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Geek Culture / What are numbers?

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Libervurto
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Posted: 11th Jun 2013 03:28 Edited at: 11th Jun 2013 09:17
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This image is the work of a madman (me):


I wont try to explain the image but as you read this you might pick up on what I was trying to represent with it.

I've been thinking about something that requires a lot more expertise than I have, but still it is interesting to ask questions. My question is "What are numbers?"
If everything began from a single point then how did it ever become two points? What distinguishes two points as unique and not part of the same point? What allows numbers to exist in the first place?
There must be something "else" which creates a division between entities, it seems natural to call this stuff "space", but then if it is distinguishing entities it can't purely be nothing, it must have some sort of value otherwise it creates no boundary at all. So are the gaps between entities part of their identity? Is 1+1 = 2 + x where x is the space between, which has no practical value but must logically be worth something.
Is space itself a continuous foamy entity that fills the gaps between matter, or is it too made up of "atoms", that are just like matter except with different properties?
Did space create matter or did matter create space?

In the top of the image there are a series of dots connected by lines, it occurs to me that for numbers to be valid all dots must interconnect. To add a fifth dot we would need to place it in the third dimension "above" the triangle. I can't figure out how to add a sixth dot but that might be because it could require a fourth dimension. In any case, there is one characteristic that we are able to plot from the data we have so far: the number of connecting lines.



The difficulty in learning is not acquiring new knowledge but relinquishing the old.
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Dark Java Dude 64
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Posted: 11th Jun 2013 03:37
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This video might be interesting to you:

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Neuro Fuzzy
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Posted: 11th Jun 2013 04:45
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Why must all the dots interconnect?

Heheh but since I know a bit of set theory (which, does nothing to help the existence of numbers or what assumptions we "really" can make about them, but does everything to discuss their properties), I can say that, even if you had an infinite number of dimensions, and an infinite number of spheres, that still wouldn't be enough to represent all real numbers/a true continuum.
(due to cardinalities - the cardinality of the set of spheres [whatever they're supposed to represent] is still smaller than the cardinality of the reals. Cardinality can be taken to mean "size" and it extends to infinite sets.)

I could go on at length :3


"I <3 u 2 bbz" - Dark Frager
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Libervurto
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Posted: 11th Jun 2013 05:24
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Quote: "Why must all the dots interconnect?"

They must interconnect to be a valid structure. Look at the diagrams at the top of the image, take one dot away from each, in the valid structures you are left with the same structure as the number -1 but in the square you break the structure. The only way this does not have to be a rule is if dots can share "space", which I showed in the diagrams below (white dots are space).

From what you say about set theory I think space between must be shared and so space is not made from "atoms". But if space is a single entity how can it surround everything? How does it expand?

The difficulty in learning is not acquiring new knowledge but relinquishing the old.
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Pincho Paxton
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Posted: 11th Jun 2013 15:10 Edited at: 11th Jun 2013 15:27
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I work on this sort of thing every day, but my answers are never understood, and usually cause threads to be locked. So I can't answer you. What annoys me about these questions though is that the thread will never be complete without the answer that gets it locked.

Instead I shall give you some ingredients of a possible solution that you can work out yourself...

1/ The Universe could be infinite.
2/ The structure of the Universe could be a grain structure.
3/ An infinite grain structure fills all locations.
4/ Filling in all spaces requires a stacking system.
5/ An infinite stacking system must also obey Newton's 3rd law.
6/ For every stack in one direction there is an opposite force stacking in the other direction... sort of symmetry.
7/ The parts do not overlap.
8/ Infinity has no overlap.
9/ Scale must obey Newton's 3rd Law.
10/ For every scale down, there is a scale up.
11/ The scale causes the numbers to have location.
12/ The numbers are spherical to complete Newton's 3rd Law.
13/ Add to this list the rest of the pattern with the gaps.
14/ What are the gaps in the corner of the sphere?
15/ The background is the same as the foreground.
16/ Density is a force.
17/ Force is propagation of movement.

The whole thing is a stacking system of sphere that is infinite, and therefore has only one solution, a pattern that obeys Newton's 3rd Law. Our senses evolved to use this stacking system, and create an illusion that is different to reality. For example that light is bright, but is in fact force.

.. and then just work it out.

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TheComet
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Posted: 11th Jun 2013 15:57
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What about a stack overflow?

Quote: "What are numbers?"


Steven Wittens summed it up nicely:
Quote: "You cannot point to anything in the world and say, "This is a 3, and that is a 5." You can point to three apples, five trees, or chalk symbols that represent 3 and 5, but the concepts of 3 and 5, the numbers themselves, exist only in our heads. It's only because we are taught them at such a young age that we rarely notice."


Numbers represent a system we can all agree on, but other from that, they're meaningless.

TheComet


Yesterday is History, Tomorrow is a Mystery, but Today is a Gift. That is why it is called "present".
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Libervurto
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Posted: 11th Jun 2013 16:43
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@Comet - I don't really mean it in that sense of the word. I am asking what allows plurality to exist, how are we able to define values at all for our number system? Why are there prime numbers? Is our concept of mathematics accurate, or are we only seeing a small part of the bigger picture?

I had the thought that maybe what we define as numbers are just the shadows (fingerprint, side-effect or however you want to call it) of true mathematical structures and we've developed this theory of numbers because it is practical for our needs and aids our survival, but is not necessarily totally accurate.

I don't know where I'm going with this now but it's fun to think about.

The difficulty in learning is not acquiring new knowledge but relinquishing the old.
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Pincho Paxton
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Posted: 11th Jun 2013 19:27 Edited at: 11th Jun 2013 19:28
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Today's science news shows Fractals from cell growth...

http://www.sciencedaily.com/releases/2013/06/130611084115.htm

I put this in here because that's how I feel that we get numbers. Sphere create order from stacking, and we used pebbles, then abacus to create order from stacking patterns.

Then the natural occurrence of numbers is spherical stacking.

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Neuro Fuzzy
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Posted: 12th Jun 2013 01:41
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Now that sounds closer to epistemology (which, if you find info on that doesn't come across as a dry philosophy book, let me know!)

Obese, you say shadow of a mathematical structure: One interesting thing that is ruled out, is to ask, "Are numbers unique? Can we define them in a fundamentally different way, with the same properties?" It turns out that you would have to break some important properties of numbers in order to stop using the reals. https://en.wikipedia.org/wiki/Real_number#Axiomatic_approach (given those assumptions, the reals are unique, up to "isomorphism", which means that, if you have some set A and B that satisfy all those properties, with addition and multiplication somehow defined (possibly differently on each set), then if one element corresponds to, say, sqrt(3) in A, there's also a unique element that corresponds to sqrt(3) in B. So there's no real difference, as far as practice is concerned, between the two sets.

In the case of complex numbers (which I don't know that much about!), ordering is left undefined (it makes no sense to define 1+3i<2+4i, for various reasons). In vectors, multiplication and ordering are both left undefined.

I have no idea what's true in string theory. It would be interesting to ask things like, "is time a real valued parameter" etc. But if you start thinking about what properties a number should have, and you wind up with the same properties as in the link, you'll get the real numbers, period.


"I <3 u 2 bbz" - Dark Frager
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Pincho Paxton
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Posted: 12th Jun 2013 02:34 Edited at: 12th Jun 2013 02:37
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Quote: "Now that sounds closer to epistemology..."


I think so. It is what is outside of our senses that I am interested in.

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