zero, relative zero, infinity and so on...

For example of analoguous use:
pete agrees with Sam [ p = S]
however P is not the same as Sam etc etc you get the idea...
IMO reality is the only proof, as everything else such as philosophy and mathematics is merely abstraction and and only "mind" tools to help achieve and change reality.

So in my defense I am not seeking mathematical justification but merely mathematical analogues.

However your summation helps proves my point regarding the issue of infinitesmal and zero [ as an analogue and in abstraction ] and I appreciate your effort.

You cannot apply physical constraints to a mathematical system. There are no infinitesimals in physics.


I agree and this is exactly my issue with PJ use of an infinitesmal time moment of actual dimensions. He has applied limitations to a mathematical system and thus limited the use of infinity.

Quantum Heraclitus:


So if we have two of your infinitesimal time segments and consider them to be analoguous with the knives would you agree that nothing or zero separates those time segments?

Yes, there is nothing that separates past from present, or present from future.


The next question is if both knives are infinitely sharp and we agree that if they are touching and the separating distance is zero then what is there to prevent us from claiming them to be one object [knife] instead of two objects?
If zero is separating them then they are one are they not?
Yet we definitely have two knives yes?

Touching does not imply oneness. The knives are still very much real on their own.


Are the two cones touching in the center as with the knives gendanken.
Is your answer the same?
That if they are touching the separation is zero?

No. There are three things in play: Past, present, and future.


So what is the time duration of the imaginary point between past and future?
[given your answer to the two knives gendanken.]

It isn't imaginary: It is real. It is the present. It is infinitesimal in duration, as I have answered before.


"Can you have a past without a future?

You can discuss only present and past, so yes.


Can you have a future with out a past?

No. A future point depends on past points for its existence.


Are the cones really demonstrating mathematicaly an event horizon of potentiality at their center?
Are they one or are they two?"

They are three.

If we accept your proposition that time has no real segments, then we must conclude that Kettle A and Kettle B boil at the same time.

Quantum Heraclitus:



Yes, there is nothing that separates past from present, or present from future.



Touching does not imply oneness. The knives are still very much real on their own.



No. There are three things in play: Past, present, and future.



It isn't imaginary: It is real. It is the present. It is infinitesimal in duration, as I have answered before.



You can discuss only present and past, so yes.



No. A future point depends on past points for its existence.



They are three.

If we accept your proposition that time has no real segments, then we must conclude that Kettle A and Kettle B boil at the same time.
OK thats it for me...Thanks PJ and others I can see we have no where to go with this discussion....

Suddenly the two knives have gone from a zero separation to an infinitesimal separation. If the separation is zero then why are they not one? The answer is obvious.

The light cones have a zero separation as described by AE and others, yet PJ you require the separation of past and future to have an infinitesimal separation without adequately supporting the notion. As the two cones have zero separation we have a the ability to label the whole thing as "time" and notice I do not use the plural "times"

I have attempted to clarify a good arguement to the contra but obviously have failed to convey it in a way that makes sense.
If the cones are separated by an infinitesimal duration then the whole of science is effectively in deep shit. IMO

I already hold that SRT has problems etc but in this regard, AE and those that subscribe to e=mc^2 have got it totally correct.
So PJ, I guess you shall have to take your arguement to someone else....

Maybe someone else would like to explain what would happen if the two lightcones had an infinitesimal gap between them called the NOW. As far as I am concerned I have other things to do...

Quantum Heraclitus:


Suddenly the two knives have gone from a zero separation to an infinitesimal separation. If the separation is zero then why are they not one? The answer is obvious.

Because they are touching - not one. Touching is a distinct phenomenon. Are A and B the same? They touch. There is no space between them.

I shbll endebvour to replbce "b" with "b" for one sentenbce.


The light cones have a zero separation as described by AE and others, yet PJ you require the separation of past and future to have an infinitesimal separation without adequately supporting the notion. As the two cones have zero separation we have a the ability to label the whole thing as "time" and notice I do not use the plural "times"

Light cones have a zero separation? This impossible. The present moment is real - it is not imaginary. It is here, right now, where we are standing, doing, et cetera, all the time. In fact, many presents past by in a second of awareness. AE cannot have meant the present did not exist - if so, we might commend his works to the flames for such blatant absurdities (which I do not believe that spectacular mind ever intended).

If it is not infinitesimal, then it doesn't exist. As such, we are left with absurdity after absurdity of a time continuum made up of one moment, with no past or future, as it has nothing to build on. 0 + 0 + 0 = 0.


I have attempted to clarify a good arguement to the contra but obviously have failed to convey it in a way that makes sense.
If the cones are separated by an infinitesimal duration then the whole of science is effectively in deep shit. IMO

I contend the exact opposite: You would have kettles which are indistinguishable from one another.

Quantum Heraclitus:



Because they are touching - not one. Touching is a distinct phenomenon. Are A and B the same? They touch. There is no space between them.

I shbll endebvour to replbce "b" with "b" for one sentenbce.



Light cones have a zero separation? This impossible. The present moment is real - it is not imaginary. It is here, right now, where we are standing, doing, et cetera, all the time. In fact, many presents past by in a second of awareness. AE cannot have meant the present did not exist - if so, we might commend his works to the flames for such blatant absurdities (which I do not believe that spectacular mind ever intended).

If it is not infinitesimal, then it doesn't exist. As such, we are left with absurdity after absurdity of a time continuum made up of one moment, with no past or future, as it has nothing to build on. 0 + 0 + 0 = 0.



I contend the exact opposite: You would have kettles which are indistinguishable from one another.

No not a correct assessment.
However if we subscribe to your infinitesimal moments the universe would cease to change nor would we be able to move as every moment is a moment of stasis....with out any ability to change.
In which moment is there change PJ and if all moments have change then they must have time and if every moment has change then each moment must have a past and a future and ..you guessed it....a zero duration point in between.

SO my last question for you on this subject is:

When does movement occur if every moment is static or in stasis?

Light cones have a zero separation? This impossible. The present moment is real - it is not imaginary. It is here, right now, where we are standing, doing, et cetera, all the time. In fact, many presents past by in a second of awareness. AE cannot have meant the present did not exist - if so, we might commend his works to the flames for such blatant absurdities (which I do not believe that spectacular mind ever intended).
The present moment is a continous event horizon that is ungoing constant and continuous change. of course it is real but at the same time it is zero duration [ stasis ] It has no stasis. IT is a continuum. And most importantly, IT is a continuum of change. [thus the expression Time Continuum]

what else can I say?
AE's work is fine...it is in the interpretation that needs to go to the flames....and unfortunately your interpretation needs a thorough burning...:)

The whole of SRT and reality relies on energy being in continuous flow with out stasis of any description.
In fact all energy systems require it.

Just need to get your head around the idea of a continuous event horizon.
[like watching a continuous sunrise or clouds continuously streaming off the horizon towards you]

An example of your 'infinitely sharp knife' would be . No matter how much you zoom into x=0 you find it's a perfect wedge. So what about the two functions f(x) = |x| and g(x) = -|x|. They touch at one and only one point, (0,0).
to quote Alpha's contention, which I find to be very appropriate.

Quantum Heraclitus:


No not a correct assessment.
However if we subscribe to your infinitesimal moments the universe would cease to change nor would we be able to move as every moment is a moment of stasis....with out any ability to change.

Not at all. Time is eternal. Possibilities in the present propel the necessity of the next moment ad infinitum. Every moment may be static, but every moment is necessitated by the ones prior and necessitates the ones after.


In which moment is there change PJ and if all moments have change then they must have time and if every moment has change then each moment must have a past and a future and ..you guessed it....a zero duration point in between.

Change is a result of comparison of two moments in time. There is no change in any moment.


SO my last question for you on this subject is:

When does movement occur if every moment is static or in stasis?

Movement is the comparison of one moment to another. It is caused by the possibilities.

bah! sorry I m out of here.....

my moment is calling me....
and my moment is sending me
to where oh where I shall never know
except as a memory:):D

Quantum Heraclitus:


The present moment is a continous event horizon that is ungoing constant and continuous change. of course it is real but at the same time it is zero duration [ stasis ] It has no stasis. IT is a continuum. And most importantly, IT is a continuum of change. [thus the expression Time Continuum]


You cannot have zero duration and it existing. This is a contradiction of terms.


The whole of SRT and reality relies on energy being in continuous flow with out stasis of any description.
In fact all energy systems require it.

Not at all. Your system would have no movement whatsoever, as time has no meaning. Again: We have kettles which are equal to one another.

Quantum Heraclitus:



You cannot have zero duration and it existing. This is a contradiction of terms.



.
which is why I have claimed that we and Mass are temporal. Which is why mass exists in the first place

Quantum Heraclitus:


which is why I have claimed that we and Mass are temporal.

Which I am frankly sorry, my good man, but it is a very wrong headed theory at this point.

Quantum Heraclitus:



Which I am frankly sorry, my good man, but it is a very wrong headed theory at this point.

Hi P_J; QQ.

I believe what he is claiming is that a mind can effect another mind and at a high level. I am not aware of this high level in your conversations, however, I am aware I think of what he is proposing.

That said, is there anything left I can say?
What I believe he is saying is
one That if the body is the source of life
two That if minds exist only as memory
three If all of these things can be concieved of at a certain extent and proven to be true then the mind in this way is shown to allow certain break outs.
Just an opinion okay?
But durring these statements being proved what will happen is you'll find of course he is thinking that and knows sincerely that telepathy is real. That is another thread once again. Perhaps I should start that thread. Of course QQ will likly not post as I am currupting his valid data by even posting this right here... *pant*
If he can read your mind and go inside of you to do things to your body then it is a for sure thing that physics is having a lot on it's hands.

:eek:

(irrelevant post)

deleted voluntarilly with appologies

Hi P_J; QQ.

I believe what he is claiming is that a mind can effect another mind and at a high level. I am not aware of this high level in your conversations, however, I am aware I think of what he is proposing.

That said, is there anything left I can say?
What I believe he is saying is
one That if the body is the source of life
two That if minds exist only as memory
three If all of these things can be concieved of at a certain extent and proven to be true then the mind in this way is shown to allow certain break outs.
Just an opinion okay?
But durring these statements being proved what will happen is you'll find of course he is thinking that and knows sincerely that telepathy is real. That is another thread once again. Perhaps I should start that thread. Of course QQ will likly not post as I am currupting his valid data by even posting this right here... *pant*
If he can read your mind and go inside of you to do things to your body then it is a for sure thing that physics is having a lot on it's hands.

:eek:

(irrelevant post)
Sisyphus,
I have not been talking about anything else but the what was stated in the OP with the exception that we have included time instead of just mass .

I am not discussing Zero Point Theory and if anything I am attempting to help PJ get over his incredible use of infinity. [ unfortunately I have failed and will learn from the experience]

deleted voluntarilly with applogies

You cannot have zero duration and it existing. This is a contradiction of terms.
It certainly isn't a contradiction in terms. And event horizon that exists between future and past is in continuous change which is why it exists as we see it [ duh continuous change is what we see is it not] all you are doing is highlighting your inability to understand what a continuous event horizon is. if the change is not continuous then the universe would cease to exist. As once you stop energy from moving therfore changing it is over red rover.

Which is exactly what the light cones decribe. [ quite correctly imo]

Now if you can't get your head around the logic of a continuous event horizon that has zero stasis [ therefore the point at the horizon has zero duration] then that's a problem you gotta work on...
Of course if you are fixated on an "infinitesimal time segment" then you will never be able to get your head around it. Remember the story about the natives and the tall ships that they failed to see due to preconceptions..well a bullet in the head fixed that one...
You see I understand your position and have declined to agree because it is unworkable therefore unexplainable however you have failed to indicate any understanding of the light cones so it is little wonder you cannot grasp any of what I am saying.

I look forward to your explanation of how possibilities just "miraculously" appear when according to you every time moment for all of eternity is static and unchanging.

Sisyphus:

Yeah, at this point, I don't think that QH is doing anything regarding mind. You shold make anothre thread about that, though.

Quantum Heraclitus:


It certainly isn't a contradiction in terms. And event horizon that exists between future and past is in continuous change which is why it exists as we see it [ duh continuous change is what we see is it not] all you are doing is highlighting your inability to understand what a continuous event horizon is. if the change is not continuous then the universe would cease to exist. As once you stop energy from moving therfore changing it is over red rover.

How can something with zero duration have change? Change takes place over long time spans.


I look forward to your explanation of how possibilities just "miraculously" appear when according to you every time moment for all of eternity is static and unchanging.

Possibilities propel time along by virtue of the necessity of possibilities (in order to be possible) to manifest. As not all probabilities can exist at any given time (water cannot be ice, water, or steam at once) it requires more than one instance. As such, time is the unravelling of possibilities ad eterniam (as somethingness cannot vanish and if once possible than it always is). Time is what permits space to undergo change. Without it, existence would be an eternal frozen picture.

Moreover, possibilities are needed because infinity (which is made up of an infinite amount of parts) is prior to finiteness (in as much as existence as such is infinite).

Quantum Heraclitus:



How can something with zero duration have change? Change takes place over long time spans.



have already explained how.....

How can something with zero duration have change? Change takes place over long time spans.
define your use of "long time spans" before I go onto a rant.

Quantum Quack:


define your use of "long time spans" before I go onto a rant.

At least two moments.

There is no change in one moment. The next moment will have some change from the first one, though.

Two moments = minimum of change. Most real change, however, occurs over an unimaginable amount of moments. Throwing a baseball, for instance.

so assuming a photon travels across vacant space how many segments of the photons travel are there. Or should I ask instead :
Do you think the photon stops and starts through it's journey across space?

Quantum Quack:



At least two moments.

There is no change in one moment. The next moment will have some change from the first one, though.

Two moments = minimum of change. Most real change, however, occurs over an unimaginable amount of moments. Throwing a baseball, for instance.
and where did you dig this stuff up James, sounds facinating....

Quantum Heraclitus:


so assuming a photon travels across vacant space how many segments of the photons travel are there. Or should I ask instead :
Do you think the photon stops and starts through it's journey across space?

It doesn't stop and start. It goes through sequences of moments.

The movement is uniform, but time is made up of segments.


and where did you dig this stuff up James, sounds facinating....

If a moment of time = space then it requires two moments in order to have change (as space cannot change in one moment).

Quantum Heraclitus:



It doesn't stop and start. It goes through sequences of moments.

The movement is uniform, but time is made up of segments.



If a moment of time = space then it requires two moments in order to have change (as space cannot change in one moment).
and you believe this to be absolutely true? Yes?

Quantum Heraclitus:


and you believe this to be absolutely true? Yes?

I am convinced of it, yes. I have no doubts, but I am open to refutation.

How can movement be uniform if it is made up of static moments? just curious

Quantum Heraclitus:


How can movement be uniform if it is made up of static moments?

It never "skips" space. It is continuous - it is a flow. The infinitesimal moments of time are simply the smallest segments of time and change that it goes through it. In essence: It is very single "step" of the way.

I'll make a suggestion,

that we both contribute to a thread that asks the board to make a comparative assessment.
Your static momento and my continuum of change via an event horizon...using the light cones as an example...

what do ya think?

Quantum Heraclitus:


that we both contribute to a thread that asks the board to make a comparative assessment.
Your static momento and my continuum of change via an event horizon...using the light cones as an example...

what do ya think?

To be quite honest, I see no rational reason to do as such. Votes do not determine reality and winning such means nothing.

This is the fallacy of appealing to the gallery. I'm not primarily interested in winning games of popular opinion. If anything, I am opposed to it for moral reasons.

If you really really really want to do it, I'll do it. But I see no reason. If we do it, however, I'd ask that we both write up exactly what we are postulating. Interpretations necessarily are biased. But again, I do not want to do it.

Quantum Heraclitus:



To be quite honest, I see no rational reason to do as such. Votes do not determine reality and winning such means nothing.

This is the fallacy of appealing to the gallery. I'm not primarily interested in winning games of popular opinion. If anything, I am opposed to it for moral reasons.

If you really really really want to do it, I'll do it. But I see no reason. If we do it, however, I'd ask that we both write up exactly what we are postulating. Interpretations necessarily are biased. But again, I do not want to do it.
what say we just think on it for a while hey?:)
but until we do I see no point in continuing this discussion....do you?

Quantum Heraclitus:


but until we do I see no point in continuing this discussion....do you?

You were evidently leading yourself to a point based on my answers to your questions.

Don't you have one to make still?

And I'll give it some thought and get back to you. It is just rather meaningless to me to appeal "to the mob".

Quantum Heraclitus:



You were evidently leading yourself to a point based on my answers to your questions.

Don't you have one to make still?

And I'll give it some thought and get back to you. It is just rather meaningless to me to appeal "to the mob".
yeah I guess I do...as usual...ha

There was a book published years ago with the title:
"All the things I need to know I learned in Kindergarten"
it was a book used in the highschool reading list year 11 I think.
I often think back to it when I get into situations like this one.
I remember one of the most important lessons in life that one can learn is the lesson of futility.

To know when it is futile to proceed and when it is not. A two year old child throwing a tantrum on a supermarket floor is an example of such learning in progress.
To continue this discussion with out peer review is one such occassion.
there I made a point....

I don't see how our argument would change with other people voting?

Are you seriously expecting reality to be demonstrated by vote?

Anyway, yes, if you think this is futile, let us be done with it.

I have to go for several hours anyway. I shall post in 7+ hours from now.

Farewell for now.

I don't see how our argument would change with other people voting?

Are you seriously expecting reality to be demonstrated by vote?

Anyway, yes, if you think this is futile, let us be done with it.

I have to go for several hours anyway. I shall post in 7+ hours from now.

Farewell for now.
never mentioned anything about a vote....nothing to do with popularity and ego but all to do with good thinking and scientific process.

bye

Quantum Heraclitus:


never mentioned anything about a vote....nothing to do with popularity and ego but all to do with good thinking and scientific process.


that we both contribute to a thread that asks the board to make a comparative assessment.

What's this but a vote?

Quantum Heraclitus:





What's this but a vote?
a vote for what?

Just requesting other intellects to apply their knowledge and skills to this issue.

I know for example that most persons fail to understand the light cones and in making their comparitive mathematical assessments we could all learn something about them.

Also in the process we would see mathematical approach to your infitesimal time segment issue.
Also in the process you may come to understand how a continuously changing event horizon even though generating a continuous event of zero duration can still present what we experience around us daily.

I'm not especially interested in spectating/contributing to a huge debate on the matter. It is frankly something which would be too much to handle and I don't especially see as very fruitful.

We'll have two sides. One will support mine, the other yours. If it is as intractable as between us, we'd get no where. I also don't suppose much support will be drummed up on either side.

I'm not especially interested in spectating/contributing to a huge debate on the matter. It is frankly something which would be too much to handle and I don't especially see as very fruitful.

We'll have two sides. One will support mine, the other yours. If it is as intractable as between us, we'd get no where. I also don't suppose much support will be drummed up on either side.
Of course it would not be fruitful as you have quoted:

Quantum Heraclitus:


“ and you believe this to be absolutely true? Yes? ”

I am convinced of it, yes. I have no doubts, but I am open to refutation.

There is no way any one no matter how incorrect you may be is going to change your position.

Doubt is always necessary, in the right balance of course, but once I hear "I have no doubt what so ever" then that is when I reach for my book about futility.:) and notes on psychiatry.

Am I wrong in my assessment of the situation....most probably and not only am I open to refutation I am open to change. Which is why I post to these fora any ways.

Quantum Heraclitus:


There is no way any one no matter how incorrect you may be is going to change your position.


I am convinced of it, yes. I have no doubts, but I am open to refutation.

Read the bold carefully, my good man.

Quantum Heraclitus:


I am convinced of it, yes. I have no doubts, but I am open to refutation.

Read the bold carefully, my good man.
yes I read " you are open to arguement to the contrary but that does not mean you would change your position regardless of that arguements validity.

So far science is telling you that the light cones are touching.

You have agreed that if the infinitely sharp edges of two similar analogues are touching the separation is zero.

Then you state that the light cones cannot be touching as the present would not exist if the separation between past and future was zero. [ contradiction #1]

I say that it can exist and am willing to explain how this is so as an event horizon of continuous change. You have declined to accept the offer.

You refuse to entertain the possibility that the Light Cones are right therefore fly in the face of conventional and well accepted science.

And you say you are open to refutation....[contradiction #2] .....sorry but this has proved not to be the case...at least not when talking with me on the subject.

Which is why I suggested a peer assessment [ to remove me from the situation], which again you decline to participate in....so


......what is a person supposed to think?

Possibly if your were able to put aside your strongly held belief and deal with the problem in abstraction you may find that the light cones offers a considerably more efficient alternative to infinitesimal time segmentation.

Quantum Heraclitus:


yes I read " you are open to arguement to the contrary but that does not mean you would change your position regardless of that arguements validity.

LOL. I'm sorry, but that is some blatant misreading of my position, good sir! I explicitly referenced I am open to refutation. Please, re-read twenty times over, because I seriously cannot see how you could have mistaken my words twice at this point.

I hate to say it, my good man, but truly speaking: I am thinking you are more liable to the charge of failing to admit refutation.


So far science is telling you that the light cones are touching.

Two things:

1. Science says no such thing.

2. Who are you to talk about the validity of science? You throw out photons! You have made an entirely new systems of physics! You have no right to discuss the authority of scientific gosepl even if it was gospel. Heretics cannot speak about orthodoxy.


You have agreed that if the infinitely sharp edges of two similar analogues are touching the separation is zero.

Indeed, quite so. Thta is what it is meant by "touching". That there ceases to be any space between them.


Then you state that teh light cones cannot be touching as the present would not exist if the separation between past and future was zero. [ contradiction #1]

Not a contradiction in the least. In the first case we have two things: Sword one, sword two.

In temporal relations, we have three things: Past, present, and future.

The present is sandwiched between the past and future which are both relative to it. It cannot be zero in duration, or it would not exist, and as such, neither would past or future (as they are relative to it). Also, as time would cease to have any moments, everything would be 0 + 0 + 0...or in other words, time itself would have zero duration, leading to a collapse of time as a whole.

You also have never given a refutation for how temporal relations are really two, not three. If you would care to do that, please do so. But do not simply affirm the opposite, while I present a contrary view with reasoning behind it. It's somewhat rude.


I say that it can exist and am willing to explain how this is so as an event horizon of continuous change. You have declined to accept the offer.

You're affirming absurdity: Zero-duration cannot have "continuous change". Change cannot occur in zero-duration.


You refuse to entertain the possibility that the Light Cones are right therefore fly in the face of conventional and well accepted science.

Again: Heretics cannot preach orthodoxy.

“ I say that it can exist and am willing to explain how this is so as an event horizon of continuous change. You have declined to accept the offer. ”

You're affirming absurdity: Zero-duration cannot have "continuous change". Change cannot occur in zero-duration.

If you are up to proving otherwise, please do so. But this stands as my counterpoint.

You're affirming absurdity: Zero-duration cannot have "continuous change". Change cannot occur in zero-duration.
Of course change cannot occur in zero duration. However what we experience in the present moment is of zero duration and do so for eternity.

imagine a peep hole in a sheet of laminate. you look through the hole at another infinitely long laminate sheet sliding underneath at the rate of 'c'.
What do you see through the hole?
You see something that has zero stasis that continues to change for eternity at the fixed rate of 'c'

If you were the observer standing on our hyperspace present as shown in the light cones diagram you would be like looking through a peep hole at the point where the cones touch watching time go by at the rate of 'c' and what you are actuallly seeing is the present moment in constant change.
Now if we take another step:
Because the observer is also changing at the same rate as what he observes the outcome is the observation of relative rest or stationary mass or even moving mass etc etc...yet change is constant yet appears to be relatively still.
so energy has zero statis and lasts for eternity [ I would anticipate this as part of an extension to the laws of thermodynamics as well - especially conservation laws]

Quantum Heraclitus:


Of course change cannot occur in zero duration. However what we experience in the present moment is of zero duration and do so for eternity.

imagine a peep hole in a sheet of laminate. you look through the hole at another infinitely long laminate sheet sliding underneath at the rate of 'c'.
What do you see through the hole?
You see something that has zero stasis that continues to change for eternity at the fixed rate of 'c'

It certainly is eternally flowing, but time is of such a nature as to discuss static points consistently. Were I to appreciate every single moment of time, I would see it as progressing past infinitesimals of space and time. I would recognize it as constant motion, but also note how very much time is like ticking seconds on the face of a clock.

We certainly experience a relative present moment (we're actually experiencing an indeterminate amount of moments all lumped together in our clumsy macroscopic time scale), but if this moment is truly "zero-duration" then all other times must be, too. One cannot get anything but zero if you keep on adding zero to it.


If you were the observer standing on our hyperspace present as shown in the light cones diagram you would be like looking through a peep hole at the point where the cones touch whatching time go by at the rate of 'c' and what you are actuallly seeing is the present moment in constant change.

No, you would actualyl see a 4-d representation of the eternity of that point in space if we were in hyperspace. In essence: The shape made up from every change in that point of space ad eterniam.

Further clarification.
if we refer to the laminate and the peep hole
because the observer is changing at the same rate as the laminate under the top sheet the sheet below appears to be stationary when both the top, bottom and observer are changing at 'c'
So the observer would see no change in this case. This assumes a universe that is entirely uniform in balance [ entropy at the max ] But because energy is distributed unevenly around the universe we have movement that we can witness and change that we can witness. [ something appears to be moving when you are not sort of thing or relative v as SRT would say]

It certainly is eternally flowing, but time is of such a nature as to discuss static points consistently. Were I to appreciate every single moment of time, I would see it as progressing past infinitesimals of space and time. I would recognize it as constant motion, but also note how very much time is like ticking seconds on the face of a clock.
yet this is merely a subjective opinion and not physical reality....the universe doesn't use a clock so to speak only us humans do for our convenience too I might add.

The distinction needs to be made as you can segment time however way you want.
BTW delete the words zero duration and replace with zero stasis. Should clarify things a bit easier.

No, you would actualyl see a 4-d representation of the eternity of that point in space if we were in hyperspace. In essence: The shape made up from every change in that point of space ad eterniam.
I am making reference to the lightcone diagrams use of the word hypersurface my mistake....sorry

We certainly experience a relative present moment (we're actually experiencing an indeterminate amount of moments all lumped together in our clumsy macroscopic time scale), but if this moment is truly "zero-duration" then all other times must be, too. One cannot get anything but zero if you keep on adding zero to it.
The time of observation is zero duration however the time itself is eternal. note distinction between observation and time.

any way enough for now...gotta get on with a beautiful day back in 6 hours

but if this moment is truly "zero-duration" then all other times must be, too. One cannot get anything but zero if you keep on adding zero to it.


Tell me, is the real number line discrete?
Tell me, how many dimensions does the value 1 have? Is 1 then a discrete value?
Is 1 a point on the real number line?

-Andrew

Quantum Heraclitus:


because the observer is changing at the same rate as the laminate under the top sheet the sheet below appears to be stationary when both the top, bottom and observer are changing at 'c'

According to current theory, that'd be wrong. I believe that even at the speed of light, light appears to be going at light speed. I'm not sure of this one, actually,but the other position would be correct, owing to the nature of relative motion. But relative motion is supposed to not hold at light speed.

I do not know what would be the orthodox opinion. But I agree that if relative motion is experienced at C, then an observer moving parralel and at equal speed to something moving at C would see no movement.


But because energy is distributed unevenly around the universe we have movement that we can witness and change that we can witness. [ something appears to be moving when you are not sort of thing or relative v as SRT would say]

This also assumes we're moving at C. But we're.......well, we're not. Everything with mass (ourselves included) move significantly slower than C. In fact, we do not even break a meaningful fraction even with our rocket ships.

Andbna:


Tell me, is the real number line discrete?

Yes.


Tell me, how many dimensions does the value 1 have? Is 1 then a discrete value?

1 is an abstract object, not a spatial object. It has no dimensions as such. 1 retains a discrete value nonetheless, though.


Is 1 a point on the real number line?

Yes.

Would you also agree that the dimension of time can be abstracted as the real number line? (that is: t exists in the reals.)

EDIT: The real number line is not discrete!

Would you agree that a single moment in time is thus represantable by a single number (ie: t=0 corresponds to a moment in time, namely the presant?)



-Andrew

Quantum Heraclitus:


yet this is merely a subjective opinion and not physical reality....the universe doesn't use a clock so to speak only us humans do for our convenience too I might add.

Then you affirm, once again, that the two kettles boil at the same time? It is most certainly a physical reality, or we assume that no duration makes sense. As such, the two kettles boil at once...


The distinction needs to be made as you can segment time however way you want.
BTW delete the words zero duration and replace with zero stasis. Should clarify things a bit easier.

It doesn't seem to change the concept much. What do you distinguish the difference as?


I am making reference to the lightcone diagrams use of the word hypersurface my mistake....sorry

Oh, I thought you were refering to 4-d cubes and such. Right-o.


If you were the observer standing on our hyperspace present as shown in the light cones diagram you would be like looking through a peep hole at the point where the cones touch whatching time go by at the rate of 'c' and what you are actuallly seeing is the present moment in constant change.

One needn't speak of peepholes: We are all ready in the present. We would not be seeing "two light cones touching", but two lightcones touching a third thing: The sandwiched-between present.

It is proper to conceive of that surface of the present as very much a real plain between two cones, the points of which are separated by its infinitely thin depth.


The time of observation is zero duration however the time itself is eternal. note distinction between observation and time.

Elaborate, please? I am not sure I understand what you mean here.

Andbna:


Would you also agree that the dimension of time can be abstracted as the real number line? (that is: t exists in the reals.)

Technically, no. As infinitesimals are not part of the reals. As I affirm that time can be segmented down to the infinitesimal, then I disagree. But for all intents and purposes, I agree, if we allow "1" to represent the smallest segment of time.

Or to simplify things: Let's only deal with positive whole numbers. Any finite amount of time can be represented by arbitrary segments of time ascribed to a numerical value and plotted along a positive whole number line. An infinite amount of time, however, would require infinities.


Would you agree that a single moment in time is thus represantable by a single number (ie: t=0 corresponds to a moment in time, namely the presant?)

T = 0 for the present would only make sense on a Cartesian graph of nth dimensions where every value is 0. On a two dimensional grid: 0,0. On three: 0,0,0 et cetera.

Properly speaking, time would be best represented by one dimension, I.E. as you say, a number line. Present = 0 if we use negatives to represent the past, positives to refer to the future. This would also keep my "three" intact, as 1 - 2 = -1 (not 1 - 1).

Ok, we shall use the extended real number line then. :)


Properly speaking, time would be best represented by one dimension, Yes, this is what I wish to focus on. In your cartisian graph; let n=1.

Now, the reals (and extended reals) are not discrete. Yet, they are made up of discrete values (and I should stress the lack of dimensions of any such value, as they are points.)
For instance:
t=1.2

Hence, the view that a moment in time should have a duration is wrong: a point cannot have a dimension, by definition

-Andrew

Andbna:


Now, the reals (and extended reals) are not discrete. Yet, they are made up of discrete values (and I should stress the lack of dimensions of any such value, as they are points.)
For instance:
t=1.2

Hence, the view that a moment in time should have a duration is wrong: a point cannot have a dimension, by definition

Sneaky like a snake! Slithering silently seducing secretly. I like alliteration.

Anyway...

You are correct to reference the non-dimensionality of points as understood in geometry. These have no dimension, only the line does.

That being said, you forget that the points have value.

Let's use a simple 1-10 number line. Let each number represent a second. 1 = first second, 10 = 10th second.

Now you are correct, again, to point out that each point is zero-dimensional. But in each instance, each point represents one second. The number next is precisely one second later. Thus the value of the point is durational. If we were to discuss the quanta of time (moments) as infinitesimal in value, then the number line would represent 1-10 moments instead of seconds and the same would be true. Even if the points are zero-dimensional, they represent an infinitesimal (which is non-zero as you well know) duration.

If the points represented were zero-dimensional and were zero-duration, then it would not even be meaningful to represent it as a number line. We would be refer to no time at all.

Thus the value of the point is durational. Looking at 2 points, we can form a line segment, which definatly represents a duration. Perhaps, however, points side-by-side, of different discrete values, will allow us to see the minimum change in time possible, and hence, the only thing that can be called the 'duration of a point' (like a single frame of a movie at 27FPS represents 1/27 of a second, and is the smalles uint of time of said movie.)
Now, we know that the integers 1 and 2 are side by side in the integer number line, but that is a discrete set, a different beast than what we are dealing with.

So what can be said about 2 points side by side on the extended real number line?
Well first: is there such a thing?
There is one definition of numbers which goes something like: "Two numbers are not equal so long as there is a third number in between those two."
It would thus seem that it is impossible to find two different moments, side by side, on the real number line: there is always another in between them. Thus the one to ten analogy does not hold (at least, not as I understand it: ) I can find 1.5 in betweemn 1 and 2, and 1.25 in between those, etc...

-Andrew

Andbna:


Looking at 2 points, we can form a line segment, which definatly represents a duration. Perhaps, however, points side-by-side, of different discrete values, will allow us to see the minimum change in time possible, and hence, the only thing that can be called the 'duration of a point' (like a single frame of a movie at 27FPS represents 1/27 of a second, and is the smalles uint of time of said movie.)

This would be a useful comparison.


There is one definition of numbers which goes something like: "Two numbers are not equal so long as there is a third number in between those two."

A pretty reasonable definition of equality.


It would thus seem that it is impossible to find two different moments, side by side, on the real number line: there is always another in between them. Thus the one to ten analogy does not hold (at least, not as I understand it: ) I can find 1.5 in betweemn 1 and 2, and 1.25 in between those, etc...

If we are dealing with only positive whole numbers (as in the example) then we cannot speak of decimals.

Or if we really want to include those things, then let's talk about an infinitesimal. An infinitesimal is defined as that which is less than any value, yet above zero. As such, it ceases to be reasonable to talk about further division. One could rightfully discuss an an infinitesimal as the product of infinite division that does not lead to zero (no division would be that was to be specific). One could then describe the 1-10 in light of the indivisibility of its parts and truly find the moments.

But again, this is simply a more precise redo of the positive whole number thing. What the above infinitesimal discussion would do is only erase all rational doubts with treating the things as indivisble (we know that whole numbers are infinitely divisible really). Putting aside decimals and other such things, the 1-10 positive whole number line would represent as much just as well.

PJ,
Travelling by train into our CBD I puzzled over this infinitesimal stuff and came up with this series of questions.
As you have defined your moment:


An infinitesimal is defined as that which is less than any value, yet above zero
Thus you are saying that no-thing or no other time segment can be smaller.

Say we have segment that is the colour Blue and the next segment is the colour red.
How did blue become red if theer is no change within your segments?

Now before you say possibilities etc remember that these two segments are the smallest time segments available so you can not insert another segment.

Now as far as I can tell the colour blue segment must transform to the colour red instantaneously is this correct?

At the end of time segment blue it is still blue as no change is allowed. Yet at the start of segment red it is red so I would have to guess that the color must change instanteously by some unknowable means.
How can you logically account for this?

Say we have segment that is the colour Blue and the next segment is the colour red.
How did blue become red if theer is no change OK, how about something that's "about to" fall to the ground? At what point of time does it stop being "suspended" and be "falling", when does the disconnection happen?

(Hint: think "Isaac Newton in orchard")

OK, how about something that's "about to" fall to the ground? At what point of time does it stop being "suspended" and be "falling", when does the disconnection happen?

(Hint: think "Isaac Newton in orchard")
A bit like asking:
At what point do two objects cease to be touching, is it a conclusive point or is it an inconclusive point.

But even if it was an inconclusive point there still must be a point when the state of separation is conclusive, this must be an either / or or black and white situation. [ in the context of our discussion so far ] and by virtue of this that poitn must be zero in duration.
refer to two infinitely sharp knife edges butting each other and touching so that separation is zero. At what point does separation exist if the knives are separated?
If we subscribe to the infinitesemal of no change and static then the knives could not be separated.

Yeah, I guess that's something like what might have occured to Isaac at the time.
I 'spose he figured that if an apple is connected to a tree (isn't falling), then at some point it gets heavy enough to separate from the tree (something called abscission helps the process along) - so at some point, the apple is no longer "held" by the tree.

Next, I guess he thought about when does this happen - when is the apple no longer "connected to" or "continuous with" the tree? Which might have lead him to his intuitive idea of "infinitesimals" of time and distance.

But I'm winging it here, of course.

Yeah, I guess that's something like what might have occured to Isaac at the time.
I 'spose he figured that if an apple is connected to a tree (isn't falling), then at some point it gets heavy enough to separate from the tree (something called abscission helps the process along) - so at some point, the apple is no longer "held" by the tree.

Next, I guess he thought about when does this happen - when is the apple no longer "connected to" or "continuous with" the tree? Which might have lead him to his intuitive idea of "infinitesimals" of time and distance.

But I'm winging it here, of course.
So you think it was Sir Isacc N. thought up the infinitesimal time idea and made it popular?
I was under the impression it was early Greek...but may be mistaken.

my point being that even if we allow for the infinitesimal time segment idea the point of separation must be zero. Or that which separates the time segments thus making them segmented must be zero.

It is only this way that the light cones can be allowed to be touching.

The only issue that needs to be resolved really is why segment the infinite any way? What value does it give us to segment it? When it is uneccessary to do so.

I'm missing something; how do you get to: "the point of separation must be zero"? If something separates, there's space between it and whatever it was connected to...?

I think what Isaac figured was that the "moment" of separation could not (ever) be determined. You see an apple connected to a tree, then you see an apple that is disconnected, you can't actually see when it's "disconnected but still continuous with" the tree, you can only ever see a small interval of time/distance, or get so close to the "moment".

Yes. This is wrong. It's pretty much the definition of a continuum. If a space is isomorphism to \mathbb{R}^{n} then it's a continuum. This is why all manifolds are continuums, they are locally diffeomorphic to \mathbb{R}^{n}.

Now you are correct, again, to point out that each point is zero-dimensional. But in each instance, each point represents one second. The number next is precisely one second later. Thus the value of the point [I]is durational. If we were to discuss the quanta of time (moments) as infinitesimal in value, then the number line would represent 1-10 moments instead of seconds and the same would be true. Even if the points are zero-dimensional, they represent an infinitesimal (which is non-zero as you well know) duration.

If the points represented were zero-dimensional and were zero-duration, then it would not even be meaningful to represent it as a number line. We would be refer to no time at all.The 'duration' of t=t_{0} is zero. They are not non-zero infinitesimal in size.

I'm struggling to work out if you're someone whose done some maths education but didn't grasp it properly or you're just a crank who exemplifies 'a little knowledge is a dangerous thing' because you aren't giving any impression you're unsure about what you say.

I'm missing something; how do you get to: "the point of separation must be zero"? If something separates, there's space between it and whatever it was connected to...?

I think what Isaac figured was that the "moment" of separation could not (ever) be determined. You see an apple connected to a tree, then you see an apple that is disconnected, you can't actually see when it's "disconnected but still continuous with" the tree, you can only ever see a small interval of time/distance, or get so close to the "moment".
exactly and that is why it is zero. For if it had value it wouldn't be.
ie.
The center of a sphere can never be found because the sphere is never perfect. So as a sort of cop out we apply infinitey.
Yet we know that there is a center somewhere but it is impossible to find, as at some point we must have a left and right side to the sphere if we place a vertical plane through it.

So zero exists but can never be determined either. [ in this context] It is in this context a "relative zero". Being relative to the sphere.

I'm struggling to work out if you're someone whose done some maths education but didn't grasp it properly or you're just a crank who exemplifies 'a little knowledge is a dangerous thing' because you aren't giving any impression you're unsure about what you say.
Alpha, I have a feeling that it stems from PJ's deep personal understanding of philosophy and metaphysics which has concluded that zero is no-existant.
However as I am attempting to find out in another thread zero can be relative and non-relative [ in philosophy ] and was wondering if this could be shown in mathematics as well.
For example this text box has nothing but white space for me to fill in. The space is a relative zero IMO.
However an absolute zero offers no such concessions. [ non-relative ]
If the distinction can be shown it can be applied to philosophy and possibly assist in discussions there and here.

another example:
If I have a bar magnet with both North and South Poles, somewhere along the bars length there has to be a point where the poles swap.
But it is impossible in a four dimensional reality to determine that point, however that point exists because the poles do actually change as you move along the bar magnets length.The point of zero could be in this case be consdered a zero dimension thickness on a two dimensional slice of the magnet.

Now if we take a 100 of these magnets and throw them at random onto the floor of a small room we have what could be considered as a culminant center of attraction to iron objects. That culminant center is indefinable by measurement but definitely exists by experience. Again you would have to apply infinity in a 4 dimensional reality to even get close to the centre. However as soon as you stop the reductionalism of infinity you no longer can get closer to finding the center.
PJ has determined that a segment must have value even if it is the smallest but unfortunaetly fails to grasp that there can never be a smallest when dealing with infinity. By limiting Infinty he renders the notion useless in this situation.

As the center of our sphere or our culminant attraction of our magnets on the floor, can never be found unless infinity is unfetted but even then we end up with our two ones touching situation and even then we can not determine exactly due to infinite resolution.
So the light cones are touching this we are sure of but can the present point in time ever be exactly determined in time? nope! But it is there for certain as we have a past and a future... so reality in this sense only exists by "default" of everthing and not because of everything.

see?

Again, I'm unable to see how you get from: "there can only ever be a small interval determined", when trying to see the "moment" of disconnection or separation, to: "...exactly and that is why it is zero. For if it had value it wouldn't be."

If it's a small ("infinitesimal") interval, then it's not zero, it's always bigger than "nothing at all". This is the notion of a fundamental limit to any determination we can ever make, so it ties into our mathematical view of stuff. Newton's infinitesimals lead to the calculus, of course (ignoring Leibniz etc for the "moment").

But Newton's "very small intervals" don't actually stand up to good old "rigorous mathematical analysis"; never mind, they did do the job for a while there. But now there's something a bit more rigorous and exact - although it's much the same deal.

AlphaNumeric:


I'm struggling to work out if you're someone whose done some maths education but didn't grasp it properly or you're just a crank who exemplifies 'a little knowledge is a dangerous thing' because you aren't giving any impression you're unsure about what you say.

Kindly go fuck yourself. :)

Again, I'm unable to see how you get from: "there can only ever be a small interval determined", when trying to see the "moment" of disconnection or separation, to: "...exactly and that is why it is zero. For if it had value it wouldn't be."

If it's a small ("infinitesimal") interval, then it's not zero, it's always bigger than "nothing at all". This is the notion of a fundamental limit to any determination we can ever make, so it ties into our mathematical view of stuff. Newton's infinitesimals lead to the calculus, of course (ignoring Leibniz etc for the "moment").

But Newton's "very small intervals" don't actually stand up to good 1]old "rigorous mathematical analysis"; never mind, they did do the job for a while there. But now there's something a bit more rigorous and exact - although it's much the same deal.

We can go back to our two knives with infinitely sharp edges scenario if you like.
BTW I am open to correction and in fact looking for reason as to why I may have a wrong view point ok...

The two knives have infinitely sharp points and are finite in size.

The sharp edges are butted together like so ><

First question to deal with is:

1] Why do we consider them as two knives and not as one object?

There is in effect no way of detremining them as separate as they are separated by zero. [ touching ] [ the apple and the tree are one ][past and future are one eternity]
2] If we apply the notion of infinitesimally small then are the knives touching?

The answer could be yes but the point of touching is no longer infinity.

3] If we separate our object into two knives at what point do they become two and not one?
is that point a yes or no point? or can it be both? and if it is both when do the knives becomes definitely two?

is the apple in the tree touching the tree?
and if not the space between the apple and the tree is how big? And what stops the apple from falling?
or what makes the future the future and the past the past if there is a gap between them?

Quantum Heraclitus:


Thus you are saying that no-thing or no other time segment can be smaller.

Yes.


Say we have segment that is the colour Blue and the next segment is the colour red.
How did blue become red if theer is no change within your segments?

First blue, then red.

The change is finger-snapping instant if it is two moments.


Now before you say possibilities etc remember that these two segments are the smallest time segments available so you can not insert another segment.

Possibilities are found in every moment. "All which will be" is found in everything which is.


Now as far as I can tell the colour blue segment must transform to the colour red instantaneously is this correct?

Correctamundo.


At the end of time segment blue it is still blue as no change is allowed. Yet at the start of segment red it is red so I would have to guess that the color must change instanteously by some unknowable means.
How can you logically account for this?

The possibility of the red object must have been in the blue object.

Quantum Heraclitus:


or what makes the future the future and the past the past if there is a gap between them?

Past is relative to the present. Future relative to the present.

Quantum Heraclitus:



Yes.



First blue, then red.

The change is finger-snapping instant if it is two moments.



Possibilities are found in every moment. "All which will be" is found in everything which is.



Correctamundo.



The possibility of the red object must have been in the blue object.
so the change is instantaneous?
and time could be graphed like a stair case with verticle edges leading to the next step. The vertical edges is when all the change takes place [ no time to change yes?

yes?

Why do you think this is the case?

It seems more far fetched than my zero space ideas

ha..ha...excuse me but it is rather amusing...

You have stated that the change occurs in a finger snapping instantanous moment between segments!........... hee hee!
so the change is occuring in zero duration yes?
ha..oh boy!
So what have I been saying all the time....that the present [now] point between past and future is a continuum of constant change with zero duration.....hmmmmm what a funny little circle we are running around in....:D

so as the light cones state they are touching at zero duration separation and you have also agreed that the change occurs at this point of zero duration, so I wonder what we are argueing about....:D
You understand the light cones better than you realise me thinks.

Alpha, I have a feeling that it stems from PJ's deep personal understanding of philosophy and metaphysics which has concluded that zero is no-existant.He's making statements of a precise mathematical nature.

0 is as valid a concept as 1 or 5 or i or pi or sqrt(2). They are all constructs of systems with precise axioms and rules of behaviour. They don't exist in the sense trees or tables exist. There isn't a planet of derivatives somewhere, all they need for them to be valid concepts is consistency.


The center of a sphere can never be found because the sphere is never perfect. So as a sort of cop out we apply infinitey.
Yet we know that there is a center somewhere but it is impossible to find, as at some point we must have a left and right side to the sphere if we place a vertical plane through it.

So zero exists but can never be determined either. [ in this context] It is in this context a "relative zero". Being relative to the sphere.Do you think you're saying anything mathematical valid or are you aware you're talking waffle?

Kindly go fuck yourself. :)Given you completely avoided addressing my explaination of why I thought you were wrong and you immediately went to insults I would summise that you don't have any actual working knowledge of this stuff and you're making a lot of it up as you go along and failing to tell anyone.

Is this true? Are you not man enough to say "I haven't studied this and some of what I've been saying I'm making up".

So all we have to do is claim one of your segments as past and the other as future and we have a linea representations of our light cones....with zero duration between them....

Do you think you're saying anything mathematical valid or are you aware you're talking waffle?
so now who is doing the insulting?
:eek:

Quantum Heraclitus:


So all we have to do is claim one of your segments as past and the other as future and we have a linea representations of our light cones....with zero duration between them....

Save temporal relations are necessarily a trinity.

You can't have "past" wedged against the future. It's a sequence. Past-Present-Future.

Alpha,
maybe you would care to show how skilled you are by contributing to this thread about defining in math "relative zero and absolute zero"
http://www.sciforums.com/showthread.php?t=82071

Remember I never claim to be a mathematician in fact I am illiterate in maths so it will be interesting to see just how illiterate I am by your contributions.

Quantum Heraclitus:

Also, attempting to place "nothing" between two things, then talk about its causal efficiency, is contradictory. You're claiming two different properties for the gulf: Somethingness and nothingness. If it is truly nothing (there is no gulf) then it cannot have causal effectiveness. If it is truly something, then it cannot be "zero duration"/nothing.

Quantum Heraclitus:


Remember I never claim to be a mathematician in fact I am illiterate in maths so it will be interesting to see just how illiterate I am by your contributions.

Hey, I'm no math scholar, either. The only thing I claim legitimate knowledge in is geometry. I know enough calculus and trig to get by, and I am interested in the philosophical problems of mathematics (Frege and Russel and Godel and such). But don't bash yourself.

Quantum Heraclitus:



Save temporal relations are necessarily a trinity.

You can't have "past" wedged against the future. It's a sequence. Past-Present-Future.
So the change we see must happen in the future of what we start to see as the present. [assuming stasis]

The logic you invoke with this system is incredibly convoluted James...sorry but...

1] You claimed that change occurs instanteously between segments of infinitesimal static moments? yes
2] You claim that the present moment is static and unchanging.
3] You are therefore claiming that change must happen in the future and not the present. [ because you refuse to support your notion that change happens instantaneously between segments and not in a present moment. Thus change must happen in the future or the present.
4] You may claim that change occurs at the end of the "present moment" and takes zero duration. so therefore the present must be in the past or the change must be in the future.
it can't be both unless you want to subscribe to multiple universes and 100's of dimesnions....

Quantum Heraclitus:

Also, attempting to place "nothing" between two things, then talk about its causal efficiency, is contradictory. You're claiming two different properties for the gulf: Somethingness and nothingness. If it is truly nothing (there is no gulf) then it cannot have causal effectiveness. If it is truly something, then it cannot be "zero duration"/nothing.
so I ask myself as I agree with the thrust of this statement above why you wish to allow change to happen in a finger snapping zero duration point between segments? Do you not see it as self contradiction!?
Please explain?

so now who is doing the insulting?
:eek:'Waffle' isn't actually up there on the insulting scale. PJ has already told me to go **** myself. Reiku threated to hunt me down and fed me to his dog and he's called me a *** stain. And all in the last 48 hours or so.

Honestly, you are not talking mathematically valid stuff. Fair enough musing about it but don't kid yourself you're making headway into something or you're treading where noone else has before, on the path to discovery. If you want to talk about the idea of fields and continuums, great. But it would seem you don't, you just want to post waffle and pat each other on the back for how insightful you each are about nothing.

For example :

So all we have to do is claim one of your segments as past and the other as future and we have a linea representations of our light cones....with zero duration between them....You misuse the term 'linear representation'. Do you know what one is? For instance, if I asked you to give me a linear representation of SL(2,Z), could you? What about a non-linear representation? It's literally a one line answer.

maybe you would care to show how skilled you are by contributing to this thread about defining in math "relative zero and absolute zero"I suspect it'll go the way of this

I am interested in the philosophical problems of mathematics (Frege and Russel and Godel and such). But don't bash yourself.But you couldn't even give an example of GIT. You basically gave an example of Russel's paradox.

PJ sorry but I failed to address my counter to Alpha and I think you took it as a counter to you...apologies for the over lap in posts.
btw the thread is still open if you choose to contribute.

AN
''Reiku threated to hunt me down and fed me to his dog and he's called me a *** stain. And all in the last 48 hours or so. ''

I apologize about that.

'Waffle' isn't actually up there on the insulting scale. PJ has already told me to go **** myself. Reiku threated to hunt me down and fed me to his dog and he's called me a *** stain. And all in the last 48 hours or so.

Honestly, you are not talking mathematically valid stuff. Fair enough musing about it but don't kid yourself you're making headway into something or you're treading where noone else has before, on the path to discovery. If you want to talk about the idea of fields and continuums, great. But it would seem you don't, you just want to post waffle and pat each other on the back for how insightful you each are about nothing.

For example :
You misuse the term 'linear representation'. Do you know what one is? For instance, if I asked you to give me a linear representation of SL(2,Z), could you? What about a non-linear representation? It's literally a one line answer.
I suspect it'll go the way of this
But you couldn't even give an example of GIT. You basically gave an example of Russel's paradox.
With all due respect Alpha as I know you know your stuff OK?
The "linea representation" was directed to the language that PJ may be able to quickly understand from me. I understand that it is not used correctly and point taken. But maybe you need to understand that when communicating to various types of people one tends to accommodate their various intellectual and emotional states in ones communications. It is called tolerance, empathy and affinity and looking up the word "forebearance" might help as well.
Try it one day and you will see a whole new world open up to you...:)

Quantum Heraclitus:


1] You claimed that change occurs instanteously between segments of infinitesimal static moments? yes

The fastest change would be a Red-Blue, two infinitesimal moment, changes. Like traffic lights blinking.

Real world changes occur over much longer timespans. It takes millions of years for the Grand Canyon to be cut by the Colorado River.


2] You claim that the present moment is static and unchanging.

Yes. Every moment is unchanging in themselves. You can't change in smaller time spans than infinitesimal.


3] You are therefore claiming that change must happen in the future and not the present. [ because you refuse to support your notion that change happens instantaneously between segments and not in a present moment. Thus change must happen in the future or the present.

Any change occurs in the moment after the present moment, so the future, yes. Of course, this is relative to the present moment.


4] You may claim that change occurs at the end of the "present moment" and takes zero duration. so therefore the present must be in the past or the change must be in the future.

The present would be the moment immediatly after by the time that moment ends.

When you reach the future, you no longer are in the future, but the present.

Quantum Heraclitus:


so I ask myself as I agree with the thrust of this statement above why you wish to allow change to happen in a finger snapping zero duration point between segments? Do you not see it as self contradiction!?

I'm not affirming that it takes place between moments. That'd be absurd.

The next moment is different. The spatial properties are that way relative to the past.

''The present would be the moment immediatly after by the time that moment ends.

When you reach the future, you no longer are in the future, but the present.''

Look,that is just circular and incompete, and lack of true understanding of time.

The present would be the moment ''immediately after'' by the time ''that'' moment ends.... you say.... which sounds right, but can't you just say, ''look, the present time is the only ever real time, and no other time can suceed it or precede it?'' That would be more accurate, and easier to understand.

Secondly, you never reach the future, so again, so it's pointless to you are no longer in it.

The "linea representation" was directed to the language that PJ may be able to quickly understand from me. I understand that it is not used correctly and point taken. But maybe you need to understand that when communicating to various types of people one tends to accommodate their various intellectual and emotional states in ones communications. The problem is that if someone goes away from reading your discussion and wants to learn more they will be lead down the wrong path because you use terminology which means something else.

It is called tolerance, empathy and affinity and looking up the word "forebearance" might help as well.
Try it one day and you will see a whole new world open up to you...I can be all of those things. I've taught some people I would classify as 'a bit thick' and been patient with them. I have generally good comments from my students. That experience and having talked to more than my fair share of cranks online tells me that this thread is not really about the exchange of information attempting to be rigorous and well defined. More towards vacuous and waffling.

The problem is that if someone goes away from reading your discussion and wants to learn more they will be lead down the wrong path because you use terminology which means something else.
I can be all of those things. I've taught some people I would classify as 'a bit thick' and been patient with them. I have generally good comments from my students. That experience and having talked to more than my fair share of cranks online tells me that this thread is not really about the exchange of information attempting to be rigorous and well defined. More towards vacuous and waffling.
fair comment...thanks...

Reiku:


''The present would be the moment immediatly after by the time that moment ends.

Look,that is just circular and incompete, and lack of true understanding of time.

The present would be the moment ''immediately after'' by the time ''that'' moment ends.... you say.... which sounds right, but can't you just say, ''look, the present time is the only ever real time, and no other time can suceed it or precede it?'' That would be more accurate, and easier to understand.

One moment is not the same as the next, and thus I find that statement misleading.


Secondly, you never reach the future, so again, so it's pointless to you are no longer in it.

ONe most certainly reaches the future relative to a past moment.

Wrong. There is no real moment, as in a set of moments... relativity explains that reality may as well just happen within one time frame, because everything is frozen in time. It's the illusory of the mind that distinguishes a past and a future... but we must not be ignorant, that we ever move into the future, because we do not. WE ALWAYS exist here and now, relative to a human observer. Suffice to say, you can say that a man exists in all the states, past, present and future, so long as you state the past and future have their own present states.

But essentially, there is no real future, and no real past. Its all present stuff.

And if you reach the future, tell me, what good is it calling it the future then? Because it obviously isn't now is it?

Reiku:


Wrong. There is no real moment, as in a set of moments... relativity explains that reality may as well just happen within one time frame, because everything is frozen in time. It's the illusory of the mind that distinguishes a past and a future... but we must not be ignorant, that we ever move into the future, because we do not. WE ALWAYS exist here and now, relative to a human observer. Suffice to say, you can say that a man exists in all the states, past, present and future, so long as you state the past and future have their own present states.

Relativity says no such thing, my good man. Einsten did not say "everything is frozen in time".

And we most certainly do move into the future relative to any given present. Otherwise, we'd not be discussing change. We'd be discussing a static image ad eterniam. As there is change, there is time. As there is change, there is future and also past. WHen we are in the future, it is in the present, but relative to our prior present, it is the future.

Would someone please with knowledge in physics, back up what i said...

or perhaps prince, put your hand in your pocket, take out about 15 pounds, or 25 dollars, and go buy ''The Frozen lake,'' by Dr. Greene.

Aright, so Prince_James, while you do make a (seemingly) logical assumption that the smalles amount of time between 2 events would be non-zero, and hence, time be segmented (at an infinitesmal level,) by the argument o*x always = 0, no matter how high of x vlaue we pick.

However, your analogy to the integers does not hold because they are a discrete (countable) set.
consider the numbers between 1 and 10: In the ste of integers, I can count all 10 of the numbers presant.
Even if I extend the integers into the rationals, they are still countable. But, if I decide to venture into the reals, they are not. That is to say: even between 1 and 2, there are an infnite many numbers.
So by the token that 0+0+0 cannot ever create a change in time, I can also state that any non-zero quantity would create an infinite passage of time (since x*infnity for all x non-zero positive x, equals infnity), even over very small periodes picked (eg: between 0 and 1.)
Thus the dillemma.

0*infnity is undefined however.

That said, you do mention the infnitesmal time value; this seems to be correct (I admit, the exact definitions of infnitesmals elude me.)
I think the elapsed time between 2 moments (selected beside each other on the extended reals) can thus be best expressed as the limit of x as x approaches infnity.
Which of course, allows us to set up a function to essentialy determin the value of 0*infnity; namely, the limit of y*x as y approaches infnity and x approaches 0. y being the number of said moments in any selected periode, and x being the 'duration' of said moment.
Then of course, the rates at which each approaches thier value respective to one another corresponds to the actual periode in time selected (if y approaches infinity at 2wice the speed of x, then we have a 2 second interval.)

Alrighty then, I think we are in more or less of an agreement mathematicaly, and we have a fairly complete view of the picture?

-Andrew

just a question
what is the Δ between infintesimal and zero?

1/0 is undefined
but if you believe in paradox
then 1/0=infinity
therefore 0*infinity=1
paradox is the mathematical construction for the bottomless pit in the sky.

Andbna:


That is to say: even between 1 and 2, there are an infnite many numbers.

I agree.


So by the token that 0+0+0 cannot ever create a change in time, I can also state that any non-zero quantity would create an infinite passage of time (since x*infnity for all x non-zero positive x, equals infnity), even over very small periodes picked (eg: between 0 and 1.)
Thus the dillemma.

Ah, so you basically are throwing a sort of infinitesimal variation on Achilles and the Tortoise, yes? That is to say, because there are an infinite amount of numbers between 1 and 2, it fails. Am I correct or am I misconstruing?


0*infnity is undefined however.

Do you know the argument for why this is so or have any references for it? I have looked but never found any that sufficiently explained it to me. Why should infinity make a difference for zero? The process is itself after all: Zero + zero. If zero + zero = zero. Then zero + zero ... + zero should be the same. It seems analytically true that infinity should follow along every finite number * zero = zero.


That said, you do mention the infnitesmal time value; this seems to be correct (I admit, the exact definitions of infnitesmals elude me.)
I think the elapsed time between 2 moments (selected beside each other on the extended reals) can thus be best expressed as the limit of x as x approaches infnity.
Which of course, allows us to set up a function to essentialy determin the value of 0*infnity; namely, the limit of y*x as y approaches infnity and x approaches 0. y being the number of said moments in any selected periode, and x being the 'duration' of said moment.
Then of course, the rates at which each approaches thier value respective to one another corresponds to the actual periode in time selected (if y approaches infinity at 2wice the speed of x, then we have a 2 second interval.)

Alrighty then, I think we are in more or less of an agreement mathematicaly, and we have a fairly complete view of the picture?

I think we are indeed in agreement and I especially like your mathematical model for the specific intervals. Quite good work, my good man!

Quantum Heraclitus:



I'm not affirming that it takes place between moments. That'd be absurd.

The next moment is different. The spatial properties are that way relative to the past.
But you fail to provide a mechanism for that difference. Other than to say it happens in a finger snapping instant.
How does the diefference occur is there is no segment for it to occur in?

What is the mechanism or process that a blue segment of time can change to red with out any transition?

here is a quick image that might help:
http://bizzymate.com/uploads/images/time%20segments.gif
two segments side by side.
nothing can be smaller and both are static and in stasis according to PJ.

How does change occur?

Do you know the argument for why this is so or have any references for it? I have looked but never found any that sufficiently explained it to me. Why should infinity make a difference for zero? The process is itself after all: Zero + zero. If zero + zero = zero. Then zero + zero ... + zero should be the same. It seems analytically true that infinity should follow along every finite number * zero = zero. Let 0*infinity = a for any real (ie finite) a.

The definition properties of 0 include that b*0 = 0 for all real b.

Therefore

b*a = b*0*infinity = 0*infinity = a

So b*a = a, so a=0.

However, consider the quantity f(n).g(n) where f(n) \to 0 as n \to \infty and g(n) \to \infty as n \to \infty. What's f(n).g(n)? Depends entirely on what f and g are and how you do the limits.

For instance, \lim_{m \to \infty} \Big( \lim_{n \to \infty} \big( f(n).g(m) \big) \Big) = 0 but \lim_{n \to \infty} \Big( \lim_{m \to \infty} \big( f(n).g(m) \big) \Big) = \infty

But \lim_{n \to \infty} \big( f(n).g(n) \big) depends on the functions.

If f(n) = \frac{1}{n} and g(n) = kn then \lim_{n \to \infty} \big( f(n).g(n) \big) = \lim_{n \to \infty} \big( k \big) = k
If f(n) = \frac{1}{n^{2}} and g(n) = kn then \lim_{n \to \infty} \big( f(n).g(n) \big) = \lim_{n \to \infty} \big( \frac{k}{n} \big) = 0
If f(n) = \frac{1}{n} and g(n) = kn^{2} then \lim_{n \to \infty} \big( f(n).g(n) \big) = \lim_{n \to \infty} \big( kn \big) = \infty

So you cannot define it in any consistent way.

just a question
what is the Δ between infintesimal and zero?
Something and nothing.

Quantum Heraclitus:


two segments side by side.
nothing can be smaller and both are static and in stasis according to PJ.

How does change occur?

The second moment is the realization of the possibility in the first. As such, it turns red. The change is "blink, red!". In reality, change is far more gradual for almost anything.

Another way to view it:

Time 1: 01
Time 2: 10

why is it so important to understand the nature of nothing?
do you think your focus is improved by focusing on nothing?
If in in understanding nothing we lose our understanding of everything else, then what is the cost of knowing nothing?

We do not lose our understanding of everything else. As such, we're fine.

But yes, it is useful on a practical sense for keening the mind.

Quantum Heraclitus:



The second moment is the realization of the possibility in the first. As such, it turns red. The change is "blink, red!". In reality, change is far more gradual for almost anything.

Another way to view it:

Time 1: 01
Time 2: 10
say we have a particle travelling close to 'c' and it moves a total of 1 foot from segment blue [position B] to segment red [position R]

How did it get to position R from position B
Did it just blink and appear AT position R?
What happened in the distance in between?

just a question
what is the Δ between infintesimal and zero?
One cannot put a number on the difference (and this is a property of it by definition.) It's not quite a 0 difference, but it's as close as possible. Mathematicaly, the infinitesmal can be expressed as lim x as x approaches 0, and thus, lim x-0 as x approaches 0 is 0, and hence, the mathematical difference is 0 (at least in this function.)


Ah, so you basically are throwing a sort of infinitesimal variation on Achilles and the Tortoise, yes? That is to say, because there are an infinite amount of numbers between 1 and 2, it fails. Am I correct or am I misconstruing? Aye that's pretty much it.


Do you know the argument for why this is so or have any references for it? I have looked but never found any that sufficiently explained it to me. Why should infinity make a difference for zero? The process is itself after all: Zero + zero. If zero + zero = zero. Then zero + zero ... + zero should be the same. It seems analytically true that infinity should follow along every finite number * zero = zero.
I could make a few arguments for it, but I don't have any sources on hand; and a google search yielded no trustworthy sources (though I should point out that the general message board concensuss does affirm your position; though these matters of calculus seem to be akin to those of QM; just within the vocabulary of many, and just out of the knowlege.) Anyway; I'l hunt around for a good source, and see what it has to say.

However, AlphaNeumeric has provided a few functions in which demonstrate the fallacy in defining 0*infinity. That should be sufficient I hope.


two segments side by side.
nothing can be smaller and both are static and in stasis according to PJ.

How does change occur?
Consder this: f(x)= x! (x factorial)
It's domain is in the positive integers (inclusive of 0).
Clearly, in the smallest possible change in x, there is a change in f(x). But f(x) always evaluates to the same value given a constant x. Thus, consider f(1) and f(2), both individual points are true point (and fit your use of 'static') both are side by side, and directly beside each other in this functions domain: there can be no smaller value between them. So how does the function change?

Hell if I'm going to answer that; seems more philosophical to me, but we can easily see that it does, and that is all that matters.


What happened in the distance in between? By definition, there is nothing in between. Indeed, what happened between 1 and 2 of the above function?

Integers not doing it for you? Lets head into the reals: even in the function f(x)=x, each value is in 'stasis:' the points are truly discrete and 0-dimensional.
Yet, a change definatly happens between the points on the functions, proving that a change should just as well happen in time. Even if we use a limit to pick to find the difference between the smallest two possible points on a function; we still measure a rate of change (this is where the derivative comes from.) even if the change between those two points is incomprehensably small.


Alright, that's eanough limits for one day >.>
-Andrew

One cannot put a number on the difference (and this is a property of it by definition.) It's not quite a 0 difference, but it's as close as possible. Mathematicaly, the infinitesmal can be expressed as lim x as x approaches 0, and thus, lim x-0 as x approaches 0 is 0, and hence, the mathematical difference is 0 (at least in this function.)

Aye that's pretty much it.


I could make a few arguments for it, but I don't have any sources on hand; and a google search yielded no trustworthy sources (though I should point out that the general message board concensuss does affirm your position; though these matters of calculus seem to be akin to those of QM; just within the vocabulary of many, and just out of the knowlege.) Anyway; I'l hunt around for a good source, and see what it has to say.

However, AlphaNeumeric has provided a few functions in which demonstrate the fallacy in defining 0*infinity. That should be sufficient I hope.


Consder this: f(x)= x! (x factorial)
It's domain is in the positive integers (inclusive of 0).
Clearly, in the smallest possible change in x, there is a change in f(x). But f(x) always evaluates to the same value given a constant x. Thus, consider f(1) and f(2), both individual points are true point (and fit your use of 'static') both are side by side, and directly beside each other in this functions domain: there can be no smaller value between them. So how does the function change?

Hell if I'm going to answer that; seems more philosophical to me, but we can easily see that it does, and that is all that matters.

By definition, there is nothing in between. Indeed, what happened between 1 and 2 of the above function?

Integers not doing it for you? Lets head into the reals: even in the function f(x)=x, each value is in 'stasis:' the points are truly discrete and 0-dimensional.
Yet, a change definatly happens between the points on the functions, proving that a change should just as well happen in time. Even if we use a limit to pick to find the difference between the smallest two possible points on a function; we still measure a rate of change (this is where the derivative comes from.) even if the change between those two points is incomprehensably small.


Alright, that's eanough limits for one day >.>
-Andrew
My question may be inappropriate due to misunderstanding but,
even if we simply declare that 1 becomes 2 in math do you feel this is suffient in describing how 1 becomes 2 in physics.
To me it is far from sufficient to simply say that 1 becomes 2 and thats that.

How would blue become red when there is no time to provide for the transition?
For an object to go from point A to point B it does actually have to move, one would think unless we are declaring that somehow miraculously movement occures when there is no time to do it in.

Just because this an accepted mathematical process does not make it IMO a physical one.
Is my question inapporpriate and mistaken?

Anbna,
Can I ask if you hold to PJs notion that the light cones are separated by an infinitisemal time segment. In that the point between past and future has infinitesimal moment called the NOW or Present?
All indications suggest that this point between past and future is in fact zero duration and thus zero stasis according to the lightcone diagrams.


http://upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/481px-World_line.svg.png
Possibly you would like to speculate on what would happen if the separation between past and future had a moment of stasis [ infinitesimal small duration] and how that would effect the spacetime theory as put forward by Albert E. and his mates.

Quantum Heraclitus:


say we have a particle travelling close to 'c' and it moves a total of 1 foot from segment blue [position B] to segment red [position R]

How did it get to position R from position B
Did it just blink and appear AT position R?
What happened in the distance in between?

It could not move 1 foot in an infinitesimal time span. Only something which is travelling at infinite speed could move more than something far less than a planck length of space.

Andbna:


Ah, so you basically are throwing a sort of infinitesimal variation on Achilles and the Tortoise, yes? That is to say, because there are an infinite amount of numbers between 1 and 2, it fails. Am I correct or am I misconstruing? ”

Aye that's pretty much it.

I think the later thing we spoke about covered this, then.

But man, Zeno's paradoxes really work, with a bit of tuning from time to time, for so many things. That Eleatic bastard!


I could make a few arguments for it, but I don't have any sources on hand; and a google search yielded no trustworthy sources (though I should point out that the general message board concensuss does affirm your position; though these matters of calculus seem to be akin to those of QM; just within the vocabulary of many, and just out of the knowlege.) Anyway; I'l hunt around for a good source, and see what it has to say.

However, AlphaNeumeric has provided a few functions in which demonstrate the fallacy in defining 0*infinity. That should be sufficient I hope.

I'm going to see if I can contact a professor of mathematics and see whether he can give me a decent, quick answer to the question of why 0 * oo = ?. I think that is one of the most reliable ways to go about those sort of things. I know I have no book on hand that ought to explain that. I only have a math text book or two and Euclid's "Elements" on hand.


Consder this: f(x)= x! (x factorial)
It's domain is in the positive integers (inclusive of 0).
Clearly, in the smallest possible change in x, there is a change in f(x). But f(x) always evaluates to the same value given a constant x. Thus, consider f(1) and f(2), both individual points are true point (and fit your use of 'static') both are side by side, and directly beside each other in this functions domain: there can be no smaller value between them. So how does the function change?

Hell if I'm going to answer that; seems more philosophical to me, but we can easily see that it does, and that is all that matters.

Again, thank you for the excellent explanation.


By definition, there is nothing in between. Indeed, what happened between 1 and 2 of the above function?

Integers not doing it for you? Lets head into the reals: even in the function f(x)=x, each value is in 'stasis:' the points are truly discrete and 0-dimensional.
Yet, a change definatly happens between the points on the functions, proving that a change should just as well happen in time. Even if we use a limit to pick to find the difference between the smallest two possible points on a function; we still measure a rate of change (this is where the derivative comes from.) even if the change between those two points is incomprehensably small.


Alright, that's eanough limits for one day >.>
-Andrew

Andy you're a star in nobody's eyessss but mineee.

Yes, I am serenading you with pop music.

Quantum Heraclitus:



It could not move 1 foot in an infinitesimal time span. Only something which is travelling at infinite speed could move more than something far less than a planck length of space.
given that you know what my question is and of course the figures quoted are examples only and not actual you have still avoided answering the question!
How does one segment make the transition to the other in physics and not math?

how does blue become red with out transition?

Andbna has graceously shown why this is possible in mathematics but as yet failed to show how this is possible in physics.

Understandably math requires finite points along a line, but these are mathematical imagery and not necessarilly physics or should I say of material value.
Am I wrong or am I right?

Quantum Heraclitus:


How does one segment make the transition to the other in physics and not math?

How am I supposed to know the answer to this question? We're talking about coloured lines. What physics can be answered with things which are not objects of physics?

But I'll try an analogy to a transistor, in line with my previous pseudo-binary answer.

A transistor has two settings: On and off.

Let red represent on, let blue represent off.

Let the switch be able to take one infinitesimal moment (that is the next moment).

If red, it will be blue in the next moment. If blue, it will be red in the next moment.

From what I understand, all we are doing is demonstrating the limitations of mathematics when attempting to apply it to the real world.

Quantum Heraclitus:


Andbna has graceously shown why this is possible in mathematics but as yet failed to show how this is possible in physics.

One thing ought to be stressed: The majority (in fact everything) in physics can be translated into mathematical language. Of course, the mathematics doesn't prove the physics, but the physics is certainly speakable in terms of mathematics. The inverse square law, E=MC2, all that nonsense.


Understandably math requires finite points along a line, but these are mathematical imagery and not necessarilly physics or should I say of material value.
Am I wrong or am I right?

Logically it does follow that material substance should be infinitely reducible if it can be finitely reducible, which it is clear it can be.

I can go a mile to the mall, or half a mile to the grocery store, or a quarter of mile to the laundry, an eighth of a mile to the bodaga, a sixteenth of a mile to my neighbour's, a 32nd of a mile to my garbage can, 1/64th of a mile to my living room...

Quantum Heraclitus:



How am I supposed to know the answer to this question? We're talking about coloured lines. What physics can be answered with things which are not objects of physics?

But I'll try an analogy to a transistor, in line with my previous pseudo-binary answer.

A transistor has two settings: On and off.

Let red represent on, let blue represent off.

Let the switch be able to take one infinitesimal moment (that is the next moment).

If red, it will be blue in the next moment. If blue, it will be red in the next moment.
hmmmm...

The transistors current flow must fall quickly but not instantaneously to zero as the flow diminishes to zero,
Can a a current flow go from say 1 amp to zero instantaneously.

I do not think so....

A bit like trying to stop a river from flowing by shutting a gate in a damn. It will always take time no matter how fast you are to go from flow to no flow.

I have a funny name for a principle:

The Gandalf Principle.

Or "You will not pass!"

"Barring demonstration of the contrary, a finite process can be extended infinitely."

Quantum Heraclitus:



One thing ought to be stressed: The majority (in fact everything) in physics can be translated into mathematical language. Of course, the mathematics doesn't prove the physics, but the physics is certainly speakable in terms of mathematics. The inverse square law, E=MC2, all that nonsense.



Logically it does follow that material substance should be infinitely reducible if it can be finitely reducible, which it is clear it can be.

I can go a mile to the mall, or half a mile to the grocery store, or a quarter of mile to the laundry, an eighth of a mile to the bodaga, a sixteenth of a mile to my neighbour's, a 32nd of a mile to my garbage can, 1/64th of a mile to my living room...
However there is a limit to how mathematics can explain reality as described in the use of infinity. Regarding the 12" brick. Infinitey from what I understand can only make sense if limited in mathematics. If left unlimited it looses it's value of utility. All you are showing is this limitation IMO and not the reality.
Besides the distances you speak of are arbitary and have nothing to do with physical reality but more to do with epistemoligical conveniance.

Quantum Heraclitus:


The transistors current flow must fall quickly but not instantaneously to zero as the flow diminishes to zero,
Can a a current flow go from say 1 amp to zero instantaneously.

Ideally, yes. If we're talking about timescales and spatial sizes on the infinitesimal.

I have a funny name for a principle:

The Gandalf Principle.

Or "You will not pass!"

"Barring demonstration of the contrary, a finite process can be extended infinitely."

eh?

Quantum Heraclitus:



“ The transistors current flow must fall quickly but not instantaneously to zero as the flow diminishes to zero,
Can a a current flow go from say 1 amp to zero instantaneously. ”

Ideally, yes. If we're talking about timescales and spatial sizes on the infinitesimal.
and you do not see how static segments would prevent this fall off to zero?
hmmmm...interesting...

Quantum Heraclitus:


However there is a limit to how mathematics can explain reality as described in the use of infinity. Regarding the 12" brick. Infinitey from what I understand can only make sense if limited in mathematics. If left unlimited it looses it's value of utility. All you are showing is this limitation IMO and not the reality.

Can you explain what you mean by "limited" here?


Besides the distances you speak of are arbitary and have nothing to do with physical reality but more to do with epistemoligical conveniance.

The unit of measurement is arbitrary, but the distances are not. They relate to spatial realities. The mall really is a mile away as defined by the measurement and as correlated to space.

Quantum Heraclitus:


eh?

Unless Gandalf demonstrates the irrationality of extending the process infinitely, it'll pass.


and you do not see how static segments would prevent this fall off to zero?
hmmmm...interesting...

The switch to zero would occur in the next moment. The possibility in the first.

Let's think of it like.....a seesaw.

When one goes down, the other goes up. The next moment, one goes up, the other goes down.

Quantum Heraclitus:



Can you explain what you mean by "limited" here?




"Achilles has stopped trying to catch the hare"
In fact if you did the math more carefuly you would probably find that Archilles will not only stop trying to catch the hare but his speed will slowly reduce until he is effectively stationary as the tourtise continues along his way with out changing his speed.

any ways enough for today as must get on.....back in 6 hours

In my mind what proves in reality that the use of infinitey in this way is incorrect is the issue of metastability and how spin is produced in the first place.
refering as an example to a teetering pencil balanced on it's point.
and :
Indirectly:
How if segmentation as you suggest was possible then pseudo perpetual motion/energy devices would be able to be built by physics and we would have free energy today with out a problem.

Quantum Heraclitus:


"Achilles has stopped trying to catch the hare"
In fact if you did the math more carefuly you would probably find that Archilles will not only stop trying to catch the hare but his speed will slowly reduce until he is effectively stationary as the tourtise continues along his way with out changing his speed.

any ways enough for today as must get on.....back in 6 hours

Yes, we know that Achilles will eventually be moving infinitesimally ( after an infinite period). Thus Achilles loses analytically.

I don't see how this is a limit, though?


In my mind what proves in reality that the use of infinitey in this way is incorrect is the issue of metastability and how spin is produced in the first place.
refering as an example to a teetering pencil balanced on it's point.

You're going to have to elaborate on this, my good man. How does metastability come into play?


How if segmentation as you suggest was possible then pseudo perpetual motion/energy devices would be able to be built by physics and we would have free energy today with out a problem.

How do you figure?

Yes, we know that Achilles will eventually be moving infinitesimally ( after an infinite period). Thus Achilles loses analytically.

I don't see how this is a limit, though?
well...that's exactly what would happen to the universe if the present moment was anything other than described in the light cones.

How do I figure?

You'll have to work that out for your self ....sorry....I have already tried to explain it but failed

The infinitesimal if I am not mistaken shouldn't exist as the Achilles always tries to over take the tourtise and keeps getting closer to doing so, but never gets over the line. The fact that he eventually slows down to almost a stop as the tourtise races ahead indicates your infinity is not correctly applied to the gendanken. In fact it only proves that the limits placed on infinty actually fail the gendankens purpose.
The distance of separation between achilles and tourtise is supposed to get smaller and never quite make it, not larger...
I may be wrong though as I actually haven't studied the gendanken for any length of time nor the math...

IMO

How do I figure?
You'll have to work that out for your self ....sorry....I have already tried to explain it but failed.

In my mind what proves in reality that the use of infinitey in this way is incorrect is the issue of metastability and how spin is produced in the first place.
refering as an example to a teetering pencil balanced on it's point. ”

You're going to have to elaborate on this, my good man. How does metastability come into play?
With studies into why pseudo perpetual energy and motion devices are not currently being built it became obvious that if balance [ stasis ] is achieved at any point within a system the system will fail as it will stop.
If times segmentaion was a you describe metastability would cease to be pseudo perpetual and I would be able to balance a pencil on it's point. [ mind you the universe would not exist to find a pencil.]

So time segmentation defeats metastability and spin would be no more as eventually balance would be achieved [ actually it wouldn't spin to begin with] thus no future and by default no past and certainly no present.
Entropy over eternity however presents for other reasons...no doubt IMO
note: I may be using incorrect terminology in the above description.

Quantum Heraclitus:


The infinitesimal if I am not mistaken shouldn't exist as the Achilles always tries to over take the tourtise and keeps getting closer to doing so, but never gets over the line. The fact that he eventually slows down to almost a stop as the tourtise races ahead indicates your infinity is not correctly applied to the gendanken. In fact it only proves that the limits placed on infinty actually fail the gendankens purpose.
The distance of separation between achilles and tourtise is supposed to get smaller and never quite make it, not larger...
I may be wrong though as I actually haven't studied the gendanken for any length of time nor the math...

The idea behind the Paradox is that Achilles, by agreeing to be fettered to always going half the distance between him and the tortoise, can never then over take the tortoise.

I fail to see how this is a failure: It's the actual solution. Achilles fails. Eventually, Achilles starts moving infinitesimal distances, but cannot go any further than that.


The distance of separation between achilles and tourtise is supposed to get smaller and never quite make it, not larger...

It never does get larger. It gets smaller and smaller.

Quantum Heraclitus:


With studies into why pseudo perpetual energy and motion devices are not currently being built it became obvious that if balance [ stasis ] is achieved at any point within a system the system will fail as it will stop.
If times segmentaion was a you describe metastability would cease to be pseudo perpetual and I would be able to balance a pencil on it's point. [ mind you the universe would not exist to find a pencil.]

So time segmentation defeats metastability and spin would be no more as eventually balance would be achieved [ actually it wouldn't spin to begin with] thus no future and by default no past and certainly no present.
Entropy over eternity however presents for other reasons...no doubt IMO
note: I may be using incorrect terminology in the above description.

You're going to have to go more in depth on this whole matter. You barely explain it here, so please elaborate.

Quantum Heraclitus:



The idea behind the Paradox is that Achilles, by agreeing to be fettered to always going half the distance between him and the tortoise, can never then over take the tortoise.

I fail to see how this is a failure: It's the actual solution. Achilles fails. Eventually, Achilles starts moving infinitesimal distances, but cannot go any further than that.



It never does get larger. It gets smaller and smaller.

hmmm....if the infinitesimal is applied from the start of the race and not just at the end what happens?
You do apply the infinitesimal to all time and not just when he gets close yes?

hmmmm......
how many infinitesimals fit into half the distance?

and if you say infinity I would beg to differ.
btw how are you this fine day?

Quantum Heraclitus:


hmmm....if the infinitesimal is applied from the start of the race and not just at the end what happens?
You do apply the infinitesimal to all time and not just when he gets close yes?

Achilles is standing there for infinity moving inches over aeons as the tortoise goes further and further past him.

I don't apply infinitesimals to any distance which isn't infinitesimal. Achilles would be making strides over feet, not infinitesimal segments of space.

Quantum Heraclitus:



Achilles is standing there for infinity moving inches over aeons as the tortoise goes further and further past him.

I don't apply infinitesimals to any distance which isn't infinitesimal. Achilles would be making strides over feet, not infinitesimal segments of space.

note edit to post above.

But you have been saying that time is made up of infinitesimal segments yes?

that change occurs instantaneously between segments due to possibilities If I remember correctly.

So when you calculate the first half way point in the race t/d do you use infinitesmal segements or not?

lets have a look at andbna's math shall we?
Not that I know what I am seeing mind you....

ok so the point of the excersise is not to keep Achilles and the Tourtise separated by only a constantly reducing infinitesmal but that the tourtice actually pulls away from Archilles?

Is this corrrect?
I was under the impression which must be incorrect that the thrust of this gendanken was to prove that infinitesmal was a constantly reducing distance between Archilles and the Tourtise, other wise whats the point of the gendanken?

Quantum Heraclitus:


hmmmm......
how many infinitesimals fit into half the distance?

and if you say infinity I would beg to differ.

Which distance?

And see Andrew's post regarding the means to calculate the rate sensibly using the infinitesimals.

But yes, an infinite amount of infinitesimals would fill any distance that isn't an infinitesimal.



btw how are you this fine day?

Good, but a bit tired and achey. Lots of walking up hill on Broadway today. I don't like Northern Manhattan that much and I was tramping around there. How about you?

of course if I place an incredibly small limitation on the distance involved Archilles will find the tourtise pulling away....
but I think this defeats the gendanken....doesn't it?

But yes, an infinite amount of infinitesimals would fill any distance that isn't an infinitesimal.
But this can not be correct as you have limited the infinitesmal to a given dimension.

Maybe I should ask what your opinon is of:
Is the infinitesimal a constantly reducing distance or time?
Or is it somehow limited to a pseudo finite value?

Good, but a bit tired and achey. Lots of walking up hill on Broadway today. I don't like Northern Manhattan that much and I was tramping around there. How about you?
Similar but mood is good especialy after the quip in the relative/absolute zero thread. The irony!

Quantum Heraclitus:


But you have been saying that time is made up of infinitesimal segments yes?

Correctomundo.


that change occurs instantaneously between segments due to possibilities If I remember correctly.

Forsooth.


So when you calculate the first half way point in the race t/d do you use infinitesmal segements or not?

No. I use seconds and feet, because Achilles is going to be moving as such. Why would I use infinitesimals for something that isn't infinitesimal?

When Achilles start moving in infinitesimal increments because he must pass halfway, halfway, halfway...then we'll talk about those. But until then, no, I don't - that'd be impractical.


ok so the point of the excersise is not to keep Achilles and the Tourtise separated by only a constantly reducing infinitesmal but that the tourtice actually pulls away from Archilles?

This is Zeno's Paradox of Achilles and the Tortoise:

Achilles is met by a tortoise who challenges him to a foot race. Achilles, knowing he is a great hero and warrior, and correspondingly a fantastic athlete, is assured he'd be able to beat this sluggard. However, in his arrogance he commits a fatal flaw: He agrees to be fettered by two rules. The first is that he must give the tortoise a head start. The second is that he can never progress more than halfway to the tortoise at any time.

As such, he has all ready lost before he even begins.

This was an attempt by Zeno to show that motion was irrational: As we do have to pass through half of any distance to get to that distance, we ought to not be able to move at all. As an Eleatic, he believed both time and motion were illusions and that we lived in a perfect static sphere.


I was under the impression which must be incorrect that the thrust of this gendanken was to prove that infinitesmal was a constantly reducing distance between Archilles and the Tourtise, other wise whats the point of the gendanken?

The idea which Andrew brought up against me was the one you just attempted to: There is an infinite amount of numbers between 1-2. This translates to somewhat of a mathematical Achilles and the Tortoise paradox.

if I draw two lines in the form of a drawing cross and magnify the lines an infinite amount at what point does the intersection become separated by an infinitesimal?
Or use two cones:
If I have both infinitely pointed cones touching with zero distance separation and maginify the point of contact infinitely at what point do the cones appear to be separating?

Achilles is met by a tortoise who challenges him to a foot race. Achilles, knowing he is a great hero and warrior, and correspondingly a fantastic athlete, is assured he'd be able to beat this sluggard. However, in his arrogance he commits a fatal flaw: He agrees to be fettered by two rules. The first is that he must give the tortoise a head start. The second is that he can never progress more than halfway to the tortoise at any time.
"at any time" means what exactly?

Quantum Heraclitus:


Is the infinitesimal a constantly reducing distance or time?
Or is it somehow limited to a pseudo finite value?

Infinitesimals are finite values: They are the finite value above zero but beneath any given number.

You give me a number, an infinitesimal < it.

Constantly reducing time or space is not an infinitesimal. However, the product of infinite division of any number is an infinitesimal.

That is: 1, 1/2, 1/4, 1/8, 1/32, 1/64.........

Quantum Quack:


"at any time" means what exactly?

He is not allowed to ever pass more than 1/2 of the way to the tortoise.

Quantum Heraclitus:


if I draw two lines in the form of a drawing cross and magnify the lines an infinite amount at what point does the intersection become separated by an infinitesimal?

When you do this for an infinite amount of time.


If I have both infinitely pointed cones touching with zero distance separation and maginify the point of contact infinitely at what point do the cones appear to be separating?

Touching cones are not separated.

Constantly reducing time or space is not an infinitesimal. However, the product of infinite division of any number is an infinitesimal.
If you are in agreement with your statement above then the light cones must stand correct as the cones are decribing space/time and not a number system.
Therefore the observers point of observation is of zero stasis and therefore duration.

and our mythical photon can rest easy and travel smoothly with out segmentation and steps in it's movement.

Quantum Heraclitus:


If you are in agreement with your statement above then the light cones must stand correct as the cones are decribing space/time and not a number system.

Perhaps I misunderstood your question, as I am not seeing where you got this from whatsoever.

A constantly diminishing space is not an infinitesimal. Isn't this what you meant? Like say...a shrinking metal bar.

Quantum Heraclitus:



Perhaps I misunderstood your question, as I am not seeing where you got this from whatsoever.

A constantly diminishing space is not an infinitesimal. Isn't this what you meant? Like say...a shrinking metal bar.
oh I interpreted you as saying that if we reduce the dimensions of space or time [ and not numbers] there can be no infinitesimals as they are not a number system...

Quantum Heraclitus:


oh I interpreted you as saying that if we reduce space or time [ and not numbers] there can be no infinitesimals as they are not a number system...

No, I didn't mean that at all. Sorry.

If you reduced any segment of time or space infinitely, you'd get an infinitesimal.

I am not interested in resolving this discussion by mere confusion... gotta get it quite clear in the end...so please excuse me if I have confused as I do not intend to do so....nor will I take any advantage from doing so...

Quantum Heraclitus:



No, I didn't mean that at all. Sorry.

If you reduced any segment of time or space infinitely, you'd get an infinitesimal.
only but only if you apply a number system to it or them? yes?

Quantum Heraclitus:


I am not interested in resolving this discussion by mere confusion... gotta get it quite clear in the end...so please excuse me if I have confused as I do not intend to do so....nor will I take any advantage from doing so...

You're quite forgiven. It was an honest mistake of interpretation on both our parts.

I fully trust that neither you or I are trying to win this debate by making someone concede something by accident. We're only attempting to win the truth by forcing someone to concede the logical collapse of their given system.

But yes, the other answers are (or ought to be - they seem in order) to not have been based on confusion.

Quantum Heraclitus:


only but only if you apply a number system to it or them? yes?

No.

If I "cut" space up infinitely, I'd get an infinitesimal eventually (after an infinite time).

Same with time.

There are monads and moments that are real and actual.

Quantum Heraclitus:



You're quite forgiven. It was an honest mistake of interpretation on both our parts.

I fully trust that neither you or I are trying to win this debate by making someone concede something by accident. We're only attempting to win the truth by forcing someone to concede the logical collapse of their given system.

But yes, the other answers are (or ought to be - they seem in order) to not have been based on confusion.
yes well said....as no one wins if it is simply about winning...this to me is more about learning than winning....learning how to communicate and also how to conceptualise what I see better. I trust it is the same for you and hopefully those that are reading...

Quantum Heraclitus:


yes well said....as no one wins if it is simply about winning...this to me is more about learning than winning....learning how to communicate and also how to conceptualise what I see better. I trust it is the same for you and hopefully those that are reading...

I count it a benefit for me to either win or lose. If I win, I have given someone a better grasp on the truth and satisfied the rationality of my own system. If I lose, I can amend my flaws and be closer to a full understanding.

So yes, it is hardly about winning or losing: This is barely a competition in the least. I'm here primarily for the truth.

Last post as I gotta go....

There appears to be a conceptional problem in that we are convinced that infinitely small has to be greater than zero yet zero has no value. so why woudl infinitely small achieve a value? Other than to say that is greater than something that has no existance.
I believe that teh value subscibed to an infinitesimal should be infinitely smaller again and when you get to the next infinite infinitesimal I would say well divide it agaiin and again and I would do so for infinity and regardless of how many infinitly reduced infinitesimals it will always be >nothing yet have no real value.

so the logical paradox is that infinitesimal can never achieve value yet it must always be >zero. in a sense we have 0 substance = [ ] or zero substance = 0
Hard to word it properly.....
Thus Archilles never stops chasing the tourtise.

Quantum Heraclitus:



I count it a benefit for me to either win or lose. If I win, I have given someone a better grasp on the truth and satisfied the rationality of my own system. If I lose, I can amend my flaws and be closer to a full understanding.

So yes, it is hardly about winning or losing: This is barely a competition in the least. I'm here primarily for the truth.
however at this level of debate given the enormous philosophical and math input it is not going to be easy to to change ones view point yes?
For me it is 15 years of experience, observation and thought [ not a text book in sight ]
So it will take some doing to show cause for the need to change my view.
I assume that it is likewise with you...

Quantum Heraclitus:


however at this level of debate given the enormous philosophical and math input it is not going to be easy to to change ones view point yes?
For me it is 15 years of experience, observation and thought [ not a text book in sight ]
So it will take some doing to show cause for the need to change my view.
I assume that it is likewise with you...

Certainly! But if I am truly beat, I am going to concede with humility. As would be the same with you, I imagine.

We're all about fairness here, even if we cannot escape the fact that both oru theories are wrapped up in inertia. Also, we likely will have to face the fact that most theories never are fully expunged, but the truthful parts are added to a more complete system.

Quantum Heraclitus:


There appears to be a conceptional problem in that we are convinced that infinitely small has to be greater than zero yet zero has no value. so why woudl infinitely small achieve a value? Other than to say that is greater than something that has no existance.

Precisely because it is not nothing ,it would have a value. The infinitely small represents the smallest away from being nothing that one can be. The product of infinite division, be it mathematically, temporally, or spatially.


I believe that teh value subscibed to an infinitesimal should be infinitely smaller again and when you get to the next infinite infinitesimal I would say well divide it agaiin and again and I would do so for infinity and regardless of how many infinitly reduced infinitesimals it will always be >nothing yet have no real value.

To ape Wittgenstein again, this is tantamount to "asking what is North of the North Pole". The infinitesimal is defined as the smallest possible - therefore to speak of further division is ridiculous.


so the logical paradox is that infinitesimal can never achieve value yet it must always be >zero. in a sense we have 0 substance = [ ] or zero substance = 0
Hard to word it properly.....
Thus Archilles never stops chasing the tourtise.

Well yes: It has no value in the sense of a number like 1 would have. But I don't grasp what you mean by "in a sense we have 0 substance"?

Try to rephrase this whole thing whne you come back.

We're all about fairness here, even if we cannot escape the fact that both oru theories are wrapped up in inertia. Also, we likely will have to face the fact that most theories never are fully expunged, but the truthful parts are added to a more complete system.
now we are talking....hmmm creative synergy....is this not what all good discussions are about afterall?

Quantum Heraclitus:



Precisely because it is not nothing ,it would have a value. The infinitely small represents the smallest away from being nothing that one can be. The product of infinite division, be it mathematically, temporally, or spatially.



To ape Wittgenstein again, this is tantamount to "asking what is North of the North Pole". The infinitesimal is defined as the smallest possible - therefore to speak of further division is ridiculous.



Well yes: It has no value in the sense of a number like 1 would have. But I don't grasp what you mean by "in a sense we have 0 substance"?

Try to rephrase this whole thing whne you come back.
Shall do...:)

Quantum Heraclitus:


now we are talking....hmmm creative synergy....is this not what all good discussions are about afterall?

I'm all about the thesis, antithesis, and synthesis, GWF Hegel stylez!

Representin' German Idealism!

Quantum Heraclitus:


Now if we apply a limit to infinity as suggested there would have to be a cavity established of zero or nothing in a three dimensional sphere in three dimensional space.

How does this follow precisely?


So this is interesting if one is looking for an non-particle or an inverse particle as this is how you would theoretically show it's existance in Mathematics.
So what is interesting to me is that the use of teh infinitesimal actually proves the non-existance of nothing due to the 3 dimensional nature of space/time
IN a 2 dimesnional setting we woud not sdhoe a cavity but this is not the case in 3 dimesnions. Of this I am quite confident but beg to be correected if necessary.


I'm not really grasping the mechanism behind your argument.

Quantum Heraclitus:



How does this follow precisely?



I'm not really grasping the mechanism behind your argument.

Take a three dimensional sphere and think about it with the application of infinitesimal as you minimum size.
Magnify the sphere infiniitely and what do you get?
A cavity of zero must be formed in three dimensional spacetime.

the volume of the cavity can be expresed as a ratio of the infinitesimal, quite easilly I think...ahh! one day I am going to learn this new "language" called mathematics.

Basically, this cavity emerges because you say that an infinitesimal stops the cones?

maybe one of the math guys would like to offer some input at this point?:)

Basically, this cavity emerges because you say that an infinitesimal stops the cones?
essentially yes as the infinitesimal must be greater than zero and in 3 dimensional space time this leaves us with a problem. A cavity must be formed.

In 2 dimensions this is not a problem such as when you talk about time and distance a cavity is not the outcome.
But in 3 dimensional substance or mass this poses as the only outcome I think although I have only been pondering a short while on it...

so guess what PJ .... we have just discovered "absolutely nothing"...if we subscribe to the infinitesimal.
Congratulations....champagne any one....:D

now there's a freebee if i ever saw one...ha

The problem with this theory that immediatly jumps to mind is this:

The supposed sphere of nothingness would have a spatial value. This is itself contradictory and also implies that you're making a spatial value beneath infinitesimal, which again attacks the defition of infinitesimal. If it is the smallest possible, then you cannot speak of further division.

Furthermore, in your picture of the infinite, you do not permit values greater than infinity. As such, if the two are the same, you ought to have the same "nothingness" popping up above infinity.

The problem with this theory that immediatly jumps to mind is this:

The supposed sphere of nothingness would have a spatial value. This is itself contradictory and also implies that you're making a spatial value beneath infinitesimal, which again attacks the defition of infinitesimal. If it is the smallest possible, then you cannot speak of further division.

Furthermore, in your picture of the infinite, you do not permit values greater than infinity. As such, if the two are the same, you ought to have the same "nothingness" popping up above infinity.
shit man I am not the one who is pushing the infinitesimals reality...you are...hey...don't blame me if 3 dimensional geometry has to be followed.

Furthermore, in your picture of the infinite, you do not permit values greater than infinity. As such, if the two are the same, you ought to have the same "nothingness" popping up above infinity.
wow and that would be one hell of a big inverse particle yes? By golly.....please excuse the humor..it has been a tough day....
again it is not I that subscribes to the infinitesimal......so I am not responsible for it's outcomes.

If I take a cube that is hollow that has the sides size as infinitesimal^2, how much volume must the inside of the cube be?

if we can get some maths happening for our sphere I think we may be in for a really ironic surprise....hmmmmm does the figure pi have anything to do with it...just a hunch...mind you

Quantum Heraclitus:


wow and that would be one hell of a big inverse particle yes? By golly.....please excuse the humor..it has been a tough day....
again it is not I that subscribes to the infinitesimal......so I am not responsible for it's outcomes.

It most certainly would be a very big inverse particle.

But let's phrase it like this: There is NOTHING beyond infinity. There is NOTHING smaller than infinitesimal.

The latter describes your system of "sphere o' nothingness" beneath infinitesimal. The former provides the proper basis, if we are going to start talking about spheres of infinitesimal nothingness, for revisiting your infinity cones.


If I take a cube that is hollow that has the sides size as infinitesimal^2, how much volume must the inside of the cube be?

1 infinitesimal. 1 * 1 * 1 = 1. We're going to assume "1" works okay for this, as infinitesimals don't have a numerical value like that. I think that is fair, as "1", in terms of the positive whole numbers, does represent the smallest value above 0.


if we can get some maths happening for our sphere I think we may be in for a really ironic surprise....hmmmmm does the figure pi have anything to do with it...just a hunch...mind you

Let's see....

Volume of a sphere = 4/3 * pi * r^3

The radius of the sphere would be infinitesimal.

Soooo....

4/3 * 3.1415 * 1

4/3 * 3.1415 = 4.18866...

So the sphere's volume is not infinitesimal if the radius is infinitesimal.

I'll be back later.

The radius of the sphere would be infinitesimal.
careful, The infinitesimal applies to the inner surface of our cavity and not necessarilly the radius or diameter.

Quantum Heraclitus:


careful, The infinitesimal applies to the inner surface of our cavity and not necessarilly the radius or diameter.

You mean its volume?


The spheres radius is only an outcome of teh use of infinitesimals and it's actual volume being absolutely nothing is not relevant from the perspective of nothingess but only relevant top to the perspectiev of somethingness.

A sphere with a volume of nothing is not a sphere. Spheres have volumes. This is tantamount to asking "what is a square that has no corners?"


The point is that if you subscribe to the infinitesimal a cavity of zero must form if that is bigger or smaller is not the point nor the issue as it si a default outcome.

This isn't the case, as we are once again dealing with a question of trying to divide the indivisible. You are asking once again "what is North of the North Pole"?


In the other thread about relative and non- relative zero it was not thought to be possible to prove non-relative zero but thanks to this discussion I think we just have.

That in itself is utterly fantastic as a result.

If this comes out to be so, we've certainly happened upon a serendipitious discovery.


Can we agree that a cavity must form first before continuing?

I'm not seeing it, no. As again, my objection is that you're not applying the same principle to your infinite cones as to your infinitesimals, and that you are asking for disibility of the indivisible.

in fact if the cavity is not existant then your infinitesimals have reached zero and that is against teh rules yes?

SO lets rephrase the question:

How do you apply the principle of infinitesimals when magnifying a sphere by infinity?
How do you avoid equaling zero at it's center?

Quantum Heraclitus:


Now the interesting thing about this is that the inverse sphere has zero on the outside yet the surface dimensions at it's centre, so this means that using infinitesimal the sphere can be interpreted as zero surface with infinitesimal at it's centre thus it has no size or volume...

You kind of lost me here. What?


When handling the notion of an inverse sphere, everything is reversed or inverted.
The center is now the surface and the surface is now the center.
In this case the surface is infinitesimal and the center is zero so in effect our cavity is actually non-existant...

Why do we need to have an inverted sphere to begin with? Also, a sphere with zero-volume is...not a sphere. You're redefining the object as you go along.


1] The most economical shape that can form in 3 dimensional space is a sphere because all forces are in balance and can be created by natural means.

I agree to some extent.


2] If the above is the case then when you apply the infinitesimal to a 3 dimenwsional object no matter how much you magnify it you will always get a cavity or chamber of zero at it's center. You could magnify infinitely for eternity and you would still have a chamber at it's center. It just keeps getting smaller with out end and never reaches zero.

...Why would there be a cavity of zero?

The problem again is that you keep on misdefining a sphere.

A volumeless sphere is a circle. The definition of a sphere is a three dimensional circle - that is one which has volume.

damn interesting dev. PJ damn interesting...haven't had this much fun in ages.

Quantum Heraclitus:


How do you apply the principle of infinitesimals when magnifying a sphere by infinity?
How do you avoid equaling zero at it's center?

What do you mean zero at its center?

Where you magnify a sphere infinitely, you'd come upon an infinitesimal distance. I don't know what more you want me to elaborate here?

Quantum Heraclitus:


damn interesting dev. PJ damn interesting...haven't had this much fun in ages.

Interesting, but we're in kind of mushy circumstances.

Quantum Heraclitus:



What do you mean zero at its center?

Where you magnify a sphere infinitely, you'd come upon an infinitesimal distance. I don't know what more you want me to elaborate here?
why distance PJ?
we are talking about magnifying an entire sphere.

we are talking about a 3 dimensional solid object there is no distance beside the diamter of the sphere. Magnify it as much as you like the diameter of the sphere will still be the same.

Quantum Heraclitus:


we are talking about magnifying an entire sphere.

A segment of the sphere magnified infinitely will get you a spot of matter that is infinitesimal. "An infinitesimal distnace".


we are talking about a 3 dimensional solid object there is no distance beside the diamter of the sphere. Magnify it as much as you like the diameter of the sphere will still be the same.

Yes. The diameter will never cease to be one inch or ten feet or whatever the case might be. But you'd be dealing with going further and further into the pieces that make such up.

try this:
if you take our light cone diagram you will note that it is rendered as a 3 dimesnional joining of two cones past and future.
Accordingly if you magnify the center infinitely you wil still find the cones still touching. yes?

A segment of the sphere magnified infinitely will get you a spot of matter that is infinitesimal. "An infinitesimal distnace".
but it's a three dimensional distance not a two dimensional distance.
The distance to the surface of the sphere has to be equal in all aspects of our infinitesimal

Quantum Heraclitus:


try this:
if you take our light cone diagram you will note that it is rendered as a 3 dimesnional joining of two cones past and future.
Accordingly if you magnify the center infinitely you wil still find the cones still touching. yes?

They have a "present" between them. But assuming the two cones are touching, magnifying it infinitely should have them still touching, yes.


but it's a three dimensional distance not a two dimensional distance.
The distance to the surface of the sphere has to be equal in all aspects of our infinitesimal

What do you mean "to the surface of the sphere"?