Vladimir, I will look at your essay soon in more detail and make some comments. Here is my preliminary observation: like the last time, I see you had some translation issues regarding which English word or phrase is best to state certain concepts. If I knew more Russian I could help, but alas I do not.
PS: I apologize in general for my low activity in making comments etc. in this contest so far. More time will open up soon.
Hi Neil--
Your essay is excellent. I agree with your bottom-line: that math, being a closed set of rules, is best at handling self-consistency, but is unable to help us on matters "out there". For that, we need physics. Your analysis involving Eq. (2) was great--but why did you call the result "obscure"? Finally, I admit that I am a fan David K. Lewis and "Modal Realism". So, I was on your side from the start.
Best regards,
Bill.
William,
Thank you very much. The paradox of math indeed is that it can tell us about anything else only through itself. If our world happens to parallel (is isomorphic to) some mathematical system, that same math cannot explain why it is the model for a world - unless the world literally is that mathematical system. Then it is a case of identity, not a mysterious echo. I don't believe the world is just math or that all possible worlds exist equivalently (as per David Lewis), but at least I appreciate that such viewpoints should be respected. Too many thinkers dismiss them as obviously wrong and absurd, able to be dismissed as "obviously wrong." Yet they don't even realizing the irony that believing in the specialness of concrete existence is akin to the "mysterian" idea of accepting conscious intuition for granted, and that the mind is beyond understanding in terms of matter. Ordinary physicalism is, ironically, a form of dualism itself - as recognized by critics like John Searle (and Lewis, in his way.)
Now, that doesn't mean we have to accept there is no physical "extra," just that if there is, it is transcendent. (I think the world and our minds are "extra" together, and form their own dualism vis a vis math - a twist on the usual divisions.) The ultimate answers to our universe being the way it is, won't fall out of equations a priori. So, we have to do experiments. Although I did not propose an experimental test this time, I did analyze a specific physical question instead of just ranging over basic issues in the abstract. (Nothing wrong with that, but we need facts and insights to fit into the pattern formed by our perspectives and methodologies.)
I said the result of Eq. (2) was obscure, because I see discussions of what physics might be like in 2-D flatlands (what atomic orbitals would be like, what 2-D life might be like as in the clever model-world fantasy The Planiverse" by A K Dewdney, etc.) These writers don't tell us that such a world would not "work" because of the infinite integral of potential energy between charges etc. I probably should have said, the implications of the integral are obscure (or shirked?) However, the shift of force exerted across a gravitational potential, really is obscure as best I can tell. You just don't see it discussed.
I will look at your essay and make a comment or more, when time opens up as it will.
Well, I got unwittingly logged out, and that happens to lots of us. The reply to William Parsons was from me.
Dear Neil,
Thanks for the arguments advanced in your essay.Where I do not seem to agree with you is your proposition that "mathematics cannot tell us about anything more than itself".
What!Has mathematics ceased to be the language of nature?Are you making a nulity of the Pythagorean thesis that "numbers rule the world;and all is number"?Are you also making a nulity of the vauntings expressed by Galileo Galilei that "The book of nature is written in the language of mathematics"?Or are you in effect contradicting yourself with an allusion that NATURE IS EXCLUSIVELY MATHEMATICAL?
Grateful,please oblige.
Lloyd Tamarapreye Okoko.
Dear Lloyd,
Thanks for your comment. My statement about math is not as opposed as it seems, to the usual sense there is a parallel or isomorphism between math and the world. Math does only directly tell us about itself. Yet of course if a math structure (per Tegmark) corresponds to an ostensible "real world", the math models that world and tells us what will happen etc. What I mean is, two things. First, math can't tell us why there is (if there is) a concrete "real world" instead of MUH (there IS nothing but math structures), and second: why it would be the way it is. It cannot do the former because it has no resources to represent or explain special existential status beyond itself. It cannot do the second thing, because there are all kinds of math structures, and no way to privilege them in an existentially special way (that follows from the first. Hence, as Tegmark notes, we can't e.g. say there is a reason why octahedrons should be also correspond to "real things", but icosahedrons would not (an analogy to comparing model worlds.)
Furthermore, I don't think a math model can even fully model a world anyway, in the sense of being a complete parallel. In other writings, I bring up issues like quantum randomness (not actually resolved by decoherence/MWI or Bohmian mechanics) and conscious experience. However, math is useful as a very close match, but like "symmetry" in our universe (our universe is not quite fully symmetrical in its laws), it is a near-miss. That may be frustrating or annoying to those who think it should be a complete fit, but what I think the world of experience has already showed us: such is life.
I'll look at your essay in turn, now that I have more time opening up.
Dear Neil,
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
OK Joe, I will go to your essay after awhile and give a comment.
Hello Neal,
Quite a number of good ideas to think about and take home from your essay.
I got mixed up a bit on the inertia of charges. Are you suggesting the inertia of an electron for example is other than its mass?
Then talking of mathematical models and "stuff" that actually "exists", in which category would you put Space. Is it a mathematical model or stuff that actually exists?
In my essay., I look at the consequences where "stuff" are not eternally existing but can be created and can perish. You may want to read and comment. You may also want to volunteer your opinion on 'how to cut a line', either from a mathematical model or real world perspective.
Regards,
Akinbo
Neil,
"Mathematics cannot tell us about anything more than itself."
Tegmark would say that conscious experience takes the form of mathematical "self-aware substructures" so itself is your perception.
I guess I am just an old-fashioned guy who likes to think it's all real and not a mathematical structure.I agree, "mere 'math brains' could not have real feelings: love, nausea, itches and pains, delight, experiences of pretty color sensations, and above all: the basic "sense" of being alive and real."
My "Connections" operate in a real world which connects math, mind, and physics into spectacular accomplishments in quantum biology, DNA mapping, and LHC discoveries.
Not having a stellar math background, I certainly could be wrong, having a math-stunted perspective.
Jim
James,
Yes we agree the world is more than math, although Tegmark's MUH shouldn't be waved off a priori because of anything immediately obvious about either logic, assumptions about ontology, or the way things work in the world. It is only by appreciating subtleties of randomness, mind, and time that one can really face up to "all this" being something beyond what any abstraction can fully describe (which, IMHO would be equivalent to it just being that abstraction.) BTW MUH neo-determinism just can't extract proper Born statistics out of its structure. I'll take a look at your essay in turn.
Greetings to the Community
I've gotten fed up with the roller-coaster ride of my point ratings, as have many others. At this point the percent change may not be much, but of course it's easy to calculate what the last rating was. Please: if you think this or any essay deserves a rating of say, three or less, you really should say why in a comment. Sure, you are justified to worry about consequences (not necessarily from the person rated!), so feel free to post as Anonymous - what matters is getting an explanation out. I'll do the same for anyone else. I don't like getting dinged with no idea what turned you off.
Even better, how about discussing things first before even giving a bad rating? And note for overall perspective: for the highest-rated essay on a 10-point scale to be in the six range, is rather sad, as is two distinguished physicists rating what would be an "F" (even if barely) on a standard public school grading system!
Thanks, I think I can say that for everyone.
Correction, I meant MWI neo-determinism (because of its branch structure and the isomorphism of compared systems differing only in the various relative amplitudes.) The many-worlds multiverse just cannot fairly generate observed statistics according to the Born rule, despite elaborate gymnastics attempting to square things, so to speak.
It is interesting to prove that the three dimensional space is the only possible for an electromagnetic, field; but this is true, if I understand well, only for a space with interacting particles, so that a single particle has not a constraint on the space dimension (ever if I understand well), so that the interaction create the space dimension.
I think that the electromagnetism and gravitation have equal fields (I think that there are duality between charges-Coulomb constant and masses-Gravitational constant), so that it can be that the constraint on a multi-particle mass is true for each field.
I must read with more attention, but it is important for me.
Cheers
Domenico
Domenico,
The inconsistency isn't about being able to have an electromagnetic field at all, it's about subtle relationships pertaining to electromagnetic inertia (which are problematic even in three dimensions per the "4/3 problem.") The relationships just won't give the right answer for other dimensionalities. Gravity: it is not entirely analogous to EM so I can't assume the problem would be the same. Furthermore, self-energy works differently because it gravitates in turn, so the addition is not linear, and there are localization issues (good discussion in Penrose's "The Road to Reality." There have been extrapolations of gravitation to other dimensions. I appreciate your interest, will look at your essay.
I think that there is a complete analogy between gravitational field and electromagnetic field, because of the gravitoelectromagnetism formulation, that it is deeper for me because of:
[math]
R_{\mu \nu}-\frac{1}{2} g_{\mu \nu} R = -\frac{8 \pi k}{c^4} T_{\mu \nu}
[/math]
so that, when I read your essay some weeks ago, I saw a possible gravity inertia application; that I had forgotten to consider, because of I had not taken notes because I read dozens of essay at a time (each essay is worth reading)..
I prefer not to comment on the essays, because they affect the votes, but in any case I would have informed you after the vote; I break the rule just because I consider polite to reply to my posts.
I am thinking that if it is true that the dimension of the space is constrained by an interaction, then there is a problem with elementary particles like quark, or electron, that don't give the right dimension (following your demonstration); so that the solution is that the elementary particles must have a real probability distribution, a quantum diffusion in the space, that constrains the space dimension: an interaction between the parts of the single elementary particle
Greetings Tyranno,
I certainly agree with the 3 dimensions of reality and arrive there from a different direction. A totally worthwhile essay, thank you.
Sherman Jenkins
Dear Neil,
I appreciate the depth of your essay and its level; to my mind, it is among the top ones here. Although I disagree with some of your points, I give your essay very high rating. Your conclusions that
"math cannot either describe what "concreteness" is, nor which if any model worlds should be manifested as "actual worlds." It cannot explain why any such transcendently "more real" world should be mathematically elegant or "simple," instead of messy and not effectively accessible through math"
are extremely important and correct. However, physics is more than math, and its success with elegant mathematics tells something very important about the universe. I am inviting you to read our essay where we refute Tegmark's MUH on the ground of fundamental physics.
