Essay Abstract

Theoretical Computer Science was one of the great intellectual developments of the 20th Century and only very recently have its ideas been integrated into basic science. I argue that these ideas and tools could be vital to understanding the relationship between mathematics and physics. In particular, if we are to ask if the utility of mathematics is a trick or otherwise, then we can use methods from the theory of cryptography and computation to pitch theory and experiment up against each other. Given this perspective we can ask if an experimenter can convince us to accept the theorist's version of events. I will outline that this contest is not as simple as it initially seems. There could be a stalemate between theory and experiment and it comes in the form of undecidability: a theorist can neither confirm or deny if Nature is behaving according to our most-trusted physical theories. Surprisingly, undecidability is a very real prospect in our current theories as I will discuss, and it forces us to question the relationship between mathematics and physics.

Author Bio

Matty Hoban is currently a postdoctoral research associate in the Department of Computer Science at the University of Oxford. His research interests are at the foundational end quantum information. He enjoys computational complexity far too much for a physicist.

Download Essay PDF File

Matty -

A remarkable essay and a quite interesting finding. Does it not leave us a bit at a loss if the physics problems we are trying to study are undecidable? I tried to take this concept a but further down the road (looking at the linked issues of incompleteness, undecidability and incompatibility) and would love to know what you think of my conclusion - that there is a "Hole at the Center of Creation."

You may also find Tommaso Bolognese's essay "Two Spherical Chickens" of considerable interest.

With deepest respect - George Gantz

    Dear George,

    Thanks for taking the time to look at my essay. First of all, I don't really think this leaves us a bit of a loss in general, as long as our physical theories give us "a story" or adequate scientific explanation. If a problem is undecidable but the theory from which it results has an adequate realist interpretation, I would still be happy with the theory and accept the limitations in making predictions. On the other hand, quantum physics poses severe problems to a satisfactory realist interpretation so one often resorts to the theory in pure operational terms. When reduced to this operational description as a means to just "shut up and calculate", it is not satisfactory if the "calculate" part is not even possible. We are forced to just "shut up".

    I will have a look at your essay when I get a chance. And thanks for the recommendations.

    Best,

    Matty

    Dear George,

    My idea is a counterexample to your proposition, you will not agree to it but I hope it will be of some help.

    Essay

    Thanks and good luck.

      Dear Dr. Hoban,

      You wrote: "Many ask what good is it to have a physical theory if it cannot give us good predictions?"

      Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

      Warm regards,

      Joe Fisher

        Dear adel,

        It's probably best if you address your concerns to George directly on his entry page.

        Best,

        Matty

        Dear Joe,

        I'm not sure how your writings are a response to what I said in my essay. Thanks for the comment though.

        I doubt Astronomers have not noticed that galaxies have a unique structure. I would say that the intentions of physics are to understand the fundamental causes of this uniqueness which hopefully results from universal laws that affect all galaxies. That is, we are not interested in particular properties of a system but more how these properties come to be and how they can change.

        Best,

        Matty

        Dear Matty,

        Your essay concerned repeating some of the unrealistic abstract theories of men long dead. I wrote about reality. As you are aware, the principle question of the Foundational Questions Institute concerns how the real Universe operates. I presented you with my contention that real light is inert and there is no physical space in the hope of converting you to realism. I am sorry that you apparently did not understand what I wrote.

        Respectfully,

        Joe Fisher

        Sorry, I don't know how I got here. This reminds me of the time I fell asleep on a train to Brighton only to end up in Portsmouth!

        25 days later

        Dear Matthew,

        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