# Reality is a Set of Points

Discussion in 'General Philosophy' started by Spellbound, Apr 9, 2015.

1. ### SpellboundBannedValued Senior Member

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Reality is a set of points in Euclidean n-space Rn, represented by ordered n-tuples of real numbers.

A pair of points A and B represent the located vector or directed line segment called AB.

The Euclidean n-space Rn in which the operations of vector addition, scalar multiplication and inner product act on have distances and angles between line segments or vectors which satisfy certain conditions which makes it a Euclidean space. One of those conditions is that it must satisfy the following linear equation.

The inner product of any two real n-vectors x and y is defined by

The distance or length of a vector is real and defined by the equation

, hence is always non-negative.

A real coordinate space together with Euclidean structure is called a Euclidean space and it defines reality.

3. ### SpellboundBannedValued Senior Member

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These define space-time coordinates within hyperplanes. The question is; what is the maximum possible number of hyperplane sets within reality?

5. ### James RJust this guy, you know?Staff Member

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Is this thread about mathematics, or is it a philosophical argument about the nature of "reality" (as distinct from a discussion of "real numbers")? Just trying to work out where it should be located on the forum.

7. ### SpellboundBannedValued Senior Member

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It is more mathematics than Philosophy. Hyperplanes and their points within Euclidean spaces are real. Mathematics and reality are thus reconciled and in such a case, Philosophy is only superficially divorced from it.

8. ### James RJust this guy, you know?Staff Member

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But things like "hyperplanes" and "points" and "Euclidean spaces" are mental constructs - as is mathematics.

So, you're talking here about a mathematical conceptual "reality", rather than the external "real world", I take it.

9. ### SpellboundBannedValued Senior Member

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Any pair of points A and B in Rn describe a located vector or directed line segment. Now, although we do not actually see the points and line segments in the physical world, they otherwise exist due to the fact that we could not travel through space thereby moving with a certain velocity or vector. The forces that these vectors describe are real so the vector, with its magnitude and direction, is real.

10. ### SpellboundBannedValued Senior Member

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So we see that the dimensions of space are defined by points, and then lines, and then squares, cubes, etc.

11. ### DaeconKiwi fruitValued Senior Member

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Maybe Spellbound should have his own "Reality is X" subforum.

origin likes this.
12. ### river

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Hmmm....

I define dimensions of space by the ROOM needed to exist

Mathematics doesn't define space , space defines the mathematics

13. ### James RJust this guy, you know?Staff Member

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Do you have a question or point of discussion, Spellbound?

14. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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He already does it is called The Cesspool.

15. ### SpellboundBannedValued Senior Member

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Yes. I am simply making a philosophical argument on mathematics. Specifically Linear Algebra. I.e. Reality is a set of points in which objects exist.

16. ### SpellboundBannedValued Senior Member

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Correct. We can construct the dimensions of space by the points needed to exist.

17. ### DaeconKiwi fruitValued Senior Member

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What about all the other things that you were certain that reality was?

Were you wrong then?

18. ### James RJust this guy, you know?Staff Member

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I don't see where the thread goes from here.

What do you wish to discuss?

Or are you done?

19. ### SpellboundBannedValued Senior Member

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I'd like to look at linear equations from a Philosophical viewpoint. And perhaps use hyperplanes to describe reality.

20. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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This would all be a little more real if spellbound would just stop posting this goofy crap in the science section.

21. ### someguy1Registered Senior Member

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The core problem you have is that there's no evidence that reality, by which you must mean the physical universe that we live in, is the same as mathematical n-space. But there's no evidence that reality is a continuum, or that it's complete like the real numbers. For all we know, reality is quantized or discrete at the deepest level. It's simply unknown. We know all about Euclidean n-space, but there's no reason to believe that we can apply the word "reality" to it. At best, it's mathematical reality. There's a difference. You don't seem to acknowledge the difference.

What do you mean by looking at linear equations from a philosophical level? The ontology of Euclidean space is well-known. We start with the Zermelo-Fraenkel axioms of set theory. Using the Axiom of Infinity we show that we can model the natural numbers. We then build up the integers, rationals, and reals via standard, well-known constructions. Once we have the reals, we take n-tuples of reals to create Euclidean n-space. That's the philosophy. It's an abstract, artificial universe based on a historically contingent axiom system. It works wonderfully to model problems in the real world; but there is no way to know for sure whether it is the real world or not.

Last edited: Apr 14, 2015
22. ### LaymanTotally Internally ReflectedValued Senior Member

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I think Max Planck mathematically proved that space was particular a long time ago, and he just failed to make a big deal about it. Since he figured mathematically that it would take an infinite amount of energy to make a measurement at a certain distance, then distances smaller than that couldn't exist. It would be impossible to have an infinite amount of energy at a single point, so those distances could never take place or have an influence on anything that could be considered a "measurement". The only time that could have been possible was at the moment of the Big Bang, and then the universe would have to have certain properties that can't be known, like being infinite.

Reality check, Euclidean space wouldn't accurately describe space on the smallest scales. If someone had calculated something moving 11^-33 cm, the most affect it could have on anything would be as if it actually moved 10^-33 cm. Then reality may actually have to round down to that, because the extra 1^-33 cm couldn't influence anything for lack of infinite energy. Say something moved 19^-33 cm. It would still be 1^-33 cm away from being detectable, because it wasn't a whole 10^-33 cm. It would be indistinguishable from something moving 10^-33 cm still, so everything would always have to be rounded down to nearest 10^-33 cm to be precisely accurate. The rules of rounding wouldn't be fully correct either.

23. ### James RJust this guy, you know?Staff Member

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Ok. Since the focus is philosophy, I have moved the thread to a more appropriate subforum.

Now, can you explain your philosophy of linear equations for us?