Dear Matt Visser,

Maybe, complex numbers are already the minimal extension of the rational numbers? Anyway, already the extension of the natural numbers to the integer numbers may be interpreted as a trick to allow convenient calculation without shift operations.

In principle, 19th century physics could also be formulated without negative and complex numbers. This is not just an idea that I adopted from other engineers; it was also admitted by Pauli (cf. Der Pauli-Jung-Dialog). Don't get me wrong, I don't deny the practical necessity of using complex calculus.

While your superb essay confirms your excellence, you and virtually all physicists might nonetheless have failed to get aware of a trivial trifle; the use of complex calculus in physics and technology has been based on Heaviside's trick to attribute zeros to the not yet existing future and split the continued. This implies fourfold redundancy due to omission. Well, one can easily avoid the dilemma by following Einstein and Hilbert and denying the distinction between past and future. However, this way the logic consistency gets lost. Instead I prefer using complex calculus properly, step by step.

So far, nobody could show in what I am wrong when I state that cosine transformation of measured data is as good as their Fourier transformation.

MPEG demonstrated, it actually works. Therefore, I doubt with all unbelievable consequences that ict and ih are absolutely indispensable for physical reasons. Again, don't get me wrong. I don't claim that they can actually be replaced.

Faithfully yours,

Eckard Blumschein

Hi Matt,

I tend to agree with you that math is efficient because we have developed it for areas in which it is efficient, so it's kind of a pointless question if you interpret it literally. It's like asking why email is efficient at delivering messages.

However, I think you're missing the more relevant question, that is, are there aspects for which math cannot be used, or it is "efficient" for everything? I see you're not very convinced by the mathematical universe hypothesis. Arguably you are right that saying that there are more mathematical structures to be discovered is hardly a useful prediction, but the question is there a mathematical structure for ANY observation that we can make (natural science or any other), or not? Maybe you have a chance to look at my essay, I think you might find we have some things in common.

-- Sophia

Dear Matt Visser,

Great essay. Your comment "unnecessary and excessive obfuscation" leading to the example of "distressingly common misconception that "uncertainty relations" are intrinsically a quantum phenomenon -- utterly ignoring the fact that engineers have by now some 60 years of experience with utterly classical timefrequency uncertainty relations in signal processing, and that mathematicians have by now over 80 years experience with utterly classical time-frequency uncertainty relations in Fourier transform theory." is something I agree completely with.

The second example you mention ""tunnelling"/"barrier penetration". Despite yet more common misconceptions, tunnelling is a simply wave phenomenon; it is not (intrinsically) a quantum physics phenomenon. Under the cognomen "frustrated total internal reflection", the classical tunnelling phenomenon has been studied and investigated for well over 300 years, with the wave aspects (the "evanescent wave") coming to the foreground approximately 150 years ago .." adds more certainty to your argument.

I enjoyed the discussion on the standard model, where no one doubts it's accuracy, but perhaps time will give us a better understanding of some of the technical aspects and issues you highlight.

Finally, I agree with your comments on "usability". In my essay here, I start with the usability issue and argue that it can be greatly enhanced by providing visual models of objects that match the properties of the fundamental particles of the standard model. I would be very interested in your comments on any of the specific models provided.

Your essay was a very enjoyable and insightful read.

Thank you and regards,

Ed Unverricht

Dear Matt,

Great essay and very clear. I particularly liked your section on Quantum conundrums.

I liked the way you dealt with quantum complementarity and I also have an instinctive reaction against such ideas which do not present a unified and simple picture of natural phenomena.

In talking about the measurement problem or the problem of the collapse of the wavefunction you may be interested to read my essay "Solving the mystery". I take the position that the apparent mystery is because of our lack of understanding.

If we adopt a different interpretation of reality in which we are dealing with real physical waves, then the notional collapse of the wavefunction is in fact an interaction of a real physical wave with an atom of the detector or measuring device. The measurement problem then is resolved.

Best regards

Richard

Dear Matt,

Please find my attempt to better explain my point of view here .

Thank you for your estimated effort to respond.

Regards,

Eckard

Dear Matt,

Thank you for your essay.

I liked your point that the back-and-forth connections between mathematics and physics will continue to twist and strain not only due to technological limitations, but also due to the personalities involved (i.e. mathematics and physics are both human endeavours).

I also liked your point that theorists pay heed to experimentalists who only adjust one aspect of an experiment at a time - similarly, theorists should not overlay speculation on speculation.

Adding to your point that mathematics encodes the patterns and regularities in the data stream, I would argue that the crux of the tension between mathematics and physics is that the data stream does not include the arrow of time - and therefore mathematics is not able to model this empirical feature of nature. That is, the act of measurement and quantification (combined with the use of the continuum) eliminates from the data stream the arrow of time before mathematics can do its magic. This, in my view, is why we end up with time-symmetric theories and,for example,the measurement problem you discuss.

Thank you for writing the essay.

Kind regards

Spencer Scoular

11 days later

Hi Matt--

Your essay was a joy to read: passionately yet cogently argued and right to the point. To all of your points, I can only respond, "YES!" In particular, I subscribe to your thesis that what we do in physics is identity patterns and regularities in Nature, which we then codify using mathematics. There is no mystery here. Mathematics is so effective because we have spent the last 350 years industriously making it so.

On a minor note, I also enjoyed your use of quotations. You've got to be the only guy in the history of FQXi who has managed to work in a cite to Ken Wilber!

On a completely different note, I observe that your outstanding book, Lorentzian Wormholes, is 20 years old. To the best of my knowledge, you never put out a second edition. Don't you think that it is about time?

Best regards,

Bill.

6 days later

Dear Matt,

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

7 days later

Dear Matt,

This is a well argued and well thought out exposition. I enjoyed reading it as much as I enjoy reading your relativity papers; you always bring up interesting topics and back them up with solid research. While I can think of counterexamples to the idea that much of the mathematics we develop serves a well defined purpose, I do agree with and enjoy your no-nonsense approach to the central theme of the contest. I also found particularly satisfactory your witty critique on how speculation gets disconnected from reality. Your mention of some of the interpretations and non-interpretations of QM made me wonder (again) which is your approach to the problem. I hope one day you'll write a paper about it.

Wish you good luck in the contest! Should you have the time and curiosity to read my essay, your comments are more than welcome.

Warm regards,

Alma

8 days later

Dear Matt

30 year ago I was persuading my classmate, that a professor was wrong, I claimed, as you, that uncertainty principle is not only a quantum phenomenon. At your interpretation it is evident still more clearly something: that the purpose of hbar is also to make physics dimensionless. More is written in my essay.

I agree also with you, that Tegmark's multiverse is too speculative. It is based on a supposition that simplicity and beauty of formulae is not enough to suppose that other simple formulae exists. (As Burov's in FQXi 2015 write.) But these beatiful and simple physical formule should/must have one still unknown background explanation. I think, that dimensionless nature of physics, already reduced number of axioms, quantum gravity theory will still reduce number of physical postulates and theory of consciousness still more.

You like positivistic aspect ''shut up and calculate''. I like such view, but not 100 %. I think that interpretation of QM should be improved and clarified and that QM is not complete: it does not explain quantum gravity and consciousness. You also correctly mentioned unexplained measurement problem.

I like your realistic and simple approach to physics, except that you do not mentioned consciousness (except measurement problem). But I hope that you will read my essay and independent Poirer's essay about quantum consciousness, and that you will give opinion.

My essay.

Best regards

Janko Kokosar

Matt,

I consider your essay beautifully balanced and written, covering many important truths. Now speed-reading I may have missed much and have noted it down to return to. In particular we agree Dyson's quote is important, I think as important as Wigners.

I agree it's not new maths that's needed to resolve the issue of QM but to derive the complex physical mechanism to match the maths, and hopefully identify a viable 'quasi' classical' mechanism in my essay (and referenced paper). I hope you'll read it and advise or comment even after the scoring deadline.

I certainly consider your essay should be in the final group and found it well argued with no flaws to worthy of a high score. Best of luck.

Peter

3 months later

"QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains. This requires nonlinear mathematics that is not present in the standard formalism."

I concur. QM is due to a rotating wave or field. The wave is rotating and corkscrewing through space tracing out a long helical path. Effects of the inclined planar wave front traversing the longer path of rotation exhibits relativistic effects such as length contraction, time dilation, inductance, and mass increase.

The basic vector math I resolved was C = Vv Vr Vt

Vv = translational motion (forward motion of the partical

Vr = rotational motion of the wave

Vt = radial motion of the wave spiralling out in a gravitational field

Limit Vt goes to zero and you have just the Lorentz invariance.

I'm surprised that Dirac did not even consider this, plus Einstein as well.

Maybe others consider it a pilot wave wrapping around a particle, but it's simply a rotating wave - see attached.

Bill Christie

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