Dear Lockie Cresswell

Thank you for comments and for reading my essay. I am pleased that you enjoyed it. I am surprise that you also mention my previous entry, which by the way it was a 4th prize winner from the 2012 contest. I hope you enjoy it as well.

It will be interesting to read your essay, this contest it's been for about 10 years. If you think you have develop a relevant theory, you should try publishing it in a recognized journal. That's my advice.

Best Regards

Israel

When I burn my fingers then I conclude that I have touched something external, yes.

Dear Israel,

I enjoyed reading your essay.

It does propose various claims with which I would tend to disagree but in any case they are well argued for.

I have some questions/ comments if I may:

-You said that "For if science is not about truth, then scienti fic activity becomes meaningless and in that case I should not be writing this essay". What if science is about unravelling "facets" of the truth rather than some absolute one way of looking at the world? Would that still make it meaningless?

- In your well-thought diverse examples to show that mathematics alone is not enough and ampliative principles from physics are necessary, I would more than agree with you.

But I thought that the way it was phrased was somehow unfair to the practice of mathematics. When solving an equation, an actual mathematician would ask in what space we are looking for the solutions. In the case of the degree 2 polynomial equation for the radius of a quantum dot, physics compels us to search for solutions in the set of positive real numbers. With regards to the particle in a box problem, I would argue the same. Although I totally agree with the main message, the mathematics problem that should be posed is that we are looking for a wave function psi(x) that satisfies the time-independent Schrodinger equation, hard boundary conditions at the walls and is normalised. If one chooses n=0, the last condition is not fulfilled since the wave function is identically zero everywhere. It is not that we decide to discard it for the sake of it, it just not satisfies the properties of a wave function.

- Of course we can also come back to the while discussion on relativity of motion later on :) .

I would be happy to know your thoughts on the questions/comments above.

Best,

Fabien

Dear Fabien

Thanks for reading my essay, I am glad you enjoyed it. Indeed science has been unraveling the truth progressively, and I think that we made a lot of progress in this direction: understanding nuclear energy, electromagnetic radiation, life, evolution, gravity, matter, consciousness, etc. is astonishing. Certainly, due to space limitations it is difficult to express ideas with precision. What I mean is that the main goal of science is to find the best description of how the world works, not merely an absolute truth. For me, science would be meaningless if it were an aesthetic activity, such as art, if it were not about understanding the world. Philosophers claim that philosophy has no utility for human life, they said that it is just an aesthetic human activity, the art of reflecting about the world, human nature, etc. If science were like this, it would be meaningless to me.

You say: But I thought that the way it was phrased was somehow unfair to the practice of mathematics.

Here is where we have to draw a line between physics and mathematics. If we deal this problem in the realm of pure mathematics, negative and imaginary solutions would be legitimate; and nobody would complain about it. However, we are using algebraic rules to find an answer to a physical problem and for this reason we are forced to rule out some mathematical aspects. This is the thesis I defend that physical understanding is crucial to make sense of mathematics. My argument is that sometimes physicists, based on mathematical rules, grant physical meaning to some mathematical results. Here is where the problem arises; because many times there are physical criteria to tell if the mathematical result is meaningless or not.

This is a similar argument for the case of the electron in a box. The initial assumption is that THERE IS an electron inside the box and accordingly the electron MUST HAVE an associated wavenumber k DIFFERENT from zero. If this wavenumber were zero, that would mean that there were no electron in the box. Now, you say that the wave function has to satisfy the time-independent Schrodinger equation, hard boundary conditions at the walls and the normalization condition. All of these are physical criteria. The last condition is just another way of saying that the particle IS IN THE BOX that is why the volume integral of the square of the wave function is equal to ONE (it is the sum of all probabilities in that space). If the integral were zero, the particle would not be in the box. So, n=0 implies k=0 and k=0 means that THERE IS NO WAVE associated to the particle or that THERE IS NO PARTICLE in the box.

Regards

Israel

Dear Israel,

Absolutely agree with "If science were not about true knowledge, it would be useless." Only several hours ago I had to address this same issue on my blog:

... such misconceptions are often caused by inadequate views on the nature of physical theories (e.g. one can hear "theories are just descriptions"). Perhaps, the saddest example of how such inadequate views can prevent even great scientists from making a discovery is Poincaré's failure to discover the spacetime structure of the world. He believed that our physical theories are only convenient descriptions of the world and therefore it is really a matter of convenience and our choice which theory we would use. As T. Damour stressed it, it was

"the sterility of Poincaré's scientific philosophy: complete and utter "conventionality" ... which stopped him from taking seriously, and developing as a physicist, the space-time structure which he was the first to discover."

Best wishes,

Vesselin

Dear Israel Perez,

I enjoyed reading your essay.

Your discussion of negative solutions was very thought provoking. I think it is worth pointing out that sometimes negative solutions should not be dismissed and

do have significant physical meaning. Dirac's finding of the positron comes to mind.

I wonder if all fake negative solutions would go away if we dealt with the right mathematics. For example, we always thing of the whole set of real numbers. Maybe we should do mathematics only with positive real numbers. We always deal with groups. Maybe we should deal with the less familiar monoids.

I also enjoyed you stressing the importance of understanding. I once humorously pointed out to my thesis advisor, Alex Heller, that

there are subatomic particles in nature that follow equations of motion

that human beings cannot solve. And even though humans do not know

where the particles will go, the particles seem to know exactly where to

go. Professor Heller responded by saying that this shows that science has

nothing to do with calculating or predicting. Calculations can be done by

computers. Predictions can be performed by subatomic particles. Science

is about understanding -- an ability only human beings possess.

Again, thanks for a great essay.

All the best,

Noson Yanofsky

    Dear Izrael,

    Your essay is very interesting. I completely agree with you that physical understanding is very important and in my essay I try to prove it on concrete examples. One mathematical model can have several interpretations and one physical phenomenon can be described by different mathematical models. The force of physics is in the possibility to combine different methods of cognition in order to find the correct solution. Without experiments and math physics is philosophy as it was at the very beginning. But without physical understanding and experimental confirmations physics can turn into mathematical philosophy.

    I wish you good luck

    Boris

      5 days later

      Dear Izrael,

      Interesting essay. The message mathematics is an amazingly useful tool but that we do need to talk about the real world is an important one. Indeed, claiming the universe is made of mathematics is pure untestable metaphysics, a claim quite beyond our abilities. At the very least, our current ones.

      Best,

      André

        Dear Noson

        Thanks for reading my essay and leaving some comments. Indeed, I also mention Dirac in my essay in relation to antimatter and the negative solutions. My work stresses that physical understanding is very important. Unfortunately, in the last decades we have not worked much this understanding and instead we are betting on mathematical description. Thanks for sharing your story with your advisor, indeed, calculations are just a matter of quantifying.

        Best Regards

        Dear Boris

        Thank you for your comments. You say it very nice. Without understanding, it is pure mathematical philosophy. I will be looking forward to seeing your entry.

        All the best

        Dear André

        Thanks for your post and for reading my essay. Mathematical representation of physics can give us quantitative answers but poor qualitative ones. Certainly, we have to walk on solid ground when developing a theory.

        Best Regards

        Dear Vesselin

        Thanks for your comment. The etymology of the word science says it all: science=knowledge. But not any kind of knowledge but true knowledge, knowledge that can lead us understand as much as possible how the world works. We may deal with approaches to the truth and in that sense it might be convenient to use one or the other, however, the final goal of a scientist is to gain true knowledge that can be useful to tell reality from fiction.

        Best Regards

        Greetings Israel Perez

        To respond to your last paragraph: "... that mathematical beauty is not enough to tell the whole story, and to achieve a solid knowledge we should work out a physical understanding. The history of physics has shown that physical understanding is crucial to make headway in this field; otherwise we might continue lost in math and measurements."

        I must submit that math can and does obstruct -

        especially when that math describes things not observed in real life that becomes the basis of physics - as in de Sitter's expanding space - Friedman's creation of the world from nothing - and Lemaître notation - "If the world has begun with a single quantum..." these all obscure applicable common 3D physics hiding the physics of the Big Bang.

        It is proposed that any evidence describing the Big Bang is beyond science's reach and yet this essay of mine entered January 18th Common 3D Physics Depicts Universe Emerging From Chaos presents a plausible explanation with plenty of current replicable evidence describing 'Reality.' Check it out.

        Regards

        Charles Sven

          Dear Israel,

          Your essay is very interesting and well written. The relation of mathematics and physics is a fundamental issue. Tegmark is championing radical thesis that physics is mathematics. This of course sounds like a metaphysical belief but the "unreasonable effectiveness of mathematics" when applied to physics can not be just brushed away. Thinking along these lines I developed approach in which uncomputability is foundational, Theory of Everything has to be founded on it but in a very peculiar way. This is sketched in my essay.

          Best regards,

          Irek

            Dear Charles

            Thanks for reading my essay and commenting. My essay is about finding an equilibrium between our physical understanding and mathematical objects. In this work, I discuss a couple of instances where physical understanding sees things that math doesn't. However, the opposite is also true. Mathematical symmetry has predicted physical reality that our physical understanding was not able to foresee, for this reason both aspects are important. I will try to find some spare time to read your essay and leave some comments. Thanks again.

            Best regards

            Israel

            Dear Irek

            Thanks for your comments and reading my essay. For me metaphysics is an old term to describe aspects that are beyond the physical realm. But, accepting the existence of metaphysical entities implies the acceptance of a metaphysical world. I therefore, deny the existence of metaphysical entities along with that world, I only accept a physical world and ideas or abstractions as part of this world, after all, the process of thinking is also a physical process that demands energy consumption. So mathematics as a way our brain has for representing the world is quite acceptable. I guess, the success of applying math to physics comes from this physical essence. I will do my best to try to find some spare time to read your essay which sounds interesting.

            Regards

            Israel

            Lovely Essay,

            Checkout the long form version of my essay where I too compare the human brain to a supercomputer that is actively processing information about the physical universe

            Please take a look at my essay A grand Introduction to Darwinian mechanic

            https://fqxi.org/community/forum/topic/3549

              Dear Israel,

              what a refreshing essay. I usually do not consider to read an all-caps-title-essay, (Why did you do that?), but I'm glad I did. I think, I knew your name from your arxiv article on the physicist's view of the universe.

              I like your approach to physics. As fascinating some of more modern information theoretic approaches to quantum foundations are, I miss the physics sometimes. It is so different to read the 'old ones' on foundational questions.

              I have a few questions though. Where did Landau and Lifshitz exclude inertial frames? Didn't they just say, that between the inertial frames non is preferred?

              Regarding the rotational motion, I did not know, that statement (2) is accepted as false by most physicist. How and when did this change come? I somehow missed that.

              In my own investigations on time dependent symmetries (within quantum mechanics), I asked myself why does the translation symmetry remain a symmetry, if we make it time dependent and the rotational not. The answer I found was basically: For rotational symmetry to hold on subsystems the environment must be isotropic. Introducing a global time dependent rotation introduces a direction in the environment and hence breaks the isotropy. Group theoretical arguments where enough to show this.

              In my own essay symmetry plays a prominent role and the question under which conditions measurements are well defined and so also concepts of the laws or properties of objects or systems. It would be a pleasure if you would find the time to read and give your opinion on my essay.

              Best regards,

              Luca

                Dear Israel,

                How interesting!

                What would you say about situations where exactly the same maths describes two completely different physical interpretations? Would this not support your assertion that it's not just about the maths?

                You may be interested in a couple of things that I have discovered and that are discussed in my essay.

                First, if you imagine a world where all change travels at the same speed in an absolute space, then, clearly, that world would not be relative. However, it turns out that a clock that moves around in such a world will slow down, contract along it's direction of motion, and increase in mass, all in accordance with the equations of Special Relativity. The maths can, therefore, apply to both an absolute and a relative world.

                Second, it is possible to use the maths of quantum electrodynamics (a quantum theory about photons and electrons) to describe a Universe made of just quantity, direction and change, and where photons and electrons don't actually exist at all. The maths, therefore applies both to a world with electrons and photons, and a world without them.

                All the very best,

                David