I don't think it is. I think the idea that the natural numbers go on forever is a concept in your brain that is associated with a Platonic romantic dream of logic that doesn't hold in reality. If the total energy content of the universe was saturated into pure intelligence, there would still be a limit to the highest natural number and most sophisticated mathematical structure it could process. And since it is the largest possible to be realized in any real consciousness, in my opinion it is the highest level of mathematics that is truly real.

If you think the natural numbers don't go on forever, please post the largest natural number. Then tell me why I can't add 1 to it to get a larger number.

Really?
What would you say that limit is?
I.e. what is the highest number possible?

What prevents you from adding 1 to that number? Or doubling it? Or squaring it?

Really?
What would you say that limit is?
I.e. what is the highest number possible?

What prevents you from adding 1 to that number? Or doubling it? Or squaring it?

What prevents you from adding 1 to the number is that at the limit of the nervous firings that process numbers there is no possible new way of firing to process a next number. Since you can use hyperoperation notation for larger and larger numbers, it is so large that its impossible to start to think about it...but you would reach it eventually, and not go further.

What prevents you from adding 1 to the number is that at the limit of the nervous firings that process numbers there is no possible new way of firing to process a next number.
Pardon?
What evidence do you have for this?


Since you can use hyperoperation notation for larger and larger numbers, it is so large that its impossible to start to think about it...but you would reach it eventually, and not go further.
Or this?

How would such a thing work?
If I see the "absolutely maximum number" written down you're claiming that my brain will somehow freeze up and prevent me incrementing it by 1?
This must be false since, to give an example, if that number (regardless of how large it actually is) ends in, say 3, then what is to prevent me from ignoring the rest of that number and simply changing that "3" to a "4"? Or an "8"? :shrug:

I think you're confusing the mathematical concept of natural numbers with some other concept involving physical realisation. Maybe call it "conceivable numbers".

N=0
Loop
N=N+1
Endloop


Tell me, at what number will that stop? And why? What "neuron firing limit" is involved?

Edit: pfft yes I know. But bigger and better computers... ;)

in base ten 9 is the limit of natural whole numbers . All others can be considered larger groups of the same 9 numbers . But that is just one aspect of mathematical objects . There are many mathematical fixtures that are not real numbers .

so here you go all the natural whole numbers
123456789
246813579
369369369
483726159
516273849
639639639
753186429
876543219
999999999

o.k. thats it , all is a repeat after that to infinity . The power of nine . You can fold up every whole number and it will fall in that pattern in its precise group of power . Kind of like counting by ten over and over again but not really . The thing is all factors of whole numbers follow the rule you see right there . Multiples of 4 will follow multiples of 13 with the same pattern .
It is quite remarkable to Me . It still blows my mind . I try not to think about it . It can be very distracting when you start seeing the implications , or better to say the weird congruences in the segregation . Don't that just blow your mind ? God I don't know why that would not . I just can't get use to it all working out like that .


Edit : O.K. it is Monday morning and you all are bad for making think about the math . Bad People !!! I got things to do besides think about math .

It don't matter how big the number is it will be a product of the above posted pattern . If it was 19191919191919.191919 the multiples would still follow the first row . By reduction if the number i just displayed is x thenx1, x2,x3,x4,x5,x6,x7,x8,x9 would still be 1,2,3,4,5,6,6,8,9
or if x was 134 then x1,x2,x3,x4,x5,x6,x7,x8,x9 would still be 8,7,6,5,4,3,2,1,9.
It just blows my mind ! Can you believe that shit ? Don't you think that is unbelievable .
It gets worse!
The interval is all perfect from 0 . The distance relationship from 0 is in perfect harmony in its bigger form . You that 7 and 25 for example . Lets call them blue. We got 0 ,7,14 ,21 = x0,x1,x2,x3 . Now we got 0,25,50,75= 0,x1,x2,x3. Now by reduction what do we got ? We got the 7 pattern of the master list above that I posted . You go to the 7 list of 7,5,3,1,8,6,4,2,9 and both are congruent by reduction .

I know you all think that might be all no big deal cause of how all multiples of 9 reduce to 9 , but I can not get past the completeness of occurrence. It don't matter how big a number it is its multiples will be of just those forms above .

I know it's not his usual subject, but this thread just screams "reiku."

Really?
What would you say that limit is?
I.e. what is the highest number possible?

What prevents you from adding 1 to that number? Or doubling it? Or squaring it?


Ha-hum... well, nothing, but with these operations you will always end up with a definite, non-infinite number... Jou just start counting and come back and tell us when you have reached infinity!

:)

I know it's not his usual subject, but this thread just screams "reiku."Nah, Reiku would have tried to link it to quantum mechanics and thrown in something like

"And so the conciousness wavefunction is \int_{\Omega}|\psi|^{2} dx = 1 with gauge connection D = \partial + ie A_{\mu} for Wely spinor \chi_{s} and so we can conclude neutrinos go faster than light!"

then proceed to throw his toys out the pram when someone points out his incorrect spelling of Weyl and the complete non-sequitor nature of his post.

ZOMG!11!
AN is channelling Reiku! ;)

“
Originally Posted by Dywyddyr
Really?
What would you say that limit is?
I.e. what is the highest number possible?

What prevents you from adding 1 to that number? Or doubling it? Or squaring it?
”


Ha-hum... well, nothing, but with these operations you will always end up with a definite, non-infinite number... Jou just start counting and come back and tell us when you have reached infinity!

:)

The concept of 'infinity' as applied to numbers remains interesting to me. That a species of demonstrably finite life expectancy would contemplate such a concept which, by logic, seems impossible to verify, is an exercise in futility, IMO. :bugeye::D

Isn't life itself a rant against futility?
Life's but a walking shadow, a poor player,
That struts and frets his hour upon the stage,
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.

If you think the natural numbers don't go on forever, please post the largest natural number. Then tell me why I can't add 1 to it to get a larger number.

I think this is about as succinct a refutation as you can get.

N=0
Loop
N=N+1
Endloop


Tell me, at what number will that stop?

2^{256}?


And why?

Because I work on a supercomputer? :-)

The philosophy of mathematics is a subject for the Philosophy (http://www.sciforums.com/forumdisplay.php?f=21) subforums, not Physics & Math (http://www.sciforums.com/forumdisplay.php?f=33).

The concept of 'infinity' as applied to numbers remains interesting to me. That a species of demonstrably finite life expectancy would contemplate such a concept which, by logic, seems impossible to verify, is an exercise in futility, IMO. :bugeye::D

It is interesting. Personally, I'm not convinced by the "you can always add one"-argument, since when you do, you always end up with a completely ordinary number. I think it is a mistake to equal "indefinetly" with "infinitely".

I think we can safely disregard the original poster's idea that this has something to do with neurons. If anything, our finite brains seems to have no problem with the concept of infinity. But I do think the use of infinity is, or at least can be, problematic.

There is no doubt that infinity may be useful sometimes, but I think it is mostly shorthand for "a very big number".

There are all sorts of difficult philosophical questions here. What kind of reality do we ascribe to a number, any number, not to mention infinity? If "number" is a concept anyway, why should "infinity" be less real? What is the relation between mathematics and physics?

Many mathematicians would not be offended by being called platonists. Its truths are considered to be indipendent of any "real" world. Personally, I see mathematics as a human activity that is very much a part of our physical world. I fear that we may make some metaphysically wrong assumptions if we uncritically allow concepts such as infinity, that these metaphysic concepts will "seep" into our worldview from platonic math. That numbers and cocepts is considered more "real" than reality.

I think you're confusing the mathematical concept of natural numbers with some other concept involving physical realisation. Maybe call it "conceivable numbers".

I think you hit the nail on the head. His arguments are all based on the premise that there is some number X that is the limit of what intelligence can conceive and that somehow this fundamental limit to intelligence somehow limits natural numbers themselves.... which is ridiculous.

I think it's simpler than that. He seems to be implying that, in his opinion, when we think of a number we actually enumerate it in our heads e.g. if we think of 8 we have eight discrete "instances" in mind rather than the figure being a symbol for that number.

I think you're confusing the mathematical concept of natural numbers with some other concept involving physical realisation. Maybe call it "conceivable numbers".

If the Universe is a closed system, then it would follow that the number of objects in it has to be limited as well - including a limited number of the imagined/conceivable objects.

But numbers, qua numbers, don't have to relate to objects. :)

I think the idea that the natural numbers go on forever is a concept in your brain that is associated with a Platonic romantic dream of logic that doesn't hold in reality.
Although there is sentiment that the OP is wrong I would say he might be very generally correct. If there is no physical representation of a number and no information to access, produce, or represent a number then it does not "exist". (One could without too much difficulty make the case that the number doesn't "exist" anyway, and that all of mathematics exists as an abstract concept in the brain, but we could at the very least point out that a set of countable integers are representable in nature, while infinity certainly is not.)

It comes down to the Axiom of Choice. We are making a presumption that (HUGENUMBER + 1) exists only because we can come up with particular examples of (HUGENUMBER) and then trivially add 1 to them but that doesn't mean that they "existed" in any fashion before we came up with any particular example. In other words once we produce it, it exists as a representation in our brains (just as the OP mentioned), but if we don't produce it and it isn't somehow also represented in some other fashion (such as a hyper-intelligent being's favorite number, etc) then does it actually exist? I say possibly not.

It is certainly a philosophical question though, not a mathematical one.

But numbers, qua numbers, don't have to relate to objects.

If the Universe is a closed system, then everything in it is limited.

Including concepts?

Yes, if it is a closed system.

Interesting.
Can one think outside the box?

I just remembered an incident from school, I think we were about 12 years old. We were talking about numbers and what the greatest number would be.
A student actually took a pen and paper and tried to write it down. She started out, what it looked like in full confidence that she can write the greatest number, right there on that paper.

What number did she come up with?

Concepts do not exist in physical reality and therefore they are not bounded by it. I can conceive of the notion of infinitely many things, even if only finitely many things exist. Concepts don't exist anywhere, they are conceptual. The brain state I use to conceive of concepts is physical and at any moment there are only finitely many concepts in the minds of people but those finitely many minds can conceive of the notion of infinitely many things.

Actually, she ended up surprised, once she realized that she could just go on writing the numbers.
I remember the incident because she was so sure of herself.

Interesting.
Can one think outside the box?

If the Universe is a closed system, then one can think outside of the box as much as the limits of the closed system permit.

Concepts do not exist in physical reality and therefore they are not bounded by it. I can conceive of the notion of infinitely many things, even if only finitely many things exist. Concepts don't exist anywhere, they are conceptual. The brain state I use to conceive of concepts is physical and at any moment there are only finitely many concepts in the minds of people but those finitely many minds can conceive of the notion of infinitely many things.

But you are in this Universe, part of it, and your cognition is also part of this Universe.
If the Universe is a closed system, the number of objects (of whatever kind) in it is limited.

The box being the universe!

I agree with AN, a concept, not being physical, isn't bounded by the universe.

I agree with AN, a concept, not being physical, isn't bounded by the universe.

Then where does it exist?

Or are you asserting that the supernatural exists?

Exist? It's a concept. An electrical/ chemical signal in the brain.
But the difference in ACTUAL "space" in the brain taken up by eleventy-billion and eleventy-billion-billion isn't significant. So thinking "infinity" doesn't mean that infinity occurs as an object.

If the Universe is a closed system, then it would follow that the number of objects in it has to be limited as well - including a limited number of the imagined/conceivable objects.

That first part assumes that objects can't have size "zero," which might allow you to have an infinite number of objects in a closed system. How many times can you subdivide a line segment?

The latter part assumes that a representation of infinity would itself require an infinite set of "objects" to be concieved of. Which is obviously false - we have a finite representation. It's called "infinity."

We couldn't even be having this conversation - you couldn't even phrase the sentences quoted above, there - if it weren't already possible to concieve of the infinite.

Exist? It's a concept. An electrical/ chemical signal in the brain.

Concepts still exist.



So thinking "infinity" doesn't mean that infinity occurs as an object.

I think it does - we can and do treat infinity as an object, in fact, as a singular, countable object ("one infinity"). This is how we can talk about it at all.

But you are in this Universe, part of it, and your cognition is also part of this Universe.
If the Universe is a closed system, the number of objects (of whatever kind) in it is limited.

So, only a finite number of brains can think about infinity. This doesn't seem to me to place any limitation on the existence of infinity, as a concept.

We couldn't even be having this conversation - you couldn't even phrase the sentences quoted above, there - if it weren't already possible to concieve of the infinite.

But we cannot actually conceive of the infinite in the sense of 10000000000000000000000000000000000000000000000000 000000000000 etc. etc.

If the Universe is a closed system, then it would follow that the number of objects in it has to be limited as well - including a limited number of the imagined/conceivable objects.

Pardon my ignorance, but does "closed system" mean anything other than "limited" or "finite"? If it's simply a synonym - well, then that's a big IF, isn't it?

Is there general agreement that the universe is a "closed system"?

Anyway, I don't see why a limited or finite universe should limit what we can imagine, even if our brains are limited. Surely, we can imagine things that don't exist? We can be wrong, no?

Pardon my ignorance, but does "closed system" mean anything other than "limited" or "finite"? If it's simply a synonym - well, then that's a big IF, isn't it?

Is there general agreement that the universe is a "closed system"?

There is some agreement that it is.



Anyway, I don't see why a limited or finite universe should limit what we can imagine, even if our brains are limited. Surely, we can imagine things that don't exist? We can be wrong, no?

Our congition is part of the Universe.
If the Universe is limited, so is our cognition.

@ DonQuixote

Is there general agreement that the universe is a "closed system"?
Yes. We're in a closed system.


Our congition is part of the Universe.
If the Universe is limited, so is our cognition.
Granted.
Er, now I'm stuck on how to express what I mean and how limited cognition would still allow us to conceive of infinity. Can I get back to you on this?

Our congition is part of the Universe.
If the Universe is limited, so is our cognition.


I'm sorry, but I find these statements to be too general and oracle-like to be able to argue one way or the other. One might be tempted to say that since people can imagine infinity, then the universe cannot be limited. But then I don't think that logic holds either.

Are you saying that people aren't *really* imagining infinity?

Real infinities do not exist in the universe.

Potential infinites exist only in mathematics.

Unless it is the “universes” then I get confused.

But we cannot actually conceive of the infinite in the sense of 10000000000000000000000000000000000000000000000000 000000000000 etc. etc.

Sure we can. You just did, and wrote a sentence that I understood referring to such. It sounds like you intend to say something other than what you're actually saying, but I'm unsure what it is.

Then where does it exist?

Or are you asserting that the supernatural exists?Concepts do not exist physically somewhere. For example, there's a physical thing known as an apple. There's also a concept of an apple. There's also the physical brain state which can hold the pattern associated to the concept of an apple within it. All of these are different things.

Concepts don't have physical nature. For example, is logic physical? No. Does it exist somewhere? No.

This is a point regularly brought up in teleological arguments (attempted arguments) for a god. Some theists claim everything is either physical or conceptual and concepts require minds and since logic and truth are concepts they must exist in a mind, that of god. Of course the next question is "Is god physical or conceptual?" and the answer is neither, he is supernatural (if he/it/she/they/santa exist at all).

I recommend you watch a series of 5 Youtube videos on said argument for god, the first part is here (http://www.youtube.com/watch?feature=iv&v=v02HM_-Dz2g). It's an atheist call in show where someone pushing said argument calls in. They discuss the important distinction between concepts, physical things, logic, truth, brain states etc. It should help clear this up.

Of course the next question is "Is god physical or conceptual?" and the answer is neither, he is supernatural (if he/it/she/they/santa exist at all).
But isn't "the answer" a concept too?

Maybe I should ask if a prime number is physical or conceptual. I believe the answer to that question depends on "where" a prime number is.
If you have three apples, that's a prime number of apples. But the apples are physical, "three" isn't physical. But in order to think about--i.e. conceive of a number--you need a physical brain that can store and recall concepts.

You will need a physical computer, calculator, abacus, pen and paper etc if you want to represent a number, and so any representation would seem to be necessarily physical. So is whatever neural process that represents a number "in your mind" something physical? I think so.

Is logic physical? Yes, if you want to build a computer. Is your brain a kind of computer? Most likely it is.

Is logic physical? Yes, if you want to build a computer.
Exactly.
My warehouse is full of unused logic. A customer ordered it and then went bankrupt.
And now I find that I can't get rid of it because it's a non-standard size. :rolleyes:

It does not change 3 apples setting on one table . You can call the group-age what ever you want but the group of bing bing bing still behaves as a group of bing bing bing or what we call 3 in this case . The physical is manifested by the group . Three by it self may have no physical form but the coupling to physical objects does . 3 attempts of something would still be physical in nature . Three strikes in baseball , or what have you . The number then takes on physical relationships and becomes something more than a place maker and then it will have to follow the rules of being 3

You all need your salad as to stay healthy . Eat your salad it is good for you .

Wow counting is complicated

I don't think it is. I think the idea that the natural numbers go on forever is a concept in your brain that is associated with a Platonic romantic dream of logic that doesn't hold in reality. If the total energy content of the universe was saturated into pure intelligence, there would still be a limit to the highest natural number and most sophisticated mathematical structure it could process. And since it is the largest possible to be realized in any real consciousness, in my opinion it is the highest level of mathematics that is truly real.
You are wrong, you can google and find that Chuck Norris counted all the numbers from one to infinity (twice)

My warehouse is full of unused logic.So you mean it hadn't been tested? No wonder the guy went bankrupt.
You haven't got any used logic on inventory?

What kind of a logic supplier are you?

Exactly.
My warehouse is full of unused logic. A customer ordered it and then went bankrupt.
And now I find that I can't get rid of it because it's a non-standard size. :rolleyes:In a thread on 0.9r on a computing forum years ago someone's 'proof' it wasn't equal to 1 was because you'd eventually run out of 9s, you'd use up all the 9's in the universe before it became equal to 1.

A friend of mine who did maths and was a member of the forum at the time and I still laugh about that. I can just imagine some kid in a maths exam putting his hand up and saying "Can I have another bag of 7's please, I've run out". It's almost as bad as a punctuation recession!! (http://www.youtube.com/watch?v=xdax8uWYmnQ)

Concepts don't have physical nature. For example, is logic physical? No. Does it exist somewhere? No.

Then we're not having this conversation.



This is a point regularly brought up in teleological arguments (attempted arguments) for a god. Some theists claim everything is either physical or conceptual and concepts require minds and since logic and truth are concepts they must exist in a mind, that of god.

But you and several others are applying this same dichotomy that things are either "physical" or "conceptual."



Sure we can. You just did, and wrote a sentence that I understood referring to such.

That's right - referring to such, supposedly.



It sounds like you intend to say something other than what you're actually saying, but I'm unsure what it is.

Granted, but I am not sure it can be said as long as we agree that the Universe is a closed system.

Are you saying that people aren't *really* imagining infinity?

Well, that is one of those things we cannot show whether it is the case or not.

There is some agreement that it is.


I really had no idea about this. My impression was that science and math use infinities all the time. Could you please point me in the direction of what field of invesitgation leads to this conclusion?

It's a serious question. The only field I know talks about "closed systems" is cybernetics...

Well, that is one of those things we cannot show whether it is the case or not.

OK. Fair enough.
I wrote earlier that I'm sceptical to the use of infinities, so I'm certainly not arguing that infinity is a sensible concept. Bu I'm trying to reason from the perspective of ignorance - i.e. I don't know what the universe is like, I'm trying to find out, using reason and logic on the (few) things I do know.

For the sake of actually discussing the viablilty of the concept of infinity, I think it is best to assume that the concept actually means something.

But you and several others are applying this same dichotomy that things are either "physical" or "conceptual."


I think it was Descartes who said that "since there can be no more in the effect than in the cause, a perfect being (God) must exist, because I can have i concept of e perfect being (an effect). Since I'm not perfect myself, something else -a perfect being (God) must be the cause." Well, more or less.

I don't find this argument convincing.

It seems to me you are turnig this argument on its head. Since we are not perfect (infinite) beings, we can not conceive of infinity.

I don't fint this convicing, either.

I agree that our concepts are dependent on our brains, which are physical and limited. I just dont think it follows that "We cannot really have the concept of infinity".

OK. Fair enough.
I wrote earlier that I'm sceptical to the use of infinities, so I'm certainly not arguing that infinity is a sensible concept. Bu I'm trying to reason from the perspective of ignorance - i.e. I don't know what the universe is like, I'm trying to find out, using reason and logic on the (few) things I do know.

For the sake of actually discussing the viablilty of the concept of infinity, I think it is best to assume that the concept actually means something.

it does . It is not unlike for all eternity concepts in religion. Does that mean anything ? Does any subject on moral behavior mean anything . I like Mother Goose the best my self. A lot more modern than some writings of thought .
Kids like it too.
O.K. this is the latest in human intuition as to what eternity looks like . Universes with invisible membranes as a separation devise . We can't see past our own universe because of the membrane ( The closed part ) Theses spaces collide and create waves that give rise to matter . Crystallized structures are created by the rise of matter. This crystal like structures align and form bigger structures . These crystal structures then convert matter and energy on bigger scales. All kind of like magnets having there iron What ever's all stacked neatly the same direction .

Note : Me has taken liberties from a conglomerate of sources posted at S.F. , You Know who you are , I should not have to point out your own posts gumbled up in the above post . Gum Chewers . Detectives . Shoes with phoning home capabilities. Homeward bound soldiers.

O.K. chew it up and spit it out

Note : Me has taken liberties from a conglomerate of sources posted at S.F. , You Know who you are , I should not have to point out your own posts gumbled up in the above post . Gum Chewers . Detectives . Shoes with phoning home capabilities. Homeward bound soldiers.

O.K. chew it up and spit it outWhat..... the...... ?

It seems to me you are turnig this argument on its head. Since we are not perfect (infinite) beings, we can not conceive of infinity.

I don't fint this convicing, either.

I agree that our concepts are dependent on our brains, which are physical and limited. I just dont think it follows that "We cannot really have the concept of infinity".
God and infinity both exist as abstract concepts in our head, while neither have a physical representation as far as we are able to determine. How's that?

I apologise for all the spelling errors. It's allowed to spell it "apologise", I believe.

God and infinity both exist as abstract concepts in our head, while neither have a physical representation as far as we are able to determine. How's that?

Well, it's a complete mystery to me, but that's how it is.

Now, if infinity is not represented in physical reality, how do we justify using mathematics that allow infinities to describe our physical world?

At least, I have read that the speeding neutrinos should have ininite mass att the speed they're going...

Now, if infinity is not represented in physical reality, how do we justify using mathematics that allow infinities to describe our physical world?
Simple answer?
Because, as they say, it works, bitches. :D

Simple answer?
Because, as they say, it works, bitches.

And the only reason why something works is because it in some is aligned with "how things really are."

Simple answer?
Because, as they say, it works, bitches. :D

Hehe, that is actually a good answer!

Still, it bothers me. Unfortunately, I'm mathematically challenged, so I can't decide if it really works or not. I'm stuck with these concepts that doesn't make sense to me.

But you and several others are applying this same dichotomy that things are either "physical" or "conceptual."


Agreed, some concepts seem to refer to the "non-physical" a category which can actually be in existence.

And the only reason why something works is because it in some is aligned with "how things really are."

I suspect there's a word missing in that sentence, but I'm unclear about what you mean - surely if things "align" with "how things really are" that's a good thing, no?

Somehow, your earlier comments leads me to think you meant something else.

And the only reason why something works is because it in some is aligned with "how things really are."
Yes and no.
As Einstein (oops, sue me!) once said:
"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Mathematics, when applied to the real world, is a "description".
I.e. it's how WE make sense of things, not necessarily how reality is.

Mathematics, when applied to the real world, is a "description".
I.e. it's how WE make sense of things, not necessarily how reality is.


There's also the question that we can make sense of anything at all, so one can ask "How do we get to make sense?".

And excellently illustrated by your post.
I can't make sense of it.

There's also the question that we can make sense of anything at all, so one can ask "How do we get to make sense?".

Apparently, it is part of the Universe that we can make sense of things, or at least have the impression of doing so.

and excellently illustrated by your post.
I can't make sense of it.

+1!

Apparently, it is part of the Universe that we can make sense of things, or at least have the impression of doing so.


Or it can be that the universe generates our "reality" somehow and because it's our "reality" it provides us a way to interact with something.

Huh?
The universe is our reality: we're stuck with it.

Yes and no.
As Einstein (oops, sue me!) once said:
"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Quoting Einstein should be forbidden! That guy made so many confusing statements. Many of which appear to contradict each other. Problem is, he is so darn quotable.

Huh?
The universe is our reality: we're stuck with it.

Welcome home.

Huh?
The universe is our reality: we're stuck with it.


Our "reality" is our "reality".

Quoting Einstein should be forbidden! That guy made so many confusing statements. Many of which appear to contradict each other. Problem is, he is so darn quotable.
Hence my comment about suing me. But this particular one was apposite.


Welcome home.
Is the kettle on?


Our "reality" is our "reality".
That's more than somewhat tautological.

Our "reality" is our "reality".

A= A

So what?

Well, it's a complete mystery to me, but that's how it is.

Now, if infinity is not represented in physical reality, how do we justify using mathematics that allow infinities to describe our physical world?

At least, I have read that the speeding neutrinos should have ininite mass att the speed they're going...


This doesn't mean that infinity cannot be represented in "non-physical" existence but I doubt you're interested in discussing the intangible. I know that "non-physical" is completely unknown territory.

That's more than somewhat tautological.


Only because you assert it to be.

Only because you assert it to be.
Really?
Please explain how it couldn't be.
As DonQuixote stated, A=A.

Was I not discussing that the universe generates our "reality".

Apparently, it is part of the Universe that we can make sense of things, or at least have the impression of doing so.

@ Signal:

Could you please tell me how we know the universe is "closed" or finite or whatever? I would really like to know.

Is the kettle on?

Yes, it's on its tour around Saturn.

Was I not discussing that the universe generates our "reality".
Your point being?

How does that "explain" that your statement isn't tautological?

Could you please tell me how we know the universe is "closed" or finite or whatever? I would really like to know.

Note, I have never made the claim that the Universe is a closed system; I only presented some conclusions that seem to follow if the Universe is a closed system.

Your point being?

How does that "explain" that your statement isn't tautological?


Why are you sidetracking by focusing only on that post then?

Our "reality" is our "reality".

Why are you sidetracking by focusing only on that post then?
Maybe you didn't bother reading any other posts.
Any "focussing only on that post" is purely because you are putting the focus there.
We also responded to your other posts, but YOU came back with replies to that particular one.
Why is that?

The post:

Our "reality" is our "reality".

was in response to

Huh?
The universe is our reality: we're stuck with it.

I wish we didn't lose context so easily.

Name a "reality" we have other than the universe we inhabit.

Note, I have never made the claim that the Universe is a closed system; I only presented some conclusions that seem to follow if the Universe is a closed system.

Reading carefully, I have to admit that you did not.
I have previously disagreed that those conclusions follow.
But you did say that "There is some agreement that it is", reffering to the universe being a closed system.

So I'm only asking: among whom does this ageement take place? What is the field of inquiry that has yielded this result?

I don't really care if you personally subscribe to it. This discovery, if true, would save me a lot of headache.

I know that we inhabit the universe but in the context of my post the universe generates our reality which allows us to interact with something. I say that as a possible explanation for the reason we can make sense of the physical world through mathematics, physics etc.

But you did say that "There is some agreement that it is", reffering to the universe being a closed system.

So I'm only asking: among whom does this ageement take place? What is the field of inquiry that has yielded this result?

I don't really care if you personally subscribe to it. This discovery, if true, would save me a lot of headache.
Um, the universe, by definition, is everything that is. Therefore there cannot be anything "outside" of it.

If you claim that it's not a closed system then you have to account for what there is that's not of the universe and also account for how it could interact without being part of the universe.

I know that we inhabit the universe but in the context of my post the universe generates our reality which allows us to interact with something.
What do you mean by "generates our reality"? :shrug:

You can use your own interpretation but it's a possible explanation for how we can understand the physical world, it's an essential explanation.

Yes and no.
As Einstein (oops, sue me!) once said:
"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Mathematics, when applied to the real world, is a "description".
I.e. it's how WE make sense of things, not necessarily how reality is.

I don't know about that as in the physical plane of earth Asq +Bsq.does equal Csq. Like every fucking time it does . Oh not necessarily for all Math ? What for Maths not proofed ? Ones that have not been constructed yet? I get it I think if something falls at a right angle it will work that way in reality . Us humans are good at seeing right angles for the most part . You can just about wank anything into a right angle . Just put it all into any triangular space and wha la we got physical lines of real space as to measure by . Are the lines real ? Are they imaginary ? Well as a measuring tool they are as real as a fucking chain saw and a tape measure. We can count on it as a natural law as far as I can tell . You do this and this is going to happen kind of thing . Are we forcing it into a box . Maybe but then inside the guided cage it is isolated as to be dissected better with Me pretties . We can find out what it really is under such scrutiny. Micro scopes are a grand thing , unless you all liked living in a cave more better with out things like running water and flushing toilets. Were washing your hands is taboo

Um, the universe, by definition, is everything that is. Therefore there cannot be anything "outside" of it.

If you claim that it's not a closed system then you have to account for what there is that's not of the universe and also account for how it could interact without being part of the universe.

by bumping into it . Stretching it as it does

I don't know about that as in the physical plane of earth Asq +Bsq.does equal Csq. Like every fucking time it does
That happens to be incorrect. :p
It's true for Euclidian geometry (which deals with flat planes).
But NOT on a sphere.

Of course Einstein may have been overstating the case somewhat, but it's pertinent.

by bumping into it
How can it not be part of the universe and still bump into it?


Stretching it as it does
As it does?
You have evidence for this?

Um, the universe, by definition, is everything that is. Therefore there cannot be anything "outside" of it.

If you claim that it's not a closed system then you have to account for what there is that's not of the universe and also account for how it could interact without being part of the universe.

Hehe. Thank you for responding.
I am not *claiming* that the universe is not a closed, or finite, system.
I am actually eager to know if there is some proof, or at least reason to believe that it is.
I do not, however, believe that by giving "everything that is" a name - universe, we can limit it in any way by definition.

If this is not clear from what I have said earlier: I am highly sceptical of the concept of infinity. I do not find that the "you can allways add one" argument holds, as it always yields a completely normal, finite number. I find it deeply troubling that the mathematics we use to describe our physical world even allows infinities. Even if "it works". But since I don't believe calling itt "universe" makes it finite, I would really, really like a demonstration that he universe is finite on other grounds. Hence my question.

You can use your own interpretation
In other words you're generating word salad that you can't be bothered to defend. Okay.


but it's a possible explanation for how we can understand the physical world
Yeah. And an equally "plausible" one is: giant goldfish.


it's an essential explanation.
I bet you can't substantiate this either.

Yeah. And an equally "plausible" one is: giant goldfish.


I bet you can't substantiate this either.


It is essential if you care why we can understand the physical world, this is only telling me you don't care to give a moments thought about it. Well I don't have a problem with that, ignorance is bliss. :shrug:

That happens to be incorrect. :p
It's true for Euclidian geometry (which deals with flat planes).
But NOT on a sphere.

Of course Einstein may have been overstating the case somewhat, but it's pertinent.

Yet I might be over stepping my bounds , but you engineers got your wicked ways of compensating for curvature of the earth . I have heard urban myths that you do when you are building incredibly long ass structures Like highways and such things ? Of major magnitudes ? It must be urban myths that engineers with there alchemy bag of tricks or treat have not compensated as so . I can visualize the curved right angled space. I can just about see how I could measure it too . If I could pull a string from the center of the radi to the curved triangles surface I am positive I could at lest lay it out in in any congruency size you want or reproduce if I was to build it and make it real

How can it not be part of the universe and still bump into it?


As it does?
You have evidence for this?

no i am shooting from the hip just for the fun of it . My bullet hollow points hit right on you . You took em like a real Man too

Yet I might be over stepping my bounds , but you engineers got your wicked ways of compensating for curvature of the earth
Yeah, our "wicked ways" include mathematics.1 ;)
Spherical geometry (http://en.wikipedia.org/wiki/Spherical_geometry) helps.


I can visualize the curved right angled space.
Sure, nothing to stop you having a right-angled triangle on a curved surface (or in curved space): it's just that Euclidean geometry doesn't apply in such cases. You can even get a triangle with THREE right angles on a spherical surface.
http://www.chris-j.co.uk/images/spherical_triangle.png
A=B=C (each being one quarter of the circumference) therefore A2+B2 != C2, but 2C2. Change one angle, and that ratio alters.


1 I deliberately didn't mention the sacrificing of virgins because that tends to freak non-engineers out.

it's just that Euclidian geometry doesn't apply in such cases.

What's non-Euclidian about it? Those lines on the surface of the ball is simply not straight lines, they are curves. Those angles aren't straight 90 degrees angles, 'cause the legs are not straight. Unless you want to ivoke infinity, since infinetly close to the angles they probably are.

What's non-Euclidian about it?
The fact that it isn't on a flat plane: that's what Euclidean geometry deals with.


Those lines on the surface of the ball is simply not straight lines, they are curves.
They're straight lines on that surface.


Those angles aren't straight 90 degrees angles, 'cause the legs are not straight.
Um, if there's 90 degrees between each pair of lines (no more and no less) then, by definition, they're right angles.


Unless you want to ivoke infinity, since infinetly close to the angles they probably are.
No, they are right angles. On a curved surface. Hence we are not dealing with Euclidean geometry but spherical.
Euclidean is only one type of geometry, there are more types of geometry that aren't Euclidean than there are that are.

I do not, however, believe that by giving "everything that is" a name - universe, we can limit it in any way by definition.
Okay: what is the universe?
(I know that sounds like a diversion, but if we're going to work out whether or not it's closed we need to know exactly what we're talking about).


If this is not clear from what I have said earlier: I am highly sceptical of the concept of infinity. I do not find that the "you can allways add one" argument holds, as it always yields a completely normal, finite number.
Agreed. Any number you arrive at is finite. Infinity in this case is a process not a "result".


I find it deeply troubling that the mathematics we use to describe our physical world even allows infinities.
Hmm, why?
Maths works, we don't have a better way. We're stuck with it.

What's non-Euclidian about it? Those lines on the surface of the ball is simply not straight lines, they are curves. Those angles aren't straight 90 degrees angles, 'cause the legs are not straight. Unless you want to ivoke infinity, since infinetly close to the angles they probably are.They are geodesics, ie the shortest path between two points in the space. Geodesics in Euclidean space are straight lines and someone on the surface will view them as straight lines.

It's non-Euclidean because parallel lines cross. For example, in the Euclidean 2 plane if different lines A and B are both at right angles to line C then A and B are parallel and never meet. On the sphere pictured above the two lines going up to the North Pole are both at right angles to the equator and yet they meet. Any two lines of longitude are at right angles to any line of latitude but the lines of longtitude always meet somewhere on the globe. Such a thing is simply not possible in Euclidean geometry.

I find it deeply troubling that the mathematics we use to describe our physical world even allows infinities. Even if "it works.



What kind of infinities are allowed in mathematics e.g. the set of real numbers or the set of natural numbers. I doubt anyone can show where in the set the "infinite number" can be reached. All that happened is an attempt to identify it as a set.

The fact that it isn't on a flat plane: that's what Euclidean geometry deals with.

Euclidian geometry has no problems describing a sphere.



They're straight lines on that surface.


Or, as Euclid would have said, they are the shortest lines over the surface of the sphere. That doesn't mean they're not curves.



Um, if there's 90 degrees between each pair of lines (no more and no less) then, by definition, they're right angles.

I would agree to that, but then I disagreed that these are straight lines.



No, they are right angles. On a curved surface. Hence we are not dealing with Euclidean geometry but spherical.
Euclidean is only one type of geometry, there are more types of geometry that aren't Euclidean than there are that are.

I have heard this argument before. I have also heard that all geometries are translatable into each other. It's geometric relativity, if you like. It's just that you can sometimes simplify the math by supposing a different geometry. Well, thats what I heard anyway. I'm really just spamming you because nobody reacts to my real questions. But I did it by mention infinity, didn't I, which is what this thread is supposed to be about? (I don't know if I have got the markup on this text right).

It is essential if you care why we can understand the physical world
According to you, at least.


this is only telling me you don't care to give a moments thought about it.
On the contrary you have been informed by two different people that your remarks is essentially meaningless. Since YOU stated it and YOU claim it has meaning then it's up to... guess: YOU to explain what YOU meant. It's not up to me to define it for myself and then work out what YOU meant.

Euclidian geometry has no problems describing a sphere.
Really?
How can it since Euclidean geometry deals purely with flat planes.


Or, as Euclid would have said, they are the shortest lines over the surface of the sphere. That doesn't mean they're not curves.
ON THE SPHERE they are straight lines. They're curved in three dimensions, but on the 2D "plane" of the surface they're straight.


I would agree to that, but then I disagreed that these are straight lines.
See previous comment.


But I did it by mention infinity, didn't I, which is what this thread is supposed to be about?
Yeah, I didn't see your last post on that until after I'd done the other reply.

According to you, at least.


On the contrary you have been informed by two different people that your remarks is essentially meaningless. Since YOU stated it and YOU claim it has meaning then it's up to... guess: YOU to explain what YOU meant. It's not up to me to define it for myself and then work out what YOU meant.


I didn't ask you to define it I only allowed you to use your own interpretation. I'll have to get back to you until I find a way to explain what I meant. :rolleyes:

I didn't ask you to define it I only allowed you to use your own interpretation.
Um,

define it for myself
would that not be an interpretation?

Maybe we are using different definitions of the word define.

Really?
How can it since Euclidean geometry deals purely with flat planes.

Now, I will admit that I have never actually read Euclid. Has anyone? But i thought a sphere is described as all points at an equal distance (radius) from a point? That's easy, isn't it?



ON THE SPHERE they are straight lines. They're curved in three dimensions, but on the 2D "plane" of the surface they're straight.

Ssshhh. Don't shout. I know what you mean.

Now, I will admit that I have never actually read Euclid. Has anyone? But i thought a sphere is described as all points at an equal distance (radius) from a point? That's easy, isn't it?
It's something they never tell you at school (where they usually only teach Euclidean) - that it only applies to flat planes: i.e. it's a sub-set of 2D geometry.


Ssshhh. Don't shout. I know what you mean.
Wasn't meant as shouting, rather emphasis. :o

It's something they never tell you at school (where they usually only teach Euclidean) - that it only applies to flat planes: i.e. it's a sub-set of 2D geometry.

Didn't know that, but it's trivial to extend it to 3D, isn't it?



Wasn't meant as shouting, rather emphasis. :o
[/QUOTE]

No problem

Have to go. 0200 am in Europe. CU

Didn't know that, but it's trivial to extend it to 3D, isn't it?
Trivial-sh. But then it becomes non-Euclidean. :p


No problem
Have to go. 0200 am in Europe. CU
Pfft, I'm on BST so it's only 1 AM.

Now, if infinity is not represented in physical reality, how do we justify using mathematics that allow infinities to describe our physical world?
Just because reality can be described mathematically does not mean everything that can be described mathematically is reality.

Just because reality can be described mathematically does not mean everything that can be described mathematically is reality.

Maybe , but the potential is very exciting!! It blows my mind . To think parallel lines can intersect at the north pole gives Me warm fussy feelings . Like I have my own star like Jesus . I want my own star Waaa Waaa . I think you can buy a star if you want these days. So Go figure lots of people got stars .

I will tell you what can be frustrating is when an Engineer don't see the 3d ramifications . Architects are the worst as not as much as Engineers . 2d and 3d are a whole different animal in the evolution of mathematics . You would not believe the stories of people with specific names that have proven my point . It is not the easiest thing to think through . The average person will miss judge the spaces . Things like distance are pretty hard for the common eye to discern . There are range finders now so you check your self and see how your own eye miss judges space

I think you can buy a star if you want these days.
No you can't. But there are plenty of scam artists who will try to convince you that you can.

It's something they never tell you at school (where they usually only teach Euclidean) - that it only applies to flat planes: i.e. it's a sub-set of 2D geometry.


This just seemed to be contrary to what I learned at school, and contrary to what I think is normal use of the word "Euclidian", so I decided to look it up.

To quote Wikipedia:



Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians,[1] Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.[2] The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions.


Last sentence seems to contradict your claim.

In another thread in the physics & Math section that was started yesterday (on special relativity), the first post refers to "Euclidian space" - that is 3D.

I know that in discussions about relativity, Euclidian space is sometimes referred to as being "flat". But this has nothing to do with being limited to the plane.

Now, it is not very important what we call the thing. Point is that ordinary geometry can describe a sphere. But in ordinary geometry, those lines on the surface of the sphere are curves.

I posted earlier concerning the non-existense of infinities in universe and stated that there existed only "potential infinities" and that real infinites only exsted in mathmatics.

Can anyone name a real infinity that exists in the universe? Combinations and permutations of elementary partiles or plank volumes won't do it.They are finite assuming the universe is finite.

This just seemed to be contrary to what I learned at school, and contrary to what I think is normal use of the word "Euclidian", so I decided to look it up.

To quote Wikipedia:

Last sentence seems to contradict your claim.
My bad, I worded it ambiguously.
Euclidean geometry as taught in schools (at least when I was a lad) was purely 2D.
http://regentsprep.org/Regents/math/geometry/GG1/Euclidean.htm


Now, it is not very important what we call the thing. Point is that ordinary geometry can describe a sphere. But in ordinary geometry, those lines on the surface of the sphere are curves.
"Ordinary" geometry? :shrug:
Euclidean?

My bad, I worded it ambiguously.
Euclidean geometry as taught in schools (at least when I was a lad) was purely 2D.


"Ordinary" geometry? :shrug:
Euclidean?

Yes, I'm completely happy to continue to say Euclidean :)

I'm trying to google a reference to my claim that different geometries are translatable into each other, but it seems I cannot find it, so it may be a figment of my imagination.

My point was/is that the lines on the ball are curves in euclidian space. Curves are notoriously difficult to handle. In another geometry, such as the spherical one, these lines are concidered straight, and that makes it much easier to handle (mathematically, I think). It comes at a cost, though. In most cases on the sphere there will only be one straight (shortest) line between two points. But in the case where the two points are on diametrically oposite sides of the sphere, there are suddenly infinitely many lines between the points, and no line is the shortest.

My point was/is that the lines on the ball are curves in euclidian space.
Er no. see my link in my last post (sorry - I added it later):

Euclidean Geometry is the study of flat space
But if you live on the ball then the lines are straight: as you said -
In another geometry, such as the spherical one, these lines are concidered straight

In fact, as Me Ki Gal claimed, the surface of the Earth can be considered to be flat for "most" purposes. House plans don't need to take into account curvature, so Euclid works sufficiently well.

Er no. see my link in my last post (sorry - I added it later):

But if you live on the ball then the lines [are[/i] straight: as you said -

In fact, as Me Ki Gal claimed, the surface of the Earth can be considered to be flat for "most" purposes. House plans don't need to take into account curvature, so Euclid works sufficiently well.

No, no, no. This has nothing to do with what I said. I don't think you are getting me here. It has nothing to do with something like "Newtonian physics is actually wrong, but a reasonable aproximation at low speeds". Euclidean geometry is not an aproximation to reality on the surface of the sphere.

Different geometries are different ways of looking at objects. I have no idea of what a sphere would look like in spherical geometry, perhaps it cannot even be represented, since the speherical geometry is 2D.

Hope this is not too confuing, I'm a bit confused myself.

I posted earlier concerning the non-existense of infinities in universe and stated that there existed only "potential infinities" and that real infinites only exsted in mathmatics.

Can anyone name a real infinity that exists in the universe? Combinations and permutations of elementary partiles or plank volumes won't do it.They are finite assuming the universe is finite.
Please think about the infinitely small. What is the smallest "particle" that no longer can divide?
Infinitely large: If the universe is finite, it must have a border. What is after the border?
But this subject belongs to philosophy.

If the universe is finite, it must have a border.
If you live on the surface of a sphere where's the border of that finite space?

. . numbers 'theories' are mental constructs . . likely started when we began to 'count' our fingers and toes! tee hee!

If you live on the surface of a sphere where's the border of that finite space?
This means that the surface is curved in the third dimension.
The infinite then is in an higher dimension.
If we send a laser beam into space and it return at our back, it means that our space is curved in the fourth dimension.
It would be something great (the hyperspace?). What is the straight line in four dimensions?

This means that the surface is curved in the third dimension.
So what?
Where is the boundary of that finite space?


The infinite then is in an higher dimension.
If we send a laser beam into space and it return at our back, it means that our space is curved in the fourth dimension.
It would be something great (the hyperspace?). What is the straight line in four dimensions?
In other words you're refuting your own argument.

Emil . . . has that laser experiment ever proven successful? . . kind of like shooting one's self in the foot . . . or stepping on one's own penis. tee hee!

. . likely started when we began to 'count' our fingers ...
Out of this came base-10 of numbering. :D

My bad, I worded it ambiguously.
Euclidean geometry as taught in schools (at least when I was a lad) was purely 2D.
http://regentsprep.org/Regents/math/geometry/GG1/Euclidean.htm


"Ordinary" geometry? :shrug:
Euclidean?

Well at my school we had to construct 3d objects out of construction paper . It was one chapter devoted to just that . House construction is a great utilization of it in 3d form . When we get into building radius type buildings higher forms of math work better . Trig comes in to play real quick from my observation . Even determining a specific arch where the seconds are called out and you figure out a straight line distance cutting through that segment of seconds and you want to know how wide a perpendicular line is to the tangent mid way of the ache bisected, plus you got shit for established measurements cause the fucking supplier won't get off his lazy ass in get you the schematic of the product. Carpenters got to brake the book open and then install backing before shit gets covered up with out having proper structural integrity. I just hate it when people say ( You Carpenters need to pay more attention to what your doing . Your building our houses and we have to live in them . Do I hate the people . No ! Don't always like what they say , but hey people don't always like what I say either , so what you gonna do

Out of this came base-10 of numbering. :D

I think that is an urban myth . A favorite of peoples

So what?
Where is the boundary of that finite space?
Yes you're right. In this case the infinite is only theoretically .
Practically, space is finite without boundary.
At least until we can get to the fourth dimension. :p

. . or stepping on one's own penis. tee hee!
Can you be a little more precise and elaborate?

This is not an answer to my question.

I posted earlier concerning the non-existense of infinities in universe and stated that there existed only "potential infinities" and that real infinites only exsted in mathmatics.

Can anyone name a real infinity that exists in the universe? Combinations and permutations of elementary partiles or plank volumes won't do it.They are finite assuming the universe is finite.

I thought about it an nothing came to mind . That is why I didn't answer . My fingers were like wanting to put something in there but just could not . Chewing gum maybe or Plastic . I don't know ? I got to think about that. Energy it self ? What ever it might convert to. Motion maybe . Infinite Motion . Yet don't you guys think of Motion as being potential energy so " Potential Infinities" sounds pretty good to Me . I will go with that

MKG:

Well . . . duh!? . . . perhaps energy can convert to matter, via E=Mc^2 .. . .

I think that is an urban myth . A favorite of peoples
It seems fairly reasonable. After all, 10 is not a very good base to choose...