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I Believe The Universe Is Purely Mathematical

Here's a crude proof that math existed before the universe began. I love proofs :D They're pretty smexy :P


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.

Proposition B: Everything is made up of infinitely tiny particles or particles that can be broken down an infinite number of times.

In this situation, there is no tiniest particle. Due to the nature of infinity, the supposed "tiniest" particle doesn't exist and the resulting structure has no physical property; again, only a purely mathematical one that defines the interactions between particle structures within itself and between others, its spin, and resonant frequency.

Because these are the only two possible outcomes, being Boolean in nature, and because both have been proven to be purely mathematical, I have now proven that the fundamental particles are purely mathematical.

Corollary: Using the proof of Lemma 1, I introduce a syllogism.

Because the fundamental particles are purely mathematical, and the universe is made up of and only of these fundamental particles, the universe is also purely mathematical in nature.


Lemma 2: Fundamental particles and forces came after math.

Fundamental particles and forces have their basis in math. Fundamental particles and forces couldn't have been created without the prior existence of math, because there wouldn't be any way to define their properties, as proposed in Lemma 1. Thus math had to exist prior to the existence of fundamental particles and forces for them to exist, else they couldn't possibly defined.

Conclusion:

Because everything is made up of fundamental particles and forces, which are in turn purely mathematical, everything is purely mathematical. Because mathematics define these forces and not the other way around, mathematics had to exist first. Because these particles and forces had to be created somehow during the Big Bang, math had to be there to create them initially to define the singularity.

THUS math existed before the creation of the universe :D
atenra11
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.

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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.

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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.

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Notice the phrase, reality does NOT seem to be *absolutely* determined.

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- 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.]

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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]

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There's a somewhat crappy article on sciencemag.org that reminds me of this thread:

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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.

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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.

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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.

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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).

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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]

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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.

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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]
atenra11
- Glad to see Woit's criticism of Tegmark stated.
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Well i wasn't aware of Tegmark's existence, but i was surprised in finding him since i wanted to search for the odd use of the adjective 'purely mathematical'. And only 224,000 hits for the phrase. We speak of 'purely mathematical disciplines' or maybe some 'purely mathematical work' or 'purely mathematical approach'. Maybe it's superstrings or more recent philosophers of science with the ugly english.
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Woit, i've heard of him, and plopped some of his pop science books onto my list of books to pick up one day like, Smolin, Davies, Ferris, Susskind, Bernstein, and the rest... and well i think it's interesting that lots of people are using the phrase 'underwhelmed'.
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- Is he skilled at math?
Well, his diagrams people think are pretty crazy, and others are saying he really doesn't seem to be all that deeply into it. It's nice to talk about being purely mathematical and then having graphs that look like something out of that crazy MIT/Japanese EDM [The Encyclopediac Dictionary of Mathematics, from 1977] which has it's fair share of crazy illustrations and boxes and Dynkin Diagrams... But it sounds like Tegmark just flirts with the Modern Algebra crowd and wants to gee whiz people like he's another Kaku. [At least Kaku's hyperspace seemed a decent book, but half of his books only seem to get a thumbs up, technical and pop science]. Feynman didn't like going off the Pure Mathematics deep end, either as he was flirting from Mathematics, to Electrical Engineering and then thought Physics was right in the middle, not too pure, not too applied. Yet he seemed to plop his nose into some topology texts in the 50s or 60s or 70s by the sounds of his autobiography and other stuff. [Remember the phrase in Surely you're Joking about, okay now imagine a ball with fuzzy green hair on it, like spikes on a porcupine, which sounds like he was checking out stuff from the library and having fun discussing it with the staff]
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- But not to the point he dazzles me with brilliance or baffles me with his bullshit. The jump made from numbers describing particles to particles being numbers...Math equations give rise to quantum numbers but the particles are not identically those numbers. Because something can be stated mathematically does not ensure it is real.
I thought the whole point of textbook writers and pop science writers were to actually explain to students or readers that these things in physics are 'assumed to be real' and *these parts in physics* are the speculative gunk or wacky possibilities.
And well it makes you respect the guys who were out there like Bohm , or Theodore Kaluza [which i wish his mathematical physics book was in English, or a good biography of him].
Actually the First Time i came across Kaluza's name was in the Philosopher/Gurdjieff Student/Mathematician/Orientalist, J.G. Bennett with his 1956 book, The Dramatic Universe. Since in the late 40s he played around with a paper and obsession of Five-Dimensional Physics, and actually pleaded with Max Born to sigh and read it one day for his opinion. [He dismissed it as overly theoretical, and the PRS paper from 1949 is an in Appendix]. Bennett was casual friends with Bohm, and i think both knew Krishnamurti, and Bennett was always inviting Hindu and Sufi mystics to his place at Sherborne House. But there was some really neat bunch of essay in that paper about what qualities are there beyond Time and Space, and Kaluza gets a whole mess of talk. Bennett was a strange cat, Head of Military Intelligence in Turkey, and reading Croce the philosopher in Italian, and World War I probably messed up his chance for a more formal education [and a full set of teeth].
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I think i heard of Kaluza again with Davies' Superstrings book and maybe a few other pop science books, but my second brush was in the 1957 Dover book by Parke, Guide to the Literature of Mathematics and Physics, with Joos and Kaluza doing a 1942 book, next to Courant-Hilbert's Methods of Mathematical Physics [Interscience 1953 and 1962] and Morse and Feshbach's Methods of Theoretical Physics, McGraw-Hill 1953] and Wylie's Advanced Engineering Mathematics [McGraw-Hill 1951]. So that was my introduction to the crazy end of physics, and I still can't read Volume I of Courant-Hilbert yet, but one day I'll need to pick up Volume II in a matching grey hardcover before getting the cooler 1990s hardcover with a much prettier Wiley-Interscience cover...
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If i was go get into this crap, one day, i'd probably only get Zee's Superstrings in a Nutshell textbook, and instead focus on something that feels way more real, like the ADM Formalism, which might be known if you know of the Wheeler-Thorne-Misner's 1973 WH Freeman textbook, Gravitation with the best bad craziness illustrations I've seen this side of Altair III.
[http://en.wikipedia.org/wiki/ADM_formalism]
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[The ADM formalism, named for its authors Richard Arnowitt, Stanley Deser and Charles W. Misner, is a Hamiltonian formulation of general relativity that plays an important role in quantum gravity and numerical relativity. It was first published in 1959.]
[Using the ADM formulation, it is possible to attempt to construct a quantum theory of gravity, in the same way that one constructs the Schrödinger equation corresponding to a given Hamiltonian in quantum mechanics.]
[There are relatively few exact solutions to the Einstein field equations. In order to find other solutions, there is an active field of study known as numerical relativity in which supercomputers are used to find approximate solutions to the equations. In order to construct such solutions numerically, most researchers start with a formulation of the Einstein equations closely related to the ADM formulation. The most common approaches start with an initial value problem based on the ADM formalism.]
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You could say that this is a branch of General Relativity.
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[Equations]
[Linearized gravity, Einstein field equations, Friedmann, Geodesics, Mathisson-Papapetrou-Dixon, Hamilton-Jacobi-Einstein]
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[Formalisms]
[ADM, BSSN, Post-Newtonian]
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[Advanced theory]
[Kaluza-Klein theory, Quantum gravity]
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Last Stuff
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[Theodor Franz Eduard Kaluza (9 November 1885, Wilhelmsthal [today Opole, Poland] - 19 January 1954, Gottingen) was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in string theory.]
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[Kaluza was born to a Roman Catholic family from the town of Ratibor [present-day Raciborz, Poland] in the German Empire's Prussian Province of Silesia. Kaluza himself was born in Wilhelmsthal (a village that was incorporated into Oppeln (present-day Opole) in 1899). He spent his youth in Konigsberg, where his father, Max Kaluza, was a professor of the English language.]
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[He entered the University of Konigsberg to study mathematics and gained his doctorate with a thesis on Tschirnhaus transformations. Kaluza was primarily a mathematician but began studying relativity.]
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[In April 1919 Kaluza noticed that when he solved Albert Einstein's equations for general relativity using five dimensions, then Maxwellian equations for electromagnetism emerged spontaneously.]
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[Kaluza wrote to Einstein who, in turn, encouraged him to publish. Kaluza's theory was published in 1921 in a paper, "Zum Unitatsproblem der Physik" with Einstein's support in Sitzungsberichte Preußische Akademie der Wissenschaften 966-972 (1921).]
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[Kaluza's insight is remembered as the Kaluza-Klein theory (also named after physicist Oskar Klein). However, the work was neglected for many years as attention was directed towards quantum mechanics. His idea that fundamental forces can be explained by additional dimensions did not re-emerge until string theory was developed. It is however also notable that many of the aspects of this body of work were already published in 1914 by Gunnar Nordstrom, but his work also went unnoticed and was not recognized when the ideas re-emerged.]
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[For the rest of his career Kaluza continued to produce ideas about relativity and about models of the atomic nucleus. Despite Einstein's support, Kaluza remained at a low rank (Privatdozent) at Konigsberg until 1929 when he was appointed as professor at the University of Kiel.]
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[In 1935 he became a full professor at the University of Gottingen where he remained until his death in 1954. Perhaps his finest mathematical work is the textbook Hohere Mathematik fur die Praktiker which was written jointly with Georg Joos.]
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[Kaluza was extraordinarily versatile. He spoke or wrote 17 languages (his favorite allegedly Arabic). He also had an unusually modest personality.]
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[He refused the National Socialist ideology and his appointment to the Gottingen chair was possible only with difficulties and by protection of his colleague Helmut Hasse. Strange stories were told of his private life, for example, that he taught himself to swim in his thirties by reading a book and succeeded at his first attempt in water.]
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[Errata - In his 1999 1st paperback edition of the The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Brian Greene incorrectly attributes the Kaluza-Klein theory and the suggestion that the universe might have more than three spacial dimensions to a 'Polish mathematician named Theodor Kaluza in 1919' on p. 185.]
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[Oskar Benjamin Klein (September 15, 1894 - February 5, 1977) was a Swedish theoretical physicist.]
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[Klein was born in Danderyd outside Stockholm, son of the chief rabbi of Stockholm, Gottlieb Klein from Humennr in Slovakia and Antonie (Toni) Levy. He became a student of Svante Arrhenius at the Nobel Institute at a young age and was on the way to Jean-Baptiste Perrin in France when World War I broke out and he was drafted into the military.]
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[From 1917, he worked a few years with Niels Bohr in the University of Copenhagen and received his doctoral degree at the University College of Stockholm (now Stockholm University) in 1921.]
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[In 1923, he received a professorship at University of Michigan in Ann Arbor and moved there with his recently wedded wife, Gerda Koch from Denmark. Klein returned to Copenhagen in 1925, spent some time with Paul Ehrenfest in Leiden, then became docent at Lund University in 1926 and in 1930 accepted the offer of the professorial chair in physics at the Stockholm University College, which had previously been held by Erik Ivar Fredholm until his death in 1927.]
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[Klein was awarded the Max Planck Medal in 1959. He retired as professor emeritus in 1962.]
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[Klein is credited for inventing the idea, part of Kaluza-Klein theory, that extra dimensions may be physically real but curled up and very small, an idea essential to string theory / M-theory.]
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[In 1938, he proposed a boson-exchange model for charge-charging weak interactions (radioactive decay), a few years after a similar proposal by Hideki Yukawa. His model was based on a local isotropic gauge symmetry and anticipated the later successful theory of Yang-Mills.]
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freeed
*Sigh* If only I were as versed as are you. :(
Here are my 2 pennies:
1) " imagine a ball with fuzzy green hair on it" reminded me that topology requires one point to be null, i.e., have no hair as per "Hairy Billiard Ball Theorem" we studied.
2) geodesics - the reason singularities appear in General Relativity and avoided in the reference I gave.
3) Tegmark's use of those wacky diagrams (at the least) persuaded me his screws need tightening. What I meant was even having exact solutions of Einstein's equations available (in The Large Scale Structure of Space-Time co-written by Stephen Hawking and George Ellis and signed for me by Ellis) I couldn't solve them for all the ice cream in Persia (or China or Egypt, depending on who you believe invented it) whereas I'm confident Tegmark can.
4) OK, that's more than 2 pennies. I'm a prevaricator. LOL
atenra11
What did you do for an Analysis or Topology book/s, and did you take a General Relativity class or text like Schutz or somethings.
I dont think i would tackle Hawking-Ellis for a while even if Baez seems to say it's a textbook every undergrad should browse or own. You'd need a mathematical physics text and a GR text and probably Differential Topology to get past page 9.
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for GR easier to hardest
a. Hartle
b. Schutz
c. D'Inverno
d. Rindler [yeah he's got three books now]
[d1. Essential Relativity] [i think this was the recommended one]
[d2. Intro to Special Relativity]
[d3. Relativity: Special, General, and Cosmological]
e. Carroll
f. Wald
g. Misner, Thorne, Wheeler [only one i got on my checklist right now]
freeed
I humbly take issue with your "proof". To begin with, one does not begin with lemmas, one begins with axioms. From axioms, which are PRESUMED true, one proves theorems. From these theorems, which have been proved true within a context, one derives other theorems which can then be used to prove a conclusion.
http://mathworld.wolfram.com/Lemma.html gives the definition of lemma as
"A short theorem used in proving a larger theorem."
http://www.merriam-webster.com/dictionary/lemma has
"Definition of LEMMA
1: an auxiliary proposition used in the demonstration of another proposition ".

Unfortunately these definitions are at odds, one calling a lemma an unproved proposition, which we have here, the other describing it as already proved. In any case, your 1st lemma is neither auxiliary nor proved true and I do not accept it.

To continue, I know of no one else who accepts your Proposition B. Classical subatomic particles are fundamental in that they CANNOT be further reduced. They can be described by, but are however not, mathematical points. Even the latest formulation - String Theory - is based on tiny, tiny, tiny vibrating "strings" having the resonances you describe. These strings already are one dimensional (have extension in space) and are not reducible. This is so crucial it bears reiteration. These strings already are one dimensional (have extension in space) and are not reducible. Further, mathematical points are not reducible. You claim , then, there is such a thing as half a point. Euclid must be spinning in his grave (get the pun?) as a point has no parts. "A point is an exact position or location on a plane surface. It is important to understand that a point is not a thing, but a place." (http://www.mathopenref.com/point.html)
Moreover, your Lemma 2 IS your conclusion. It cannot be used as proof of itself!
Finally, math is man made (this position is endorsed by Max Tegmark in "Our Mathematical Universe" which you have yet to read as have I. :P)
Ergo math came only after man, who appeared after fundamental particles (of which he is made) which formed after the universe began.

QED

X,D
blargendee
I don't find this to be an adequate proof. There's a few too many assertions in here that the rest of the proof rely on in order to attempt to prove anything.
For one, why can't resonant frequency itself be a physical property? When did the definition of physical property become "something that is unable to be broken down further"?
For two, you've asserted that there are only two possible outcomes. Why? Isn't that an "argument from ignorance"? What makes this a boolean situation exactly?
For three, even if I assumed the previously mentioned assertions were correct, you basically end by saying that "because we have mathematics to explain this stuff, the stuff must therefore be made of math". Not your exact words, but that's basically what you're saying isn't it?
Yes, we have mathematics to describe the universe at this scale, but that doesn't mean the stuff itself is made out of... math. What would that even mean?
If you feel I've missed something, feel free to fill me in.
blargendee
Also, thank you for taking the time to respond. I find this very interesting!
blargendee
Oops, actually I just looked up the "fallacy fallacy", and you were right about what it is. My bad.
TetrisGuy · 26-30, M
Well yeah, that's why this is a "semi-formal" proof. Our math can do everything. The only thing is, we simply don't know the parameters of every particle in the universe, in which causes minute differences in the final condition, even with the tiniest of changes in the initial parameters. So it's *our* inadequacy that our math isn't perfect. Both we need an unrealistic amount of data about literally *everything* there is to be 100% accurate, and also, it's a matter of time before we discover a branch of mathematics to explain it. People originally thought that no math outside of sacred geometry could describe nature, yet Benoit Mandelbrot came along in the 1970s and introduced fractal geometry, which was a *very* good representation of natural structures. Fractals have always existed. As with all math, we simply discover them, not invent them. We invent *ways* of *representing* them, but we didn't invent math itself; it is intrinsic and inherently encoded into everything. This is merely a theory, and theories require you to make assumptions. That's the entire part of a formal proof. So while technically I have made assumptions, my logic isn't flawed. If my assumptions were all correct, then my proof would hold. If my assumptions were not correct, then my proof would be unstable. You are, again, missing my point. Lets say there is this hypothetical circle that represents the universe, and each "pie slice" of it represents a fundamental particle. We know that the universe is cut up into at least n number of pie slices, as we can observe them with the LHC and TEM microscopes. Would you not agree that I can either have a finite number of pie slices, or an infinite number of pie slices, or have the pie sliced such that you only halve one of the previous halves (think of 1/2ⁿ * 360 to be the arc length of a circle with unit circumference, where n is the iterations done--the number of slices of a slice done )? Some combination of finitely wide slices and infinitesimally wide slices, or just one of the other? If there's another way to cut the circle such that you don't have either a finite number of slices or an infinite number of slices, or a combination of such, do tell me, as that could completely break our understanding of mathematics, regardless of what the universe is made up of. Do you understand now?
CarefulTreading
Mostly solid proof of things indeed... om0 *Smokes puffy cigar while trying sound posh and concurring a lot wif head nod'z!!* >mO Now riddle me this copper! 0 . 0 What about the "Void" of space!! O-0 Is it math too!!?
CarefulTreading
\(0 'o)/ BUT-BUT-BUT!! IT FELL'Z IN HORSEY POO'S!!
TetrisGuy · 26-30, M
I cleaned it.
CarefulTreading
D'x Tha TONGUE is not a cleaning TOOL!!
aphroditespriestess
Hey this relates to a question I wanted to ask you because you are EP's go-to person for math! The universe is 14 billion years old or whatever, right? But a year is a cycle of the seasons and the sun's positions relative to the earth. So, what do they mean by a year before there was an earth? or a sun? Or before there was anything in cyclical motion?
Seems like it should be a simple question but I have asked a physicist who couldn't explain it. But I have confidence that you can. <3
TetrisGuy · 26-30, M
Think of it this way. Before we had a clock or any comprehension of the passage of time, a minute ticking by would still be a minute. I am not looking at a clock right now, but I know that time is still passing, regardless of whether I'm looking at the clock or not. We define a second to be what it is, and we can work backwards to see how long ago something happened. For instance, I have a video of a plate breaking. I know exactly what time the plate broke, and I know how long the plate was in free-fall. By dividing that time in free-fall into predefined intervals (i.e. seconds), we can work out how long the plate was in free fall, and as such, when it was first dropped. In a similar way, instead of subdividing time into intervals of seconds, we subdivide time into intervals of years--as defined by the amount of time it takes for earth to make one revolution around the sun. By using various techniques, we can estimate the age of the universe (measured in various other methods and then converted using dimensional analysis) by subdividing this period of existence into intervals of years, then counting the number of intervals that fit. This will give the age, and so on. For instance, lets say that you want to estimate my birth year (essentially, my age). You know that I'm in 12th grade, and you know that typical 12th graders are 17 years old. You know that this is 2014. So you can work backwards and see that I was born in 1997. See what I mean now?
atenra11
It's kinda cute isnt it, we need a physical earth and sun to have the concept of a 'year', yet a few silly cosmologists like to use phrases like think of time before time began, or similar gloopiness.
......
There is the physical reality *hits you with a rock ouch*
There is the idea *green bunnies*
.......
now imagine green bunnies before i bash them with the rock
and then imagine
me doing this before rocks were invented.
RipperKing
That's not proof, because math is subjective.
atenra11
That's pretty similar to the criticisms of Descartes, where one gets into how a lot of our mental states are subjective things. We ponder, we appeal to intuition and commonsense and in things like mathematical analysis and topology there are lots of counterexamples that are counterintuitive. Happens in economics as well.
........
A lot of truth boils down to what is consensus.
.......
Which can be subjective humans. Who can agree the sky is blue, but analytical deductions usually work out, ethical ones less so, even harder is stuff on metaphysics/reality/spiritual/religion where we arent too sure of what the statements mean and can have lots of trouble with verification.
........
And well how objective or subjective or obvious is Godel's Proof?
.......
And what of the paradoxes and contradictions in mathematics or logic?
Russell used to have nightmares about the paradoxes.....
atenra11
"Math is purely objective, and is the ONLY thing that's purely objective"
.........
.........
You think so?
I think someone could argue that any Analytical Statement could be purely objective.
..........
Now how about a comment on this one:

- Kant claims that 7+5=12 is a synthetic statement.

- No matter how much we analyze the idea of 7+5 we will not find there the idea of 12.

- We must arrive at the idea of 12 by application to objects in the intuition.

- Kant points out that this becomes all the more clear with bigger numbers.

- Frege, on this point precisely, argues towards the opposite direction.

- Kant wrongly assumes that in a proposition containing "big" numbers we must count points or some such thing to assert their truth value.

- Frege argues that without ever having any intuition toward any of the numbers in the following equation: 654,768+436,382=1,091,150 we nevertheless can assert it is true.

- This is provided as evidence that such a proposition is analytic.

- While Frege agrees that geometry is indeed synthetic a priori, arithmetic must be analytic.

Was Kant purely objective?
Was Frege purely objective?

- Although Bertrand Russell later found a major flaw in Frege's work (this flaw is known as Russell's paradox, which is resolved by axiomatic set theory), the book was influential in subsequent developments, such as Principia Mathematica.

- The book can also be considered the starting point in analytic philosophy, since it revolves mainly around the analysis of language, with the goal of clarifying the concept of number.

..............

so how can the concept of number be purely objective, if you have to look deeply into language?

and was Frege purely objective?
And if so, why did Russell find flaws in his work?
and did Godel find flaws in Russell?

Maybe Morris Kline was onto something about Mathematics and the Loss of Certainity.
atenra11
Cauchy liked his rigor, and his total dislike of intuition and diagrams and anything geometric.

Yet he was later to have a few careless mistakes, oh and much much later
not rigorous enough.
I guess he wasnt analytical and objective enough.
Elitevenkat8kashyap
Then, is mathematics the God particle?
AxeRoberts
God created the math that defines the physics of this universe and life
TetrisGuy · 26-30, M
A theistic God is merely a human delusion caused by the want of comfort, even if by the needs of false security as is with religion and any form of theism.
AxeRoberts
Where's your proof of that statement
Vic01
Hello, I need some help in a problem that me and my teacher couldn't solve, I tried msging u but u put that u won't msg underage people, help plz
TetrisGuy · 26-30, M
Talk using proper grammar, and then we can talk.
aphroditespriestess
To me the universe is purely sexual but that may amount to the same thing :)
TetrisGuy · 26-30, M
Ah, your and your Freudian mind x'D
TetrisGuy · 26-30, M
Whoops. Added an extra r to that first you. xD
Randy1a
If you're so smart, couldn't u find better 'friends' than us?
TetrisGuy · 26-30, M
There are a few intelligent people on EP.
Randy1a
I'm sorry:>)
tesla47an
Logic and logical deduction exists before and without need for a physical universe.
attcia
summery anyone?
attcia
ok....
i just cba to read all that :/
i mean i bet its interesting and all but...
TetrisGuy · 26-30, M
Read the last paragraph.
attcia
ok
lifetime201
How you doing in school? Fellow gr12 student

 
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