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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)

#21

I believe there’s a reasonable explanation for this effectiveness: mathematics is created by brains. Brains have evolved to track and entrain to various physical phenomena, and the internal dynamics of the brain resonate with the dynamics of the world around that is perceptible through sensory channels. It hardly seems odd that the mathematics created by the physics and chemistry of the brain is very good at describi…

In pre scientific times people mostly thought it was driven by spirits. God told things to exist, the devil made bad things happen, the rain god made rain and so on. It was a bit of a surprise when experimental investigation found mathematical laws, starting mostly with Newton. Also human brains are pretty bad at some of the maths. I can't figure out renormalization.

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

#22

Earlier quoted context omitted.

But why? Why are the rules of the universe consistent? What orders them? These are some of the most baffling questions in philosophy. This is even more of mystery if you take non-theist interpretation of the universe. If all possible universes (including ones with changing rules) are equally probable, then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical model…

> then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical models referred to the in the paper have such predictive power and the rule are not changing over time. Could conscious life capable of asking such a question evolve in a world with volatile rules? Also, math spots patterns. It makes sense that we would spot patterns with it. But these patterns could eith…

The article makes a more subtle point. You can still have deterministic physics but not necessarily explained by simple math equations. For instance, physics could have worked through small algorithms with results that can't be captured in elegant math equations like E=mc2.

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

#23
post #6

Earlier quoted context omitted.

It's that it's surprising physical behavior fits with mathematical equations so well. My guess is it's because the universe is maths in some sense.

Max Tegmark is chatting elsewhere

Yeah he wrote a lot about that.

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

#24

Earlier quoted context omitted.

But why? Why are the rules of the universe consistent? What orders them? These are some of the most baffling questions in philosophy. This is even more of mystery if you take non-theist interpretation of the universe. If all possible universes (including ones with changing rules) are equally probable, then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical model…

> then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical models referred to the in the paper have such predictive power and the rule are not changing over time. Could conscious life capable of asking such a question evolve in a world with volatile rules? Also, math spots patterns. It makes sense that we would spot patterns with it. But these patterns could eith…

A sibling comment to my reply made the point already about deterministic not being simple, so let me address your first point that there could be a filter causing it.

First, a disclaimer. I'm a theist. I like arguments like the so-called "modal ontological argument" and find them convincing. That said, I love explore philosophy especially non-theistic positions because I'm already convinced of theism.

Second, your arguing that there is a filter, and, yes, I agree that one of the possible explanations is a filter. But just asserting that filter with a simple claim as the original commenter did dismisses what is a fascinating exploration of why? How do we know that's a sufficient filter. How do we know that volatility prevents life from existing and asking the question? Is it not possible that there is a volatility that preserves our existence. When your dealing with infinite possible "worlds" this paper becomes more interesting.

Third, if I could put on my non-theist hat (and do it without my biases affecting me), it seems that discoveries such as those made in the paper require non-theist explanations to depend on the existence of a multiverse.

Fourth, there is something else that always get's missed. In a non-theist philosophical framework that forces us to consider all logical possible worlds and universes there is no restriction that a universe begin in a simple state such as a singularity that causes a big bang. A universe can logically begin to exists in an infinite set of states. And again, if every possible universe is equally probable. Why should we be in a universe where what we see can be logically extrapolated backwards to imply that there was a history that follows the mathematical models that we construct. Even a life filter like what you suggested is not capable of answering why we should end up in such a universe. That's a deep and fascinating mystery to be explored.

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

#25

Earlier quoted context omitted.

But why? Why are the rules of the universe consistent? What orders them? These are some of the most baffling questions in philosophy. This is even more of mystery if you take non-theist interpretation of the universe. If all possible universes (including ones with changing rules) are equally probable, then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical model…

> then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical models referred to the in the paper have such predictive power and the rule are not changing over time. Could conscious life capable of asking such a question evolve in a world with volatile rules? Also, math spots patterns. It makes sense that we would spot patterns with it. But these patterns could eith…

> Also, math spots patterns. > ... you can only see what you can see. ... undiscoverable with a math mind.

It's not that we believe that we have a math mind. It's that we believe that we have logical minds. Math is just one part of the abstract domain of logic. I agree that there are limitations to our ability to observe and limitations with the capacity (storage depth and processing depth) of our brains. If our brains can be trusted then they are logical, and nothing illogical can exists. It seems to me like this is a very hard argument for you to make.

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

#26

Earlier quoted context omitted.

But why? Why are the rules of the universe consistent? What orders them? These are some of the most baffling questions in philosophy. This is even more of mystery if you take non-theist interpretation of the universe. If all possible universes (including ones with changing rules) are equally probable, then what are the odds that we would be in both a universe with simple rules such that the elegant mathematical model…

You don't have enough information to simulate and predict what goes on in an arbitrary 10 cubic cm part of your tissues for an arbitrary purpose (things are different if you had sensing instruments and are satisfied measuring something easily measurable for that purpose). Doctors can't predict, either. Yet many lives could be greatly improved it we were able to do this cheaply. But you and I have ignored all that and…

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.

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

#27

Earlier quoted context omitted.

You don't have enough information to simulate and predict what goes on in an arbitrary 10 cubic cm part of your tissues for an arbitrary purpose (things are different if you had sensing instruments and are satisfied measuring something easily measurable for that purpose). Doctors can't predict, either. Yet many lives could be greatly improved it we were able to do this cheaply. But you and I have ignored all that and…

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 before where neat Newtonian physics was found to fail at edge cases detectable by more precise instruments.

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.

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.

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

#28

I believe there’s a reasonable explanation for this effectiveness: mathematics is created by brains. Brains have evolved to track and entrain to various physical phenomena, and the internal dynamics of the brain resonate with the dynamics of the world around that is perceptible through sensory channels. It hardly seems odd that the mathematics created by the physics and chemistry of the brain is very good at describi…

> It hardly seems odd that the mathematics created by the physics and chemistry of the brain is very good at describing the physics and chemistry of the world the brain’s physics and chemistry is evolved to track.

You just assigned intent to evolution. Evolutionary theory emphatically avoids, even precludes, intent.

Furthermore, the "mathematics created by the physics and chemistry of the brain" is only our modeled attempt to describe the actual "physics and chemistry of the world". The two ideas are separated by so many layers of complexity that work should be shown to establish that there is, in fact, circularity in the process. (Water molecules are bound by electromagnetism, but this did not cause us to build Maxwell's Laws with our watery brains.)

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

#29
post #7

Never seemed unreasonable to me - math is “rule-based” and so is nature. The later is perhaps mysterious, but Occom’s Razor makes it more likely than lawless.

Interesting typo: math (the study) is "later" than nature.

Also, Occam's Razor, but here I risk Muphry's Law.

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