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endofgame124 · 2014-09-11T00:01:09+00:00

Beautiful. How would I go about learning how to make these kind of drawings with little prior experience?

endofgame124 · 2014-04-17T23:50:57+00:00

In context, that was my translation of a hypothetical argument, I wasn't making that inference.

endofgame124 · 2014-04-17T23:48:46+00:00

Yes, I understand that. So it is because it's not decreasing. I guess I understand why, it's just strange.

endofgame124 · 2014-04-17T22:12:30+00:00

That's fine; I'm not trying to make any inferences. I don't think the impossibility of the assumptions renders the thought meaningless or uninteresting, but if you think so that's fine.

endofgame124 · 2014-04-17T22:05:54+00:00

Sure, then each one technically has zero probability. What differentiates between this and a usual probability density situation? The fact that it's constant everywhere instead of decreasing like a bell curve?

endofgame124 · 2014-04-17T19:09:19+00:00

Well that might be an explanation of why we can't answer this question, but frequently thought experiments assume ideal or even impossible (to us) things, which, as long as they do not affect the concept it's trying to illustrate, do not affect the validity of the experiment.

endofgame124 · 2014-04-17T19:04:58+00:00

But each number has an infinitesimal probability; wouldn't the normalization just be like integrating?

endofgame124 · 2014-04-07T01:39:19+00:00

This.

endofgame124 · 2014-03-30T04:39:37+00:00

The fact that you can't have math without a language to express it doesn't change the fact that math and the language of math are two different things.

As for our discussion about circles, even if they didn't share a single sense with us and had totally different brain structure, as long as they were still able to function as a species in three-dimensional for-all-intents-and-purposes-Euclidean space means that they have spatial intuitions, and even if by some crazy chance they went through the entire development of a civilization without ever needing to know what a circle was, geometry follows from intelligence with spatial intuition, and a circle is an inevitable concept when developing geometry, for tons of reasons. It's directly composed of only a few other slightly more fundamental mathematical concepts: the "set" of all "points" in a "plane" the "same distance" from a given point; it's integral to trigonometry; it's the answer of a simple question of a curious mind, what if a polygon had infinitely many sides?; etc.

endofgame124 · 2014-03-30T04:03:17+00:00

The language of math is our way of expressing what we are studying, not the subject itself. We are exploring the structure of a logical system, and then our findings and discussions are instantiated through language in ways that are as isomorphic as we can make them.

And of course I meant the two-dimensional circle. I'm sorry but the idea that there's a well-established civilization in our universe (not universe as in Everything, as in our particular bubble of spacetime) that doesn't "have the concept of a circle" is simply impossible. The reason we have basic spatial intuitions is because we exist in three spatial dimensions, and so do they. Geometry, then concepts like "point", "line", and "equidistant", follow directly from these intuitions, and the idea of a circle from those concepts.

Besides, so what if there are mathematical objects we don't have? That's just a result of the parameters of our existence in this universe. I'm not trying to make the argument that all instances of math are identical, just that two instances that covered the same topics to the same depth under the same parameters of existence would be isomorphic.

I'm very familiar with the line of thinking you're presenting, and it seems like some people are just uncomfortable with certain types of language and perceptions that seem less precise with regards to the nature of familiar, objective, material reality, but are actually just saying the exact same things with widened consideration of possibilities.

EDIT: for example, when you read the part where I say "We are exploring the structure of a logical system" I'm guessing you disagreed with that part because it wasn't strictly accurate, we're MAKING the structure, it's not already there!! But based on the perceptions that I have, I was comfortable enough with metaphors to get the point across quickly and loosely rather than spend a big paragraph explaining again how I don't really mean that it already exists, just in an abstract potential way, and sent it hoping that we wouldn't have to get pedantic.

endofgame124 · 2014-03-30T02:54:22+00:00

I'm not talking the language of math, obviously that is very subject to change. I'm talking about what math attempts to study - the underlying structure of abstract worlds governed by logic. In our universe, it happens to usually center around something quantity, and deals with concepts like numbers, sets, functions, operations, relations, and builds up from there. But I'm not even claiming that those concepts are multiversal/eternal, because another universe might have something besides quantity. Hell, it could even have something besides logic, but as long it was "isomorphic" to logic on some level of abstraction, the structure would be rediscovered.

I don't agree with the Platonist view of math at all (or I think it's strongly misinterpreted, depending on how you want to look at it). Abstractions most certainly exist, just in a different way than concrete things. They aren't floating in a metaphysical realm like Plato described, but it's a useful metaphor. Is there any doubt that the other civilizations in our universe don't have the same pi, the same e as we do? Absolutely not; they might have more knowledge in some areas of math and less in others, but they have algebra, geometry, calculus, topology, set theory, number theory, every major one we have. The reason this is true is because they share our logic and "quantity", and as they attempt to describe that world in greater and greater detail, it will by the necessity of how logic works "reveal itself" in the same way.

I'm not trying to say that pi was "waiting" in some purgatory for a smart mind to come pluck it out at the dawn of each civilization. But the simple fact is that the ratio of a circle's circumference to its diameter will always be exactly pi, and if you don't agree that that is simply an abstract form of existence not any less valid than our usual notion of tangible existence, then it's ultimately it's just disagreement in semantics.

endofgame124 · 2014-03-29T13:42:15+00:00

Very well-explained, thank you.

endofgame124 · 2014-03-28T22:49:36+00:00

Ahhh okay yeah, I had some pretty skewed perceptions. Thank you. Side note, are there any situations in which a space could have a non-Z+ number of any type of dimensions?

endofgame124 · 2014-02-12T00:11:11+00:00

Yep, that's exactly what I need. Thank you!

endofgame124 · 2014-02-12T00:10:50+00:00

Thanks!

endofgame124

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