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[Bumber]

If the laws of physics in said universe are so unstable I must question how self-aware observers would come to exist in the first place.

Because of complex interactions between the physics.

This also allows them to construct the simulation, which is not typical of their universe.

[Bumber]

It is necessary that they must be able to use all of our math. (Not efficiently! They might need equations describing our universe to do so.)
It is not necessary that our math be able to describe all of theirs. By that very nature, we cannot come up with such an example.

Obviously if you can describe something it's not entirely inconceivable, is it?

[dragdeler]

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[Reelya]

All math that's not related to real-world phenomena would work the same under any set of physics.

Spoiler (click to show/hide)

For example the concept of number theory would all be the same, since that's completely invariant to your choice of physics.

Math about things would be different, but that's just applied math. For example we use 3D geometry a lot because it's useful, whereas in a universe with different topology or number of dimensions then different math would be more useful. However if some aliens in a non-euclidean universe worked out the solutions to euclidean math problems, they'd get the same results we get.

But the underlying theory is the same. 1+1=2 and that's completely independent of your physics.

~~~

as an aside: note that something like prime numbers don't change depending on base-10 system or any other system. The property of primes is that they cannot be divided evenly by any number except themselves or 1. That property is independent of how numbers are written down which is all that base-10 depends on. So the sequence of prime numbers is universal. Even in a universe with weird physics.

So is the sequence of e.g. doubling: 1,2,4,8,16 ... It's the same sequence of values, except different representations are possible. For example you could write it in binary as 1, 10, 100, 1000, 10000, 100000, which is pretty neat. But they're representing the same numbers. Or you could write it in ... Roman Numerals as I, II, IV, VIII, XVI ... just to make the point. The numbers did not change, only how we write them down.

pi is also the same value in all number systems. It's just a representation issue. But that's no different to saying for example that 1 third is 1/3 or 0.333333... or 4/12 or any other value. They are written down differently, but they're all the same thing. Similarly, pi would be written differently in binary vs decimal or any other system, but that's just how its written down, not the value itself. When you put PI (or any number) into a computer or calculator its actually stored in binary notation, and all calculations happen in binary then are converted to decimal only for display, which really proves the number systems don't give different answers to math.

[dragdeler]

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[dragdeler]

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[dragdeler]

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[Max™]

This statement is false.

Incidentally if you're talking about impossible squares you probably mean complex numbers which is much easier to understand if you just look at it as being another axis on a graph, and performing operations with those numbers allows one to move about the graph via linear paths or rotations.

[dragdeler]

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[Max™]

None of that was any help to them.

In simpler terms he was just talking about how you can classify one infinity as being larger or smaller than another infinity.

Take basic counting numbers like 0, 1, 2, 3, ... which can be continued to infinity, but in between 0 and 1 or 1 and 2 is an infinite number of fractional numbers.

If you take those fractions and look in between them you could do another infinite count of numbers just slightly different than those fractional values, 0.1111112, 0.1111123, 0.1111234, etc and you can then take all of that infinite set of numbers and write them out before drawing diagonal groups from say, the first place of one, to the second of the next, to the third of the next, and so forth. That set of numbers is also infinite but wasn't in the one you produced it from, and after a hop skip and jump you find yourself in a densely packed set of numbers called the Reals.

The counting numbers and whole numbers are infinite, as are the real numbers, but there are an infinite number of real numbers for every whole number, so the cardinality of the reals is greater.

I may have mangled some of that but hopefully not too badly.

[dragdeler]

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[wierd]

Already has. Good statistical analysis on conspiracies already exists, and gives good framing to the rationality (or lack there of) behind belief in decades long terms on government conspiracies.

[Bumber]

Even conspiracy theory analysis shall fall to mathematics someday.

A. It was inevitable.
B. It must be met with violent force!
Subjects who choose A might be sheeple.

[Trekkin]

Of course, even if all human effort was explicitly mathematical, mathematicians don't actually control mathematics, so they'd be no closer to global control.

[wierd]

There are mathematicians who work on that stuff that dont know how it all works.

(We are approaching a point where the collective whole of a project is incomprehensible to individual humans, and requires a group of specialists, and some interdisciplinary persons to glue them together with for inter-specific communication of ideas. General AI, should it ever appear, will be so complicated on the "how it works", that no single human will be capable of holding a complete picture of that understanding.)