Axioms [LWN.net]

Axioms

Posted Feb 24, 2021 18:28 UTC (Wed) by Wol (subscriber, #4433)
In reply to: Axioms by rschroev
Parent article: An introduction to lockless algorithms

Whoops. I didn't mean to say there aren't other solutions for the equations. Just that the possible universes are seriously constrained by the maths.

Cheers,
Wol

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Axioms

Posted Feb 24, 2021 21:54 UTC (Wed) by mathstuf (subscriber, #69389) [Link] (3 responses)

That we had such a firm grasp on physics at that level to tell a "broken" from a "working" universe given a set of "knob settings" is news to me. That we even know all of the relevant knobs is news even. I thought we were still at the "we have a working universe on our hands…what makes it tick" stage about the fundamentals. Do you have any journal papers about this you could cite?

Axioms

Posted Feb 24, 2021 23:22 UTC (Wed) by Wol (subscriber, #4433) [Link] (2 responses)

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

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.

Axioms

Posted Feb 24, 2021 22:24 UTC (Wed) by Cyberax (✭ supporter ✭, #52523) [Link] (4 responses)

Not really. Math is just a language, it basically restricts nothing.

If you want to read something mind-blowing, try the "Clockwork Rocket" series by Greg Egan. It's accompanied by a thesis-sized exploration of its (fictional) physics: http://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html

Axioms

Posted Feb 24, 2021 23:26 UTC (Wed) by Wol (subscriber, #4433) [Link] (3 responses)

Maths is just a language, true. But if we try to define a - six-dimensional universe, say - the maths just doesn't add up. So yes the maths does restrict our universes - it says six dimensions just won't work.

Cheers,
Wol

Axioms

Posted Feb 24, 2021 23:34 UTC (Wed) by Cyberax (✭ supporter ✭, #52523) [Link]

> Maths is just a language, true. But if we try to define a - six-dimensional universe, say - the maths just doesn't add up. So yes the maths does restrict our universes - it says six dimensions just won't work.
Who told you that? A six-dimensional classic (Newtonian) universe works just fine. Sure, you won't have stable orbits but apart from that it's OK.

You can also construct a quantum field theory for such a universe, it also would work just fine.

Axioms

Posted Feb 25, 2021 15:16 UTC (Thu) by mathstuf (subscriber, #69389) [Link]

I think you're confusing the physics of our universe versus those of any possible universe. Sure, *ours* might not make sense with 5-9 dimensions, but that makes no conclusion about *any possible universe* having such a number of dimensions. Maybe you're just being imprecise with your language in places?

Axioms

Posted Mar 8, 2021 14:59 UTC (Mon) by LtWorf (subscriber, #124958) [Link]

I think you are very confused about the dimensions thing in physics.

Physics tries to model measurements.

So for example you measure a planet that is orbiting, make an equation, and see if tomorrow the equation and the position are the same (within a certain range of precision).

Before Galileo saw that Jupiter had satellites, they had perfectly fine equations that predicted where everything would be in the sky. The problem arose because new data could not fit the model.

You can absolutely model an orbit of a planet using 3 dimensions, or you can model it in an higher space with an equation of a lower degree. Both work. We can't really know which is "exact" if both work.

You can keep adding dimensions and make equations that work, but we don't really know what the "truth" is.