LOL. Right you are. Like I say I'm new around these parts. But it's still the case that math and physics are different subjects, even though "everything is related" and "all is one" as you say. There are no zero-dimensional points in the physical universe, but there are in math. If you and I can't agree on that then we will make no progress. When you ask how the circumference of a circle can exist yet have no area; the answer is that in math it can and in the physical world there's no such thing as a dimensionless circle having no thickness.
Pi - No Patterns, because Pi is the pattern
- Thread starter Quantum Quack
- Start date
LOL. Right you are. Like I say I'm new around these parts. But it's still the case that math and physics are different subjects, even though "everything is related" and "all is one" as you say. There are no zero-dimensional points in the physical universe, but there are in math. If you and I can't agree on that then we will make no progress. When you ask how the circumference of a circle can exist yet have no area; the answer is that in math it can and in the physical world there's no such thing as a dimensionless circle having no thickness.
Fedris,
Can you say with absolute certainty that a given length of a line from a central zero point to another zero point can be quantified so concisely?
for example say we draw a line 50 mm long and wish to consider this to be a radius.
center point is a zero point .
the 50mm point is a zero point.
How can precision be achieved that is absolute given that we are talking about values at 1/infinity or less than.
Does 49.9999999999999... repeated infinitely, equal 50
On that basis how can a perfect circle be constructed when the "error margin" of 1/infinity is present?
I agree , if agreement over the zero point is not achieved we will indeed get bogged down ingoing around in dare I say imaginary circles [chuckle]
Regarding the physical existence of zero point.
Physics:
The center of Mass [commonly referred to as the [center of gravity] is what?
Does this center of mass exist?
If so how big is the this point?
It's Physical reality is evident in everything of substance.
It's exact location can NEVER be nailed in absolut-um [ re: Uncertainty Principle for example]
=======
Math:
If I draw a line 60mm long A to B
and wish to identify it's middle point M [30mm]
Does this Middle point M exist?
If so how big is this point?
Can this middle point ever be found if it is a zero point?
It's physical reality is in every line or geometric shape ever drawn. Every shape manufactured or crafted etc etc...
Zero does indeed both exist and non-exist simultaneously in both fields, math and physics. IMO
In other words zero exists but can never be found except by Reductio ad absurdum. Therefore zero can only be deemed to exist by deductive reasoning, by default of everything else being considered but never deemed to exist directly. [both for math and physics ]
To me this is exposed by the sheer brilliance of Zeno of Elea's paradoxes, which indicated the need for calculus and the invention of the infinitesimal.
Zero is both imaginary and real simultaneously.
The use of the term infinitesimal proves the Physical and non-physical existence of zero "by default".
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I'm not talking about physics. To the extent that you are having a conversation that involves physics, I'm not involved in that conversation. I don't know much about physics, for one thing. My training is in math and I'm trying to present and explain the mathematical point of view.
I make no representation that anything I say has the slightest bearing on actual, physical reality. All I'm doing is explaining the math. Since the discovery of non-Euclidean geometry in the 1840's, math and physics have been two separate but interrelated disciplines. Math is not physics. I'm just talking about the math.
However to answer your questions: The exact location of any object in physical space can never be determined. This is true not only in quantum physics; but also in classical physics. All measurements are made by humans using the technology they're capable of making. All real-world measurements are approximate.
Yes. It's halfway between A and B.
It's a dimensionless point. It has zero length. If it's living in 2-space it has zero length and zero width. If it's living in 3-space it also has zero height. It's a point. It's modeled by a real number (in 1-space) or by an n-tuple of real numbers in n-space.
Yes, it's (A + B) / 2. That's true whether A and B are real numbers or vectors in n-space. That's how you find the midpoint of two points. Didn't they teach you this in high school? I'm sure they teach this in 2 dimensions. I'm really curious, when you were in class did you have these conceptual objections to mathematical objects? Or is this a more recent set of beliefs?
It definitely exists mathematically. Physically we cannot say, for all physical measurement is approximate. What would it mean in physics to ask if a "point" exists? How would you build an apparatus to measure one? The question itself is meaningless.
Look, you want math to be about physics. You have the same opinion the typical educated person did in 1840. Today we simply don't have that belief anymore. Math is not about physics. Some philosophical theories of math regard math as a complete fiction, a made-up story that happens to be useful to people.
You want math to be about physics; but it simply isn't.
Tell me something, do you at least understand what I'm trying to say? In other words even if you think I'm wrong ... can you at least comprehend that in math, (A + B) / 2 is the midpoint of the vectors A and B in any finite dimensional Euclidean space. Whereas in physics, firstly we can never know exactly where objects are; and secondly, the objects of study are not dimensionless points, but rather galaxies, planets, atoms, quarks, etc., that each have many complex properties and behaviors of their own.
Physics studies the real world. Math studies the abstract mathematical world.
Math is not physics. I haven't got much to add, except for details.
oh, I accepted your explanations ages ago... not a problem. However we are not here to discuss the veracity of (a+b)/2. I thought we were discussing the reality of that mid point as being zero..
Does zero exist or not or both, that is the question.
I hold that zero is paradoxed regardless of discipline you refer to. It both exists and non-exists simultaneously.
Pi - Zero - Pi^3 -STOP Go No Further Into Infinite Irrationality
Hi QQ, I may be to far off base for you thread topic but wanted to through my thoughts into the this pi-ratio as random pattern.
Yeah, it is random pattern.
Non-occupied space = zero fermions, bosons and gravity
Zero is symbol or word used to represent a the count of beads in this column of abacus is 10, so move on to next column and place these beads in this column back to there zero( not counted yet ) starting place aka zero.
The perfect circle or perfect sphere are mathematical constructs of mind/intelligence only ergo Pi is of a mind/intelligence mathematical nature only.
That said, let us take mathematical Pi^3 and round off the irrational parts selectively at various places to see if it approximates nature when so doing.
Pi^3 = 31.00 62 7.......
^3 = a 3rd powering ergo a XYZ cubing or ABCD tetrahedroning as a volumetric quantity.
For starters, counting both sides of the decimal point, we have a total of 7 integer places ending at #7
The regular/symmetrical, 5/phi-fold icosa(20)hedrons 6, 10 and 15 great/equaltoria, circle-like planes( GrCP's ) total 31.
There exists fundamental left and right skew set of these 31 GrCP's ergo 62
There exists a primary axi setof 7 GrCP's, The above 5-fold icosahedron has 15, 10 and 6, and the 4-fold cubo(6)-oct(8)ahedron has 12, 6, 4 and 3 for a total of 56 GrCP's and so that is 7 sets.
Humans have 31 bilateral( left and right ) spinal nerves ergo 62 total and 62 follows the set of double zero's aft the decimal point in Pi^3.
12 cranial nerves that-- originate in and around the brain stem --- sits atop the spinal cord and coincidentally the above mention 5/phi-fold icosa(20)hedron and the 4-fold cubo-octahedron, are both defined by 12 close packed sphere's/sphericals around either one or none set of spheres.
31, 331, 33 31, 33 33 1, 33 33 33 1, 33 33 33 31 continuation of the prime number 31 extends out to seven places of 3 and one of 1 a total of 8 integer places.
The torus has a cosmic maximum set of 7 areas/faces that can be mapped onto its surface
For me, I think that Pi^3 contains information that tells us to STOP at this 3D set i.e. proceed not further into infinity and potential madness.
31 in Pi^3 the first cosmic clue for rationality i.e. stop here and go no further into irrationality.
And then the dual zeros( 00 ) isolate the 31 even further away from proceeding on further onto this infinite linear irrationality.
Then we have the 62 ergo potential bilateral left and right expression of 31 again another cosmic clue to STOP go no further into infinite irrationality.
Then, if all that was not enough, we get to the number 7--- a the 7th integer place ---and it has various cosmic implications that are associated with a cosmic primary and finite set.
By the time we get to the 7th integer place, we get the number 7. STOP go further into infinite irrationality.
r6
Hi QQ, I may be to far off base for you thread topic but wanted to through my thoughts into the this pi-ratio as random pattern.
Yeah, it is random pattern.
Non-occupied space = zero fermions, bosons and gravity
Zero is symbol or word used to represent a the count of beads in this column of abacus is 10, so move on to next column and place these beads in this column back to there zero( not counted yet ) starting place aka zero.
The perfect circle or perfect sphere are mathematical constructs of mind/intelligence only ergo Pi is of a mind/intelligence mathematical nature only.
That said, let us take mathematical Pi^3 and round off the irrational parts selectively at various places to see if it approximates nature when so doing.
Pi^3 = 31.00 62 7.......
^3 = a 3rd powering ergo a XYZ cubing or ABCD tetrahedroning as a volumetric quantity.
For starters, counting both sides of the decimal point, we have a total of 7 integer places ending at #7
The regular/symmetrical, 5/phi-fold icosa(20)hedrons 6, 10 and 15 great/equaltoria, circle-like planes( GrCP's ) total 31.
There exists fundamental left and right skew set of these 31 GrCP's ergo 62
There exists a primary axi setof 7 GrCP's, The above 5-fold icosahedron has 15, 10 and 6, and the 4-fold cubo(6)-oct(8)ahedron has 12, 6, 4 and 3 for a total of 56 GrCP's and so that is 7 sets.
Humans have 31 bilateral( left and right ) spinal nerves ergo 62 total and 62 follows the set of double zero's aft the decimal point in Pi^3.
12 cranial nerves that-- originate in and around the brain stem --- sits atop the spinal cord and coincidentally the above mention 5/phi-fold icosa(20)hedron and the 4-fold cubo-octahedron, are both defined by 12 close packed sphere's/sphericals around either one or none set of spheres.
31, 331, 33 31, 33 33 1, 33 33 33 1, 33 33 33 31 continuation of the prime number 31 extends out to seven places of 3 and one of 1 a total of 8 integer places.
The torus has a cosmic maximum set of 7 areas/faces that can be mapped onto its surface
For me, I think that Pi^3 contains information that tells us to STOP at this 3D set i.e. proceed not further into infinity and potential madness.
31 in Pi^3 the first cosmic clue for rationality i.e. stop here and go no further into irrationality.
And then the dual zeros( 00 ) isolate the 31 even further away from proceeding on further onto this infinite linear irrationality.
Then we have the 62 ergo potential bilateral left and right expression of 31 again another cosmic clue to STOP go no further into infinite irrationality.
Then, if all that was not enough, we get to the number 7--- a the 7th integer place ---and it has various cosmic implications that are associated with a cosmic primary and finite set.
By the time we get to the 7th integer place, we get the number 7. STOP go further into infinite irrationality.
r6
You mean physical reality? The question's meaningless. How would you measure it?
I don't understand what you mean. It's clear to me that mathematically, a point exists because the existence of a point follows from the rules of math. Physically, the question is meaningless because I can't imagine any physical apparatus that could measure a dimensionless, propertyless point.
You keep saying that zero both exists and doesn't exist in both math and physics. I don't understand what you mean.
How does a mathematical point not exist in mathematics? And how could you measure a physical point even if such a thing did exist? In physics, "to exist" means "is capable of being measured." Otherwise you're doing metaphysics.
ever seen a picture of Pi?
Did this on sciforums about 6 years ago.
250k placeholders each number given a grey scale gradient. [top left to right] [both pi compared with random - a sophisticated random number generator [can't recall the details]]
Images are controlled as to "contrast and lightness" as being equal [not tampered with]
The test was for a number of reasons
1] for something to be truly random pattern forming should NOT be inhibited. [ie. for randomness to be absolute patterns are most likely to form over an infinite series.] [slight re: Chaos theory]
2] see if a hidden message could be garnered [ whoo whoo ] [chuckle]
3] To compare visually the difference between the apparent fixed randomness of Pi [the pseudo random sequence is constantly able to be repeated exactly] and an actual variable random sequence. [random outputs are infinitely variable every time the algorithm is run.]
or in other words;
Every time we repeat this exercise the image for pi stays exactly the same where as the random image generated will always change.
Thus pi it self is a pattern and quite fixed [ certainly not random ]
and who says you can't have fun with physics and math?
It is actually really simple but damn hard to grasp [ a paradox yes?]
If you are sitting at a desk grab a pen if you can.
now hold the pen and observe it has length and no doubt it has a middle point.
You have a left side and a right side to the pen.
Note that middle point has to be a zero point to be exact.
Now ask you self, "Does that zero point in the middle of your pen exist or not?"
At some point [zero] the left side becomes the right side..it is that exact point that is in question.
Your answer will be most enlightening... IMO
No, you just need to explain yourself better so I can understand you.
There are four things you claim.
1a) A dimensionless point exists in the physical world.
1b) A dimensionless point does not exist in the physical world.
That's your physics paradox. And
2a) A dimensionless point exists in the mathematical world.
2b) A dimensionless point does not exist in the mathematical world.
That's your math paradox.
Now I believe in the truth of 1b and 2a. Regarding 1b, you could never design a physical apparatus to measure a dimensionless point; so the question of its existence is -- by the very nature of science -- meaningless.
And having been trained in math, I have an unshakable belief in the mathematical existence of dimensionless points. And if required, I could demonstrate their existence from the rules of logic and the axioms of set theory.
So I am on board 1b and 2a.
However I do NOT see any justification from you for 1a and 2b. You can't show a dimensionless point exists in the physical world; and I really can not understand how you can deny the existence of a dimensionless point in the mathematical world.
What do you mean here by a zero point? Do you mean a midpoint? If so, then of course a pen does not have a precise midpoint. For one thing, the "pen" is made of subatomic particles that keep jumping around. Just by putting your finger near it you cause all kinds of molecules to be exchanged between the pen and your finger. It's not possible to specify with complete precision exactly how long the pen is or what shape it is; let alone to determine the existence of some hypothetical midpoint.
And even if you could play God for a moment and precisely freeze one instant of time and then note the precise location of the theoretical midpoint of all the particles ... there might not be any pen-particles there! You might identify a region of empty space. There might not be any points there!
The question is clearly meaningless at best. There is no midpoint of a pen. It may or may not exist but you have no conceivable way of identifying it or proving it exists. It's metaphysics, not physics.
Well then I hope you are enlightened
I never claimed that. In fact using the double reduction method of the circle in a box as described earlier Proves the existence of Zero [< 1/infinity] In Math and physics.
And I would further go on to suggest that at any time the infinitesimal is used zero is proved by default. [ No-thing (zero) can be less than the infinitesimal ]
see post: #42
x= y+z+(< 1/infinity)
&
x= y+z+0
and it is this difference that we are embroiled in discussing
There is a surprisingly big difference between these two :Steps
1] Calculate the area of the Square.. = x
2] Calculate the area outside the circle[but inside the square] = y
3] Calculate the area of the circle = z
Then you will find if I am not mistaken logically the following:
x= y+z+(< 1/infinity)
The end result is a circle [line] that is both non-existent and existent simultaneously.
The circle line becomes an event horizon or vanishing point and nothing more
As shown in exaggerated form below:
Of course this is on the premise that Pi can not ever be resolved finitely
x= y+z+(< 1/infinity)
&
x= y+z+0
and it is this difference that we are embroiled in discussing
Every time we repeat this exercise the image for pi stays exactly the same where as the random image generated will always change.
Thus pi it self is a pattern and quite fixed [ certainly not random ]
and who says you can't have fun with physics and math?
QQ, I think your confusing random generator--- that is quasi-variable ergo not totatly, fixed so yes it will produce various random patterns -- with a fixed the fixed random pattern i.e. your mixing changing random pattern of apples with a fixed random set of oranges.
Pi is rational three( 3) 1D + irrational infinite 1D.
Pi^3 is rational 31, 3D( physics and nature ) + irrational infinite, with inherent 6 numerated places that inhibit, or shy away from or some other terminlogy that I don't have a word for to discourage further continuance of irrational exploration.
Perhaps 3D Pi--- 31.00827 --- is not enough to convince you to consider/ponder/reflect, so, perhaps if we go to Pi^4 and see if we can work time into the nature and/or physics of Pi.
Pi^4 = 97.4 0 90 91 0 34 00 24 37236440332688705
I'm not a mathematician QQ, and certainly know or can do any physics math.
So I'm left to wander in the dark so to say, when it comes to mixing 3D space with time. And to be clear here, I've not even consider this next pathway I'm about to go on.
97.4090910340024 minus 31.00627 = 66.4028640340024, so, I guess what I've done here, is to say that the value 66.402864 etc....is some associated with time based on all my given linear progressions of Pi > Pi^3 > Pi^4.
I dunno if that would be reasonable, rational or logical way to approach adding time into the powering of Pi. Again, that is my first ever approach at such an association. If there was a consenus on a way to integrated time into this Pi powering scenario, then perhaps we could then attempt to discern what we can gleen from those numbers we might find consenus on.
Were seem to be doing linear 1D, 3D and possibly time as a 4th-D mathematics here as related to Pi. I dunno but not afraid to explore. Conceptual explporation does not lead to following over a edge of cliff....ha ha
r6
With all due respect rr6, I'll refer to a motto I have tried to keep [And failed many a time I might add]QQ, I think your confusing random generator--- that is quasi-variable ergo not totatly, fixed so yes it will produce various random patterns -- with a fixed the fixed random pattern i.e. your mixing changing random pattern of apples with a fixed random set of oranges.
Pi is rational three( 3) 1D + irrational infinite 1D.
Pi^3 is rational 31, 3D( physics and nature ) + irrational infinite, with inherent 6 numerated places that inhibit, or shy away from or some other terminlogy that I don't have a word for to discourage further continuance of irrational exploration.
Perhaps 3D Pi--- 31.00827 --- is not enough to convince you to consider/ponder/reflect, so, perhaps if we go to Pi^4 and see if we can work time into the nature and/or physics of Pi.
Pi^4 = 97.4 0 90 91 0 34 00 24 37236440332688705
I'm not a mathematician QQ, and certainly know or can do any physics math.
So I'm left to wander in the dark so to say, when it comes to mixing 3D space with time. And to be clear here, I've not even consider this next pathway I'm about to go on.
97.4090910340024 minus 31.00627 = 66.4028640340024, so, I guess what I've done here, is to say that the value 66.402864 etc....is some associated with time based on all my given linear progressions of Pi > Pi^3 > Pi^4.
I dunno if that would be reasonable, rational or logical way to approach adding time into the powering of Pi. Again, that is my first ever approach at such an association. If there was a consenus on a way to integrated time into this Pi powering scenario, then perhaps we could then attempt to discern what we can gleen from those numbers we might find consenus on.
Were seem to be doing linear 1D, 3D and possibly time as a 4th-D mathematics here as related to Pi. I dunno but not afraid to explore. Conceptual explporation does not lead to following over a edge of cliff....ha ha
r6
"If you are prepared to write your thoughts in a way that can be comprehended by a "linguistically programmed Robot" then I am prepared to decyper them as best I can."
After all please consider that your readership are all linguistically programmed.
I personally don't see how time can be, or should I say, needs to be, added to this discussion on Pi, however if you can explain it in an appropriate thread in pseudo science as if talking to linguistically programmed robots then I am more than happy to have a read of it.
I see your issue. You should read up on the subject of boundary in the field of general topology.
For example if I take the closed interval of numbers [0,2]; that is, the set of real numbers greater than or equal to 0 and less than or equal to 2; I could then cut it into two disjoint pieces:
[0, 1] and (1, 2]. That is:
a) The set of real numbers between 0 and one, inclusive; and
b) the set of real numbers strictly greater than 1 and less than or equal to 2.
Now you want to know how the point 1 can be an endpoint of (a); and also "sort of" the endpoint of (b), yet 1 is defined as not an element of b.
The answer is that 1 is regarded as being on the boundary of both (a) and (b). This is exactly the kind of issue general topology addresses. So in fact the point 1 is only an element of (a) and is not an element of (b); yet 1 is on the boundary of both (a) and (b).
I hope that contemplation of this example will clarify this point; or at the very least, motivate you to look up "topological boundary" on Wikipedia. I can't post links yet.
(edit) Hey I can post links now. Thanks QQ for this conversation that has helped me to boost my post count
https://en.wikipedia.org/wiki/Boundary_(topology)
Is this the issue that's concerning you? It's actually a good insight on your part; and it's answered by the mathematical concept of boundary.
And to extend this to the unit circle x^2 + y^2 = 1; I could partition the plane into two disjoint subsets:
(a) x^2 + y^2 <= 1; and
(b) x^2 + y^2 > 1
Now (a) is the closed unit disk; that is, it's the area enclosed by the circle plus the circumference.
(b) is everything other than (a). So it does not contain any of the points on the unit circle; yet, the unit circle is regarded as being in the topological boundary of both (a) and (b).
This is actually a subtle point, and it took mathematicians a long time to get the definitions exactly right. But now we have vocabulary to say that the unit circle is the boundary of both (a) and (b), even though only (a) actually contains the points of the circle.
pi^3 = 31.00627... and a human has 62 spinal nerves. [Thanks for that factoid, I didn't know that!] And 62 are the first two nonzero digits to the right of the decimal point in the decimal representation of pi^3. I can see that.
Can you explain to me why you think this is meaningful; and in what way?
Pi > 3D > 3D + time
QQ, I've showed rational logical progression of 1D Pi to 3D and is well establised methodolgy of powering that gives to get a volume.
If you don't understand taking a number to the 3rd power to arrive at a 3D volume( space ) then I can help with that.
3D( space ) is very commonly accepted phenomena of our known Universe. If you don't understand that I can help you there also.
Following the above common accepted processes--- and plenty of associated rationale and logic ---I then moved on to trying to arrive reasonable way of adding in time to my already given volumetric Pi as 31.00627.....
If you do not understand that space and time are related to physics and nature in most intimate way I can help there also. Begin with the notion of gravitational spacetime. Some might if see that has having a relationship to geodesics.
That said QQ, if there is word or concept you don't understand, please specify and I can attempt to help you.
All of my given words were in English and the math is so simple even I can do it, with a calculator.
I don't know that time can be expressed in similar way that I have done with volumetric Pi. Again, I'm not a mathematician of and certainly not a physics mathematician by any means. Just and explorer looking for cosmic truths.
Pi^4th seems like a rational way to approach the issue of time, based on 3D volume( space ) plus a dimension of time.
Sure the 4th dimension of time of a differrent nature and that is why I stated, I dunno what a correct approach to adding time to P^3 would be.
If you have or no one else has any ideas then I will gladly bow out of your Pi disscussion revoling around a zero of some sort or another. There are two zeros in the beginning of the irrational side of Pi^3 = 31.00.
r6
QQ, I've showed rational logical progression of 1D Pi to 3D and is well establised methodolgy of powering that gives to get a volume.
If you don't understand taking a number to the 3rd power to arrive at a 3D volume( space ) then I can help with that.
3D( space ) is very commonly accepted phenomena of our known Universe. If you don't understand that I can help you there also.
Following the above common accepted processes--- and plenty of associated rationale and logic ---I then moved on to trying to arrive reasonable way of adding in time to my already given volumetric Pi as 31.00627.....
If you do not understand that space and time are related to physics and nature in most intimate way I can help there also. Begin with the notion of gravitational spacetime. Some might if see that has having a relationship to geodesics.
That said QQ, if there is word or concept you don't understand, please specify and I can attempt to help you.
All of my given words were in English and the math is so simple even I can do it, with a calculator.
I don't know that time can be expressed in similar way that I have done with volumetric Pi. Again, I'm not a mathematician of and certainly not a physics mathematician by any means. Just and explorer looking for cosmic truths.
Pi^4th seems like a rational way to approach the issue of time, based on 3D volume( space ) plus a dimension of time.
Sure the 4th dimension of time of a differrent nature and that is why I stated, I dunno what a correct approach to adding time to P^3 would be.
If you have or no one else has any ideas then I will gladly bow out of your Pi disscussion revoling around a zero of some sort or another. There are two zeros in the beginning of the irrational side of Pi^3 = 31.00.
r6
With all due respect rr6, I'll refer to a motto I have tried to keep [And failed many a time I might add]
"If you are prepared to write your thoughts in a way that can be comprehended by a "linguistically programmed Robot" then I am prepared to decyper them as best I can."
After all please consider that your readership are all linguistically programmed.
I personally don't see how time can be, or should I say, needs to be, added to this discussion on Pi, however if you can explain it in an appropriate thread in pseudo science as if talking to linguistically programmed robots then I am more than happy to have a read of it.
ahh, thank you for that...
the link in question:
Topological boundary
lead on to:
Manifolds
lead on to
Differential manifolds
ok I get the general picture... it would take years of serious study to work through it all and many more to become proficient at it.
and to be honest it is IMO an utterly amazing achievement.To logically prove [in math] the above which Archemides, Zeno and a few others of Ancient Greece may have alluded to so many years ago.
Time out needed to absorb and re-appraise... thanks
I've seen the light.
pi^4 = 97.409...
And in 1962 the Beach Boys released a song called ... 409.
http://www.youtube.com/watch?v=xKKP_cZuk54
Coincidence? I think not. Clearly the Beach Boys were sending the future a coded message that they knew all about the fourth dimension.