Lemma 1: Particles are purely mathematical.
Proposition A: Everything can be broken down into a single or a class of elementary particles.
In this situation, the tiniest particle cannot have any physical property, else it could be broken down further. Its properties can only be mathematically described in terms of its resonant frequency and spin. There are no physical properties at this level; everything is just a modeled interaction between said particles with given formulaic patterns.
...........................
Firstly,
What do you mean by 'purely' mathematical, Im going to guess, and you tell me if I'm right. This sounds like the philosophical bullshit pedalled by the MIT scientist Max Tegmark who likes to claim the universe is a mathematical structure.
I was going to be extremely critical here about how sloppy the philosophy was but i was so curious at your odd usage of talking about particles as *purely* mathematical objects, i thought i should see if there was any cult out there using that phrase.
At the end of my rant, i'll include some interesting quotes about the Grade Z Philosophy by some Grade B Physicists. It's one thing to be open minded but when it's bordering on embarassing philosophicals and a near absolutism, someone has to seriously call in the bullshit and reign in some egos.
.....................................
A particle is a physical object, it is rooted in something empirical and existing. Mathematics is nothing more than a language for showing relationships of numbers or measurements.
And yes there are mathematical structures, which are abstract, and may or may not have a basis in reality.
Yet i think there is a problem here of Absolutism here, and it's used here to pure the purely mathematical relationships of physical particles and then magically say, it's all mathematical. And suddenly you got asswipes magically waving their magical wand saying, the magical appeal of Order is so strong with mathematical structures we can be reductionist and say it's all rooted in the mathematical.
A particle is a representation of a physical object. Yes we can have theoretical particles, but is it not meaningless if they did not exist? The physical reality is the significant part here.
Basically someone is taking something extremely trivial, that physical matter shows a lot of mathematical relationships, and they feel that the laws of physics are mathematical in nature and this is the actual reality. I would say this is basically a sloppy physicist trying to nothing more than an awkward Mathematical Platonist.
He thinks the 'forms' are reality, and that the physical is oh, never mind....
Pretty much he's saying, math is pretty, and he's very certain, almost absolute in saying, all reality can be reduced to mathematics.
So he's an Absolutist, and a Reductionist, and well maybe a Platonist.
[the math is more pretty than the reality, and maybe the math is the reality, yawn]
........
And well, im sure he'll sweep the Decline of Mechanism, and of the Absolute with Quantum Theory and the Uncertainity Principle.
Particles are nice physical objects, yet on the quantum level we might need to use different models and constructs. With Heisenberg's uncertainity relations, you are going beyond the classical concepts of describing atomic processes. This is what i mean by a decline of the absolute, sometimes you have problems with say, measurement, or cause and effect. And even in statistical mechanics [the more detailed stuff in heat and thermodynamics] you use unintuitive mental models.
Wiki has some interesting comments under Determinism:
- A particle's path simply cannot be exactly specified in its full quantum description.
- "Path" is a classical, practical attribute in our every day life, but one which quantum particles do not meaningfully possess.
- The probabilities discovered in quantum mechanics do nevertheless arise from measurement (of the perceived path of the particle). As Stephen Hawking explains, the result is not traditional determinism, but rather determined probabilities.
- In some cases, a quantum particle may indeed trace an exact path, and the probability of finding the particles in that path is one (certain to be true).
- In fact, as far as prediction goes, the quantum development is at least as predictable as the classical motion, but the key is that it describes wave functions that cannot be easily expressed in ordinary language.
- As far as the thesis of determinism is concerned, these probabilities, at least, are quite determined.
- Thus, quantum physics casts reasonable doubt on the traditional determinism of classical, Newtonian physics in so far as reality does not seem to be absolutely determined.
- This was the subject of the famous Bohr-Einstein debates between Einstein and Niels Bohr and there is still no consensus.
.......................
Notice the phrase, reality does NOT seem to be *absolutely* determined.
.......................
- According to some, quantum mechanics is more strongly ordered than Classical Mechanics, because while Classical Mechanics is chaotic, quantum mechanics is not.
[one interesting conclusion when you argue about determinism, and how ordered matter or mathematics is.]
........................
Secondly, these statements have little meaning:
- Particles are purely mathematical.
- the tiniest particle cannot have any physical property, else it could be broken down further.
- There are no physical properties at this level; everything is just a modeled interaction between said particles with given formulaic patterns.
Purely mathematic or not, there is a physical reality to particles, and particles are measured, and this measurement is what gives us those mathematical relationships.
Maybe he likes to say, the math comes first, but i think it's best to say that physical reality shows mathematical relationships and laws of the physical universe.
He seems to be stuck on the tinkertoy model of reality, and has the perverse conclusion that observable physical properties are only shown for large objects and fundamental particles cannot be broken down, and would magically have no physical properties.
Sounds like perverse atomism, that we assume there are fundamental particles and if fundamental would be lacking some physical property. uh sure, great.
The next statement is the goofy one, there's patterns, but they are modelled interactions. We assume by modelled interactions, they can't be measured, and somehow he magically hops to the shopping cart of certain levels of the universe lacking physical properties.
Now i think i have two asswipes on my hate list
a. Max Tegmark of MIT - cosmologist
b. Lubos Motl of Harvard - string theory
Pie in the sky bullshit and third rate philosophy, but at least Max sounds like a nice guy, but for my money, Wheeler was not a flake [though he defended Tegmark's paper that people rejected three times], and Feynman was a skeptic of superstrings and scowled at pretty much all philosophy, he seemed to be pretty pragmatic.
I think we need better mathematicians and physicists, who can suggest the crazy but at least state their presuppositions more clearly so you know where the craziness starts [aka where the weird assumptions start]
......................
......................
......................
There's a somewhat crappy article on sciencemag.org that reminds me of this thread:
.................
Do We Live Inside a Mathematical Equation?
BOSTON - From the arc of a baseball to the orbits of the planets, mathematical patterns are everywhere. But according to physicist Max Tegmark of the Massachusetts Institute of Technology in Cambridge, it’s not enough to say that math governs our universe. Rather, he believes that reality itself is a mathematical structure. What the heck does that mean? We caught up with Tegmark after his presentation at yesterday's symposium "Is Beauty Truth?" at the annual meeting of AAAS (which publishes ScienceNOW).
Q: What makes a mathematical theory beautiful?
M.T.: For me, it’s usually when there’s an unexpected connection between two things I thought were unrelated. Imagine if you walked into an art museum and saw a very beautiful sculpture in one corner, and something else in the other corner, but there’s a big veil between them. And then suddenly someone lifts the veil and you see that the two things are just parts of a much grander structure. Seeing that whole makes you understand the pieces much better.
The beautiful mathematical regularities that have been uncovered have typically been unifications, where instead of having one mathematical description for this and a different one for that, we realize there’s a single mathematical structure that encompasses all of it. So for me, it would be a natural conclusion if everything could be unified, if there’s a single mathematical structure that is our reality, and all of the mathematical structures that we’ve discovered before are part of this more beautiful whole.
Q: Wait a minute. What do you mean, the universe is a mathematical structure?
M.T.: So right now, I’m eating an orange, which is made of cells. Why do they have the properties they do? Well, because they’re made of molecules. Why do the molecules have their properties? Because they’re made of atoms put together in a certain way. Why do the atoms have those properties? Because they’re made of quarks and electrons. What about the electron? What properties does it have? And the cool thing is, all the properties that electrons have are purely mathematical. It’s just a list of numbers. So in that sense, an electron is a purely mathematical object. In fact, there’s no evidence right now that there’s anything at all in our universe that is not mathematical.
.............................
The Physicist and Pop Science Author Woit at Columbia says on his site:
Our Mathematical Universe
Posted on January 17, 2014 by woit
Max Tegmark has a new book out, entitled Our Mathematical Universe, which is getting a lot of attention. I’ve written a review of the book for the Wall Street Journal, which is now available (although now behind a paywall, if not a subscriber, you can try here). There’s also an old blog posting here about the same ideas.
Tegmark’s career is a rather unusual story, mixing reputable science with an increasingly strong taste for grandiose nonsense. In this book he indulges his inner crank, describing in detail an uttery empty vision of the “ultimate nature of reality.” What’s perhaps most remarkable about the book is the respectful reception it seems to be getting, see reviews here, here, here and here.
........................
Tegmark’s innovation is to postulate a new, even more extravagant, “Level IV” multiverse. With the string landscape, you explain any observed physical law as a random solution of the equations of M-theory (whatever they might be…). Tegmark’s idea is to take the same non-explanation explanation, and apply it to explain the equations of M-theory. According to him, all mathematical structures exist, and the equations of M-theory or whatever else governs Level II are just some random mathematical structure, complicated enough to provide something for us to live in. Yes, this really is as spectacularly empty an idea as it seems. Tegmark likes to claim that it has the virtue of no free parameters.
........................
I think an accurate way of characterizing this is that Tegmark is assuming something that has no reason to be true, then invoking something nonsensical (a measure on the space of all mathematical structures). He ends the argument and the paragraph though with:
"In other words, while we currently lack direct observational support for the Level IV multiverse, it’s possible that we may get some in the future."
This is pretty much absurd, but in any case, note the standard linguistic trick here: what we’re missing is only “direct” observational support, implying that there’s plenty of “indirect” observational support for the Level IV multiverse.
The interesting question is why anyone would possibly take this seriously. Tegmark first came up with this in 1997, putting on the arXiv this preprint. In this interview, Tegmark explains how three journals rejected the paper, but with John Wheeler’s intervention he managed to get it published in a fourth (Annals of Physics).
........................
A very odd aspect of this whole story is that while Tegmark’s big claim is that Math=Physics, he seems to have little actual interest in mathematics and what it really is as an intellectual subject. There are no mathematicians among those thanked in the acknowledgements, and while “mathematical structures” are invoked in the book as the basis of everything, there’s little to no discussion of the mathematical structures that modern mathematicians find interesting (although the idea of “symmetries” gets a mention). A figure on page 320 gives a graph of mathematical structures which a commenter on mathoverflow calls “truly bizarre” (see here).
[What on earth are double fields and triple fields??? Also, why does the dodecahedron group belong to that chart? ...strange choices. - Andre Henriques]
[However much I respect physics and physicists, I personally think the article in question is a truly bizarre choice of a reference when it comes to dealing with algebraic structures. - Vladimir Dotsenko]
...........................
Multiverse mania goes way back, with Barrow and Tipler writing The Anthropic Cosmological Principle nearly 30 years ago. The string theory landscape has led to an explosion of promotional multiverse books over the past decade, for instance
Parallel Worlds, Kaku 2004
The cosmic landscape, Susskind, 2005
Many worlds in one, Vilenkin, 2006
The Goldilocks enigma, Davies, 2006
In search of the Multiverse, Gribbin, 2009
From eternity to here, Carroll, 2010
The grand design, Hawking, 2010
The hidden reality, Greene, 2011
Edge of the universe, Halpern, 2012
Watching these come out, I’ve always wondered: where do they go from here? Tegmark is one sort of answer to that.
..........................
I’m still though left without an answer to the question of why the scientific community tolerates if not encourages all this. Why does Nature review this kind of thing favorably? Why does this book come with a blurb from Edward Witten? I’m mystified. One ray of hope is philosopher Massimo Pigliucci, whose blog entry about this is Mathematical Universe? I Ain’t Convinced.
[What I can tell you now is that I find Max a fascinating person, a wonderful conference organizer, someone who’s always been extremely nice to me personally, and an absolute master at finding common ground with his intellectual opponents - I’m trying to learn from him, and hope someday to become 10^-122 as good. I can also say that, like various other commentators (e.g., Peter Woit), I personally find the “Mathematical Universe Hypothesis” to be devoid of content. - scott aaronson]
[Scott, Glad to hear that you also find the “Mathematical Universe Hypothesis” devoid of content. This is an example highly relevant to the “falsifiability” question. Are those willing to argue against falsifiability to prop up the string theory landscape also willing to include the MUH and the Level IV multiverse? Or is going from Level II to Level IV too far and they’d be willing to agree this is not science? Will we hear from them publicly on this? More generally, if the physics community agrees that Tegmark’s proposal is empty pseudo-science, will this news get to the public, or does the fact that he’s an eminently nice and reasonable guy mean no one is willing to say anything? .... it certainly seems to me that the theoretical physics community is not presently suffering from an unwillingness to consider highly speculative ideas that are at and sometimes past conventional boundariess of what is testable science. - woit]
[woit - www.math.columbia.edu/~woit/wordpress/?p=6551]
