The Dot, the Point, the Dot — the Intention by Arved C. Huebler

Dear Arved Huebler,

thank you also for your reply.

If mathematics has evolved from some empty set, at first glance it seems as if the rest of mathematics follows necessarily. The latter should be indeed true, because otherwise one couldn't trace it back to its origin - namely to the empty set. But what does this demand of necessity imply? For me, it implies that the empty set somehow contains already the whole of mathematics. But this would mean that mathematics didn't evolve, but was already hidden in the empty set. This would further mean that the empty set is not really an empty set, but could be identified with the whole of mathematics. Surely, mathematics could also have been arisen out of the blue and once it exists with its main properties (namely being a network of necessary relationships between its consituents), these relationships must be considered as necessary.

But let's prove this a bit more in detail. Think about the number Pi. In the case of mathematics having evolved out of an empty set, its value 3.14159... is not a necessity, it could well be 4.14159... or any other string of digits. Because, as outlined above, necessity implies that the whole of mathematics exists already hidden in the empty set. Surely, if the value of Pi would be different from our known value, all the other mathematical relations also had to be other than they are to guarantee the consistency of maths and/or the consistency with our physical theories. The question here is how the value of 3.14159... comes about, if there is no maths around in an empty set. If this value is logically necessary, on what basis other than on the relation between the circumference and the diameter of a circle does it 'emerge'? If true, how did this circle have been emerged from an empty set? But if the existence of circles and alike are not logically necessary, what has determined their shape and values? It cannot be mathematics itself, because from the point of view of an empty set, there is no maths around anyhwere other than potential being (of some kind). So it seems to me that in both cases, the necessity of such mathematical values or their sheer 'randomness', their has to be some kind of existence beyond mathematics which has determined such values, either intentionally and / or by necessity, or randomly. The same is valid for the existence of circles and all kinds of geometrical shapes. Randomness cannot have achieved this, because without mathematics there is no definition of randomness (in an empty set). And on what ontological properties should this 'randomness' be based, i am forced to ask (if it really does exist, what i doubt).

This leads me to the conclusion that if mathematics has somehow emerged, this could be only possible due to some entity that has more intelligence than mathematics itself. Mathematics, due to its inherent properties, cannot explain how it came about, because it cannot differentiate between a necessity and a possibility. If its existence is logically necessary, how can this be justified other than by a circular argument with the known existence of mathematics? And if it was just possible that it exists in the form we know it, what mechanism / or entity has decided which possibility to choose?

You wrote

"And finally, you have criticized my argumentation regarding non-existence. Perhaps it was wrong to confuse the reader with this more philosophical stuff within this few eight pages. The idea was to define the initial starting point of mathematics. It can be the existence itself, which is unfolded to the infinite complex structure of mathematics. But if you assume non-existence as first entity ever, in the same moment existence is logically included as a second entity. For the main hypotheses, this question seems not crucial."

I agree, as far as the natural numbers are concerned. But for all other features of mathematics, i would pose the questions i wrote above. Anyways, thank you very much for your detailed reply and good luck in the contest!

Best wishes,

Stefan Weckbach

Dear Professor Arved C. Huebler,

Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

Joe Fisher, Realist

Nice essay Huebler,

Your ideas and thinking are excellent for eg...

At this macroscopic systems complexity and singularities play an important role. The idea is obvious to identify the singularity M as a candidate for the emergence of the physical universe.

But singularities are mathematical problems, do you feel it is necessary that they exist in the real universe also?............

..................... At this point I want you to ask you to please have a look at my essay, where ...............reproduction of Galaxies in the Universe is described. Dynamic Universe Model is another mathematical model for Universe. Its mathematics show that the movement of masses will be having a purpose or goal, Different Galaxies will be born and die (quench) etc...just have a look at my essay... "Distances, Locations, Ages and Reproduction of Galaxies in our Dynamic Universe" where UGF (Universal Gravitational force) acting on each and every mass, will create a direction and purpose of movement.....

I think intension is inherited from Universe itself to all Biological systems

For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

http://vaksdynamicuniversemodel.blogspot.in/

Best wishes to your essay.

For your blessings please................

=snp. gupta

Greetings Arved,

I was attracted to this essay, as I am also a fan of the HoTT program, and I am glad I took the time to read it. I like the idea you are presenting and the first few pages of the paper very much. The way the paper wraps up fails to give the reader a clear idea of how this thesis fits into the assigned topic, and honestly it gets a little scattered, but it is an interesting exploration in its own right.

Your comments on page 3 "The impossible existence (_) leads logically to its opposite, the possible or potential existence (т--Л). From this, real existence is derived (т--П), and then two existences are logically true (т--Пт--П)." are a precise re-statement of the ancient Chinese philosophical doctrine of Wu Ji and Tai Ji as taught by Taoist philosophers. In my essay, I argue that some of the ancient philosophical texts might encode secrets put there by mathematicians.

But what you describe is broadly supportive of the main thesis in my own essay, Putting the Elephants to Work where I assert that evolutive trends observed in nature arise from properties of higher Mathematics. I would invite your comments. After reading your essay; I have the impression that HoTT offers rigorous proofs for some of the statements I made as logical arguments in my paper. But my work is also highly speculative, so it might be nice to know where my ideas are well supported.

All the Best,

Jonathan

As it turns out..

I got to spend a lot of time hanging out with printing presses as well.

Warm Regards,

Jonathan

I am wondering..

Could you elaborate on your usage of the word 'Dasein' in this essay? There is a substantial difference between the usage of Heidegger and that of Karl Jaspers, where you seem to be leaning toward the latter. This would be in accord with the original usage, if indeed Heidegger first encountered the notion in the Taoist works of Zhuangzi - as some assert. But this seems to be the key point, or at least a hinge in your argument.

Let me summarize; by imposing the impossibility to exist (in a particular state or at a certain location in real or parameter space) we are creating an openness which is effectively the opportunity for something to exist - which is the possible or potential existence. Only when the possibility exists, or the potentiality is non-zero, can existence assert itself - so an entity or identity can come into being. One could also say; only when the space is available can something come to exist within that space.

In Chinese philosophy; Tai Ji is the grand ultimate, representing the form of the universe as a divided collection of forms. Wu Ji is the eternal unity, beyond and before the existence of form. Philosophers talk about Wu Ji as being "neither hot nor cold, neither light nor dark, and neither large nor small" which presents an analogy with non-commutative geometry. This fits with the notion that there is a process of becoming, which brings forms into being, and that this process is dictated by Math.

All the Best,

Jonathan

The word for Physics in Chinese is..

Wu Li

Regards, JJD

Dear Jonathan,

i read your comments here and i would like to add some thoughts of mine to your contributions.

I think that 'impossible existence' does only make sense if one defines it as the impossibility for mutually excluding things to exist. For example, if God is existent beyond space and time in his own eternal realm and God is an eternal entity, it is impossible that he should be caused by something at a certain 'time'. He just is. Impossible existence says that it is not ontologically sound to attribute to something some self-contradictory properties. So for example God should not be able to anihilate himself, otherwise he would not be eternal.

So, we have an 'impossible existence' here, namely that God cannot anihilate himself. This will never become reality (if God does indeed exist, but let's assume it here for the sake of the argument). One also can say that if there is a multiverse out there, it is impossible that at the same time the claim that there isn't a multiverse out there is equally true.

'Impossible existence' is really just another terminus technicus to indicate the impossible existence for mutually excluding alternatives. As i argued elsewhere, therefore one cannot deduce from impossible existence to possible existence other than to presuppose something already being existent - namely logics. If 'impossible existence' does necessarily lead to possible existence, there has to be some logics around to make this step possible. But if there is some logics present in an empty set, this empty set would not be empty. So, deducing from an empty set to possible existence and then to actual existence does not explain the origins of mathematics, because the very basis of mathematics, namely logics, is already there. And with the same logics one then can trace back to hopefully arrive at the origins of mathematics, finding that it obviously is rooted in logics. So what has been achieved is simply to say that logics is logic, since otherwise (logics being illogical) would lead to mutually excluding alternatives.

'Impossible existence' therefore is equal to the logical connective 'NOT', 'impossible existence' and 'possible existence' together are equal to the logical connective 'AND'. Both connectives are sufficient to built all logics from it. What follows is that if an empty set can generate all of mathematics, there had to be logics inherent within it and the question remains where this logics does come from, if not from mathematics itself. But if the latter would be true, then mathematics hasn't evolved, but would be an eternal fact just like God would be.

Dear Huebler,

Fantastic ! What creativity and fertility of mind ! No, I am not offering these generous words for your line of thinking that Mathematics or order alone must be the cause of the existence [I too have been worrying about it for quite sometime], but rather for the jugglery and ingenuity of associating the elements of logic with elements of physical universe, and for the attempt to bind the unlimited scope of mathematics to the realm of observable physicalism.

Our minds are built to parse pattern and build models, arriving at a rational viewpoint that without a pattern, one cannot derive or predict anything. Therefore, we necessarily seek to understand how universe must have a rational beginning; we just cannot reconcile with the arbitrariness of nondeterministic 'process' to create the universe. Certainly, if a process does not have a degree of determinism, we cannot even call it a process.

Mathematical rationality of emergence of the universe is riddled with several difficult issues.

1. Eternity. Even the induction rule has an eternal existence. It does not matter what mathematics develops out of induction, but what ever develops is not bounded by time. Given the eternity, every notion would have played out in the past and continue to do so for ever. Only truly cyclic processes can be allowed. But then, again what fixes the periodicity of such cycles? A periodicity of infinity, or frequency of 0, could be of particular interest.

2. There does not exist uniqueness in mathematics. So, I am not sure which dynamical, or induction based mathematics should one consider as the basis for the existentiality of the universe.

3. Randomness allows unpredictable variations to occur. If randomness does not exist then following issues emerge. A static null configuration remains null for eternity. Changes are required to bring in time. Regular changes with finite elements may bring in time but it may create endless cycles. but then, if randomness is allowed then it does not remain mathematical. Of course, in our mathematical thinking, inifinity is the only savior to bring in whatever fundamental indeterminism. However, bringing elements of indeterminism via the concept of infinity and zero, would render the universe entirely non deterministic, and it would be difficult to bring in order, without an arbitrary rule.

4. The reason that we cannot reconcile with the idea of indeterminism is that once there is a breakdown of rule, we cannot employ rational thinking to resolve issues. Yet, we cannot do without indeterminism. One way to handle it is to hypothesize a limited indeterminism of certain specific 'kind' and 'limit'. For example, we may allow the most fundamental level of entities to have analog / continuous detail, which cannot be defined with finite number of parameters, yet they could change only in quanta, and have finite number of measurable states -- something like infinity modulo N. Furthermore, these entities may have constancy of relation among measurable states, individually they do not have entirely deterministic description, only relations have consistency.

5. It would be interesting to know if author believes that the process could be simulated even at smaller scale?

The most fundamental trouble that one faces is that nothing comes out of absolute null, cipher. Point to pixel posses an infinite abyss in logical construction. No matter what we do with objects of measure zero, we cannot bring about a finite dimensional object from it. The unfathomable leap in the argument is in this statement, "but as soon as the newly generated mathematical points are connected in very large dimensions and categories with a huge number of different meta-information paths, we can expect a delay of the mathematical frequency."

HoTT defines, "'a' is a point of the space A'. A bit circularity exists here. How do we first define A? We cannot, unless we consider A as a class whose members are constituted of 'a's. 'a' does not receive an independent qualifying definition from A. So, I take it as that 'a' and A have existence in mutual relation, in particular that of relation between a class and its members. Since no object can be defined with any absolute reference frame, therefore, this mutual existential relation is acceptable. You have used this consideration to get rid of physicalism.

The empty set is just an information, if we give it a status of the realism of substratum, then why only points, what cannot be imagined to have an empty set of. Information requires a substratum of its own -- e.g. registers for bits, quantum states of particles for qubits, and neurons for everything. That is to say, it is always the physical state of an entity that correlates with, or represents information, as I have worked out in my essay. And all interactions resulting in definitive consequence carry out information processing by virtue of natural causation. Without this physical substrate, information has no basis, no existence. One is able to talk about empty set, only because such a notion can be conceived of by the function of neurons.

"The impossible existence (_) leads logically to its opposite, the possible or potential existence (т--Л)". This is a pure magic of a magician working on the minds of the readers (audience). It took me so much to understand this. If the meaning, or notion, or information of 'the impossible existence' exists then of course, it leads to its own opposition. In a context of nothingness of all existence, even this information has no basis. I could grant this under the notion of 'cogito, ergo sum'. But then, we all already know, we exist. The existence is brought about by simply asking the right contradictory question, a discrete question, leads to discrete contradictory existence.

As you sought -- a logical step forward could be to seek an evolutionary path for laws or function (natural causation) of universe, such that starting from nearly no determinism, the laws acquire (evolve) greater determinism, without ever achieving absolute determinism. The absolute determinism is as much of a trouble as absolute null to begin with. Or, a hypothesized limited determinism may also work.

By the way, natural causation is non-violative, as the information processing emerges from it as I have shown. Therefore, one has to show exactly how this version of causation may come about.

Rajiv

P.S. I had to read your essay so many times, yet do not understand fully.

I did read this..

And I thank you Stefan for sharing your thoughts in this lofty manner. I do think that Math has somewhat the same attributes of eternal nature as God. If I was asked to choose "are the fundaments of Math evolving or eternal?" I'd have to say the latter is more nearly true. Perhaps even beyond and before the existence of time, Math did exist in some manner. But obviously, it can only have expression within some kind of physical or other enduringly structured existence.

All the Best,

Jonathan

Dear Sirs!

Physics of Descartes, which existed prior to the physics of Newton returned as the New Cartesian Physic and promises to be a theory of everything. To tell you this good news I use spam.

New Cartesian Physic based on the identity of space and matter. It showed that the formula of mass-energy equivalence comes from the pressure of the Universe, the flow of force which on the corpuscle is equal to the product of Planck's constant to the speed of light.

New Cartesian Physic has great potential for understanding the world. To show it, I ventured to give "materialistic explanations of the paranormal and supernatural" is the title of my essay.

Visit my essay, you will find there the New Cartesian Physic and make a short entry: "I believe that space is a matter" I will answer you in return. Can put me 1.

Sincerely,

Dizhechko Boris

Hi Arved... ;)