Dear Paul,
Congratulations! Your bold an thought-provoking essay is one of the best I've read so far in this contest. Contrary to many entries, that try to play it safe (or rehash the same alt-physics theories contest after contest, irrespective of the contest theme), you actually hold strong and original positions concerning the question of fundamentality. I do not necessarily agree with everything that you are arguing for, but I find the questions that you raise and the examples that you give worth thinking about. Moreover, you conclude that general mathematics/logic appears to be more fundamental than the particular "physics" that our world "runs on", which has interesting similarities to my own views on the subject, views I have hinted at in my essay in the current contest...
"Fundamentality here, there, everywhere" (2018) : fqxi.org/community/forum/topic/3132
...but elaborated more fully in the essays I wrote in the previous two FQXi contests:
"The Co-Emergence of Lawfulness" (2017) : fqxi.org/community/forum/topic/2912
"Living in a Mathematical Universe" (2015) : fqxi.org/community/forum/topic/2497
For my comments, I will be using the format that Terry Bollinger uses --- he also has a very wise "essay contestant pledge" that I fully agree with and that can be found here: goo.gl/KCCujt
What I liked the most about your essay:
- Your definition of 'fundamental', to mean not only underlying our observations and theories of the world as we know it, but also EXPLAINING them.
- Your "running gag" of the imaginary band "Hawking and the Reductionists", that were supposed to be the opening act for "The Theory of Everything", a band that never showed up!
- Your definition of 'strong emergence' as applying to systems that are "not completely defined at the microscopic level, but in which additional causal behavior kicks in on larger and more complex scales".
- Your use of Conway's Game of Life as a toy-model of a world where the "Theory of Everything" is completely known and not in the slightest way ambiguous or uncertain, yet that clearly possesses interesting higher-level behavior, which demonstrates that this kind of behavior can "easily" occur via "mere" weak emergence.
- Your statement that, since the Game of Live is Turing-complete, its phase space contains all possible software, including World of Warcraft and the software that guided Apollo 11 to the moon!
- Your statement of the delightful circularity of the Game of Life being able to implement a Turning machine, and a Turing machine being able to implement the Game of Life.
- Your mention of the crucial importance of the idea of "multiple realizability", and your description of it: "the complex behavior on the phenomenal level can be implemented in multiple ways by different microscopic realities (noumenal level)."
- Your deep insight that it is no more necessary to scrutinize the rules of the Game of Life to understand Turing machines than it is necessary to have five coconuts to establish that 2 3 = 5, or, more provocatively, than it is necessary to know about the details of quantum mechanics to understand and use the Navier-Stokes laws of fluid dynamics.
- Your clever use of Laplace's Demon to personify an extremely powerful computer that can analyze the evolution of anything, as long as the problem is specified by using ONLY the concepts of the base-level (reductionist) description of reality.
- Your explanation, using the Taylor expansion, of the "naturalness" of Hooke's law for elastic objects, irrespective of the actual details of microscopic physics.
- Your clear, 4 bullets point phrasing, without referring to biology, of what it takes for a system to be able to undergo natural selection.
- Your bold conjecture that general aspects of mathematics (formal logic, geometry, algebra) could be said to be fundamental (if anything deserves to be called fundamental).
What I liked less / constructive criticism:
- In your analysis of Putnam's peg and board set-up, you rightly say that the notion of rigid bodies is prerequisite to understanding the situation, but you go on to say that it is impossible to make the step from Schrodinger's equations to rigid bodies --- not merely so difficult that we cannot hope to do it in the foreseeable future, but outright impossible... I am not sure I would go that far. Arthur C. Clarke said that any sufficiently advanced technology is indistinguishable from magic... could it be that sufficiently advanced scientists would have powers of deduction that so dwarf ours that all the higher-level laws and behaviors of physics would seem to trivially follow from Schrodinger's equation (or an even deeper, more advanced formulation of the basic reductionist laws of our universe)?
- You use the word "exist" to mean "exist at the most fundamental level", so you can make provocative claims, for example, that rigid objects do not exist or that concept of force does not exist. You certainly are not the only one to use "exist" in that way --- which leads, for instance, to the often-encountered claim made by physicists who study foundational issues that "time does not exist". I prefer a less spectacular phrasing: "force is a concept that is not fundamental" or "force is a concept that does not exist at the fundamental level" instead of "force is a concept that does not exist". That said, I like your bold claim that force is the phlogiston of the 20th century... As someone who has a degree in history of science, I find this analogy very thought-provoking... I am not sure I would go that far, but I'll certainly have to think about this!
- I really like how you show that the linear form of Hooke's law makes a lot of sense if you analyze the elasticity of an object by using a Taylor expansion. But when you say that Hooke's law can be derived PURELY from mathematical considerations and would be valid whatever underlying microscopic laws we have, I am not sure I agree. It seems to me that to derive Hooke's law, you need a lot of implicit physical baggage, the notion of rigid bodies, or at least of shape (space), change (time)... If mathematics is the most fundamental level, it seems to me that it must span/generate a wide spectrum of "physical" worlds (Max Tegmark's level 4 multiverse), some of which are so radically different from ours that they could very well contain "rigid bodies" whose elastic behavior does not obey such a linear and simple rule as Hooke's law. I agree with you that mathematics/logic can teach us a lot about how the world behaves, but when you say that it can teach us how ANY possible world behaves, I have doubts...
- You conclusion that Hooke's law is not REDUCIBLE to the underlying microscopic laws is quite a bold claim, and few physicists would agree to go this far... But I guess it all hinges on what is meant precisely by "reducible"...
- You claim that "the Theory of Everything wouldn't make a shred of difference for applied physics and chemistry, let alone biology and the social sciences". Of course, you may be right. But the future could prove you incredibly wrong: imagine, for instance, that the ToE leads to a new source of energy that solves all of humanity's problems, or to efficient ways to travel between the stars, or to contact with parallel branches of the universal wavefunction, allowing for fascinating cultural exchanges between divergent worldlines of humanity's history. Of course, all these scenarios are very unlikely, but who knows? ;)
You conclude that "this very world seems at least partly understandable by thinking about it, not looking"... a very Platonist view... but I like it! Of course, like many of us in the FQXi community, we are fascinated by the more speculative fuzzy areas at the margins of currently well-established knowledge... and in many cases, before we can look, we have to think about it... if only to know what to look for. Your essay certainly made me think!
Welcome to the FQXi community --- I am glad you "came-out" as a philosopher with this essay, and I hope your ideas generate debate and get the recognition they deserve in this contest!
Best wishes,
Marc