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FQXi Administrator Max Tegmark wrote on Jan. 7, 2014 @ 17:11 GMT
The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Why does our universe seem so mathematical, and what does it mean? In my new book, Our Mathematical Universe, which comes out today, I argue that it means that our universe isn't just described by math, but that it is math in the sense that we're all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison.

Max Tegmark ponders the mathematical universe
At first glance, our universe doesn't seem very mathematical at all. The groundhog who trims our lawn has properties such as cuteness and fluffiness--not mathematical properties. Yet we know that this groundhog--and everything else in our universe--is ultimately made of elementary particles such as quarks and electrons. And what properties does an electron have? Properties like -1, 1/2 and 1! We physicists call these properties electric charge, spin and lepton number, but those are just words that we've made up and the fundamental properties that an electron has are just numbers, mathematical properties. All elementary particles, the building blocks of everything around, are purely mathematical objects in the sense that they don't have any properties except for mathematical properties. The same goes for the space that these particles are in, which has only mathematical properties--for example 3, the number of dimensions. If space is mathematical and everything in space is also mathematical, then the idea that everything is mathematical doesn't sound as crazy anymore.

That our universe is approximately described by mathematics means that some but not all of its properties are mathematical, and is a venerable idea dating back to the ancient Greeks. That it is mathematical means that all of its properties are mathematical, i.e., that it has no properties at all except mathematical ones. If I'm right and this is true, then it's good news for physics, because all properties of our universe can in principle be understood if we're intelligent and creative enough. For example, this challenges the common assumption that we can never understand consciousness. Instead, it optimistically suggests that consciousness can one day be understood as a form of matter, forming the most beautifully complex structure in space and time that our universe has ever known. Such understanding would enlighten our approaches to animals, unresponsive patients and future ultra-intelligent machines, with wide-ranging ethical, legal and technological implications.

As I argue in detail in my book, it also implies that our reality is vastly larger than we thought, containing a diverse collection of universes obeying all mathematically possible laws of physics. An advanced computer program could in principle start generating an atlas of all such mathematically possible universes. The discovery of other solar systems has taught us that 8, the number of planets in ours, doesn't tell us anything fundamental about reality, merely something about which particular solar system we inhabit--the number 8 is essentially part of our cosmic ZIP code. Similarly, this mathematical atlas tells us that if we one day discover the equations of quantum gravity and print them on a T-shirt, we should not hübristically view these equations as the "Theory of Everything," but as information about our location in the mathematical atlas of the ultimate multiverse.

It's easy to feel small and powerless when faced with this vast reality. Indeed, we humans have had this experience before, over and over again discovering that what we thought was everything was merely a small part of a larger structure: our planet, our solar system, our galaxy, our universe and perhaps a hierarchy of parallel universes, nested like Russian dolls. However, I find this empowering as well, because we've repeatedly underestimated not only the size of our cosmos, but also the power of our human mind to understand it. Our cave-dwelling ancestors had just as big brains as we have, and since they didn't spend their evenings watching TV, I'm sure they asked questions like "What's all that stuff up there in the sky?" and "Where does it all come from?". They'd been told beautiful myths and stories, but little did they realize that they had it in them to actually figure out the answers to these questions for themselves. And that the secret lay not in learning to fly into space to examine the celestial objects, but in letting their human minds fly. When our human imagination first got off the ground and started deciphering the mysteries of space, it was done with mental power rather than rocket power.

I find this quest for knowledge so inspiring that I decided to join it and become a physicist, and I've written this book because I want to share these empowering journeys of discovery, especially in this day and age when it's so easy to feel powerless. If you decide to read it, then it will be not only the quest of me and my fellow physicists, but our quest.

--

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark is now available to buy.

(The groundhog image above is courtesy of Max Tegmark and Meia Chita-Tegmark. He's not really called "Max Tegmark" either, but "Mr Hoggles.")

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Pentcho Valev wrote on Jan. 7, 2014 @ 17:30 GMT
"If space is mathematical and everything in space is also mathematical, then the idea that everything is mathematical doesn't sound as crazy anymore."

Unfortunately the mathematics depends on purely physical assumptions. For instance, if the speed of the light pulses (relative to the observer) varies with the speed of the observer, as shown in the following videos, the Einstein-Minkowski mathematics is simply wrong:

"Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

"Doppler effect - when an observer moves away from a stationary source. ...the velocity of the wave relative to the observer is slower than that when it is still."

Pentcho Valev

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Pentcho Valev replied on Jan. 7, 2014 @ 20:46 GMT
The "mathematical universe" can be based on a single mistake:

Max Tegmark: "Does c depend on observer motion (frame)? No first order effect has been seen. Michelson-Morley experiment hammered it - let's see how..."

Max Tegmark, if you knew that, originally, the Michelson-Morley experiment had shown just the opposite - that the speed of light is variable - your "mathematical universe"...

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Pentcho Valev replied on Jan. 9, 2014 @ 15:30 GMT
Max Tegmark: "In Section III, we discussed the challenge of deriving our perceived everyday view (the "frog's view") of our world from the formal description (the "bird's view") of the mathematical structure, and argued that although much work remains to be done here, promising first steps include computing the automorphism group and its subgroups, orbits and irreducible actions. We discussed how the importance of physical symmetries and irreducible representations emerges naturally, since any symmetries in the mathematical structure correspond to physical symmetries, and relations are potentially observable. The laws of physics being invariant under a particular symmetry group (as per Einstein's two postulates of special relativity, say) is therefore not an input but rather a logical consequence of the MUH."

I am afraid Einstein's postulate of constancy of the speed of light is absurd and for that reason cannot be a logical consequence of any reasonable "bird's view":

When the observer starts moving towards the light source with speed v, the wavecrests start hitting him more frequently - the frequency he measures shifts from f=c/L to f'=(c+v)/L, where L is the wavelength. Yet special relativity says that, even though the wavecrests hit the observer more frequently, their speed relative to him has somehow remained constant, Divine Einstein, yes we all believe in relativity, relativity, relativity.

In other words, no reasonable "bird's view" will have the following incompatible consequences:

1. frequency shifts from f=c/L to f'=(c+v)/L

2. speed of wavecrests shifts from c not to c'=c+v but to c'=c, Divine Einstein, yes we all believe in relativity, relativity, relativity

Pentcho Valev

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Pentcho Valev replied on Jan. 11, 2014 @ 09:25 GMT
Max Tegmark: "Einstein, for example, was the first person to really question the idea that time was just this boring thing that ticks at the same rate for everybody. That led to relativity theory. And I suspect that also today there are a lot of assumptions that we're making about reality which just aren't true."

Unfortunately, the "idea that time was just this boring thing that ticks at...

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Florin Moldoveanu wrote on Jan. 7, 2014 @ 17:31 GMT
The Mathematical Universe idea is correct and can be used to solve Hilbert's sixth problem. The first installment of that is deriving quantum mechanics but more can be proven. For details, see the ongoing series of posts at http://fmoldove.blogspot.com/

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Thomas Howard Ray replied on Jan. 11, 2014 @ 14:28 GMT
Florin,

I think you have a fundamental misunderstanding of relativity.

You write: "How is special theory of relativity derived? One starts with the invariance of the laws of nature to changing inertial reference frames. From this you get either the Lorentz transformation or the Galilean transformation, and use the second postulate, that of the constant value of the speed of light, to select between the two choices."

Special relativity is derived from Newtonian mechanics and the Galilean transform, to the limit of the speed of light. One doesn't choose between Galilean and Lorentz transformations -- the domain is continuous. This is important, because it begs the continuity of space with time; i.e., special relativity generalizes to accelerated motion (general relativity) because inertial frames are *not* invariant ("all physics is local").

"But are the laws of nature invariant only to changes in inertial reference frames? How about a trivial invariance: the laws of nature do not change during time evolution?"

However, also because inertial frames are invariant only under the mathematical artifacts of spacetime transformation, whether Galilean or Lorentzian, time does not evolve with the state evolution of invariant inertial frames. This is, in fact, what keeps quantum mechanics from being a mathematically complete theory -- the assumption that t = 1, a trivial constant. The laws of nature are in fact invariant under *space*time evolution.

Tom

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Pentcho Valev replied on Jan. 11, 2014 @ 15:06 GMT
Florin Moldoveanu: "How is special theory of relativity derived? One starts with the invariance of the laws of nature to changing inertial reference frames. From this you get either the Lorentz transformation or the Galilean transformation, and use the second postulate, that of the constant value of the speed of light, to select between the two choices."

True, even trivially true.

Thomas Howard Ray: "Special relativity is derived from Newtonian mechanics and the Galilean transform, to the limit of the speed of light. One doesn't choose between Galilean and Lorentz transformations -- the domain is continuous. This is important, because it begs the continuity of space with time; i.e., special relativity generalizes to accelerated motion (general relativity) because inertial frames are *not* invariant ("all physics is local")."

Not a single sentence makes any sense (at least to me).

Pentcho Valev

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Thomas Howard Ray replied on Jan. 11, 2014 @ 22:36 GMT
"Not a single sentence makes any sense (at least to me)."

That should surprise no one.

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John Brodix Merryman wrote on Jan. 7, 2014 @ 18:07 GMT
Max,

Math is a tool box, not a particular tool. We keep finding the limits of particular tools and then have to invent new ones. It could be many of the assumptions stated here, from space being three dimensional, to multiverses, is more a function of the limits of our current set of tools, than it is about the fundamentals of nature. Those who think the current tools answer everything are like the person with a hammer that thinks everything is a nail.

Why is space three dimensional? Doesn't it grow from the use of a three vector coordinate system to measure space. Measurement only describes features, it does not create the whole. Possibly we could start from the other direction and just assume space is space, an empty void and then accept that dimensions are the tools we find convenient to describe it. We are points of reference and so lines, planes and areas are how we project out from the point that is our view.

How does nature describe space? Looking out on the cosmos; physical spheres, radiant energy and convective processes connecting the two would seem to be nature's most popular 'mathematical' devices. Yet we have this 'blocktime' which reduces the dynamics to static measures of duration. Measurement is not causal, it is only descriptive. Does that mean blocktime is physically real, or does it point to the limits of a particular tool?

Maybe multiverses are simply a consequence of space not fitting into our current tool box.

Regards,

John M

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FQXi Administrator Max Tegmark replied on Jan. 15, 2014 @ 17:10 GMT
Thanks John for this interesting comment. Perhaps I'm misunderstanding you: are you arguing that the number 3, the dimensionality of space, is actually not a property of nature but merely some sort of human invention or construct, and might come out to be 2 or 4 or some other number if we developed different mathematical tools (as opposed to simply defining dimensionality differently)?

/Max

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Eckard Blumschein replied on Jan. 15, 2014 @ 19:15 GMT
John M, Max,

Particular Cartesian coordinates are definitely to be chosen arbitrarily. Nonetheless, there seems to be no alternative to a description of space in terms of three orthogonal to each other variables. Moreover, I see such description still not entirely in agreement with the obvious fact that there seems to be no preferred point in space to which we could refer anything. The problem does already occur with the 1D line between minus infinity and plus infinity. Mathematicians do not understand the real numbers IR likewise unrelated; they always refer to zero and one. Accordingly, the air can be identified as the reference for acoustic waves. The speed of acoustic waves in air refers to a "block" of air with finite boundaries.

Michelson's 1881/1887 experiment didn't find a corresponding "block" of space. Instead of accepting that there is simply no absolute point of reference for electromagnetic waves in space, FitzGerald, Lorentz, Poincaré, Einstein, Tolman, and many others arrived at the mathematical tool of covariance theory (Michelson spoke of a monster) and spacetime because other alternatives like dragged aether or emission theory proved untenable and leading Wilhelminian mathematicians were self-delighted having created a non-Euclidean geometry as description of the world.

Max, are you aware of Wolfgang Mueckenheim in Augsburg? Mathematicians called him a ultra-finitist because he argues that there is no absolute infinity. I slightly disagree: I am an EE, and to me infinity is a valuable mathematical fiction and also the most appealing option to conceive the universe.

Regards,

Eckard

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John Brodix Merryman replied on Jan. 15, 2014 @ 21:44 GMT
Max,

First let me thank you for the reply. We don't get much input from the powers that be here in the gallery.

Yes, 3 dimensions is a very useful descriptive property of space, especially our relationship to it, just as 'blue' and '4 tires' are properties of my pickup truck. The issue is whether it is somehow foundational, or an effective description of particular properties. Rather than attempt to debate the nature of space(typing on a phone), let me argue that it blurs the functionality of said coordinate system for mapping spatial relations. Unless you are going to specify the particular vectors used, space is effectively infinitely dimensional, since multiple systems can be used to define the same space. For example, you could say the Israelis and Palistinians use different coordinates to define the same space.

Then of course there is that timeline used as the fourth dimension. To be continued.

Regards,

John M

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Robert H McEachern wrote on Jan. 7, 2014 @ 19:30 GMT
"That our universe is approximately described by mathematics means that some but not all of its properties are mathematical"

Nonsense. It simply means that it is describable by mathematics. Consider the following substitution (mathematics = english):

That our universe is approximately described by english means that some but not all of its properties are english

Rob McEachern

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FQXi Administrator Max Tegmark replied on Jan. 15, 2014 @ 18:22 GMT
Thanks Robert for your comment. I'd be curious to hear whether, after reading my complete argument in the book, you still feel that my point of view is nothing more than a nonsensical play with words, or if you feel that there really is more than one logical possibility for how things can be and that it's interesting to study nature further to find out.

/Max

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Robert H McEachern replied on Jan. 15, 2014 @ 19:35 GMT
Max,

I don't feel that your point is mere word-play. But regardless of "how things can be", I do believe that it is possible to DESCRIBE "how things can be", in multiple ways, all of which are mathematically exact. I can fit a straight line to a set of data points, and I can also fit a Fourier Superposition to them; both may fit the data precisely. But one makes much more intuitive sense (Occam's Razor) than the other.

For this very reason, communications engineers, long ago, abandoned the use of Fourier Superpositions, when attempting to DESCRIBE information carrying signals. It is time that physicists do the same.

Rob McEachern

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Robert H McEachern wrote on Jan. 7, 2014 @ 19:34 GMT
"consciousness can one day be understood as a form of matter"

Consciousness is much more likely to be proven to be a process taking place within matter, than a "form of matter"

Rob McEachern

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Roger Granet replied on Jan. 15, 2014 @ 06:35 GMT
Robert,

Well said. If consciousness isn't occurring within the matter and energy in the brain, could someone please point out where it is taking place or provide some experimental or logical evidence that it is it a new form of matter.

Roger

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FQXi Administrator Max Tegmark replied on Jan. 15, 2014 @ 18:29 GMT
Dear Robert & Roger,

It sounds like we're all in agreement here. In http://arxiv.org/pdf/1401.1219v1.pdf, I used "state of matter" in the same way as we that we refer to solids, liquids and gases as "states of matter" (or "phases of matter"): not new substances made of new types of elementary particles, say, but traditional particles arranged to be able to process information in certain complex ways.

/Max

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Robert H McEachern replied on Jan. 15, 2014 @ 19:53 GMT
Max,

I think that even likening consciousness to a ""state of matter" in the same way as when we refer to solids, liquids and gases", is one giant step too far. However, if one were to say the activity of "traditional particles arranged to be able to process information in certain complex ways", as in neurons and integrated circuits, then one would be a lot closer to the truth.

Rob McEachern

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Robert H McEachern wrote on Jan. 7, 2014 @ 19:43 GMT
"An advanced computer program could in principle start generating an atlas of all such mathematically possible universes."

An eighth grade student could also START this project. But neither would ever finish.

Unless all those universes are virtually devoid of information, our own universe lacks the information storage capacity to model "all such mathematically possible universes."

Rob McEachern

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James A Putnam wrote on Jan. 7, 2014 @ 22:25 GMT
Our Mathematical Universe?

"And what properties does an electron have? Properties like -1, 1/2 and 1! We physicists call these properties electric charge, spin and lepton number, but those are just words that we've made up and the fundamental properties that an electron has are just numbers, mathematical properties. All elementary particles, the building blocks of everything around, are...

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FQXi Administrator Max Tegmark replied on Jan. 15, 2014 @ 18:33 GMT
Hi James - wouldn't you agree that the Coulomb is a somewhat arbitrary unit made up by us humans, and that if we'd discovered that all electric charge is quantized before we defined the Coulomb, we might have instead defined it so that the electric charge was -1 (or +1)?

For the other electron quantum numbers, e.g., spin and lepton number, we've indeed opted for such dimensionless definitions.

/Max

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adel sadeq wrote on Jan. 8, 2014 @ 01:50 GMT
Dear Max,

My theory proves that reality is indeed a particular mathematical structure.

I was very happy when you replied to my email few years back. As my theory matured I tried to get your attention to no avail. My guess is that you did not get the chance to see it, OR, the way my theory is presented is unacceptable in the mainstream and hence an...

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FQXi Administrator Max Tegmark replied on Jan. 15, 2014 @ 18:37 GMT
Thanks Adel for your encouraging words. I hope you can post a detailed description of your model online somewhere and link to it here so that others can give it careful scrutiny!

/Max

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adel sadeq replied on Jan. 17, 2014 @ 15:40 GMT
Hi Max,

Thank you for the reply. I think you were in a hurry and did not push the "view entire post" link which FQXI's way to expand the shortened reply display. There you would have seen the links and the abstract. I repost the links here again to my theory.

Fundamental Theory of Reality

Reality is nothing but a mathematical structure, literally.

QSA theory

FQXI contest

Thanks

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Thomas Howard Ray wrote on Jan. 8, 2014 @ 18:23 GMT
Max,

" ... if we one day discover the equations of quantum gravity and print them on a T-shirt, we should not hübristically view these equations as the 'Theory of Everything,' but as information about our location in the mathematical atlas of the ultimate multiverse."

Maybe not everything -- yet vastly enough. For if we actually possess a specific location, and given special relativity, we should know for certain that the world is classical at foundation, and that "All physics is local."

Glad to see your book as a sciam book club featured selection. My order is in, and I look forward to a great read.

Best,

Tom

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Rodney Bartlett wrote on Jan. 11, 2014 @ 13:43 GMT
About our mathematical universe, and about the "diverse collection of universes obeying all mathematically possible laws of physics" (I don't believe this diverse collection exists, Professor Tegmark). Also, the Higgs boson certainly exists but I don't think it gives ANY particle mass (see the part below where I mention DNA). We could say the Higgs FIELD bestows mass if we think of it as a...

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Eckard Blumschein wrote on Jan. 11, 2014 @ 15:09 GMT
"The essence of mathematics is its freedom". May I ask Max Tegmark to comment on this utterance by Georg Cantor who plays a similar role in mathematics as does Albert Einstein in physics? Both created a lot of paradoxes.

Eckard Blumschein

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FQXi Administrator Max Tegmark replied on Jan. 15, 2014 @ 18:44 GMT
Although I'm a great fan of George Cantor, and fell in love with his hierarchy of infinities as a teenager, it's important to remember that mathematics` doesn't give you complete freedom. For example, if a civilization develops an interest in 3D shapes built out of identical polygons, they'll discover the five Platonic solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron. They have the freedom to invent whatever names they wan for them, but they don't have the freedom to invent a 6th Platonic solid - it simply doesn't exist!

/Max

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Eckard Blumschein replied on Jan. 16, 2014 @ 19:33 GMT
Thank you for responding, Max.

Fraenkel's 1923 textbook revealed to me that Georg Cantor made a naive mistake when he assumed the entity of "all" of infinitely numbers like something that can be considered as tangible and fix. While I consider aleph_0 (potentially infinite) and aleph_1 (actually infinite, continuous) as reasonable, I wonder if there is any serious justification already for aleph_2. Cantor's naive ideology is not consistent with my logical reasoning. The finitist Hilbert admitted having replaced it by a clever designed set of axioms.

I appreciate you clarifying that in contradiction to Cantor's naivety, "mathematics` doesn't give you complete freedom."

We may hopefully agree on that one has to carefully check what mathematics fits to physical reality.

/Eckard

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Sydney Grimm replied on Jan. 25, 2014 @ 22:18 GMT
Max Tegmark,

Some years ago I read partly your publication about 'The mathematical universe'. I assume that your book will explain the subject in a more popular way. That I did not read the whole publication had a reason; I was already familiar with the subject for many, many years. So I agree with your conviction that our universe is totally mathematical. Moreover, your assumption that consciousness can be understand by knowing the mathematical rules that form reality do not shocked me at all. I have the same opinion.

At the other hand, because of your publication I suppose that you are not familiar with the foundational mathematics that rules reality. This is not surprisingly because studying physics is not the easiest way to understand reality, albeit it is impossible to do any research about the subject without some insight in physics.

The main reason that hinder an easy perception of the mathematical reality is the human projection of the sensorial observations within our imagination. We simply have a wrong concept about reality. And when someone - like Parmenides - draw our attention to the discrepancy between our concepts and reality, we refuse to consider the arguments. Because we are - unfortunately - convinced that natural concepts are the right concepts. But we do not realize ourselves that the natural concept is only formed by our physical orientation in space and time.

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Akinbo Ojo wrote on Jan. 12, 2014 @ 15:28 GMT
Hi Tom,

First, I do not wish to deny your devotion and your right to the "continuous view" rather than the "discrete possibility". I would however hope that you give some consideration to the latter as well, even if just a tiny bit, and see where it could lead. This is in keeping with an eminent mathematician like Penrose's advice, that we should at the least harbour some suspicion that: "If we continue to divide up the physical distance between two points, we would eventually reach scales so small that the very concept of distance, in the ordinary sense could cease to have meaning. It is anticipated that at … 10-35m this would indeed be the case", "We should at least be a little suspicious that (despite the logical elegance, consistency, and mathematical power of the real number system) there might be a difficulty of fundamental principle on the tiniest scales", "This confidence – perhaps misplaced- …", etc. All on p.113, The Emperor's New Mind.

Having tried to cajole you with this preamble, I found this in one of Max Tegmark's published papers (2007), not the book:

"We found it important to define mathematical structures precisely, and concluded that only dimensionless quantities (not ones with units) can be real numbers".

What is your or the possible interpretation of this Tegmark's statement?

Akinbo

(I am posting here rather than the Classical Spheres blog, so as not to distract from Joy's work). I will post my interpretation after yours for comparison.

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Thomas Howard Ray replied on Jan. 12, 2014 @ 16:13 GMT
It's straightforward, Akinbo. As Max Tegmark explains, after noting that the manifold R, metric space R, number field R and vector space R occupy four symmetry groups in a single representation, "Quantities with units may instead correspond to the 1-dimensional vector space over the reals, so that only ratios between quantities are real numbers."

In other words, the universe of relations among dimensionless points is a real structure independent of internal thought processes. Max's philosophy is an extreme realist position, which I share.

Best,

Tom

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John R. Cox replied on Jan. 12, 2014 @ 17:20 GMT
Mad Max,

"...so that only ratios between quantities are real numbers."

Sweet! jrc

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Akinbo Ojo replied on Jan. 13, 2014 @ 09:42 GMT
Thanks Tom,

My own literal interpretation of "We found it important to define mathematical structures precisely, and concluded that only dimensionless quantities (not ones with units) can be real numbers" is that Length itself being a quantity that is certainly not dimensionless, with the metre as its unit of measure, has a mathematical structure that is not fully in accord with the real number system, even though ratios of length according to Tegmark and yourself can be described by the real number system, (whatever that means).

This is unlike dimensionless quantities such as temperature, colour or ocean salinity to which the real number system is fully applicable on their own without resorting to ratios. Thanks all the same. How about that little suspicion Penrose talked about, is it an unfounded paranoia by the eminent mathematician?

Akinbo.

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Thomas Howard Ray wrote on Jan. 13, 2014 @ 14:22 GMT
Akinbo,

I ran across a comment in Google groups that I think summarizes what you, John, Florin and others have said about a fundamentally discrete reality:

"Tegmark is arguing for finite mathematics, not just finite physics to defeat Godel incompleteness theorem which he sees as fatal to his idea that all reality is mathematics. That's why he moved to a computational universe. But I find it surprising that Tegmark hasn't incorporated quantum computing in his proposal because ultimately reality is quantum. (Bob Zannelli)"

I think the correspondent has realized something that all of you have missed: that were reality fundamentally discrete, quantum computing should be easy.

On the other hands, the continuous functions of a chaotically deterministic universe falsify the illusion of irreducibly discrete entangled elements in superposition.

Best,

Tom

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Akinbo Ojo replied on Jan. 13, 2014 @ 20:11 GMT
Tom,

"Tegmark is arguing for finite mathematics", which I believe must include finite geometry. My essay, if he cares to read it might be of help to his argument but he dislikes philosophers who can help him out of his troubles...

Then, when you say, "something that all of you have missed", does that include Penrose, Fredkin, Wolfram, etc. These are highly qualified mathematical physicists. But I observe your 100% unwillingness to even give these suspicions on discrete physics a consideration. Why not just 99% and give 1% or 0.5% please? I beg of you as a new year resolution :)

Akinbo

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Thomas Howard Ray replied on Jan. 14, 2014 @ 13:31 GMT
Akinbo,

My comment was confined to the issue of quantum computing. However:

Keep in mind that Fredkin and Wolfram are computer theorists, whose research programs depend on the discrete nature of computation and computable functions. Fundamentally, if one were to extrapolate this philosophy (Fredkin calls it digital philosophy) to the foundations of nature, the universe itself should be a computable phenomenon.

Sir Roger Penrose is a different case -- a mathematical Platonist in the tradition of Godel. That is, for Penrose mathematics lives in a world apart from the physical; physical reality could never fit into the mathematical world. Consider the Penrose triangle in this context: one can draw it in two dimensions, or construct it by a set of computer instructions, yet it cannot possibly exist in the three dimensional physical world. I've read Penrose's work on physics and mind; much of it is inaccessible to me, yet of what I do comprehend, I reject the premise that brain-mind and external nature are identical.

Max Tegmark's view conforms to my own of what the world "should be." Though often wrongly confused with Platonism, it is realist in the extreme, such that mathematical structures -- all of them -- are objective external representations of the underlying reality we all share. For this to be true, there must also be a unifying principle in mathematics, identical to the principle that unifies nature.

That's why I think Joy Christian's measurement framework for quantum correlations is a model clue to finding that principle -- a simply connected space of continuous measurement functions. We cannot get such a picture with an assumption of discrete functions that are disconnected or multiply connected. The Christian-Roth computer simulation makes the case for a smooth stable function with discrete random input -- just the way nature appears to work.

All best,

Tom

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Thomas Howard Ray replied on Jan. 14, 2014 @ 14:10 GMT
Hi Akinbo,

I went to your essay site to remind myself of my comments:

"I would make a note that the mathematical point at infinity is actually realized in the compactification of the complex plane, which shifts the discrete and probabilistic measure functions of the complex Hilbert space to the continuous and deterministic functions of a topological model. You might want to look into that to help further strengthen your argument.

"Something else that caught my eye in regard to Newton's idea of spatial translation: ' ... unless we postulate that there are two spaces that everywhere coincide, a moving one and one that is at rest, so that the movement of a part of the moving one involves a translation of that item from the corresponding part of the resting one to a different part of the resting space ... That is crazy (translator's inclusion) ... ' I have to disagree with the translator's editorializing -- Newton's conception is not crazy; it follows directly from his belief in absolute space and absolute time. The duality is necessary -- which Einstein fixed, with Minkowski's model of continuous spacetime, in which neither space nor time are independently real, but rather preserve physical reality in a union of the two."

I hope you see that I am not "suspicious of infinity." I am just suspicious of the idea that there is more than one infinity in the physical world.

All best,

Tom

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Robert H McEachern wrote on Jan. 16, 2014 @ 16:41 GMT
Max,

In your new paper, "Consciousness as a State of Matter", that you cited in response to an earlier post of mine, you repeatedly ask the question:

"why do conscious observers like us perceive the particular Hilbert space factorization corresponding to classical space (rather than Fourier space, say)"

If you would take off your "math hat" for a moment, and consider the following, you would have a lot better chance of answering that question:

Biological systems cannot accurately measure or even utilize "phase".

Hence, they cannot employ cleverly crafted phase relationships, as in Fourier Analysis, to either analyze or synthesize ANYTHING. Furthermore, they have no need of such non-causal, infinite basis functions, in order to represent the finite, causal world they inhabit.

The biological senses and their associated processing are almost entirely "Amplitude-Modulation-Only" characterizations of input signals.

Your comment that "human consciousness may have evolved as an accidental by-product of error correction." is closer to the mark. However, it is not random noise, but multi-path and multi-source interference that are the problem. And the solution rests in the use of modulation types that alleviate this problem, rather than sophisticated mathematical coding, to detect and correct errors after they occur.

Ask yourself why the visual system lowpass filters light amplitudes down to a bandwidth of only 10 Hz. When you come upon the correct answer, you will have answered your above question.

I'll give you a hint. While your "physics from scratch" problem may "come without any a priori physical interpretation", the same cannot be said of the "biology from physics" problem.

Rob McEachern

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John Brodix Merryman replied on Jan. 16, 2014 @ 17:01 GMT
Rob,

"The biological senses and their associated processing are almost entirely "Amplitude-Modulation-Only" characterizations of input signals."

E.O. Wilson described the insect brain as a thermostat. Yet it has been shown ants count their steps as a navigation tool. I see the right brain as a thermostat and the left brain as a clock. The non-linear, scalar side to approximate conditions and the linear, sequential side to navigate a path through them.

Regards,

John M

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Robert H McEachern replied on Jan. 16, 2014 @ 22:51 GMT
John,

Counting amounts to amplitude detection. The phase does not matter: you will get the same final amplitude/count regardless of the rate or change-of-rate of the counting. Similarly, a thermostat is sensitive to the amplitude (amount) of heat, but does not need to be referenced to any other event, (which is what phase is all about) in order to determine a temperature value.

Rob McEachern

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John Brodix Merryman replied on Jan. 17, 2014 @ 00:36 GMT
Rob,

"a thermostat is sensitive to the amplitude (amount) of heat, but does not need to be referenced to any other event, (which is what phase is all about) in order to determine a temperature value."

Exactly. Thermostats don't count.

Yes, clocks measure phase, irrespective of the count, but in order to have discrete amplitudes, ie. counting, you need that phasing to separate them.

The point is that insect minds are not just thermostats, they register and record those events. Given they measure distance by footsteps, the phase is spatially regular. While frequency is temporally regular, it is due to crossing distance at a regular rate and arriving at the detector at a constant rate.

So the counting is not just the sequence, but the spacing as well.

Regards,

John M

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Akinbo Ojo wrote on Jan. 16, 2014 @ 19:34 GMT
Rob & Tom,

Rob brought up some interesting issues on "something" and "somewhere" on the Fluctuations, Schmucuations blog and I asked if Rob were a something or a somewhere or both? I now post this as a dialogue hoping it will bring out any new insights...

The State Vs. Tom McEachern

Judge: May Prof. Tom McEachern step into the dock. Please be reminded that you are on oath to...

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Robert H McEachern replied on Jan. 16, 2014 @ 22:31 GMT
Akinbo,

If you like putting science on trial, you might enjoy this book Paradigms Lost

A typical dictionary definition for "somewhere" is: "in, at, or to a place not known, named, or specified"

Since I am known, named and specified, I am not somewhere.

I guess I must be some sort of mysterious quantum superposition; simultaneously everywhere, but, alas, nowhere to be found. But that's only a guess. ;)

Rob McEachern

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Anonymous replied on Jan. 17, 2014 @ 08:49 GMT
Rob,

Your reply gave me some food for thought. You are known like an electron is known, you are named like an electron is named and you are specified like an electron's charge is specified but the truth is only you (and the electron) know where you are. So to me the observer you are somewhere. It is only when I look for you and measure you that I can really say categorically where you are, that is your probability and wave function finally collapses to me the observer. In short to me you are somewhere, something and sometime. To a fundamental particle, it does not care where it is, does not care what it is and does not care what time it is, its time is its time. To it all these are absolute to it and not relative to that of other 'its'.

Cheers,

Akinbo

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Robert H McEachern replied on Jan. 17, 2014 @ 14:18 GMT
Akinbo,

Now you have seen; "wave function finally collapses to me the observer"

If one must speak of wave-function collapse, then one must realize that one is speaking about the "collapse" of the purposeful activity within the observer's mind, as it contemplates an observed, not a collapse of the observed. The observed simply continues to be whatever, wherever and whenever it is. It is always "in phase" with itself.

Rob McEachern

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adel sadeq wrote on Jan. 17, 2014 @ 15:40 GMT
Hi Max,

Thank you for the reply. I think you were in a hurry and did not push the "view entire post" link which FQXI's way to expand the shortened reply display. There you would have seen the links and the abstract. I repost the links here again to my theory.

Fundamental Theory of Reality

Reality is nothing but a mathematical structure, literally.

QSA theory

FQXI contest

Thanks

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John Brodix Merryman wrote on Jan. 18, 2014 @ 19:07 GMT
Peter Woit has an interesting blog post reviewing Tegmark's book. Max has some responses in the comments section.

The comments mostly deal with whether and to what extent reality is platonically mathematical.

I've been banned for making comments Peter deemed crackpot, so I'l just raise my crackpot ideas here. I wonder how much the problem of reality being seemingly mathematical, but none the less unpredictable, is due to information necessarily being conceptually static and reality/the energy manifesting it, is inherently dynamic. Part of this supposition goes back to complexity theory and how reality is that juxtaposition of order and chaos. Obviously math being the (stable)order defining everything, while the dynamics being the chaotic element constantly upsetting and pushing through the cracks in the system.

?

Regards,

John M

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adel sadeq replied on Jan. 19, 2014 @ 03:29 GMT
I think Peter is on a rampage, attacking everybody in sight. He is accusing people of doing things as if for money and yet he wrote a book that makes money and I don't see anything wrong with that. He accuses people of acting as science spokesman and yet he increasingly doing the same thing to the extreme.

He only allows posts that support his point of view (at least 95%), very strange, never seen that even with Lubosh.

I like some of his work, but I don't know what is eating him.

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John Brodix Merryman replied on Jan. 19, 2014 @ 11:12 GMT
Adel,

I don't knock Woit for his editing. It's his prerogative. I certainly agree there are problems in physics, but I think it is deeper than those in the field appreciate, because the 'fabric of spacetime' is built into the foundations and it is the grandaddy of projecting mathematical patterns onto the physics. It makes the same conceptual leap of faith as epicycles, assigning agency to the pattern. So Woit is like one of those 80's Russian Communist officials, promoting glasnost and perestroika and thinking it will clear up a few problems and everything will be just fine.

Regards,

John M

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Akinbo Ojo wrote on Jan. 24, 2014 @ 12:07 GMT
Max Tegmark, author of The Mathematical Universe wrote in 2007, "When considering such examples, we need to distinguish between two different ways of viewing the external physical reality: the outside view or bird perspective of a mathematician studying the mathematical structure and the inside view or frog perspective of an observer living in it.…If the frog sees a particle...

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Thomas Howard Ray wrote on Jan. 24, 2014 @ 14:20 GMT
Max,

I got around to reading your "Edge" comments on the subject "What scientific idea is ready for retirement?" which I found poignant, particularly on inflation and the measurement problem:

"The theory of inflation has been spectacularly successful, and is a leading contender for a Nobel Prize. It explained how a subatomic speck of matter transformed into a massive Big Bang,...

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Plato Hagel wrote on Jan. 24, 2014 @ 21:50 GMT
Max Tegmark:"For example, this challenges the common assumption that we can never understand consciousness. Instead, it optimistically suggests that consciousness can one day be understood as a form of matter, forming the most beautifully complex structure in space and time that our universe has ever known. "

I have my own reasons for believing what Max is saying. While consciousness in itself may question the proponent states given as matter distinctions, as consciousness may use it, it still to me questions the state of the most rarefied in order to say what exactly consciousness is at that point.

In a way there is this esoteric feeling of what is transmitted, has a logical and consistent manner, that is somehow lost in it's translation. As a concept/idea of something that is very simple and beautiful, asking for, a description of the reality we live in? So, there is always this attempt to see nature as a partial view of reality, layered, as this expression of consciousness in action, settled to some state of as that defined matter.

In that rarefied form, it is an intellectual struggle to define something that is within, and emotively cast as a fluid state of expression being formed as the person who is restraint to the the final form of there choosing. Memory induced toward repeatability in remembrance of time.

Plato's mathematical foundation is an example of the foundations with which reality is being chosen to be describe as. All attempts to describe reality, as a complex view regarded as a simplistic expression, as the choosing of the mathematical framework?

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Plato Hagel replied on Jan. 24, 2014 @ 21:58 GMT
This then goes toward the subject of foundation, now defined as a matter state descriptor as an attempt to understand reality. It's process seeks to be a foundational one. What then ensues as a emergent product from the beginning so as to surmise, that the universe is the way it is, or, that it has a foundational description, of it's possibility. This as a functional expression of the vacua?

Anthropologically this forces one back to question of the relevance of such a stated view, with reality, as to where it is to begin?

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Eckard Blumschein replied on Jan. 25, 2014 @ 10:10 GMT
Plato Hagel's comment on Plato's mathematical foundation is hard to read for someone whose native language isn't English. Maybe, it is elegant to use only an unexpected question mark after a describing rather than asking sentence.

Isn't the verb missing in the sentence "All attempts to describe reality, as a complex view regarded as a simplistic expression, as the choosing of the mathematical framework?"?

Eckard

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Plato Hagel replied on Jan. 25, 2014 @ 17:14 GMT
Hi Ekard,

"All attempts to describe reality, as a complex view regarded as a simplistic expression, as the choosing of the mathematical framework??"

Physics is about a mathematical approach? Then, from the list of mathematical approaches, which one? The mathematics chosen can only be part of a larger context reality while only revealing "a partial view." It can never be a complete "theory of everything?"

To me, it is a selection based on the idea that, that particular selection, will have a direct affect on what you are doing in physics in terms of it's description of reality.

The inductive, toward simple and beautiful.....as a equation? The complex, to the simple. What "genus figure" resides in the valley.

Also to point toward the understanding of that rarefied state of matter that Tegmark is referring too. The trend toward vacua should have been a clue? Also, that with regard to the Anthropic principle how would such a math be chosen?

In general then, what portion of the population believe in Platonism? SEE: Answers to Question-Interesting

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Plato Hagel wrote on Jan. 25, 2014 @ 20:07 GMT
Hi Eckard,

Why do you write "Physics is about a mathematical approach?" instead of "Is physics about a mathematical approach?"?

In the sense I know that mathematics as a question related to physics is a affirmative. For those recognize this, the answer is obvious as it was to you. To others who would not understand that question, it may be posted as a second option.

The foundational recognition is important. People have debated the struggle with what counts as reality, and to be faced with the question of foundations it is to understand that this push toward describing reality. Albeit a theoretical one, it is based on the information that such a theory is constructed from.

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Eckard Blumschein replied on Jan. 26, 2014 @ 06:22 GMT
Is the meaning of both sentences different? To me the sentence "The meaning of both sentences is different?" would be bewildering unless your background isn't English.

I guess,"?" stands for "Really?" rather than for "Isn't it?".

Eckard

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