This One Moved Me

[bhobba]

See:


Thanks
Bill

 

[Jaime Rudas]

Frenkel says (4:32):

"Mathematics does not come to us from physical reality."

Is there really anything that could not come from physical reality?

 

[Paul Colby]

Frenkel says (4:32):

"Mathematics does not come to us from physical reality."

Is there really anything that could not come from physical reality?

I would say (imo) no. But, geometry is definitely an approximation or idealization of what we see in nature. Developing the logical consequences of these idealizations is what mathematics is.

 

[bhobba]

Is there really anything that could not come from physical reality?

I think, at rock bottom, math is motivated by an abstraction of physical reality. Why that abstraction was chosen, and even why to some people it has appeal, and others go 'yuck', is a matter for psychological research. You see this in things like the small minority of people that firmly support LET, and those like me who prefer an abstract presentation based on symmetries:

https://physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Thanks
Bill

 

[jedishrfu]

“To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.”
― William Blake, Auguries of Innocence

Such is Mathematics.

 

[djmanicbadger]

M

I would say (imo) no. But, geometry is definitely an approximation or idealization of what we see in nature. Developing the logical consequences of these idealizations is what mathematics is.

Math is cool but it dont " matter" lol

 

[symbolipoint]

M

Math is cool but it dont " matter" lol

We see your feel in usage of "lol", but Mathematics gives us great, great predictive power.

 

[Jaime Rudas]

Mathematics gives us great, great predictive power.

I believe that for a model of reality to be predictive, its fundamental principles must correspond to reality and its mathematical development must be correct. However, simply having correct mathematical development will not make a model predictive if its foundations don't correspond to reality.

 

[symbolipoint]

I believe that for a model of reality to be predictive, its fundamental principles must correspond to reality and its mathematical development must be correct. However, simply having correct mathematical development will not make a model predictive if its foundations don't correspond to reality.

We become aware of how well certain mathematical situations correspond to things we find, work we do, and such very difficult to generalize. Certain situations for mathematical things just work too well and work very logically. I do mean, many practical situations. We often find some examples of situations which fit, like when we deal with "Applied Problems" in our studies of "Elementary/Introductory Algebra", and "Intermediate Algebra".

 

[bhobba]

I believe that for a model of reality to be predictive, its fundamental principles must correspond to reality and its mathematical development must be correct. However, simply having correct mathematical development will not make a model predictive if its foundations don't correspond to reality.

You might like to read Hardy's - A Mathematician's Apology.

He was, in a sense, proud that what he did had no application, but even he was wrong - there is the so called Hardy Weinberg Law. This is a very strange thing about math captured in Wigner's famous essay, which, if you have not read it:

https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf

Thanks
Bill

 

[jedishrfu]

One trap in math that physicists fall into is relaxing a rule as a practical expedient to solve a problem. But to a mathematician, you have taken a shady shortcut that might come back to bite you.

I remember Feynman's story of the physicist who asks his mathematician friend about some math for 3D problems. The mathematician says I have just the math you're looking for, and says it can handle any dimension, but the physicist says, "No, no, I only want the 3D version."

Some time later, the physicist realizes that a 4D model would solve the problem if only he had the right math, and he goes back to the mathematician to ask about the multidimensional math he had previously sheepishly rejected.

 

[Paul Colby]

I view mathematics as a rather substantial collection of intellectual tools. Looking at a problem and selecting a 3d tool when a 4d one was more appropriate is just being a poor mechanic. Both are valid tools but only one of them fits the circumstance. The thing about developing mathematical tools is, they need not fit any given purpose. What is or is not interesting mathematics is rather beyond me to characterize.

 

[jedishrfu]

You might like to read Hardy's - A Mathematician's Apology.

He was, in a sense, proud that what he did had no application, but even he was wrong - there is the so called Hardy Weinberg Law.

I remember reading it and wondering he was so proud of the fact his math served no useful purpose other than to view it's elegance and marvel at its insight.

I came to the realization that Hardy and others of the time were appalled by war and it's use of the latest scientific and mathematical discoveries that killed, maimed or psychologically damaged so many promising young men and women and generations of families.