Dear Scott Guthery,

i enjoyed your essay a lot. I agree much on your statement about rational numbers.

Although in the pysical theories are "flaws" too, but they are effect of physicist being conditioned to use wrong mathematics.

To me it looks like we must at least go back to Pythagoras Mathematics, but scientific community is in fear to do so, because physics and mathematics then become connected to political influence and economic system.

Physics about space and time is Philosophy ... not attached to Reality (physical)

"Physical" Physics is different mathematics, as each number (each °1°) must be connected to a "measurement" (empirical data).

irrational mathematics : 1+1=2 ???

rational mathematics :

1+1=1 (1 bread + 1 butter = 1 small meal)

1+1+1+1+1 = 1 (1 bread + 1 butter + 1 egg + 1 orange juice = 1 big meal.

one can find 1 piece of butter and create 1/3 + 1/3 + 1/3 = 3* 1/3 = 1 Piece

same concept is possible for Astronomy:

one find one sphere (sky) and can find 4 (or 4 Million) stars (shining objects) and use them as 4 million "clocks". Using them, there a 4 (million) different times at the same time.

in general, (as said by others too) "math" is our universal language and also "animals" are using maths as language: They use "waves" (sound, EM) to communicate.

Our mathematics (language-puzelling might be completely disconnected from physics at least for 2020 years.

Best wishes

Manfred Pohl

Dear Scott Guthery,

Do mathematicians like you consider a reference point an irrelevant detail because it is considered outside pure mathematics?

Eckard Blumschein

5 days later

Hi Dr. Guthery!

This is an excellent point, that math should be driven by physical observations! I definitely agree with this. Our models should inform us about the world around us, but we should also let the world around us inform us about new models. Actually, this is why I was so happy to be a data scientist for a few years! It gave me a very good perspective on the data-driven world and the advantages it has to offer. Now returning back to academia, I see a very big need for a two-way street between models and observations! It seems like it should be an iterative process between refining models and giving a causal explanation to data.

Cheers!

Alyssa

Dear Dr.Guthrie,

Let me suggest another topic that applied mathematicians should address: Nonlinear dynamics.

In particular, I believe that the behavior of solitons is central to a proper understanding of quantum mechanics, and solitons can occur only in certain nonlinear differential equations.

Note that the entire Hilbert space formalism of orthodox quantum theory is based on linearity. Linear algebra is well known as a powerful mathematical tool, but it does not apply to nonlinear systems.

In my own essay, "The Uncertain Future of Physics and Computing", I point out that an electron can be presented as a soliton-like wave, rather than a statistical distribution of point particles. The exclusion principle can be understood as a classical soliton-soliton interaction, rather than as a mysterious entanglement in Hilbert space. But we need the mathematics to address this.

Alan Kadin