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SW-User
Surely mathematics is simply a human derived shorthand (thanks particularly to middle ages Islamic scholars who gave us the modern method for writing it and for algebra etc.) to explain the natural world around us.
I have 1 Goat my Wife's Dad gives me another goat - I have ... 1+1=2
It's then that along comes the lord of the manor and says - You all need to pay me 1 groat for every goat you have... so writing down maths is important... etc.
In the same way the two pages of squiggles my son publishes explains (probably) how Saturn's current fields interact with it's gravity etc. It's a language to explain a concept in a way people can interpret uniformly
I have 1 Goat my Wife's Dad gives me another goat - I have ... 1+1=2
It's then that along comes the lord of the manor and says - You all need to pay me 1 groat for every goat you have... so writing down maths is important... etc.
In the same way the two pages of squiggles my son publishes explains (probably) how Saturn's current fields interact with it's gravity etc. It's a language to explain a concept in a way people can interpret uniformly
SomeMichGuy · M
@SW-User That's an explanation of bookkeeping/low-level accounting, which is very different from mathematics in general.
That the idea of number can be tied, in counting, directly to real objects (and through this, you can demonstrate positive integers & real numbers) demonstrates that THAT aspect of mathematics is definitely reality-based. Add in trade and the notion of owing someone something, and you have justified negative numbers.
Counting & trade give you addition & subtraction. Multiplication is fast addition, division is fast subtraction, so the four basic math functions are easily derivable.
But the theoretical side--à la Descartes, etc.--is grounded enough that solutions to equations used to model reality end up describing things we may not yet have even seen, showing that our mathematics models reality amazingly well. Examples include Newton's mechanics & law of universal gravitation; Laplace's & Hamilton's reformulations of Newtonian mechanics; Maxwell's compilation of results from studies in electricity & magnetism to give the equations of electromagnetism; Hertz's derivation of electromagnetic waves; Bohr's model of atoms; Sommerfeld's quantization rule; Einstein's derivations & explanations of Special Relativity, E = mc^2, Brownian Motion, the Photoelectric effect, General Relativity; Planck's generation of his constant; Bell's derivation of his inequality; the predictions in particle physics of Gellman & Nishijima's "Eight-fold Way"; the particle predicted by Higgs et al.; etc., etc., etc.
It is discovered, uncovered, created, but based enough in reality that it describes it well, including the use of imaginary numbers to represent real waves...
That the idea of number can be tied, in counting, directly to real objects (and through this, you can demonstrate positive integers & real numbers) demonstrates that THAT aspect of mathematics is definitely reality-based. Add in trade and the notion of owing someone something, and you have justified negative numbers.
Counting & trade give you addition & subtraction. Multiplication is fast addition, division is fast subtraction, so the four basic math functions are easily derivable.
But the theoretical side--à la Descartes, etc.--is grounded enough that solutions to equations used to model reality end up describing things we may not yet have even seen, showing that our mathematics models reality amazingly well. Examples include Newton's mechanics & law of universal gravitation; Laplace's & Hamilton's reformulations of Newtonian mechanics; Maxwell's compilation of results from studies in electricity & magnetism to give the equations of electromagnetism; Hertz's derivation of electromagnetic waves; Bohr's model of atoms; Sommerfeld's quantization rule; Einstein's derivations & explanations of Special Relativity, E = mc^2, Brownian Motion, the Photoelectric effect, General Relativity; Planck's generation of his constant; Bell's derivation of his inequality; the predictions in particle physics of Gellman & Nishijima's "Eight-fold Way"; the particle predicted by Higgs et al.; etc., etc., etc.
It is discovered, uncovered, created, but based enough in reality that it describes it well, including the use of imaginary numbers to represent real waves...
SW-User
@SomeMichGuy not sure Saturn Aligned Current Fields is low level accounting.
My point being that much of maths is used to relay the physical world whether counting goats or determining the power within the atom.
My point being that much of maths is used to relay the physical world whether counting goats or determining the power within the atom.
SomeMichGuy · M
@SW-User No, the goat & lord of the manor thing.
Yes, mathematics has a level of reality behind it as shown by the fact that predictions we make with it can be born out in reality, even in realms where we have no direct experience (macroscopic/cosmological & microscopic length scales).
Yes, mathematics has a level of reality behind it as shown by the fact that predictions we make with it can be born out in reality, even in realms where we have no direct experience (macroscopic/cosmological & microscopic length scales).