Every Mathematical Theory Is Held Inside a Physical Substrate(nav.al)
nav.al
Every Mathematical Theory Is Held Inside a Physical Substrate
https://nav.al/substrate
15 comments
I’m not partial to the “I say the universe is infinitely subdividable; since we can obviously move despite Zeno’s paradox, then there must not be a tension between these two” logic - it’s weak.
FWIW, I believe that I can move. I have no idea on how small things get.
FWIW, I believe that I can move. I have no idea on how small things get.
Zeno's Paradox is apparently not easy to state in terms that are accessible to a present-day lay person. The versions I usually see, and the only ones I understand, are the ones that depend on the implicit assumption that a finite quantity cannot be expressed as the sum of an infinite number of other finite quantities. The versions that are formulated to avoid that mistake are completely impenetrable to me, because they depend on Greek philosophical concepts that framed the terms of debate for Zeno and his contemporaries.
Anyway, the article's take is a bit of a cop-out:
> If the laws of physics say that we can cover one meter in a certain time period, then that’s exactly what we’ll do. And our current understanding of the laws of physics says precisely that. So Zeno’s paradox is resolved simply by saying that we can cover this space in this amount of time.
Zeno accepted that we observe objects moving through space. He would not have to change his position an inch to accept classical physics as a valid and successful description of such observations. The paradox comes from accepting such observations and trying to reconcile them with the logical soundness of Zeno's argument. So, if you aren't looking at the logical structure of his argument, you aren't addressing the paradox at all.
Anyway, the article's take is a bit of a cop-out:
> If the laws of physics say that we can cover one meter in a certain time period, then that’s exactly what we’ll do. And our current understanding of the laws of physics says precisely that. So Zeno’s paradox is resolved simply by saying that we can cover this space in this amount of time.
Zeno accepted that we observe objects moving through space. He would not have to change his position an inch to accept classical physics as a valid and successful description of such observations. The paradox comes from accepting such observations and trying to reconcile them with the logical soundness of Zeno's argument. So, if you aren't looking at the logical structure of his argument, you aren't addressing the paradox at all.
I don't think current physics works below the Planck length. There aren't all that many infinities in physics in general, and where the do pop up, they're problematic.
Whereas in mathematics, infinities are a rich field of research, which goes way beyond anything that could ever be physical.
Besides, the tension doesn't exist, because whether or not spacetime is infinitely subdividable, going a certain distance takes a certain time, and going a fraction of a distance takes a fraction of time. The two series will converge in both the discrete and the continuous scenario.
Whereas in mathematics, infinities are a rich field of research, which goes way beyond anything that could ever be physical.
Besides, the tension doesn't exist, because whether or not spacetime is infinitely subdividable, going a certain distance takes a certain time, and going a fraction of a distance takes a fraction of time. The two series will converge in both the discrete and the continuous scenario.
Plank length was found because it fixed equations.
I don’t think any equivalent has been found for time units. Not that can be experimentally proven yet.
Would love to see time proven one way or the other.
I don’t think any equivalent has been found for time units. Not that can be experimentally proven yet.
Would love to see time proven one way or the other.
Unless you discover time crystals in old sense of the word, everything we know about time is related to momentum, esp. thermal equilibrium and symmetry breaking.
This means it is subject to Planck scale and uncertainty principle.
This means it is subject to Planck scale and uncertainty principle.
[deleted]
What the hell am I reading? Two people discussing whether to seriously tackle Zeno's Paradox or not?
And their conclusion is... don't bother? Ok awesome. These two people can go about not bothering... and other people will try to figure it out. Why am I reading this?
And their conclusion is... don't bother? Ok awesome. These two people can go about not bothering... and other people will try to figure it out. Why am I reading this?
Lay philosophy posing as mathematics. I doubt he understands Kurt Gödel's work. (Most mathematicians don't, either.)
[deleted]
It seems the claim here is that physics is more fundamental than mathematics. It may be an open argument, but anyone who wants to make this claim today really has to address John Wheeler's "It from bit."
Skip this one. An article written by someone who doesn't understand math, logic, or philosophy, and thinks stamping his foot and saying "general relativity" is the height of explanatory sophistication.
Naval‘s pseudo-intellectualism at its height.
oh wow, much arrogance here..
it's not about Gödel, it's not about wether physics or mathematics is more fundamental, it's just about how we develop and refute scientific theories in order to describe nature in the best possible way.
it's not about Gödel, it's not about wether physics or mathematics is more fundamental, it's just about how we develop and refute scientific theories in order to describe nature in the best possible way.
And I would say, “General relativity.”
0. https://www.thebeginningofinfinity.com/
1. https://en.wikipedia.org/wiki/The_Beginning_of_Infinity
2. https://www.goodreads.com/book/show/10483171-the-beginning-o...
3. https://brettroberthall.podbean.com/