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The Unreasonable Effectiveness of Mathematics in the Natural Sciences [pdf] (1960)

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Re: The Unreasonable Effectiveness of Mathematics in the Natural Sciences [pdf] (1960)

#31

Earlier quoted context omitted.

I think your conflating emergent behavior that results from complex physical states / arrangements of matter with the surprisingly simple laws of physics which can be modelled with mathematics and are the foundations that such complex emergent behavior operate according to. Discoveries since the paper was created have not changed that.

Let me ask you this: 1. what makes you confident that the rules of particle physics alone can lead to a perfect simulation of macroscopic phenomena? (as you call it "emergent behavior") 2. what makes you confident that our universe is not "turtles all the way down", that as soon as we develop more precise and powerful instruments we will discover new "fundamental phenomena" that requires new theory? This has happened…

Interesting questions. I'll try to take a shot.

> 1. what makes you confident that the rules of particle physics alone can lead to a perfect simulation of macroscopic phenomena? (as you call it "emergent behavior")

Given the general axiom of science that the same experiments under the same conditions will yield the same results, I do think we can trust the standard model because of how successful it has been at matching real world tests. That doesn't mean that the standard model is "correct" or complete--we know that we still don't have a quantum theory of gravity--only that model is amazingly predictive, which is all that we could ask of a mathematical model. There are also philosophical explanation of quantum physics that need to be factored in (Copenhagen, many-worlds, pilot wave).

All that said, I think your mixing up the need for a perfect simulation with the fact that the currently understood quantum level interactions of matter and space produce produce the lions share of influence at the larger macroscopic levels. The fact that medical science has been massively successful at using our understanding of chemistry and physics to explain so much of what we know about the details of the body is evidence of how amazing our understanding already it, even if it's not perfect.

> 2. what makes you confident that our universe is not "turtles all the way down", that as soon as we develop more precise and powerful instruments we will discover new "fundamental phenomena" that requires new theory? This has happened before where neat Newtonian physics was found to fail at edge cases detectable by more precise instruments.

All of physics is dying to be the one who discoveries the next level or foundation or theory of everything in physics. No disagreement there, but if that next level turns out to be indescribable with simple mathematical models as is the case with the currently understood quantum level, then that make the effectiveness of relatively simple mathematical models at the quantum level and in relativity/Newtonian physics all the more astounding. How amazing it would be that the complexity would produce such elegance. That would answer one of the whys that we wish to answer!

> 3. considering that we have no feasible way of snapshotting a 1 cubic inch of the world, and even if we have done that, no feasible way of simulating its dynamics at the qft level for one second, and yet we have "approximate" physical theories with less invasive instruments that can do that (for specific purposes), is the ideology of calling macroscopic phenomena an emergent behavior of particle physics still relevant? In a similar bent, there exists a Starbucks in certain places in the world, and there does not exist a Starbucks in other places. This is a fundamental truth of the present world, and many peoples' lives are oriented around that and affected by it. Nevertheless, it cannot be precisely predicted by mathematics where there exist Starbucks and where there does not exist Starbucks one year into the future.

"...is the ideology of calling macroscopic phenomena an emergent behavior of particle physics still relevant?" How did this become an ideology? That said, yes, even with all that said, the effectiveness of mathematics in the physical sciences is still amazing. How the universe came to have it's current arrangement is a fascinating question with it's own mysteries, but that doesn't take away from the points about the effectiveness of mathematics.

"Nevertheless, it cannot be precisely predicted by mathematics..." The ontological naturalists would push back on that claim. Although, I do my best to explore naturalism under it's own terms and conditions, I'm a theist who believes that humans have a soul. For that reason I would agree that we cannot predict such a scenario because there are inputs from outside the physical universe. That said, if we are just talking about physics only, it would be an assumption on your part that it cannot be precisely predicted by mathematics.

> 4. I hope you can see that just as Newtonian physics was useful for describing an approximation to the world but still fails at giving knowledge about sufficiently complex systems and sufficiently small scales, you now see that likewise particle physics is just an "effective lens" for a particular genre of human activity.

I think my other comments have addressed this. Thank you. I enjoy these discussions & debates.

Re: The Unreasonable Effectiveness of Mathematics in the Natural Sciences [pdf] (1960)

#32

Earlier quoted context omitted.

Let me ask you this: 1. what makes you confident that the rules of particle physics alone can lead to a perfect simulation of macroscopic phenomena? (as you call it "emergent behavior") 2. what makes you confident that our universe is not "turtles all the way down", that as soon as we develop more precise and powerful instruments we will discover new "fundamental phenomena" that requires new theory? This has happened…

Interesting questions. I'll try to take a shot. > 1. what makes you confident that the rules of particle physics alone can lead to a perfect simulation of macroscopic phenomena? (as you call it "emergent behavior") Given the general axiom of science that the same experiments under the same conditions will yield the same results, I do think we can trust the standard model because of how successful it has been at match…

I'm sorry, I cannot continue this conversation. To do so we need an intense back-and-forth that this format is too asynchronous to provide. Either that, or I will need to spend hours trying to anticipate your responses and address them, and I am not sufficiently motivated to do that. I can state my position succinctly in that my view on science and knowledge is very close to philosophical pragmatism.

Re: The Unreasonable Effectiveness of Mathematics in the Natural Sciences [pdf] (1960)

#33

Earlier quoted context omitted.

Interesting questions. I'll try to take a shot. > 1. what makes you confident that the rules of particle physics alone can lead to a perfect simulation of macroscopic phenomena? (as you call it "emergent behavior") Given the general axiom of science that the same experiments under the same conditions will yield the same results, I do think we can trust the standard model because of how successful it has been at match…

I'm sorry, I cannot continue this conversation. To do so we need an intense back-and-forth that this format is too asynchronous to provide. Either that, or I will need to spend hours trying to anticipate your responses and address them, and I am not sufficiently motivated to do that. I can state my position succinctly in that my view on science and knowledge is very close to philosophical pragmatism.

No problem. I enjoyed the discussion we had. These conversations do tend to blow up...
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