1. Why does mathematics works?

Why does mathematics works?

All is said in Wikipedia's article on Mathematics:

Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.
https://en.wikipedia.org/wiki/Mathematics
Mathematics works because, and only to the extent that, it is logical.

We got our logic through natural selection so, presumably, it was thoroughly tested over something like the 525 million years of the evolution of neuronal systems over the entire biosphere.

This doesn't mean that it should therefore work in all situations, only that it could be difficult for us to find one where it doesn't work.

Mathematicians can also invent theories that don't "work" because it just happens that there is nothing in the universe that works like that.

When a mathematical theory works, it can be thought of as a model of something real. For any such mathematical model, there is no good reason to claim that we know that it will work for ever, as if it was somehow a perfect model. In effect, we may believe that it will work for ever when in fact it won't because at some point in the future the model will be falsified by new facts. And we don't know the future.

In this case, we just don't know when it will stop to work. So, we can only believe that mathematical models will work. And then, that a model works doesn't mean that it is correct. Newton's laws of gravitation worked beautifully but then were effectively falsified by the more precise observation of Mercury's orbit.

Thus, we don't really know whether mathematics works since we don't know if it works for things we haven't been able to observe yet.

It may well be that we won't find anything ever for which mathematics doesn't work. However, this should be no surprise. I don't know of anything in nature that would somehow be illogical. So, again, as long as mathematics is logical, we should be safe.

This isn't specific to mathematics either. Language works, too, at least as long as you keep it logical. Any model works, as long as it is logical.

For example, you can try to think of Russian dolls. No mathematics. No language. Just your mind's power of imagination. Think of three dolls: doll A, doll B, doll C. Try to imagine a situation where doll A would be inside doll B and doll B inside doll C, while doll A wouldn't be inside doll C. Me, I can't. Our mind seems a pretty good model of reality and this before any mathematics at all.

So, the question of why mathematics works is trivial. It works because human logic works, and mathematics works only to the extent that it is logical.

The reason that logic works is less trivial. It works because it has been thoroughly tested by nature itself and finding a flaw in it is probably not easy at all. It seems safe to believe that finding a flaw in logic is beyond our current technological powers and will remain so for a very long time.

However, here too, there is no eternal guaranty. Only the future will tell.

I don't think I need to dwell on the question of the role played by abstraction in mathematics.
EB

2. Originally Posted by Speakpigeon
Why does mathematics works?

All is said in Wikipedia's article on Mathematics:

Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.
https://en.wikipedia.org/wiki/Mathematics
Mathematics works because, and only to the extent that, it is logical.

...

EB
Mathematics works because it relates to physical world in an operational way. A cubit is a cubit and a knot is a knot wherever and they are applied and always relate to object treated operationally. Mathematics actually serves as the inspiration for logic. Logic is a discipline that often wraps up itself in irrational outcomes. Logic can apply to an imaginary world with little or no benefit to those who apply it beyond being some sort of gotcha game. Applying mathematics as a logical tool breaks the link between discipline and the real world.

Put the cart behind the horse sir.

As for the link between logic and natural selection you have no evidence for such. Natural selection is always material, treatable by systems linking the physical to observational tools - mathematics. Logic is not. For instance logic would tell us the next coin flip with be either different or the same as the previous for some personal causal reason (contradiction of terms). On the other hand mathematics shows us that coins will tend to fall equally heads or tails with just a skosh of edge probability as the result of observation.

3. Effectively falsified?

It’s a Law!

4. Damn electron microscope and MR techniques.

Not a law a solution that works for what was known at the time. The theory has been extended by such as mercury observations and light bending showing that energy was better than force as a measure. The relationship between force and energy is
Work done is equal to force * distance. And, energy is equal to work done in unit time, which is equal to force*diatance/time, which is equal to force * velocity.
e=Fv

5. HeeHeee.what does he think it was based on. illogic? Tarot Cards, reading goat entrails?

Reasoning and logic are the same for all. Creationists use logic and draw technically valid conclusions, conclusion follows premise.

The difference between science and creationism is the set of premises which in science are usually based in part at least in experimental observation.

Math is based in logic, well no shit Sherlock. What does that have to do with the price of eggs?

Look at formal logic. You have AND, OR, and NOT(negation). From a basic principle in Boolean Algebra all logical expressions can be written as combinations of AND, OR, NOT.

and
or
not
if then else

Everybody uses the same logic. It is inescapable. Formal logic is a symbolic structured form of common informal logic.

The problem is one of synthesis. Simply deriving premises and drawing a conclusion such as a mathematical proof works sometimes, a lot of times it does not. It is part experience and intuition from experience, part trial and error, and part logic. The trial and error part is now compurterized.

In the early 20th century Hilbert posed the question, are all mathematical truths provable, and is there an algorithm to find all mathematical truths. The question in part was the genesis of the Turing Machine, an algorithmic general purpose engine.

Göedel postulated in any logically consistent system, no ambiguities, there will be truths not provable in the system.

Aristotle thought given first principles he could logically deduce the universe, he was wrong. Linear logic is not a universal solution. The numerous syllogistic problems and fallacies demonstrate that.

P1 math is based on logic
C therfore math works becuase it is logical.

Conclusion does not follow from premise. Why does logic work, same quetion. The anwer is who knows. It is a combination of our brains plus evolution of thought passed on through culrure IMO.

Both logic and math in the end are empiracly validated by suage over time.

If I say ‘if it is raining and I am outside and I have no cover I will get wet’ why is it true?

A True if I am outside
B It is raining
C True if I am noit under cover
Dtrue if I am wet

Why is this logic true, why is logic true? How does logic 'work'?

If ( A & B & C ) then D

6. Originally Posted by fromderinside
Damn electron microscope and MR techniques.

Not a law a solution that works for what was known at the time. The theory has been extended by such as mercury observations and light bending showing that energy was better than force as a measure. The relationship between force and energy is
Work done is equal to force * distance. And, energy is equal to work done in unit time, which is equal to force*diatance/time, which is equal to force * velocity.
e=Fv
Not to be pedantic but energy = E, e for me usually refers to the electron unit charge or voltage. Just sayin

7. Gotta be true. I was tired when I wrote my comment. So E's to you.

8. Originally Posted by fast
Effectively falsified?

It’s a Law!
Laws can be changed.

And what else could you possibly falsify?

Facts? But facts themselves are laws. Each fact is a law whose scope is limited to the fact itself: A implies A. (Thank you to have helped me think of that one! ).

Laws can be changed. You only need to have a majority, as Boris Johnson is being taught the hard way at the moment, to the enjoyment of the whole of Europe.
EB

9. Well, on lawfulness being changed I find that to be so. Until about a year ago I agreed that hearing movement was just a function of spectral detectability. Then in a swoop I realized that results I found back in 1976 meant the whole hearing sensing mechanism was involved in finding moving objects as the result of our ability to detect changes in tone as sounds moved through space near us, to hear doppler effects. Yes. The facts were the same but understanding of mechanisms changed in how they evolved to process them. A implies A changed to A implies B.

I won't bore you with why because this is not the place for that. But, if you are interested consider outer hair cell function both in bringing linearity to perception and to detecting correlated minute changes in acoustic activity.

As for facts being changed by perceptions of many you should consider GBs history rather than the discomfort they feel in making it. You are wrong on your perception of change.

10. Originally Posted by fromderinside
As for facts being changed by perceptions of many you should consider GBs history rather than the discomfort they feel in making it. You are wrong on your perception of change.
You don't know what you are talking about.
EB

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