A dialogue concerning undecidability, uncomputability and unpredictability by Gabriele Carcassi

Gabriele Carcassi

Essay Abstract

At a physics conference break, a group of three participants discuss the impact on physical theories of Turing's halting problem, the uncertainty coming from chaos and quantum theories and Godel's incompleteness theorems. They try to differentiate between limitations of formal systems and limitations of what is accessible through experimentation, the latter of which, one of them argues, should be taken as foundational starting points in physics.

Author Bio

Gabriele Carcassi is a researcher in the Physics Department of the University of Michigan. There, with Prof. Christine Aidala, he leads a project on the foundations of physics called "Assumptions of Physics", his main research interest. He also has been working on numerous technical projects in support of the High Energy Physics community, including accelerator controls, data management and Grid/Cloud software infrastructure.

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Satyavarapu Gupta

Dear Gabriele Carcassi,

Wonderful simple essay as a dialogue form !!, Uncomputability is not only just non-terminating infinite loop of calculations, but also those physical situations where it is not possible to fit a mathematical function to some physical happenings, what do you say?

Some of your beautiful dialogues.........

B: I understand now. You can separate what is physically relevant from athematical junk.

C: That's a rather harsh term... Time and time again, what was seen as mathematical junk turned out to be useful to physics later

B: And a lot of it didn't ..............

..... is extremely correct, Physicists are searching for mathematical singularities in Physical universe!!!

In my essay "A properly deciding, Computing and Predicting new theory's Philosophy" I discussed much similar concepts in a different way....

Gabriele Carcassi

Thanks for the kind words.

>also those physical situations where it is not possible to fit

>a mathematical function to some physical happenings, what do you say?

I am not sure I understand... maybe an example?

Satyavarapu Gupta

Dear Gabriele Carcassi,

Thank you for your reply. For example there is a Mass and it is under gravitation. For Gravitation of that body we made a mathematical equation. That equation is complex and explains Gravity well. But that mathematical equation has some undefined points where some infinite values are coming.

Does that mean we should search for such infinite vales in physical world or try to change mathematical portions?

Is that what you said in your Dialogue is it not? I also discussed some thing similar in my essay.

I request you to have a look at it

Best

=snp

Vladimir Rogozhin

Dear Gabriele,

A very interesting, exciting Dialogue ... Is this a crisis of understanding in the basis of "fundamental knowledge"? ... Your opinion: what to do with the Big Bang hypothesis? I believe Carlo Rovelli is right: Physics Needs Philosophy / Philosophy Needs Physics ... Do you agree with the conclusions of Carlo Rovelli?

Sincerely, Vladimir

Gabriele Carcassi

Dear Vladimir,

Thanks! Given that I have attended philosophy of science conferences and that I am starting to contribute to the philosophy literature, it seems I do think some philosophical aspects are indeed useful.

But I am not a philosopher myself, so most of the things you talk about in your essay, for example, are things I do not have enough background for. Also, there are many questions in philosophy that I am not personally interested. For example, "what is space?" and other similar ontological questions I do not find interesting.

The question I am interested is "how do we, in practice, construct a coordinate system?". This is both a philosophical question, as it delves into epistemological issues, but it is also very practical engineering/physics questions, as it delves into the practical aspects of setting up an experimental device, calibrate it, etc...

Gabriele

Vladimir Rogozhin

Dear Gabriele,

Thanks so much for the quick reply and reading my essay. I, too, am not a philosopher, but an engineer, but life made me back in 1990 to begin to answer the most extreme questions of being and knowledge. Moreover, when science imposes on society a philosophically naive model of the "beginning" of the Universe, and knowledge in general, and especially mathematics, does not have an ontological basis ... Especially in modern conditions, when existential threats and risks for Mankind are constantly increasing.

You write: "The question I am interested is" how do we, in practice, construct a coordinate system? ""

This question also interests me.

I have three questions:

What is the coordinate system in the heads of birds that fly in the north in spring, home to their homeland, and in the south to fall?

How could a coordinate system arise as a result of the "Big Bang"?

Is there an absolute (natural) coordinate system in Nature? How to construct it?

Sincerely, Vladimir

Gabriele Carcassi

Dear Vladimir,

A coordinate system assigns labels (in the form of numbers) to objects to quantify their spatial position. Nature does not do this. We do it. The principle of relativity is a consequence of that: since nature does not assign numbers to objects, the laws we write down based on those numbers should not care of that assignment is done. Therefore, the laws should be independent of the choice of coordinate system.

Birds do not do that either. Though they will use a system of references to know where they are with respect to different objects. A system of references is what I use to approach the problem of defining a coordinate system. The idea is that, if you assume you have enough references that can be arranged in a particular way, you can construct a continuous scale. At a technical level, it meas writing down a few formal definitions and run the math to see you can derive the appropriate structures.

The fact that mathematics captures only abstract formal relationship does not bother me. What I like to do is have the physics justify those formal relationships in mathematical starting points (i.e. axioms and definitions) and then use it to make conclusion.

So, that's more or less how I approach the question "how do we, in practice, construct a coordinate system?" and the type of problems I work on.

Gabriele

Vladimir Rogozhin

Thanks a lot, Gabriele! I wish you success in your research and contest. I hope that mathematicians, physicists, poets and musicians will nevertheless have a single picture of the world and together we can overcome the crisis of understanding in the philosophical basis of fundamental science. My highest rating. If you have time, please give your critical comments on my ideas . I wonder how different we see our Universe.... I remembered studying the beautiful sketches of Matteo Carcassi on a guitar in my youth. I believe that the guitar will win the "big bang".

Best regards, Vladimir

Gabriele Carcassi

>I hope that mathematicians, physicists, poets

>and musicians will nevertheless have a single picture of the world

I very strongly feel the same way. All these disciplines are like the blind men and the elephant: all focusing at the same object (our experience of reality) from different angles. It's only the combinations of all those angles that can give us a complete picture.

Music is very dear to me as well.

Gabriele

Mozibur Ullah

Dear Gabrielle,

I liked the use of a dialogue format - it makes the issues come alive more. I especially liked:

shrugs, silence.

and

Newton's second law and Ohm's law have, formally, the same structure. The math itself is not enough to characterize the physics.

I very much agree with that. Physics is so much more than mathematics, though of course, the mathematics helps a great deal.

I wish you all the best with the contest.

Warm wishes

Mozibur Ullah

Gabriele Carcassi

Dear Mozibur,

Thanks for the feedback and encouragement! And I am glad to see the dialogue format achieved the desired effect!

>Physics is so much more than mathematics, though of course,

>the mathematics helps a great deal.

Indeed! To me, the math captures the part and only the part of physics that can be formally characterized. Which I feel is a small part.

Gabriele

Rick Searle

That was a great piece Gabriele!

It managed to be engaging, thought provoking, and funny at the same time.

The line "Pardon my math..." made me laugh out loud.

Seeing the Halting Problem in terms of experimental verification, or scientific verification as analogous to Incompleteness was new and eye opening for me.

Thanks for your dialogue- and best of luck in the contest!

Rick Searle