Mathematics as unifying force for science by Torsten Asselmeyer-Maluga

You wrote:

"... numbers as an abstract count of objects was the beginning. ... But math is in particular a relational theory. Let us consider Euclid's geometry. One needs some obvious basic objects like point, line or surface which is not defined. Then the axioms are given by the relation between the three objects (like: the intersection between two lines is a point). In principle all axiom systems are of this kind."

Euclid's math was built directly on modeling structure in the world of phenomena, and therefore has phenomena as it's "referent". The same cannot be said for much of math that comes since, although it certainly has been adapted (with great effort and creativity) to the task of modeling phenomena.

Before you can claim otherwise, can you answer the question: what is a number?

Also, Euclid's axioms and postulates have the quality of encoding the law-like behavior of phenomena. Does that get carried forward into any subsequent math?

You might want to check out the entry "The Mathematics of Science" by Robert MacDuff.

Dear Torsten,

You didn't confirm agreeing agree on that alephs in excess of aleph_1 didn't find any application in science.

What about non-Dedekind but Euclidean (Maudlin's) numbers?

Regards,

Eckard

Dear Torsten,

Please find Euclid's famous, plausible, and compelling definition of a point as "something that has no parts" via Ref. 1 of my essay. Euclid summarized the still useful definitions and axioms of ancient mathematics.

Naive point set theory was logically untenable and therefore substituted by competing among each other i.e. rather arbitrarily chosen systems of axioms (NF, ZF, ZFC, NGB, ...) that were fabricated with the only intention to avoid paradoxes, cf. Fraenkel 1923 and 1984.

Regards,

Eckard

Dear Torsten Asselmeyer-Maluga

You wrote very exhaustive presentation of mathematics in physics. At this search it is also importantly to find the most precise words, which describe our intuition. One good example of your precise words is: ''Without abstraction, our species with a limited brain is unable to reflect the world.'' Thus math is a process of abstraction. Thus, my conclusion is that the essence of math in pyhsics is to be abstract and simple as much as possible. Because foundations of physics should be simple, the task of math is to describe quantum gravity on a t-shirt. Or, answer, why universe exists, should be short one. This would also confirm trend in physics until now. Smolin is also naturalist, as I am, but he think that elementary physics is not simple. What do you think about this?

My essay

Best regards,

Janko Kokosar

Dear Torsten,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear Torsten,

I just red your post to me about a wild embedding and a corresponding quantum state. Although my familiarity to your field is weak at the moment I am fully confident in your approach.

Cheers,

Michel

Dear Torsten,

Yes: Quantum studies: mathematics and foundations.

The editor in chief Yakir Aharonow writes in the preface:

"Finally, there is the approach championed by Dirac and repeated successfully by Feynman and later by Freeman Dyson, namely "playing with equations" as Dirac puts it. This approach sometimes causes equations to reveal their secrets as in the Dirac equation. Dirac took this approach and created results that mathematicians and physicists are still digesting. Feynman, first with the Lagrangian approach to quantum mechanics, the so-called path integral approach, and later with QED and most of the subsequent papers he wrote, operated in this manner. The same could be said of what Dyson did when he "cleaned up "QED into a methodology usable for calculations. Playing with the problems of quantum mechanics often leads to the creation of new mathematics."

and "Think, reconsider, explore, create deep questions, use paradoxes as a tool for understanding, and finally: publish in this journal!"

A priori this is a good journal for us. My own essay has quotes from Dirac and Dyson, and implicitely to Feynman that anticipated quantum information theory: "There's Plenty of Room at the Bottom" (in 1959). May be I can submit my Monstrous Quantum Theory and you?

Best,

Michel

Dear Torsten

Thank you for 7 points, but I gave you 10 points yesterday. I did not send message, thus this is in rules of FQXi. :) Thus, this that you give points to me today, is a coincidence.

The main reason is because you used right words, that I continue to describe relation between math and physics.

Dear Torsten,

I very much enjoyed your thorough exposition and your conclusions. Math is indeed a creative process that evolved from a need to have abstract unifying representations of the world. Your speech seems full of passion for the topics you study and that is very admirable for me. Your encyclopedic knowledge is just as impressive. I wish you best of luck in your research and in the contest!

You are more than welcome to read my essay and leave a comment, should you have the necessary time.

Alma

Dear Torsten,

Your essay is very good. I want to comment on your attitude:

„As described above, the relation between math and physics is not accidental. But the discussion above also implies that math is a general concept for whole science. But at the first view, only physics has this strong relation, why?

I see the reason in the different complexity in science. Physics describes the dynamics of simple objects."

This is a clear position and the answer is correct. The basis for your answer, you can look at the RuÄ'er BoÅ¡ković, who some consider the father of modern science and the creator of the first theory of everything. You research as a hobby; you do not have shown references which I think is good. I bring you my experience that in literature even more can be understood from the theories of giants of natural philosophy than current scientists. With this approach I have come to a result in my essay.

Regards,

Branko

Dear Torsten,

Great essay! You offered a nice historical review of math and physics, and gave strong arguments for why math is a creative process of the human mind. We seem to agree in many points as my essay reflects. For example, I don't believe in the Platonist view of mathematics, and I think that mathematics only provides models for describing nature not an exact correspondence. I would be glad to take your opinion in my essay.

Best regards,

Mohammed

Dear Torsten,

This is: „in medias res":

„Of course I'm influenced by many other thinkers (Hegel, Russel, Gödel, Einstein, Planck, Helmholtz etc.) but I don't find direct places to cite them. I'm sure that my thoughts were also thought by others but I had no time to find the places in the literature." Me too.

Sorry for researcher, I thought in the sense of the obligation of professors at the university.

Essentially, I assume importance just a one number, which I call the Cycle, exp (2pi).

Relationships between physical values are essential, not any particular phenomenon, which is a consequence of those relationships.

It is wrong to bind the fine structure constant with one phenomenon, electric charge. This constant appears in many relationships. The more we know of those relationships, getting closer and closer we know that constant. Nobody has an explanation for this constant, me too.

I did not calculate the fine structure constant. I followed two physical constants: the relationship between the mass of protons and electrons and inverse fine structure constant. Sure, I could use some other two constants.

My Table is not numerology and do not need dimensions. It uses three fundamental properties of matter: mass, length and time.

From it we can conclude:

That the Mach principle is good, i.e. My statement is: "The whole and parts are immanently dependent on each other";

To grasp the essence of the Planck values;

That the singularity in physics, as well as in mathematics is not possible, because there will always be referring within the cycle.

That is irrelevant story about the number of dimensions;

The connection between physics and mathematics is true;

That the relations between physical constants are immanent;

With the Table can be determined and the relationships between other physical values;

And much more.

Note that: the Table does not deal with quantum gravity.

Note that: Math that I use (seven main mathematical operations and two natural constants) is not an invention. It should be the same for the aliens.

Regards,

Branko