Essay Abstract

Based on physical sensations the human brain manufactures mental structures leading to a theoretical framework that is used to make sense of life and external reality. Such framework turns out to be our physical understanding. To quantify and model physical systems humans have also invented both mathematics and experimental instruments. The physics developed in the last decades has trusted its validity on these two aspects above our physical understanding. I argue that undecidability and unpredictability might not be relevant for physics. Math and measurement are not the sole players in apprehending natural reality. Physical understanding should play a prominent role in physics if we wish to make headway.

Author Bio

Israel Perez is a physicist in hard condensed matter. He works for the National Council of Science and Technology and does research at the Physics and Mathematics Department at the Autonomous University of Juarez City in Mexico. For this contest he has written a thought-provoking essay.

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Dear Israel Perez,

Thanks for an insightful and enjoyable essay. I agree with you completely and my current essay supports your discussion. I consider the fact that space and time can be described mathematically as four dimensional or as (3+1)D. The math is correct in either case, so human understanding is needed to choose between these two. My essay is here: Deciding on the nature of time and space.

If we assume that there is a unique physical reality (ontology) and there is an alternate imagined reality, there is nothing that prevents math from describing both 'realities' in detail. Measurements may do the trick, but some measurements are hard to perform perfectly. In that case only intuition will guide us, and many physicists, as you point out, have been warned to ignore intuition -- 'shut up and calculate'.

Your essays are usually insightful, and I'm glad you focused on this issue. There are too many imagined realities [a dozen in QM?] and the best way to navigate through these is human understanding.

Thanks again and good luck.

Edwin Eugene Klingman

    " For if science is not about truth, then scientific activity becomes

    meaningless..."

    We may never know the "truth" or the ontology. Science is about helping humanity survive. Its realm is to be useful which requires prediction and creating models of how the universe works.

      Dear Israel Perez,

      I enjoyed your essay very much. Although I am a mathematician, it is clear to me that mathematics alone does not provide a complete picture of physical reality, and that physical understanding as you explain it is also required. I have also been wrestling with the fact that while rectilinear motion appears to be relative, both in theory and in practice, rotational motion appears to be absolute. Taking this physical understanding to its logical extreme in quantum mechanics leads me to some very surprising, but I believe inevitable, conclusions about the nature of mass. This argument, and its conclusions, form the subject of my essay, which I hope you will find interesting.

      Robert Wilson.

        Dear Israel Perez,

        Your essay is perfect clear and to the point. Personally I like the last part about Einstein's lectures by his friend Paul Ehrenfest at the University of Leiden the most. For me it was an eyeopener when I read about it some 15 years ago. Before I had already discovered that the curvature of space isn't real, it "terms" the visualization of Einstein's model.

        With kind regards, Sydney

          Dear Israel,

          since Paul Feyerabend we know that there is no golden methodology to do physics, because scientific effort is either gap-filling (Th. Kuhn) or in the worst case just permutation of existing knowledge - or it is making observable what so far was unobservable. In the latter case absolute novelty comes into play, the invention/discovery of which can not possibly be traced back to some methodology. Gravitation and el. mag. waves, for instance, came out of the blue.

          The above does, however, not exclude the existence of methodologies how physics (science if you will) should not be done. Now, with the help of Google and lots of estimation I believe that at least the order of magnitude holds, that the intellectual (let alone monetary) efforts put into theoretical physics since QM and relativity have been one million times higher than all the time before. And yet no substantial progress has been made beyond the tautological confirmation of what lies hidden in the axioms of those theories.

          So, I disagree with your conclusion that "a better understanding of physics" (beyond mathematics) will do the trick. Rather I think that physics has embarked on a necessarily unsuccessful methodology. Basically the title of your essay neatly puts it together, without providing the overarching clamp, however. So allow me to complete it:

          Lost in math... and measurements = Lost in models

          That this runs counter your intentions becomes clear right from the beginning of your essay:

          "Our physical understanding of nature is strongly rooted in sensory perception. Our senses provide us with information of different nature such as on shape, color, light intensity, motion, space, weight, sound, temperature, force, taste, smell, and so on. From these stimuli, or raw data..."

          Since this view is the pseudo-empirical model-view of the world and since models have no explanatory, intuitive or understanding powers, your plea for more physics must remain wishful thinking under the assumptions you make.

          best,

          Heinz

            Dear John

            Thanks for reading my essay and leaving a comment. As I said,theories should reflect the true reality because this is the only way science can be used in favor of humanity. If science were not about true knowledge, it would be useless.

            Regards

            Dear Robert Wilson

            Thanks so much for reading my essay and leaving your comments. I am glad that you recognized that math is not enough to prescribe reality.

            Regarding motion, I think Newton was right, there is absolute and relative motion and one can be distinguished from the other by forces and accelerations. Uniform motion appears to be relative because we were taught that there was no preferred frame. I do not think this is correct you may want to check one of my previous entries

            I would be happy to read and comment your essay, I also did some research on mass some time ago, I guess it would be exciting to see your view.

            Regards

            Dear S. E. Grim

            Thanks a lot for your comments and reading my essay. I am glad that you enjoyed it. Einstein theory of relativity is just a geometrization of space which in that context is understood as curvature and in some sense can be seen like that. But I guess there are other approaches that not resort to geometry. I wonder how you discovered that there is no space curvature. In what sense you say it.

            I would seek for your essay and comment asap.

            Best regards

            Dear Edwin

            Thanks for reading my work and for your comments. I wonder what you mean by (3+1)D, as far as I understand it is already that way; but I will read your essay asap to make this clear. Certainly quantum mechanics is a theory that requires deeper understanding. I have also worked out this theory to deeper understandt it, especially entanglement and its spooky action at a distance. I am looking forward to seeing your essay.

            Best regards and good luck!

            LOST IN MATH ... AND MEASUREMENT sounds a bit hopeless.

            I claim having FOUND among others a possibly important mistake by Fourier.

            Eckard

              Dear Heinz

              Thanks for reading my work and leaving your important comments. I would like to ask in what sense Gravitation and el. mag. waves came out of the blue. To my understanding there was a gradual process for the development of these theories.

              You mention that: no substantial progress has been made beyond the tautological confirmation of what lies hidden in the axioms of those theories.

              Definitely I agree, no much progress, but as always, attacking the principles will lead to progress. For instance the question on the origin of the particle spin.

              Regarding your disagreement, certainly, measurements and math might compose a model, but what kind of model? Current models are merely mathematical and the explanations are also mathematical, with barely no physical insight, this is why nobody understands quantum mechanics. I argue that we should work out a physical understanding to make physical sense. This would help us, for instance, to rule out the different interpretations in quantum mechanics and make some progress in this field.

              As for your last comment, I wonder why you call it pseudo-empirical model-view of world. Why pseudo? Where is the pseudo part? and what is your understanding of a model?

              I will be looking forward to seeing some feedback.

              Best regards

              Dear Eckard

              Thanks for your comment, I hope you enjoyed my work. I will take a look at your writing, it sounds interesting.

              Regards

              Dear Israel,

              as regards concepts it is difficult to see how they could evolve. Until Newton it was uncontested knowledge that force can only be conveyed by collision. Accordingly was his gravitation, which is action at a distance, initially ridiculed by some. I also don't see a viable trajectory from Newton's to Einstein's gravitation. Further, Huygens' superposition of unit waves explaining diffraction etc. can't be derived from then prevailing geometrical optics. Also from Huygens to Fresnel I see no change of principles, only refinement. Rather, if concepts were soft, I believe that nothing at all could be observed. Models, on the other hand, are indeed soft and for this reason no laws of nature - just models. Let me explain in some more detail and bore you with a little bit of philosophy...

              Irrespective whether model or natural law, any speculation beyond the given requires pre-knowledge. How otherwise could we express such speculation? The task then at hand is the weighing of such speculation in light of pre-knowledge. There was a 17th century philosopher, Baruch de Spinoza, who held the following: "A thing necessarily exists, if no cause or reason be granted preventing its existence." What he says is, that a thing exists, if it is non-contradictory. Popper said that we can accept a theory as long as it hasn't been falsified. Falsification, however, is contradiction. So, are Spinoza and Popper saying the same?

              It is important to recall that Popper's theory of falsification (and Spinoza's assertion per se) is a theory over propositions (Sätze). "Only propositions can falsify propositions. Measurements, experiments and data as such have no place in Popper's theory, i.e. falsification is an armchair job. This means mere facts can neither verify nor falsify theories. The first stage of attempting the falsification of a theory consists according to Popper in its consistency check, which I call the semantics-check. Can we reasonably speak about what the theory pretends to claim? In the case of quantum mechanics his conclusion was: no we can't, unless we consider statistical quantum ensembles in a frequentist's sense. Well, it doesn't really need super-intelligence to find that any other traditional interpretation is a-semantic, thus failing the pre-test. Also recent QM and relativity interpretations/extensions would not pass the semantic test and hence end up dead in the water even before reaching the core of the falsification procedure, the weighing of two semantically consistent theories against each other. I guess Spinoza would buy this.

              But then there is a difference: the important word in Spinoza's assertion that things exist "if no cause or reason be granted..." is the word NO! whereas Popper suggests falsification against so called Basissätze, i.e. a set of fundamental propositions that is believed to be 'true'. This is where Popper changes over from falsification to affirmation, which is super-critical not because the chosen set may contain false propositions, but because it reduces the totality of human knowledge down to almost nothing and entirely excludes human experience in the world, i.e. the phenomena. This is what Spinoza would have rejected, for other knowledge domains (e.g. biology) and the phenomena make up for an estimated 99.9% of our daily propositions.

              What Popper effectively proposed is the minimization of pre-knowledge and physicists increasingly began to substitute propositions by facts (data), which eventually led to the outcry of physicists 'we cannot possibly falsify our theories', while they actually meant 'we cannot possibly falsify our data'. Now, empiricism is a posteriori rule-making over data censored by the phenomena, i.e. modeling (e.g. of the climate), which is to be distinguished from a priori (Spinozean or Kantian) laws of nature, which value the whole of knowledge and experience. In the absence of phenomena, which is the case for all of theoretical physics, the modeling turns into pseudo-empiricism, for data are no empirical evidence of whatsoever..

              the best for your essay,

              Heinz

              Writing a function as F(x,y,z) does not mean that F really exists in physical space, even though x, y and z seem to refer to physical space.

              Israel,

              Excellent essay. Nicely expressed and argued, and we're in very close agreement yet again.

              You well describe the issues of Absolute v Relative motion etc, but it seems may not recall that you (with others) briefly grasped the solution I posited, consistent with Einsteins final (1952) rationale. That's proved powerfully resolving so I'll outline it again here for your view;

              Physical systems only have ONE assignable state of motion k, and occupy bounded 3D spaces. Each is mutually exclusive, but can be embedded within a larger one, and also contain smaller ones. So forming a hierarchy. Now Einstein's (Appx.V) words; "..there is an infinite number of spaces , which are in motion with respect to each other...so..an infinite number of spaces in motion relatively to each other. This latter idea is indeed logically unavoidable, but is far from having played a considerable role even in scientific thought."

              When we actually look for the boundaries they're hiding right before our eyes, literally! Fine surface structure electrons play the same role as astrophysical shocks, modulating LOCAL propagation speed to c in each system.

              NASA's E H Dowde and C Su found the same, i.e. (Eur. Phys. J. C 21, 701-715 (2001))

              That explains observed CSL, with ALWAYS a 'local background' frame but no accessible 'absolute' frame. I recall you agreed that logic, but fqXi essays are hard to remember!

              I write all that as it's so important, (consequences presented in my essay) but very well done for your own essay of which I can find no criticism! I'm sure you'll like mine again, and as our ratings are close

              agree as gentlemen both are worth a high score (mine was hit by an annoying 1.0 again!)

              Finally ref your abstract. I showed one implication of the above last year, that A & B can reverse their OWN outcomes by reversing their dial. That needs thought, but a PHYSICAL sequence producing it was described in last years essay, outlined again in this years.

              Very best regards

              Peter

              Dear Heinz

              Thanks for your comments. Despite your explanation I still don't see any justification of your claim that those theories came out of the blue. For instance, Newton was aware that gravitation was not conveyed in total emptiness, he always held that there was aether. However, his theory does not include it and for this he was criticized. So why at the end was his theory established? First because it made testable predictions and explained known phenomena. Besides, at that time people discovered that it was possible to create vacuum with machines and that light and gravitation could travel through the vacuum. This was an argument that many invoke to justify Newton's gravitational theory. When one studies relativity one easily realizes from analyzing Newton's theory that this formulation suggests that gravitation and acceleration are strongly related: [math]F=ma=G\frac{mM}{r^2}[/math]

              by eliminating the inertial mass

              [math]a=g=G\frac{M}{r^2}[/math]

              we see arrive at the Galilean equivalence principle(Einstein's happiest thought). The rest was just to put these ideas in mathematical terms following the four dimensional formulation of special relativity derived by Minkowski. So, I see no "out of the blue" and similarly for the theory of electrodynamics. For this was also a long and complex process that one can trace back. I do agree that some ideas may come out of the blue, but as you put say it they came from some pre-knowledge.

              As for your comments on philosophy, I am aware of Popper, I have read his most important works on the philosophy of science. I have not read much about Spinoza. I know that sometimes propositions cannot be tested for they seem to be beyond experience or data, but as I said, data requires a theoretical framework to have meaning. Experimentation itself cannot rule out propositions because data itself depends on the theoretical framework where laws (principles, propositions) and definitions are embedded. So, in my opinion a model, understood as an abstract construction of some phenomenon, can be useful to understand something about reality (this is how we have built it). For instance, I suppose that materials are composed of atoms with a given arrangement. The atomic composition and the arrangement of the atoms define the physical properties of the material. If I check such or such property of that material and fits with my predictions it means that my model is correct and therefore my model does have explanatory powers because it is helping to understand the observed phenomenon. Models along with the principles help us understand reality.

              Israel

              Dear Martin

              Thanks for your comment. For instance, the electron density [math]\rho (x,y,z)[/math] depends on the spatial variables, and exists because electrons exists, so if the density exists why not its mathematical representation? The problem as I argue in my essay is that we think that what exists is what we can detect with instruments or our senses but that just half of the story. I think you should first start by telling what you understand by "exist".

              Regards

              Dear Peter

              Thanks for reading my essay, I am glad you find it interesting. Definitely you have a very good memory, I do recall we discussed these matters in the past. I am sorry for not recalling the details and thanks for the reminder. The reference appears to be interesting, I will take a look at it asap. As I argue in my essay, math does not tell the whole story. The preferred frame is sound and can be used to make some progress in physics, let's see what happens in the following years in this respect. The article you cite seems to be in agreement with this view.

              As for Einstein's arguments, it seems that he was happy with the mathematical formulation of general relativity but not very much with references frames. In the book Relativity authored by Pauli, it is clear that Einstein's tried several times to remove any trace of the absolute frame, without success.

              Thanks again, I will read your essay and leave some comments asap. I am sure you did a good job.

              Regards

              Israel I appreciated your essay. Perhaps because my creation theory came from "physical understanding" and then finding the mathematics to explain the measurements. In my essay I describe a flowing "picture" of compositional changes that originate in chaos and become our universe. It also creates the mathematics that can be used to describe it and match the its measurements. I would appreciate your comments (coming from your perspective) on my "revised" essay. John Crowell.

                Dear John

                Thanks for reading my essay. I am happy that you found it interesting. Certainly, I will take a look at your work and leave some comments. To make some progress in physics either mathematical or physical understanding is valuable.

                Regards

                Israel

                Dear Israel,

                I indeed meant that the actual density is not the same "thing" as its mathematical representation. In models of the density, the model is commonly only an approximation of the real density, due to all sorts of approximations that are necessary for being able to calculate a result. E.g. the exchange-correlation functional of an interacting many-particle system can only be approximated, e.g. by assuming the local density approximation, etc. So the model density is not even numerically identical with the actual density.

                I only said this as I see this as being a problem in foundational physics. In general relativity there is a curved spacetime, but this is just a mathematical representation. And what is, in quantum field theory, the field PSI(x,y,z,t)? Why assume that this is a physical field? Historically, this field has only been created in order to describe experimental results.

                Another question is what is meant with "exists". In what sense does the number 5 exist? I think it means that we have a formalized manner of using the symbol "5".

                Dear Martin

                Have you read my essay? There I explain that our brain builds reality according to experimental data that is interpreted in our brain with electrochemical patterns leading to a theoretical framework. The interpretation can be given in terms of sensory-data or in terms of abstractions, such as mathematics. Mathematics can be seen just as a codification of sensory data which is used to model and quantify our physical representations. But physical representations, are just electrochemical patterns, similar to strings of bits in a computer. So, why should we narrow our view to believe that what are senses/instruments detect "exists" and the mathematical codifications of this same information doesn't?

                It is as if we were giving more physical significance to a program that is written in fortran and ignoring another program that does the same as the former but it is written in C++. Why should we think that the program written in C++ is just a representation of the other just because it is written with different symbols and different grammar?

                Best regards

                Israel

                Israel

                I have answered your post on my page.

                Regards ________________ John-Erik

                Yes, OK, "mind" is physical. And so are feelings.

                But I meant: why assume that our mathematical representations exist "out there"?

                Dear Israel,

                Thanks for this essay, whose main point cannot be stressed enough - indeed even Einstein did not appreciate it, especially in his later life. An interesting and polemical analysis in this direction is also contained in Sabine Hossenfelder's book Lost in Math. As you say, it is all about balancing physics, math and measurement, Newton understood this! Best wishes, Klaas Landsman

                  Because we assume that our "physical" representations exist out there!

                  Dear Klass

                  Thanks for leaving some comments, I appreciate it. I hope you enjoyed it.

                  Best Regards

                  Israel

                  Dear Israel,

                  Your enjoyable essay makes a very good case for more ontological reasoning in physics, rather than just remaining lost in the maths wilderness, where we have been stuck for decades in many areas of physics.

                  My particular areas of interest are particle physics, time and the aether. By complete chance, back in 2002, I discovered a new preon theory, which I have named gimli theory. You quote Feynman "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." Gimli theory works and gives consistent outcomes that agree with experiment.

                  The point here is that a reductionist theory that works (agrees with experiments) can give new structural insights into the world of particles, and these insights can lead to a dismantling of much of the patchwork of quantum field theories of the Standard Model. Gimli theory is not based on heavy mathematics at all, yet it can provide many answers to big questions because of its ontology.

                  My grumble is that mainstream physics journals do not want any "maverick" theories challenging the status quo, unless put forward by a Nobel laureate, and even then it may still be difficult. New physics theories heavy in math tend to be only read by the few in the clique, and are often beyond the grasp of philosophers of physics.

                  You state that physical understanding is crucial to make headway; otherwise we might continue to be lost in math and measurements. I fully agree with you!

                  As my entry is my first ever FQXI essay, I tried to stick to examples of undecidability, computability and unpredictability, in my considerations of a TOE, although I do wander on to the philosophical time topic of presentism which I currently endorse.

                  I am currently reading your 2012 FQXI essay "The preferred system of Reference Reloaded" which is a brilliant essay. It is a pity that I have only just discovered FQXI, partially due to me working in almost total (physics) isolation for the last twenty years developing my 'structural' theories of space, time, aether and particles. The advantages of being a hermit (not visiting physics forums) is that you can keep ideas pure during development. Of course, one needs good reference material to work with from the start.

                  Good luck with your essay and 'may physical theoretical frameworks come into prominence'! (ie. may the force be with you)

                  Lockie Cresswell

                    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