Why is math effective? Because there is structure to the world that is describable with mathematics.
Why is the world describable with mathematics? Because there are regular, consistent physical relations between objects that have an inherent mathematical component (like an inverse square law). — Relativist
the fact that there is structure to the world does not mean that the world comes to our awareness packaged an ‘inherent’ way that is already mathematical. Nature became mathematizable when we contributed our own peculiar interpretive structures to it. — Joshs
I'm guessing that Wigner's use of "unreasonable" was ironic or tongue-in-cheek. In view of the randomness & uncertainty of its Quantum foundation, it is perhaps surprising that on the Macro level of reality, its structure & processes are predictable & consistent. In other words, there is an underlying logic to the order of reality. And mathematics is simply an abstract form of Logic.I think all participants here know about the statement of the unreasonable effectiveness of mathematics. Shouldn't we, rather, speak of it's reasonable effectiveness? I can't see nothing unreasonable about it and can't even imagine how else it could be. — Landoma1
No, it's not packaged in an inherent way, but the success of our inferred mathematical relations suggests there is an ontological basis to it.I was with you in your first paragraph. But the fact that there is structure to the world does not mean that the world comes to our awareness packaged an ‘inherent’ way that is already mathematical. Nature became mathematizable when we contributed our own peculiar interpretive structures to it. — Joshs
I'm also not a Platonist. I have an Aristotelian view of immanent universals (more directly: an Armstrongian view).As you can see, I’m a mathematical constructivist, not a platonist.
I think all participants here know about the statement of the unreasonable effectiveness of mathematics. Shouldn't we, rather, speak of it's reasonable effectiveness? — Landoma1
No, it's not packaged in an inherent way, but the success of our inferred mathematical relations suggests there is an ontological basis to it.
“As you can see, I’m a mathematical constructivist, not a platonist.”(Josh)
I'm also not a Platonist. I have an Aristotelian view of immanent universals (more directly: an Armstrongian view). — Relativist
I don't follow you, but I'll elaborate on my view: laws of nature are relations between kinds of things. Kinds are universals, and laws of nature are universals. This is the metaphysical theory of law realists.What I reject is the idea that the regularity and consistency of physical relations reduces to differences of degree that are not at the same time differences in kind.
Put differently, quantitative measurement introduces qualitative change at every repetition of the counting. — Joshs
Your first sentence sounds consistent with law realism. I don't know what to make of your second sentence, other than that it sounds like an interpretation of quantum mechanics. Please explain.
Are you a nominalist? — Relativist
Isn't "electron" a kind? Do they not all have an electric charge of quantity -1?A ‘kind’ is not a category, object, identity. It is a differentiation. There are no quantities within kinds. — Joshs
Isn't "electron" a kind? Do they not all have an electric charge of quantity -1? — Relativist
Nature is undead.Nature is not dead. — Jackson
As you say, you've never heard of (Wigner's paper) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" and you should start doing your own homework so that you can contribute intelligently to the current discussion.look up Eugene Wigner.
— Joshs
Why? — Jackson
:up:As you can see, I’m a mathematical constructivist, not a platonist. — Joshs
Look at the period at the end of this sentence. Now keep on staring at it. — Joshs
Our mathematics begins only after we have concealed what happens within ‘kinds’. — Joshs
I think all participants here know about the statement of the unreasonable effectiveness of mathematics. Shouldn't we, rather, speak of it's reasonable effectiveness? — Landoma1
This (case) originated when Max Born noticed that some rules of computation, given by Heisenberg, were formally identical with the rules of computation with matrices, established a long time before by mathematicians. Born, Jordan, and Heisenberg then proposed to replace by matrices the position and momentum variables of the equations of classical mechanics. They applied the rules of matrix mechanics to a few highly idealized problems and the results were quite satisfactory.
However, there was, at that time, no rational evidence that their matrix mechanics would prove correct under more realistic conditions. Indeed, they say "if the mechanics as here proposed should already be correct in its essential traits." As a matter of fact, the first application of their mechanics to a realistic problem, that of the hydrogen atom, was given several months later, by Pauli. This application gave results in agreement with experience. This was satisfactory but still understandable because Heisenberg's rules of calculation were abstracted from problems which included the old theory of the hydrogen atom.
The miracle occurred only when matrix mechanics, or a mathematically equivalent theory, was applied to problems for which Heisenberg's calculating rules were meaningless. Heisenberg's rules presupposed that the classical equations of motion had solutions with certain periodicity properties; and the equations of motion of the two electrons of the helium atom, or of the even greater number of electrons of heavier atoms, simply do not have these properties, so that Heisenberg's rules cannot be applied to these cases. Nevertheless, the calculation of the lowest energy level of helium, as carried out a few months ago by Kinoshita at Cornell and by Bazley at the Bureau of Standards, agrees with the experimental data within the accuracy of the observations, which is one part in ten million. Surely in this case we "got something out" of the equations that we did not put in. — Eugene Wigner, Unreasonable Effectiveness...
The father of antimatter was the remarkable English physicist Paul Dirac (1902-1984), considered by many to be the greatest British theorist since Sir Isaac Newton.
His research marked the first time something never before seen in nature was “predicted” – that is, postulated to exist based on theoretical rather than experimental evidence. His discovery was guided by the human imagination, and arcane mathematics.
For his achievement Dirac was awarded the Nobel prize for physics in 1933 at the age of 31.
Let's not forget though where we apply it. To dead Nature. In the human realm it seems unreasonable if effective indeed. — Landoma1
Why is math effective? Because there is structure to the world that is describable with mathematics. — Relativist
However, Richard Hamming's thought experiment gives a powerful reason why heavy objects should fall at the same speed as lighter ones. This thought experiment allows us to predict that universally a heavy object should fall at the same speed as a lighter one, not only on Earth today, but on the far side of the universe and millions of years from now. Such thought experiments can predict both what cannot be seen and what cannot be experimentally foreseen.— RussellA
Look into this box of apples. They are all Delicious apples, a kind of apple. Now look closely at each one after carefully counting them - there are 24. Each apple is unique, being distinguished from the others in small ways. We see this as we contemplate these apples, a particular kind of apple. After a bit each apple seems to turn its best side toward our gaze, and we begin to contemplate what may lie on their opposite sides. In so doing we drift into a meditative state in which apples prevail, even those not Delicious. — jgill
Never heard of it before you. — Jackson
Why Wigner says it is 'unreasonable' is because of the sense in which mathematical conjectures sometimes produce completely unforseeen predictions which turn out to be true — Wayfarer
As soon as there are ANY differences in the world, you have a structure describable by mathematics — litewave
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