For a Final total TOE, it must consist of, at least, three pillars:

One, physics-TOE

Two, life-TOE

Three, math-TOE

It must arises from a single FIRST PRINCIPLE.

And, it must make contact to ALL known facts (not theories).

This criteria is simple enough and is verifiable by every street walking person.

**Section one: the philosophy**

Wigner (in a 1969 essay) argued that {“the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious”, and that “there is no rational explanation for it”.}

Wigner’s statement shows the current status of math which has a BASE totally disjoined from NATURE. The modern math INVENTed a set LANGUAGEs and plays a language game internally. Language by definition is recursively defined and is a machine for producing paradoxes and riddles.

Furthermore, the key point here is that the math-universe is a multiverse, with infinite many sub-universes while THIS physical universe is unique with many known attributes: nature constants, Planck CMB data, SM particle zoo, etc.

So, the key issue here is that:

One, is math ONLY as a great tool and language for describing physics? Or,

Two, {math universe} is totally isomorphic to the {physics universe}, the total universal structural realism.

Or, three, THIS unique physical universe of ours is just a happenstance in the physics-multiverse.

The answer from nature is {Two}, and this was the key point in the book {Super Unified Theory, US copyright TX 1-323-231} which describes this issue with three Chapters:

Chapter Seven – Colored numbers (page 53 – 61)

Chapter Eight – Chromology (page 62 – 69)

Chapter Nine – Unilogy (page 70 – 74)

Some of discussions of this issue were also post online over 20 years ago, see,

Unification of physics and mathematics, http://www.prequark.org/Mlaw.htm

and, Law of Creation, http://www.prequark.org/Create.htm

As the criteria is that all these three TOEs must arise from a single ‘First Principle’, there is no way to prove that the third TOE (math) is correct if we cannot show the details of two other TOEs. Thus, I will show the validity of math-TOE by showing the two other TOEs first.

**Section two: physics-TOE**

One, the first principle: {The essence of THIS universe is ‘NOTHINGNESS’, and it must remain to be nothingness}

Two, definition of ‘nothingness’: {timelessness and immutability}

Three, manifestation of timelessness: at every t, it must be ‘timelessness’ in essence.

Four, the equation of this ‘timelessness’: {Delta S = (i^n1, i^n2, i^n3) x C x Delta T} … Equation zero

S, space; T, time (real); C, light speed. (n1, n2, n3) take the value of {0, 1, 2, or 3}

Five, Equation zero generates 48 SM fermions, see http://prebabel.blogspot.com/2012/04/48-exact-number-for-number-of.html

Six, the manifestation of ‘immutability’: via Ghost-rascal, see http://prebabel.blogspot.com/2014/02/ghost-rascal-conjecture-and-ultimate.html . Again, it generates 48 SM fermions.

Seven, the manifestation as force(s):

F (unified) = K*ħ/ (delta S*delta T), K is a coefficient constant … Equation one

This force (gravity) has two parts:

First, it moves the entire universe from {[here (now), now] to [here (next), next]}, and it causes the expansion of universe with acceleration.

Second, every individual particle interact with ALL particles in this universe via the {Real/Ghost symmetry}, with the strength measured with Newton’s gravity equation (distance is measured in the world (real) sheet).

See http://www.prequark.org/Gravity.htm

This physics-TOE has the following consequences:

Consequence one: universe expands with acceleration. See, http://prebabel.blogspot.com/2013/11/why-does-dark-energy-make-universe.html

Consequence two: uncertainty principle is the emergent of Equation one.

Consequence three: calculation of Alpha

See https://www.linkedin.com/pulse/totally-blind-deaf-googlefacebookblogosphere-era-jeh-tween-gong

Consequence four: calculation of Planck CMB data

See, https://tienzengong.wordpress.com/2015/04/22/dark-energydark-mass-the-silent-truth/

Consequence five: calculation of Cosmology constant, see https://tienzengong.wordpress.com/2016/04/24/entropy-quantum-gravity-cosmology-constant/

Consequence six: the Hierarchy problem

See https://medium.com/@Tienzen/why-making-something-easy-so-difficult-aae8e3715b6d#.6ko3u5dlf

Consequence seven: the physics-TOE,

See https://tienzengong.wordpress.com/2016/01/18/the-final-toe-theory-of-everything/

**Section three: life-TOE**

The highest EXPRESSION for life is {intelligence and consciousness}.

One, definition of ‘intelligence’:

Necessary condition: there is a ‘counting’ device (counting strews, abacus or Turing computer).

Sufficient condition: the ability to distinguish self from others.

See http://www.prequark.org/Biolife.htm

Two, definition of ‘consciousness’:

Necessary condition: the ability to distinguish self from others.

Sufficient condition: there is a ‘counting’ device (counting strews, abacus or Turing computer).

More about this ‘Theorem of Consciousness’, see Metaphysics of Linguistics, http://www.chinese-word-roots.org/cwr018.htm .

Now, intelligence and consciousness are SEEDed in physics. Yet, the utmost EXPRESSION of life has a structure as a topological torus, having 7 color-codes.

With embedded intelligence and consciousness, life evolves INTELLIGENTly, see DEATHS OF TWO GODS, https://tienzengong.wordpress.com/2016/04/20/deaths-of-two-gods/ and, INTELLIGENT EVOLUTION, https://tienzengong.wordpress.com/2014/10/11/intelligent-evolution/ .

With {intelligent evolution}, life-TOE is complete, and it unifies with the physics-TOE.

**Section four: the math-TOE**

There are three key points for the current mainstream math:

One, number line has the cardinality of continuum; that is, between any {two points}, there are ‘infinite’ numbers between them.

Two, there is ONE ‘number’ for each ‘point’ of the number line.

Three, Continuum Hypothesis is undecidable.

On the other hand, this math-TOE must have the followings:

One, number line has the cardinality of continuum; that is, between any {two points}, there are ‘infinite’ numbers between them.

Two, there are at least ‘TWO’ numbers for each ‘point’ of the number line. This is the key for the math-TOE.

Three, Continuum Hypothesis is false. I will not prove it here in a traditional way but will give an example (the bridge between two cardinalities).

First, we should renormalize the Godel’s incompleteness to regain the completeness in TOTALITY, see http://www.prequark.org/Create.htm . More detailed discussion is available at http://www.prebabel.info/lifesys.htm , completeness is regained in life-system via a renormalization process.

See http://www.prebabel.info/lifesys.htm

Second, there are at least two NUMBERs in each number-line POINT.

In the above graph, the ‘X’ point is the point A = 0. The point B is a moving point. When B moves to ‘X’, B = 12. That is, the point ‘X’ in fact has two numbers (0, 12).

Third, Continuum Hypothesis is false; there is a bridge between two infinities.

See http://www.prebabel.info/newmath.htm

Fourth, more entanglement:

One: 1/3 = 1/2 – 1/4 + 1/8 – 1/16 + 1/32 – 1/64 + 1/128 – 1/256 + 1/512 – 1/1024 + 1/2048 -… +…

For 1/3 (with an odd number as the denominator), it can only be “reached” with the sum of a sequence of numbers with only the even numbers as the denominators, see http://prebabel.blogspot.com/2011/05/source-of-spontaneous-symmetry-breaking_13.html and http://www.prebabel.info/newmath.htm

Two: prime numbers cannot be reached via multiplication with nature numbers.

Three, Fermat’s last theorem: the sum of two nature number cannot be reached via the same algebra operation.

Each point (number) is in fact entangled with (or reachable by/from) infinite number of other numbers. For example, 3 is linked to 1/3, {3^n, integers}, {3 ^ (-n), irrational}, etc.

This ‘number entanglement’ is the base for the third cardinality.

Fifth, the ‘HOLE’ point contains infinite number of geometrical points.

See http://www.prequark.org/Create.htm

With the above, we can reconstruct the NUMBER line as follow:

One, with the “number entanglement’, there are three cardinalities: countable, uncountable, the bridge (pseudo-uncountable).

Two, there are three ‘zeros’, in correspondence to the three infinities.

0 (c) = 1/countable

0 (u) = 1/uncountable

0 (p) = 1/pseudo-uncountable

Three, every POINT on the number line has three different NUMBERS.

4 + 0 (c) = C4

4 + 0 (u) = U4

4 + 0 (p) = P4

Yet, these three different ‘4’ cannot be distinguished algebraically or by any known math operations. That is, for some numbers A < > (not the same as) B, {A – B = 0}.

Now, there are two theorems:

Theorem 1: between two ‘points’ of number line, there are infinite ‘numbers’.

Theorem 2: between two ‘numbers’, there could have either infinite or finite numbers.

Four, this ‘number entanglement’ does show up by having three different kind of numbers:

First, with countable digits, such as 3 = 3.0000… (the c-number).

Second, with uncountable digits, such as Pi = 3.14… (the u-number)

Third, with pseudo-uncountable digits, such as 2 ^(1/2) = 1.414… (the p-number)

Five, with a seed number {1}, we can construct the entire number line (including three infinities) with a 7-color code system.

See http://www.prequark.org/Fermat.htm

**Section five: The map of Final TOE**

I have constructed the physics-TOE from the first principle together with two manifested equations, as below.

The first principle: {The essence of THIS universe is ‘NOTHINGNESS’, and it must remain to be nothingness}; definition of ‘nothingness’: {timelessness and immutability}

{Delta S = (i^n1, i^n2, i^n3) x C x Delta T} … Equation zero

F (unified) = K*ħ/ (delta S*delta T), K is a coefficient constant … Equation one

At this point, there is seemingly a major difference between math and physics.

Physics manifests IN time/space (the equation zero), and thus it is constrained in Energy (an expression of space/time). Thus, physics universe is a FINITUDE.

On the other hand, math manifests IN nothingness {the union of zero(s) and infinities)}.

Thus, the evolution of math has no physical constrain and can have infinite expressions while physics universe is unique (no multiverse). The physics-multiverse is denounced at here, http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html

While math evolution can lead to multi-math-universe (arbitrary constructions, such as the Grassman, Quaternion and Octonions numbers), its BASE (the basic lego pieces) is totally NATURE (total Platonism: basic math lego pieces are timeless entities, independent of the physical world and of the symbols used to represent them.) while the human-math is all about the ‘construction’ of ‘structures’.

As the Continuum Hypothesis is undecidable in the set theory, it is valid to select a third cardinality as a new axiom. But, no. This third cardinality is not a humanly selected axiom but is a part of nature’s math basic lego pieces. The reason for the insistence of this is that it is the only way to DERIVE the physics universe from math-universe.

By knowing the difference between the two, the only way to DERIVE the physics universe from math-universe is by transforming infinities into FINITUDE (same as creating something from nothing).

In math universe, the finite numbers are produced by the INVERSE operation of infinities. Yet, transforming infinites into physics-universe (a finitude), they (infinities) must be transformed into CONCRETE objects. And, this was done with two Platonic equations.

One: 1/3 = 1/2 – 1/4 + 1/8 – 1/16 + 1/32 – 1/64 + 1/128 – 1/256 + 1/512 – 1/1024 + 1/2048 -… +… (trisecting an angle, taking countable steps); countable infinity is now transformed into a concrete object (A: angultron, a trisected angle)

Two: pi / 4 = 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + 1/13 – … + … (with “countable” infinite steps to reach ‘uncountable digits’); uncountable infinity is now transformed into a unit circle (which gives rise to space/time equation zero; the 64 subspaces: 48 fermions and 16 dark energy).

See, http://www.prebabel.info/newmath.htm ,

http://prebabel.blogspot.com/2011/05/source-of-spontaneous-symmetry-breaking_13.html and

http://prebabel.blogspot.com/2011/05/source-of-spontaneous-symmetry-breaking_11.html

That is, the math-universe (infinities) gives rise to the physics-universe. Of course, I will give more evidences to show this point.

One, the generalization of a circle is elliptic curve, and the fermion is described with elliptic curve.

See https://tienzengong.wordpress.com/2016/03/16/nothingness-vs-nothing-there-the-quantum-gravity/ .

Two, In addition to this {infinite to finitude} transformation, the key essence of these two equations is the {number entanglement: odd numbers can only be reached by even numbers, and vice versa}. This number entanglement is also the source for quantum (gravity) entanglement.

The essence of the math-universe to physics-universe transformation is all about infinities and the pathways of their concretization. That is, the key equation is,

A – b = 0, but A is not b.

This means that most of numbers are unreachable by finite means (arithmetic and algebra operations), as every *finite* number is the concretization of infinities, and it does carry a tail with infinite digits. That is, for any selected number *A*, it is surrounded by zillions (at least two) neighborhood numbers which are not distinguishable from the number *A* by all means. Thus, all those unreachable (indistinguishable from the number *A*) numbers must be color-coded, such as, b = A (red), = A (blue) or = A (green), etc.; that is, A (x) – b = 0.

Yet, there is always a number C, and

A – C > 0

The largest C cannot truly be determined with finite means. But, in principle, there is always *a* largest C in the physical universe *with* finite means (by measurement). That is,

A – C = g

Although we do not know the exact value for g, g is larger than 0 (g > 0). In the math universe, g is un-determined and can approach the concept of *continuity*. Yet, in the finite (physical) universe, this g becomes the smallest *deterministic unit*, distinguishing the number *C* from the number *A*. Indeed, for the *physical* universe, the g can actually be determined. Let,

X-axis as space, thus, the (delta S > =g).

Y-axis as momentum, the (delta P >= g).

So, (delta P) x (delta S) >= g^2

In physics, the photon is the medium for causality (see Constants of Nature, http://www.prequark.org/Constant.htm ). Thus, the smallest *deterministic* unit (for causality) in the physical universe is (photon / c), c is the light speed. That is, in the physical universe, g^2 = (photon / c).

Yet, photon is the result of the interaction of e (electron).

So, g^2 = (photon /c) = (e^2/c), e is electric charge.

In the article “The Rise of Gravity and Electric Charge, (http://www.prequark.org/Gravity.htm )”, the e-charge is,

e (charge) = (L * C)^(1/2) = [(1/2) ħ * C]^(1/2); L the angular momentum, C light speed, ħ (Planck constant).

So, g^2 = ħ * C / C = ħ,

Thus, (delta P) x (delta S) > = g^2 >= ħ

Now, the uncertainty principle of physics is the direct consequence of the *Nature math*, the essence of infinities and of unreachable of numbers (the number entanglement), see http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html

With this *derivation*, this new paradigm is fully verified. Yet, there is one very important additional point. That is, this major essence of the *unreachable numbers* is swept away in the human math by the concept of *continuity*. That is, the human math is completely unaware of this *Nature math*.

Three, this {number entanglement} is also the source for Fermat’s last theorem and abc-conjecture, and they are closely related to the elliptic curves. Fermat’s Last Theorem was proved by using elliptic curves but still not knowing the essence of the theorem: the entanglement caused by the colored numbers. In fact, this colored number is the SOURCE for the Fermat’s last theorem, see The Philosophical Meanings of Fermat’s Last Theorem, http://www.prequark.org/Fermat.htm .

Four, topologically a complex elliptic curve is a torus (can be defined with 7 color-codes) which is the BASE for consciousness via the Theorem of consciousness (Ringel-Youngs theorem).

**Section six: conclusion**

**One: Physics TOE**

**First principle**: {The essence of THIS universe is ‘NOTHINGNESS’, and it must remain to be nothingness}; definition of ‘nothingness’: {timelessness and immutability}

Consequences:

First, Nature constants: Cosmology constant (https://tienzengong.wordpress.com/2016/04/24/entropy-quantum-gravity-cosmology-constant/ ), Alpha = (1/137.03599…), etc.

Second, Planck CMB data (DE=69.22 % 、D=25.90 % 、V=4.86 %)

Third, expanding universe with acceleration

Fourth, SM fermion zoo

See, http://prebabel.blogspot.com/2013/11/why-does-dark-energy-make-universe.html , https://tienzengong.wordpress.com/2015/04/22/dark-energydark-mass-the-silent-truth/ and http://prebabel.blogspot.com/2012/04/alpha-fine-structure-constant-mystery.html

**Two: Math-TOE** — First principle in math as {nothingness = 1/infinit(ies)}

Consequences:

First, {colored number/number entanglement: 0 (c) = 1/countable; 0 (u) = 1/uncountable; 0 (p) = 1/pseudo-uncountable} with 7 colors {1, c-numbers, p-numbers, u-numbers, countable, uncountable, pseudo-uncountable}.

Second, Fermat’s last theorem, ABC conjecture, etc.

Third, describing physics TOE

Fourth, as a base for life TOE

Math-universe is built up with arbitrary constructions by using a “lego base”, but this **{Lego Base} is not a construction but is totally nature**, expressed from the {First Principle} which gives rise to physics-universe too.

**Three: Life TOE** — Intelligence + Consciousness

First, definition of ‘intelligence’:

Necessary condition: there is a ‘counting’ device (counting strews, abacus or Turing computer).

Sufficient condition: the ability to distinguish self from others.

Second, definition of ‘consciousness’:

Necessary condition: the ability to distinguish self from others.

Sufficient condition: there is a ‘counting’ device (counting strews, abacus or Turing computer).

See http://www.prequark.org/Biolife.htm

**Four**, on a deeper level, physics TOE is derived from math by concretizing infinities.

Five, physics/math/life are totally unified.

See http://www.prequark.org/Create.htm

Note 1: in 2014, Max Tegmark published a book “Our Mathematical Universe” which promotes an idea of {the mathematical universe hypothesis (MUH)} with the central point as: {Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and “in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically ‘real’ world”.} His key idea is similar to mine but with the following giant differences.

One, Tegmark does not and did not know any physics-TOE; so, his idea is just a philosophy, no way to unify physics and math.

Two, this math-TOE is totally based on the colored numbers (the third cardinality) and the number entanglement, and Tegmark does not have any idea of these.

Three, Tegmark reached his conclusion for multiverse from two confusions:

First, (1/Alpha) is not computable, at least not in countable steps, and this is absolutely wrong.

Second, that there are unlimited (if not infinite) math-structures in comparison to a unique physical universe. In my math-TOE, math and physics have the same BASE lego set while physics manifests in the arrow of time (being constrained by energy) while math manifests in the essence of nature (the timelessness). The multiverse bullcrap is denounced in the article {Multiverse bubbles are now all burst by the math of Nature, http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html }.

Note 2: this article is written as a part of presentation {(Modeling universe by G-string theory) at “Strings 2016 (http://ymsc.tsinghua.edu.cn:8090/strings/ )” held at Tsinghua University, Beijing China (from August 1 to 5, 2016)} and will be handed out as handout at {The 7th International Congress of Chinese Mathematicians (ICCM 2016), held from Aug. 6 to Aug. 11, 2016 in Beijing} by my colleague Dr. Li xiaojian (Professor of North China University of Technology, Beijing, 100144, China).

**Note added on August 7, 2016 (after the new LHC 2016 data was released):**

My Protégé Dr. Li xiaojian (Professor of North China University of Technology, Beijing, 100144, China) discussed “The Final Total TOE” with Dr. David Gross (Nobel laureate) on August 5, 2016; see photos below.

“The Final Total TOE” was presented at {Strings 2016 conference (http://ymsc.tsinghua.edu.cn:8090/strings/ )} held at Tsinghua University, Beijing China (from August 1 to 5, 2016), by my Protégé Dr. Li xiaojian too. The key points of this presentation is available at https://tienzengong.wordpress.com/2016/08/01/the-final-total-toe-theory-of-everything/ .

**Note (added on August 29, 2016):**

The current (2016) mainstream physics status is this: #PostCheckmateTTF (Post Checkmate temper tantrum fit).

See https://tienzengong.wordpress.com/2016/08/26/vision-eulogy-the-post-checkmate-temper-tantrum-fit/

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**Copyright © August 2016 by Tienzen (Jeh-Tween) Gong**

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