Dear Terry,
Congratulations for the essay contestant pledge that you introduced (goo.gl/KCCujt) --- I think we should all follow it, and I will certainly attempt to from now on. Congratulations also on the truly constructive comments that you have left so far on the threads of many of the participants in this contest. I thought I would use a similar format and comment on your essay!
What I liked:
- Your essay is well written and interesting to read: at the end, I wanted more of it!
- You introduce vivid/memorable expressions to describe your main points: the principle of binary conciseness, the trampoline effect, foundation messages. I specially like the trampoline effect, defined as the bouncing-off of the near-minimum region of Kolmogorov simplicity by adding new ideas that seem relevant, yet in the end just add more complexity without doing much to solve the original simplification goal. I think you will agree that, when you read some of the essays submitted to your typical FQXi contest, you can observe spectacular examples of the trampoline effect. It seems easy to diagnose a trampoline effect in accepted theories that we find lacking, or in alternative theories that we find even more flawed. True wisdom, of course, would be to be able to become aware of the trampoline effect in our own thinking... which is so hard to do!
- You directly address the specific essay contest question, "What is fundamental?" (at least, in the first half of your essay)
- Nicely worded and accessible introduction to the famous equation E = mc²
- Pedagogical presentation of Kolmogorov complexity for the reader not already familiar with the concept
- Interesting parallel between the increased difficulty in reducing Kolmogorov complexity in an already well-compressed description and the increased difficulty in improving an already well-developed theory
- It was interesting to end with challenges to the physics community, although it fits only tangentially with the essay topic (it would make a great essay topic for a future contest!)
- Your challenges #2 and #3 are profound questions: WHY the spin-statistics theorem? WHY the three generations in the Standard Model? There is certainly much to be learned if we can make progress with these fundamental "Why?" questions --- although the particular physics of our particular universe might just be arbitrary at the most fundamental level, forever frustrating our hopes of ultimate unification and simplicity.
What I liked less / constructive criticism:
- You say that the content of foundation messages (data sets expressing structures and behaviors of the universe that exist independently of human knowledge and actions) must reflect only content from the as-is-universe, despite the extensive work that humans must perform to obtain them. But this presupposes that we can have a reasonably access to the "as-is" universe, which many historians and philosophers of science would deny, saying that observations are always more-or-less theory-dependent (no such thing as a pure observation, independent of the previous knowledge of the observer): see for instance the articles "Theory-ladenness" and "Duhem-Quine Thesis" in Wikipedia.
- You say that in physics, the sole criterion for whether a theory is correct is whether it accurately reproduces the data in foundation messages. It is true that reproducing data is an important criterion, but is it the sole one? For example, a modern, evolved, computer assisted epicycles-based Ptolemaic model (with lots and lots of epicycles) could probably reproduce incredibly well the planetary positions data, but we could use other criteria (simplicity, meshing with theories explaining other phenomena) to strongly criticize it and ultimately reject it.
- I am not sure that the map analogy and the associated figure helps clarify the concept of a Kolmogorov minimum. Maybe it's because I was distracted by the labels: Why pi-r-squared in one of the ovals? Why Euler's identity? Why the zeros and ones along the path? Why is the equation E = mc2 written along a path that goes from Newton to Einstein, since it is purely an Einsteinian equation?
- Your short section on the "Spekkens Principle" is very compact and will probably remain obscure to many readers (it was for me). It might have been beneficial to expand it (I understand there was a length limit to the essay...) or to drop it altogether.
- Concerning your challenge no. 1... Like many mathematicians and physicists, I am in awe with Euler's identity, but I am not sure that there is explicit undiscovered physics insight hiding within it. Once you understand that the exponential function is its own derivative, that the exponent i in e to the i*t comes in front when you derive with respect to time, that multiplication by i rotates a vector by 90° in the complex plane and that the velocity vector in uniform circular motion is perpendicular to the position vector, it becomes "evident" that you can model circular uniform motion (hence, the trigonometric circle) with an exponential function with an imaginary argument: Euler's identity then follows from the fact that pi radians corresponds to half a turn, which is the same as multiplying by -1! If there is anything truly remarkable in all this basic math, it is perhaps that the ratio pi (or, more often, 2 times pi) appears so often in the fundamental equations of physics, even in phenomena that do not seem related in any way to circles or rotations.
And finally, a question:
In your expression "principle of binary conciseness", what does the "binary" stand for exactly? The fact that it deals with TWO (or more...) theories that address the same data, or the fact that Kolomogorov complexity is often applied to strings of BINARY digits?
Congratulations once again, and welcome to the FQXi community! I hope you have the time to take a look at my essay and leave comments --- especially constructive criticism, which is unfortunately so hard to get in these contests, because of the fear of rating reprisal.
Marc