Tegmark's Mathematical Universe

Ray ,

You are right ,alone we are nothing in fact .

I repeat I don't critic the skills but the models .

You can do the same with mine ,between us ,you know what my Theory is correct .

Why an other logic in 3D ?It is impossible .

This reality will rest .It is not a reason it is finished for the discoveries ,no it is the begining of a real research with pragmatism about our real universe .It is more essential to study what we can study in fact and not extrapolations behind the walls ,that has no sense .The unknew is the unknew and our 3d are our 3d ,it is like that since the begining .And never that will change .

When I say that about pseudo sciences ,I insist yes all that is pseudo sciences .And the skills have others things to do I think.

It is sad all that in fact ,very sad for the sciences .

Friendly

Steve

Steve,

You said "The physicality is more foundamental than maths because there only the reals exist. The imaginaries are thus humans in conclusion."

Many of my models are based on crystalline lattices that exist in Nature. They are fundamental, not imaginary. If Nature uses a structure once, she might use it again. Is a sphere really more fundamental than a buckyball? Nature can make a buckyball with a mere 60 atoms of Carbon. In contrast, a perfect sphere is a mathematical abstraction that can never be perfectly attained in this world. Try polishing a piece of wood or marble into a perfect sphere.

Our most significant differences lie in multiple dimensions. I introduce extra degrees-of-freedom and call them new dimensions. You introduce new degrees-of-freedom and call them spin. If I am correct, then part of hyperspace is a 3-brane that mirrors 3-D space such that it is easy to confuse the two different concepts. Note that on page 10 of my book, I obtained a 3-dimensional momentum space density of states. This is a hyperspace effect, not a spacetime effect. The numbers can trick you if you mix up cause versus effect.

Have Fun and continue to evolve!

Ray

I am going to try to get to the matter of the associator and its implications for physics by Sunday.

Cheers LC

Although he begins with the External Reality Hypothesis (ERH) that claims reality actually exists outside of us humans, it appears to me self-evident that Tegmark's Mathematical Universe Hypothesis (MUH) is in the realm of meta-physics. For example:

"Mathematical structures do not exist in an external space or time, are not created, or destroyed..."

can be replaced by:

"God does not exist in an external space or time and is not created or destroyed..."

with no significant change in 'provability'. With this (negative) definition of mathematical structures, Tegmark goes on to state in his Mathematical Universe Hypothesis that "our external physical reality is an abstract mathematical structure."

The closest dictionary meanings that link these two words are:

Reality = actual fact

Abstract = insufficiently factual

So what he is saying is:

(MUH) => (ERH)

abstract is real

or

insufficient fact = actual fact

This has exactly the same sense as:

"This statement is false."

That is, it's nonsense.

Thus, on the face of it, Tegmark's basis appears to be nonsense. This leads me to wonder if Tegmark has written a Sokal Hoax for physicists! The idea that he is all the while laughing up his sleeve almost prevents me from responding to his paper, but I will do so anyway.

A Mathematical Universe?

If I believe in God, my friend John believes in the flying spaghetti monster and Tegmark believes in 'mathematical structures' existing outside of space and time, these are called meta-physical beliefs. They are non-physical and cannot be tested by physical means. These beliefs cannot be proved or disproved physically.

Ignoring my belief and John's belief, let's look at mathematics "in" the physical world. One aspect is Wigner's appreciation of "the unreasonable effectiveness" of math in physics. Another is Kronecker's remark that 'God made the integers, all else is the work of man.' Tegmark quotes Wigner and Kronecker. In the 1970s these (and similar) quotes inspired my dissertation, 'The Automatic Theory of Physics', in which I present 'natural numbers' as artifacts, created by 'counters' and subject to 'logic', where both counters and logic are physical devices that can be implemented via silicon, proteins, or neural networks. Based on these numbers we can derive rational numbers, then, using the concept of limits, we can derive irrational numbers, and all the rest of mathematics. Nowhere in this process do we need to step 'outside space and time'.

This process serves us two-fold: first, using thresholds or triggers on the counters, we can make 'observations', that is, obtain mathematical 'data' that 'represents' a physical system. Second, we can mathematically process this data via clustering algorithms to obtain a 'feature set' and create a corresponding 'feature vector'. Through the use of pattern recognition algorithms we can derive equations that represent the dynamical data changes, if any. These become the 'laws of physics' subject to further change or confirmation by additional observations.

I developed this scheme in 1979 and 30 years later (April 2009) Science has just published two papers on 'Automating Science' based on the same theory. In this scheme mathematics is an artifact, created in the physical universe.

Physical reality -> counter/logic -> mathematics

The reality of this approach is easily demonstrated. Tegmark, on the other hand, wants to invert the scheme as follows:

Abstract mathematics -> physical reality

He cannot possibly demonstrate this (according to his own definitions) any more than I can demonstrate that God, acting outside of space and time, created the physical universe. These are effectively religious beliefs, but one (his) is apparently taken as serious physics commentary, so I will try to analyze it here.

To summarize: Mathematics, as described above, is an artifact used to describe or map the territory of physical reality. In contrast to this Tegmark claims that physical reality is mathematics.

In order to make this claim he wishes to get rid of human 'baggage'. He doesn't define baggage but seems to consider it to be the concepts or interpretations that physicists typically associate with the features of the physical universe based on observations, claiming that:

"For a description to be complete, it must be well-defined also according to non-human sentient entities (say aliens or future super computers)..."

Since my Automatic Theory of Physics uses a (non-sentient) robot to derive the laws of physics from measurement data (observations) my approach satisfies Tegmark's basic requirements for the External Reality Hypothesis. The robot works with math only, it has no human baggage.

But Tegmark's Mathematical Universe Hypothesis is a horse of a different color. It states:

"Our external physical reality is a mathematical structure."

In fact, in his abstract he goes further to state that:

"Our physical world is an abstract mathematical structure."

Recall that he defines a mathematical structure as an abstract, immutable entity existing outside of space and time, being neither created or destroyed.

One would think that the conversation would terminate at this meta-physical point, but it does not.

So where do we go from here?

---Klingman analysis of Tegmark's theory of reality continued in next comment:

---Continuation of Klingman analysis of Tegmark's theory of reality:

Although I believe we are in the realm of religious argument, Tegmark makes a number of statements that appear to be recognition of potential problems in his argument, so we consider these next. I will list these problems below and then treat each one in detail [ER = external reality, MU = mathematical universe].

A. Other rational explanations than MU

B. Uncomputable ER

C. Embarrassing if TOE

D. Insufficiency - ER has properties not described by MU

E. Unpredictable ER

F. Non-observable MU

G. Non-consciousness MU

H. Unsymmetrical ER

The following comments will address each of Tegmarks potential trouble spots.

(A) Other rational explanations than MU

Tegmark says Wigner argued that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious", since "there is no rational explanation for it". Tegmark claims the MUH provides this missing explanation, since "I know of no other compelling explanation for this...than that the physical world is completely mathematical."

The Automatic Theory of Physics provides the rational explanation. In a nutshell, I describe the way that any set of measurements can be clustered to form a feature space and then entropy-based pattern recognition principles can derive 'physical laws'. The ability to derive mathematical descriptions, using only physical devices, from any set of physical observations (without baggage) provides the rational explanation Wigner and Tegmark are looking for. [An updated edition of The Automatic Theory of Physics should be available on Amazon shortly after these comments are published].

(B) Uncomputable External Reality

Tegmark says: "There are only two possible origins for random-looking parameters in the Standard Model Lagrangian like 1/137.0360565: either they are computable from a finite amount of information, or the mathematical structure corresponds to a multiverse..."

In 'Chromodynamics War' and elsewhere I derive the fine structure constant from straightforward equations, based on the simple assumption that there is a limit to the curvature of a field in space-time. In this theory the limit of curvature of the gravito-electric field produces black holes, and the limit of curvature of the gravito-magnetic field produces charged particles. The alternative is that there is no limit to field curvature, in which case every vortex will end as an infinitely dense 'point'. Our universe appears to exhibit more charged particles than infinitely dense points, so we assume the limit applies, in which case the fine structure constant falls out rather simply.

Tegmark first asks whether parallel universes are within the purview of science or merely silly speculation. I believe silly speculation, since they are by definition unobservable and not measurable. He then claims his Level 3 model of the multi-verse is the rather uncontroversial cosmological standard model. Uncontroversial it may be within a certain class of physicists, but it is nevertheless a meta-physical belief that differs not a whit from a Jesus-based or a flying spaghetti monster universe.

Anyone who has "evidence for" rather than "belief in" such a multi-verse should respond here.

---Klingman analysis of Tegmark's theory of reality continued in next comment:

---Continuation of Klingman analysis of Tegmark's theory of reality:

(C) Embarrassing Theory of Everything

Tegmark says a TOE must address Wheeler's embarrassing question:

"Why these particular equations, not others?"

My essay addresses this as follows: unless one believes, as Tegmark appears to, that math somehow exists 'outside' of space and time and yet derives the 'laws of (space-time) physics', then one must assume that the laws of physics are derived from the universe interacting with (operating on) itself.

Ask, as Tegmark and others do, why our laws of physics are so simple. My approach is the opposite of Tegmark's. He believes that the laws derive from mathematical structure outside of time and space. As I develop elsewhere, this idea of law is an anthropomorphic hangover from the 'King' and modern science has driven the king (God) concept out of physics, retaining only the king's 'laws'. I reject this anthropomorphism. I believe that the laws of physics are built into the universe, as did Wheeler. If we then start with one thing, the primordial field, then any law that the field follows must derive from self-interaction. That is, if we presume a mathematical operator, D, whose operation describes the evolution of the field (i.e., the universe) then the operation on the field G is described by D (dot) G while the interaction of the field G with itself is G(dot)G. If these are identical, then

D(dot)G = G(dot)G

This is our Master equation of the universe. It does not come from outside of space and time. Of course we do not know what form the operator D has, but it is not difficult in the real world to show that the Master equation is isomorphic to Newton's equation and hence we assume that D is the familiar divergence operator. This grounds us in reality.

Although Tegmark claims that, if a Theory of Everything is one day discovered, then Wheeler's embarrassing question remains: why these particular equations, not others? But Wheeler also claimed that the laws must be built-into the universe and NOT derive from outside of space and time. It seems clear that Wheeler would prefer the above approach to Tegmark's mathematical structure outside space and time.

Could there in reality be a fundamental, unexplained ontological asymmetry built into the very heart of reality, splitting mathematical structure into two classes, those with and without physical existence? Tegmark states that his theory implies that in his Level 4 multi-verse of 'all mathematical structures exist' as physical realities.

In fact, this question is only important for Tegmark's theory. If math is merely descriptive of real relations, then whatever math best describes physical reality is appropriate. Descriptions of non-physical relationships are still mathematical, but there's no 'ontological asymmetry' problem! The self-consistency of the physical universe is real, while the ability of this universe to mentally or logically construct limited 'truth systems' (limited by Godel) is simply a measure of the almost miraculous open-endedness of the universe.

But, to avoid this threat to his belief that mathematical existence and physical existence are equivalent, Tegmark concludes that, "In the context of the MUH, the existence of the level IV multiverse is not optional."

Yet our highly encoded Master equation allows us to derive both cosmology and particle physics (see essay). Instead of embarrassing, it is self-evident that built-in laws of physics MUST derive in this fashion.

(D) Insufficiency - ER has properties not described by MU

Tegmark states: "If...one could argue that our universe is somehow made of stuff perfectly described by a mathematical structure, but which also has other properties that are not described by it...then Karl Popper would turn in his grave, since these properties would make the universe non-mathematical by definition, having no observable effects whatsoever."

In his abstract and in his paper, Tegmark comments on human consciousness, and says his theory has implications for consciousness, but then he claims it is not necessary for a theory of physics. I do not agree with this claim. My FQXi essay exhibits the Master equation that describes our physical universe. The C-field described by this equation represents the field of consciousness, defined as awareness plus free will (volition).

Neither awareness nor free will is a mathematical structure--yet these properties have observable effects, watch me raise my arm.

---Klingman analysis of Tegmark's theory of reality continued in next comment:

---Continuation of Klingman analysis of Tegmark's theory of reality:

(E) Unpredictable External Reality:

Tegmark realizes that true randomness in the laws of physics would be a severe problem for his Mathematical Universe Hypothesis.

Since Darwin, people have been looking for schemes to which everything can be reduced. The Darwinian scheme depends on randomness, which basically means that things happen "for no reason at all". But this doesn't fit well into a 'structural' scheme, so Tegmark banishes randomness from his mathematical universe. In fact, "a convincing demonstration that there is such a thing as true randomness in the laws of physics...would therefore refute the MUH."

This is probably Tegmark's strongest statement concerning refutability, so it's worth expanding upon.

The essence of his argument is that if such randomness exists, then things 'happen' for no reason at all. And the essence of mathematics is that logic, through the concept of 'implication', provides a 'reason' (cause) for every happening. To examine this, we must bring 'consciousness' into the equation. This is legitimate since Tegmark, in his abstract, claims that the MUH has implications for consciousness, hence we assume that 1.) consciousness exists, and 2.) consciousness has implications for the mathematical universe.

In my FQXi essay, 'Fundamental Physics of Consciousness' consciousness is 'awareness plus volition'. In the simplest sense, awareness in its essence is 'built-in' to any multi-body physics.

Either two (or more) bodies are somehow 'aware of' each other and interact, or they do not. A physics of non-interacting bodies (free particles) is an interesting toy physics but is not sufficient for our reality. In the same sense, the essence of awareness is implied by observation. To observe something is to somehow be aware of it. The real trick is 'self-awareness', as described in Gene Man theory via the C-field, which both has mass (E=mc2) and is aware of mass. But this 'self-aware' field also acts on mass (see essay).

The combination of awareness and volition is consciousness.

There are those who declare volition (free will) to be an illusion. I don't argue with these zombies (their own technical term for this theory) as it does not describe my reality.

My reality is one of consciousness, and the most fundamental theory of consciousness (insofar as it can be described in 10 pages) is given in my FQXi essay, A Fundamental Physics of Consciousness.

In this theory volition replaces randomness as the source of unpredictability. Tegmark does not consider volition (free will) but does state that "A convincing demonstration that there is such a thing as true randomness in the laws of physics...would therefore refute MUH".

Because the essence of randomness ('for no reason at all') is unpredictability, then volition, as a randomness substitute refutes MUH. This is consistent with:

Consciousness gives rise to math.

Math does not give rise to consciousness.

ANY existence of free will is sufficient to refute Tegmark's MUH. So it boils down to whether Tegmark and his defenders are 'zombies', for whom free will is an illusion. If so, then MUH again descends to the level of religious claim, since proof for or against free will is not only lacking, but will likely always be lacking.

(F) Non-observable Mathematical Universe

Tegmark concludes that "MUH follows from ERH that there exists an external physical reality completely independently of us humans...the opposite of physics where human-related notions like observation are fundamental."

I confess to not understanding what he's talking about here, although I assume that he is addressing the Copenhagen interpretation of quantum mechanics, specifically, the collapse of the wave function. Else he is saying that the concept of observation does not even apply. In physics this means the measurement and recording of information from 'experiment'. If he is throwing this away, then he has left the realm of physics, not just humans. If aliens or other sentient entities do not in their appropriate way 'observe' (measure) the physical universe then "we're not in Kansas any more, Toto". So he must be referring to the collapse of the wave function above.

But as I state in my essay and elsewhere, there is a quantum interpretation that involves neither 'collapse' or 'many-worlds' and is compatible with reported non-dispersing Bohr wave functions and with entanglement.

(G) Non-conscious Mathematical Universe

Finally, I remark that in his abstract, Tegmark claims that MUH has implications for "broader issues like consciousness" but he never touches on these implications or even discusses consciousness, except to say in his notes that an understanding of consciousness is NOT necessary for a theory of physics. As far as a working theory goes, he is surely correct, but as far as ultimate physics (as in the recent essay contest) then he is almost certainly wrong. And since his theory that the physical universe is an abstract mathematical universe is certainly an ultimate theory, then he is inconsistent to a fatal degree.

---Klingman analysis of Tegmark's theory of reality continued in next comment:

---Continuation of Klingman analysis of Tegmark's theory of reality:

(H) Unsymmetrical External Reality:

Tegmark says: "...the Mathematical Universe Hypothesis implies that any symmetries in the mathematical structure correspond to physical symmetries..."

If this is the case, why are there no right-handed neutrinos? And why has QCD only approximate symmetry?

I also make the case that the non-symmetrical modified set of Maxwell's gravito-electro-magnetic equations, not his symmetrical set, describes reality. I suspect there are other examples, but these are a good starting point.

In 'The Chromodynamics War', chapter 114, 'Conservation or Symmetry?', I state that "conservation implies symmetry" whereas, since Noether, physicists have tended to believe that "symmetry implies conservation". Since "the MUH implies that any symmetries in the mathematical structure correspond to physical symmetries" I believe this is potentially proof that MUH is wrong.

Similarly, "Wigner and others have explained that to a large extent, symmetries imply dynamics". I believe it is more correct to say that conservation laws imply dynamics and conservation laws imply symmetry. But symmetry does not imply physically realized conservation laws.

Symmetry is a mapping, conservation is the real territory.

Maps derive from the territory.

Territory does not derive from maps.

This is the essence of the MUH mistake.

Thus on all of the points where Tegmark realizes there might be a problem, we show there is an alternate approach to the problem.

From the above, it may be apparent that I view the Mathematical Universe hypothesis as silly, and the logical response to this would be, then why do so many well known physicists seem to take MUH seriously. I discuss this below.

The Mathematical Universe begins with considerable attention being paid to the 'baggage' that the observer in physics brings to the party. This is supposedly banished by hypothesizing an external reality completely independent of us humans. One supposes that this is meant to banish 'consciousness' from the scene, although the only reason to even consider an 'external reality' is that we humans can agree that we observe (and are conscious of) the same objective phenomena.

This is followed by hypothesizing that 'mathematical structure' exists outside of space and time. This is surely just as legitimate as considering the universe to exist in the 'mind of God', but no more scientific. I do not believe in Tegmark's 'god', his 'mathematical structure'. Is there only one super-structure or are there Cartesian, cylindrical, radial, etc? I believe that mathematics is an artifact and have written several books demonstrating this point.

Nevertheless, let us ignore humans. Does this mean that there is no consciousness? Tegmark continually refers to birds and frog 'observers'. Is this baggage? Are they conscious? I think so. Can he, without consciousness, describe any universe with mathematics?

I can show Tegmark how to start with a physical world and derive math as an artifact. He has not succeeded in showing me how to start with math and derive a physical universe.

Existing in a physical universe, manifesting consciousness, he draws map after map after map, and claims, 'all is maps'. Aside from the declaration of equivalence, there is no explanation of how the physical universe comes to be. There is even less 'explanation' of consciousness.

He claims that a 'key prediction' of MUH is that physics research will uncover regularities in nature. I showed in 1979 and Science published in 2009 how automata can derive the equations of physics from observations. No MUH needed or implied.

Tegmark thinks resistance to his simplistic idea is due to 'vanity'. Not much of an argument.

In his abstract, Tegmark claims MUH has implications for consciousness, but his paper fails to address consciousness.

I believe that to discuss physical reality -- the very conception of which is based on conscious observation and awareness, whether this is called 'baggage' or not -- and to equate this reality to 'mathematical structure' (outside time and space) which is a figment of his consciousness, without any real consideration of the nature of consciousness, is missing the point. I agree with Penrose and others that any 'ultimate' physics must take consciousness into consideration.

My theory (sketched in my essay and expanded in 'Gene Man's World') begins with consciousness as an innate feature of the universe and derives the Master equation, the quantum flow principle, Newton's equation, Maxwell's gravito-electro-magnetic equations, and all known particles, as well as provides an inflationary force for cosmology.

My theory offers an alternative to Tegmark that explains far more without postulating any meta-physical entities such a 'mathematical structure' or 'parallel universes'. It does not depend on any undiscovered particles or principles, and it explains dozens of physical facts that are otherwise mysterious today.

And, most important, it predicts no new particles will be found at the LHC.

What does Tegmark predict?

---Klingman analysis of Tegmark's theory of reality continued in next comment

---Continuation of Klingman analysis of Tegmark's theory of reality:

There also appears to me to be 'practical' problems in his formulation. Let us assume for a moment that Tegmark is correct --- a mathematical structure is physically real:

Which mathematical structure 'is' the hydrogen atom?

A Cartesian structure?

A cylindrical structure?

An elliptical structure?

A radial structure?

A structure in some other coordinate system?

How do you choose, or are they all the same?

I once needed to evaluate an integral (representing a physics energy) by expanding it as an infinite series over 3 indices. Being young and gung-ho, I expanded it in all eight possible ways. Seven of these series were infinite, but one of the expansions truncated after a finite number of terms (all following terms contained a zero multiplier). Which of these eight structures 'was' the physical energy?

Tegmark mentions 'pi in the sky', which I take to be a reference to the Platonic belief that pi 'exists' somewhere outside time and space. I believe that the physical universe is so constructed that we can measure pi to an arbitrary number of places and compute it even further, but pi does not 'exist' as a mathematical structure.

Tegmark discusses the question "Is reality a computer simulation?"

Although my books on Computer Design and The Automatic Theory of Physics lead me to dismiss the 'universe as computer' arguments, I'd like to point out that it has been realized for decades that algorithms and data structures are merely tradeoffs of time for space. That is, one can save space at the expense of time by computing a value algorithmically, say the cosine of an angle, or one can save time by fetching the value from a (pre-computed) table of cosines at the expense of the 'space' required to store the table. As Tegmark says, "it (the universal computer) could simply store all the 4-dimensional data, i.e., encode all properties of the mathematical structure that is our universe. Individual time slices could then be read out sequentially if desired..."

This model cannot accommodate 'free will' and hence is only of interest to Zombies. The rest of us can dismiss this without looking any further. Please spare me the "it's an illusion" responses. If you believe that you have no free will, you shouldn't be arguing with real conscious beings.

Tegmark gives a convention for encoding any finite mathematical structure, involving arbitrarily many entities, as a finite sequence of integers. He also claims that infinite mathematical structures can be encoded as a finite-length bit string. I contend that these bit strings can be implemented in physical logic (silicon, rtc). Thus the physical universe, in and of itself, can produce any mathematical structure that Tegmark wishes to use. I can (and have) explained how one designs physical structures that instantiate mathematical structures. Can Tegmark explain how mathematical structures instantiate, ie, reify, physical structures?

It's important to realize that Tegmark is arguing meta-physics, not physics, and physicists who argue meta-physics can not automatically claim expertise or authority that they may have in other fields as applicable to meta-physics. However Marcel-Marie LeBel's essay in the last FQXi contest, "Physics Stops Where Natural Meta-physics Starts", makes a beautiful case for logic as a natural meta-physical requirement.

The question is, is physical behavior logical? And, if so, does this imply an abstract realm of logic, or is logic simply 'abstracted from' reality?

By creating real structures that (always!) implement logic one can show that the physical universe is logical in its behavior; to counter this, one must create an illogical physical structure. Via the use of logic circuits, one can then create mathematical machinery, of which counters are the most elemental, with adders, subtracters, and comparators at an equivalently basic level. Per Kronecker, all of mathematics arises from these physical structures.

Thus one can demonstrate that math arises from physical reality. How will Tegmark demonstrate that physical reality arises from (is) math?

This is so simple. Why do a significant (greater than zero!) number of physicists have difficulty grasping this fact?

---Klingman analysis of Tegmark's theory of reality continued in next comment

---Continuation of Klingman analysis of Tegmark's theory of reality:

If it's so simple, why do a significant (greater than zero!) number of physicists have difficulty grasping this fact?

My guess is as follows. Math, since Plato, has existed in the minds of man, and the conscious mind has been the ultimate mystery. When Newton and Leibnetz invented calculus, they increased the power of logical description tremendously. Because physical reality behaves logically, the logical mental models (math) corresponded sufficiently well that, in some sense, the logical behavior of the model could be pushed further than physical experiment had gone, and thus the math 'predicted' physical behavior, found to be true when experiment pushed reality as far as the model had been pushed. This is a consequence of physical reality being logical in nature.

Centuries after Newton and Leibnetz invented calculus, most new physicists tend to feel that they had 'discovered' calculus, as if it had always been there, (outside of space and time) implying pre-existence. Considering the confusion of most physics students, faced with learning mechanics, optics, acoustics, thermodynamics, quantum mechanics, and sophisticated math tools, it's not surprising that the young physicist is confused.

But Tegmark is not a young physicist, and the Platonists who have entered essays on FQXi are not young. What explains their Platonic beliefs?

As a graduate student I chose the smartest adviser I could find, and was surprised to find that he had no idea at all how computers worked. I'm sure this has changed significantly, yet theoretical physicists are not typically computer designers, and so have less feel for how logic is implemented in the real world, whether silicon, protein, or neural networks. In addition, even fewer have more than a fuzzy understanding of consciousness, yet without consciousness how does one consider meta-physical aspects of mathematics?

Another factor concerning Platonism: For almost a century physics has been based on 'point' particles and 'fields' (as many as needed!) and after convincing oneself that a 0-D point has reality, it's not much of a stretch (pun intended) to believe a 1-D string has reality, and then that reality has 26 dimensions (or so). As I explain in great detail in 'The Chromodynamics War', the belief in 'electric-analog' colors as opposed to Rutherford's 'magnetic-analog' strong force has resulted in QCD not making any physical sense at all. And the confusion from Noether's results (symmetry implies conservation rather than conservation implies symmetry), combined with required techniques of particle physics, (looking at 'points' from 'infinity') led to symmetry and gauge theories. The net effect is that theorists have absolutely no physical feel for ultimate particle interactions but unlimited mathematical tools to explore them.

As a result of this history, physicists have no physical understanding of particle interactions, treating them as 'fields' in Lagrangians. For every new phenomena requiring explanation, physicists propose another 'field'. No one knows how many or even which fields are real and the tools don't care. The math has become more real than reality to them, and their prestige comes from mathematical sophistication, not from physical explanation.

Yet Alfred Korzybsiki's definition of sanity, in essence, is the ability to distinguish the map from the territory.

To actually conceive that the map gives rise to the territory illustrates the total confusion reigning in physics today. I expect that failure to find the Higgs or any other of the proposed particles will cure this by forcing at least a few physicists to investigate a theory that does make physical AND mathematical sense -- a reality that is logically self-consistent and answers many questions that today are simply mysteries.

The above arguments separate into two classes, those dependent upon consciousness, and those dependent on 'non-conscious' physical reality. For discussions of consciousness I have assumed that my essay, 'Fundamental Physics of Cponsciousness', is correct. This will surely be challenged by tegmark's defenders. Knowing this, I still believe that presenting an alternative explanation is better than simply arguing against MUH. But the 'physico-logic' arguments above do not depend upon my theory. They are easily demonstrated. To repeat:

I can demonstrate that math arises from physical reality. How will Tegmark demonstrate that physical reality arises from (is) math?

Edwin Eugene Klingman

Lawrence,

Looking forward to it. By the way, the algebra of observables is non-associative (but power associative).

Also I have just discovered this paper: http://www.dinahgroup.com/content/jglta/v2_n4_2.pdf and it seems that I was right to speculate that lack of associativity implies hidden unobservable states. This in turn means that the Born rule is broken as well. I will need some time to digest this paper.

Hello dear Mr Klingman ,

I liked a lot reading your posts here .Thanks for this relevance .

It is well sais these words"Yet Alfred Korzybsiki's definition of sanity, in essence, is the ability to distinguish the map from the territory."

Like what the topology is essential .

Best Regards

Steve

Florin,

I have read some papers by Vladimir Dzhunushaliev on nonassociative quantum mechanics. One can interpret equation 3.1 as an associative ordering on channels determined by an S-matrix. Since the associator returns the set of states with a sign change

[φ_i, φ_j, φ_k] = φ_i(φ_jφ_k) - (φ_iφ_j)φ_k = C_{ijk}^lφ_l = -φ_i(φ_jφ_k)

nonassociative structures imply a phase ambiguity in a Taylor expansion. So this is an indication of shadow states or something similar in the S-matrix.

He does appear to be saying that the Born rule needs to be generalized in some fashion. I will try to return to this later today, maybe after I have fully read this paper.

Cheers LC

Dear Lawrence,

Have you seen this article? Quantum Criticality in an Ising Chain

The golden ratio 1.618 is based on the geometry of the pentagon. It is funny that speculators are proposing that this is experimental evidence for Lisi's E8 TOE when Lisi never specified the E8 pentality symmetry (that I've been talking about for months). This is the kind of experimental evidence that El Naschie could use to further his claims of E-Infinity (order of 685~(10*1.618*1.618)^2).

This gives me hope that I'm on the right path pursuing the pentagonal Spin(5)~Spin(4,1). I think a transition occurs that changes the system from a hexagonal Spin(6) tiling to a buckyball tiling composed of hexagonal Spin(6)'s and pentagonal Spin(5)'s.

Have Fun!

Ray

Double-triple thanks for this. I heard D. A. Tennant interviewed on NPR the other day, and spent time trying to look for this. And here it is, and I am an AAAS member, but hand not checked my AAAS email.

I really am going to try to get to the nonassociator quantum mechanics, maybe tonight.

Cheers, LC

Here is an overview of nonaxxociators and what might be called quantum homotopies.

The ordered S-matrix defines each vertex, or particle, and its neighbor. In a linear chain a general state is an S-matrix channel of the form

|φ) = |p_1,..., p_i,..., p_j ,..., p_n)

This state or S-matrix channel is related to but distinction from the channel

|φ') = |p_1,..., p_j,..., p_i,..., p_n).

The particles or vertices p_i and p_j have been exchanged, and a certain "relationship" structure to the amplitude has been fundamentally changed. The S-matrix is written according to S = 1 - 2πiT, so two states or channels |p_1,...,p_n) and |q_1,...,q_n) are related to each other by the S-matrix as

(p_1,..., p_n|S|q_,...,q_n) = (p_1,..., p_n|(1 - 2πiT)|q_1,..., q_n)

= (p_1,..., p_n|q_1,...,q_n) - 2πi(p1,..., p_n|T|q_1,..., q_n)

For the (-| the in channel and |+) as the out channel p_n and q_1 are neighbors, and are neighbors through the T-matrix. This eliminates an open vertex in the chain. The vertices or particles p_1 and q_n are the open elements in the chain and defines the "anchor" for the chain, and are thus defined as neighbors in this manner. Hence this process defines a complete linear chain, which is similar in its structure to a gauge-"Moose," which is a cycle of gauge fields on a compactified space, such as a Calabi-Yau space. Each element pi defines a particle or vertex according to a set of quantum numbers. Thus each p_i is defined by a vector space V , which is some Hilbert space. The linear chain here is an ordering on a total Hilbert space H = ­\otimes Vi. This construction is based upon relationships between p_i and p_{i+1} by bilinear operation of the form [-; -] :V x V - -> V , as a product structure for position exchange. To define physical states this bilinear operation must obey the Jacobi identity. This requires the vector space be k-equipped so the bilinear operation is an isomorphism on the vector space H = k x V, where the modulus |k| is the number of elements in the chain. This gives the isomorphism,

Y:H x H - -> H x H

Y((x; p) otimes (y; q)) = (x; p) otimes (y; q) + (1; 0) otimes (0; [p; q]):

The application of Y otimes id on H x H x H then gives

Y otimes­ id((x; p) otimes (y; q) otimes (z; r)) = (x; p) otimes (y; q) otimes (z; r) +

(1; 0) otimes (0; [[p; q]; r] + [[q; r]; p] + [[r; p]; q]):

This isomorphism on the three spaces is the Yang-Baxter equation. If the permuted double commutator sum vanishes, which is the Jacobi equation. The elements p; q; r as momentum operators D = ∂ + iA, defines Jacobi identity the conservation law

cycle[[D_a, D_b], D_c] = ε_{abcd}D_eF^de = 0:

The Yang-Baxter relationship is defined in the S-matrix by the following observation. Consider the optical theorem S = 1 - 2πiT and the projection of the density matrix according to

Ρ' = SρS^† = ρ + 2πi[T, ρ],

The neighborhood rule tells us the commutator is between elements of the |-) and the (-| with regards to the transition or T-matrix, which is a neighbor exchange rule. The Yang-Baxter equation describes braids, which are compositions of paths. In general this theory must be extended to compositions of loops. The S-matrix acts upon a loop composed of (-| and |-) to define the composition of two loops (-|-) with 2π(-|T|)i. Homotopy is the mathematical theory for loop topology. For a topological space (X; p) the loop space ΩX is defined by the continuous map

φ:[0; 1] - -> X,

with the compact open-set topology on the endpoints φ(0) = φ(1) = p. Here the vertex or particle p is considered to be the base point of the map. The composition or multiplication of points obeys the rule,

π_1 - -> ΩXxΩX1 - ->ΩX,

Higher homotopies exist for spaces with larger dimensions, where the ordering of homotopies determines the vertices of associahedra. A braid is a (ab) ¡ (ba) edgelink, and an associator is a(bc)¡a(bc) for fields defined on the vertices . The associators with three elements define two hexagons, which link vertices in associator by commutation of the elements in parentheses. Braid links between the commuted vertices defines the general system of associators plus commutators. The associahedra K_4 for four elements is a pentagon. In three dimensions the Stasheff polytope K_5 or associahedra. This polytope is constructed from pairs of three hexagons glued into "tents," which are then attached to form a solid with three squares arranged π/3 radians from each other. This polytope may also be constructed by gluing two tetrahedra together and truncating the vertices in the same plane. Similarly, to the system with three letters copies of these associator exist with commutative links between vertices.

A system of commutators and associators is extended to the K_4 pentagon of associators. At each vertex of the above pentagon with associators for the elements a; b; c; d has six possible commutator variations. This each pentagonal vertex is identified with a hexagon, for a net 30 independent vertices. The convex polyhedron with 12 hexagons, which share a vertex with an adjacent hexagon, and possesses a pentagonal symmetry is the truncated icosahedron: The K_4 elements are mutually related by a braiding (commutation) around alternate hexagon, half of the twelve in total, and are connected by cross links through the polyhedra. This obeys the icosahedral group as an octahedral with quivers of vectors at each vertex. The octahedra has Im(5); m = 3 group structure, which does not tessellate a flat three dimensional space, but will tessellate a hyperbolic space in three dimensions. The four dimensional extension of this is the 120-cell, called the hyperdodecahedron or dodecachoron, which is a polychora with 120 octahedron boundaries, 720 pentagons, 1200 edgelinks and 600 vertices, and Schl¨afli index {5, 3, 3} . The dual is the 600 cell, with 120 vertices which define a group under quaternionic multiplication. This group is sometimes called the binary icosahedral group, which is a double covering of the icoshahedral group. The symmetry group of the 600-cell is the Weyl group H_4 ~ {3, 3, 5}, a group of order 120^2 = 14400.

Cheers LC

Dear Lawrence,

WOW! It will take at least a week for me to digest this information, but everything seems to be coming together.

You said "Higher homotopies exist for spaces with larger dimensions, where the ordering of homotopies determines the vertices of associahedra. A braid is a (ab) ¡ (ba) edgelink, and an associator is a(bc)¡a(bc) for fields defined on the vertices . The associators with three elements define two hexagons, which link vertices in associator by commutation of the elements in parentheses. Braid links between the commuted vertices defines the general system of associators plus commutators. The associahedra K_4 for four elements is a pentagon. In three dimensions the Stasheff polytope K_5 or associahedra. This polytope is constructed from pairs of three hexagons glued into "tents," which are then attached to form a solid with three squares arranged π/3 radians from each other. This polytope may also be constructed by gluing two tetrahedra together and truncating the vertices in the same plane. Similarly, to the system with three letters copies of these associator exist with commutative links between vertices."

This looks like the permutohedron of type A3. I want pentagons with a triality symmetry, so I'm thinking more like a dodecahedron (H3 - has the basic triality and pentality symmetries, but doesn't explain hexagons morphing into pentagons) or a Carbon-60 buckyball.

I've been trying to get rid of a cold for the past week. I need a clear mind to focus on these ideas.

Have Fun!

Ray

Dear Lawrence,

Thanks for the information. It will take some time to fully digest it though.

Thanks again,

Florin

The business of quantum homotopies might feed into the idea of E_∞, by El Naschie. I must confess at this point I don't know what is meant by this. Yet the question did occur to me whether E_8 has some Bott periodicity structure. We might think of there being 3 SO(8)'s in there, and these have certain structure involved with Lim_{n->∞} SO(n), with Z and Z_2 homotopies and with cyclicity of 8. I studied this in depth years ago, so maybe with some review I might be able to think about this some.

Cheers LC