Axioms [LWN.net]

Axioms

Posted Feb 24, 2021 23:22 UTC (Wed) by Wol (subscriber, #4433)
In reply to: Axioms by mathstuf
Parent article: An introduction to lockless algorithms

How many dimensions does the Universe have? We know it's not three, Einstein proved that.

We think it may be four - that's what Einstein thought but that has a whole bunch of problems. If it *is* four, I believe that means string theory is correct as it's the explanation for relativistic singularities.

Or it could be ten or eleven. Anything betwen five and nine inclusive just doesn't work because we get an explosion of infinities - infinity itself isn't a problem, but there are different sorts of infinity and for reality to work they need to cancel out. For those dimensions they don't. (These universes, if I remember correctly, define mass as the fifth dimension ...)

(That's why I was moaning about computers crashing when you divide by zero. If you declare zero and infinity as non-numbers for which arithmetic doesn't work, you're in trouble. If you say "to make arithmetic work, they swap places on division", then you can do this sort of maths and come up with something that makes sense.)

At the end of the day, we have loads of maths that describes what we see. And that *constrains* what is a plausible universe. We have a local maximum or minimum, don't know which. By adjusting some values, we can force others to impossible values. Plausible universes must have all these values at maximum or minimum, not off the scale or impossible or at some non-equilibrium value.

Cheers,
Wol

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Axioms

Posted Feb 24, 2021 23:36 UTC (Wed) by Cyberax (✭ supporter ✭, #52523) [Link]

> Or it could be ten or eleven. Anything betwen five and nine inclusive just doesn't work because we get an explosion of infinities - infinity itself isn't a problem, but there are different sorts of infinity and for reality to work they need to cancel out. For those dimensions they don't. (These universes, if I remember correctly, define mass as the fifth dimension ...)
You can construct a universe with multiple time axes, with many more dimensions, and so on. The math will be internally consistent.

Axioms

Posted Feb 25, 2021 0:05 UTC (Thu) by nybble41 (subscriber, #55106) [Link]

> That's why I was moaning about computers crashing when you divide by zero.

To say that division by zero is undefined is mathematically correct and not just an arbitrary computer limitation. There is no proper answer to the question "What number, when multiplied by zero, gives the non-zero product X?", at least not in any system that would uphold basic idioms such as the product of a number and its reciprocal being equal to one. "Infinity" times zero is not equal to any particular finite number X, so that isn't a solution. Depending on the particular forms of the equations which gave rise to the infinity and the zero (or infinitesimal) the product could be another infinity or any real number; it depends on how you phrase the question. $\lim_{x \to 0+} x ln \frac{1}{x} = 0$, but $\lim_{x \to 0+} x \frac{1}{x} = 1$. In both cases you're multiplying an infinitesimal ($\lim_{x \to 0+} x$) by an infinity ($\lim{x \to 0+} ln \frac{1}{x}$ or $\lim{x \to 0+} \frac{1}{x}$, respectively) but the specific form of the equation changes the result.