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

Dear Arved Hübler,

good work, although some people may consider it as purely metaphysical.

In the past, i have considered similar lines of reasoning and came also to the conclusion that mathematics must have been created. My current answer to this question is, indeed it was, but i have to make some restrictions on what you exemplified.

Firstly, one has to recognize that even before the creation of maths, there had to be some kind of logic, because otherwise the creation process you describe would not be necessarily appear at all. If the latter would be true, mathematics would be the result of an absurd change from an empty set to a - relatively - meaningful existence. For differenciating impossible existence from potential existence - as you have done stringently - one (and i think not only a thinker, but also 'nature' at is fundamental level, means at the level of an empty set) needs some kind of logics which allows nature to differentiate between impossible and potential existence. Otherwise even impossible existence would be possible! And what could the latter mean other than that your creation process is just a lucky fluke, an appearance of mathematics without any (and i emphasize *any*) reason whatsoever, a kind of nice and consistent nightmare (for some people) out of the very blue. There could well be other such emergences, not so nice and totally devoid of any meaning and order - but with observers in it! It your creation process does not presuppose some kind of logics, the latter scenario cannot be ruled out.

My answer to the question of what initiated the creation process of maths is that it can only be a higher consciousness who has set the stage for this. I therefore take it for highly probable that there exists an intelligent entity, usually called God, from whom the needed logic originated.

Let me say that this would be consistent with what you wrote. An induction process needs, in my opinion, something more than an empty set, it needs logics. Otherwise, as already stated above, the appearance of your creation process would be some kind of magic, or if one likes, a totally irrational event from out of a nothingness which is logically not limited to further produce all kinds of irrational events - all the time.

Induction traditionally is understood as collecting some data which does form a certain pattern and then induce something from it. In the case of an empty set, one has just a half bit of information: there is an empty set (or stated from the view we humans have now: there is no pattern). For your creation process to start, you need 1 bit that can make a logical difference. But an empty set is not 1, but 0. Surely, in retrospective view, an empty set can be equated with 1, because we can now contrast it with existing things, but if we talk about 'nothing', this traditionally means that there is nothing, not even an empty set (yes, nothing in the traditional sense is very hard to imagine; i assume because it simply is impossible!). So what you have done is to induce from the fact that there is existence to the conclusion that there has always been some existence, even if it is only an empty set. So, from this perspective, you have the 1 Bit, the empty set and the consequences of it - namely, the non-empty set. But you have induced it with what couldn't be present before your creation process, namely logics. You circumvent this by saying that the empty set is a mathematical set, an homogenous background and thereby tacitly introducting the needed logics for your creation process to unfold. But if logics is already there, then also maths is potentially there. Moreover, one then has to ask where the logics came from, what i do here.

What to you appears as an empty set in your description, could well be the full gamut of God. In this empty set there would be contained all eternity. Hard to swallow and to understand, but some near-death experiences do report impressions like this. Surely this empty set would then also include the needed logic. I think if there is this entity called God, he/she very well knows what happens if his domain would be contrasted with something that is not this empty set. Therefore, in some sense, it seems to be very natural that if something (or someone) does try to transcend/leave the realm of God's existence (due to free will), it results in a very real illusion of existence that is relatively devoid of all the good properties which are ascribed to God (i think if we wouldn't have been created as eternal souls and in the picture of God's own existence, the world would be not only relatively devoid of all the good properties which are ascribed to God, but absolutely devoid of it) Moreover, this realm of existence would seem to successfully prove its own absurdity and in some sense it does indeed prove it. Only take for example what i have wrote in my essay about extrapolating mathematics to be the only fundamental level of reality. This would lead to a world which is exclusively only ruled by mathematical relationships and therefore is strictly deterministic. No free will whatsoever, but only absurdity at the core level. I don't buy such a conclusion but further stick to logics and it tells me that there must be more than a mathematical empty set at the roots of existence. Because an empty set as a stanalone feature of some existence - the existence of the set itself! and not more - does not make much sense.

Nonetheless your essay is a brave piece of work to tackle the big questions. Thanks for an enjoyable reading!

Best wishes,

Stefan Weckbach

Hi Arved

I don't know if you have seen my idea which seems to be vaguely connected to yours , but mine directly leads to whole of physics. Please, see if it makes any sense to you and I appreciate a feedback. I will grade you in due time.

"Reality is nothing but a mathematical structure, literally"

this is last years contest essay

http://fqxi.org/community/forum/topic/2451

And this is this year(please read my comment notes for missing info)

http://fqxi.org/community/forum/topic/2884

Thanks

Adel Sadeq

Dear Prof. Huebler

It is nice to get tbe scent of printing ink through your essay, I am a type designer as well as physicist, albeit an independant minded researcher as you can see from my fqxi essay. I liked your starting from a dot because in my theory Beautiful Universe Theory the building block of everything is a spherically symmetrical node or element interacring with its neighbor as a cellular automata. I could not follow your technical logical analysis (my limitations) but your approach reminded me of the artist Paul Klee (in The Thinking Eye I think) of his little diagram how a point becomes a line, lines form a plane and planes form a solid. As to mathematics I believe it owes its affinity to physics because humans (the inventors or discoverers of mathematics) evolved from organisms that interacted with the Universe at the 'dot' molecular scale, hence 'getting' how it works as they evolved.

Best wishes,

Vladimir

Arved,

I appreciate your essay for its clarity and intelligence. Unlike some other attempts to derive the universe from pure mathematics, you don't make exaggerated claims to have solved all the problems in physics, and admit that your work is "highly speculative". My own feeling is that while mathematics certainly has a universal character that transcends the particularities of the physical world, it still depends on many features of our world for its meaning. Just counting, for example, would not be meaningful if the world consisted only of continuous fields. In fact, discrete, stable, countable entities are abundant in our universe... and yet at the quantum level, "elementary particles" turn out to be far more complex than pixels.

You write, "A change is only relevant if an effect happens." I would add - "and if its effect also has an effect, in some other context." I think the basic difference between physical existence and mathematics is that the latter takes for granted that its basic concepts (point, set, number) have meaning, while the physical world actually provides all the many kinds of contexts needed to make all its concepts meaningful and measurable, in terms of each other. I explore this in my essay, which roughly sketches out the beginnings of "a generalized theory of evolution" based in empirical science rather than pure logic.

Thanks again for an interesting and imaginative piece of work.

Dear Arved,

Universe is an i-Sphere and we humans are capable of interpreting it as 4 dimensional dual torus inside a 3-Sphere, which consists of Riemann 2-sphere as Soul as depicted in S=BM^2 diagram in the attached doc. Soul is the simplest of the complex manifolds with in the 3-sphere, Mind and Body constitute the remaining complexity. Soul, Mind and Body are in a toroidal flux in human beings, exactly at the center of the 3-sphere one can experience the unity of the trinity and that is the now moment we experience. As there are 4 dimensions required for a 3-sphere, the regular 3 dimensions of space and the fourth dimension of time, it is obvious that the 2-sphere (Riemann sphere) of consciousness with in us is with out the time dimension and hence the saying "eternal soul". Poincare` conjecture implies that consciousness is homeomorphic (same or similar) in all beings manifested in all dimensions of the universe, as i have shown that Riemann sphere can serve as the fundamental unit of consciousness in [link:fqxi.org/community/forum/topic/2748] There are no goals as such its all play[/lin].

PS: i thinks therefore we are VR(Virtual Reality), i "am" not GOD but i "is".

zero = i = infinity = sqrt ( e power (i * pi) )

Love,

i.Attachment #1: 10_zero__i__infinity.docx

Dear compatriot,

You wrote: " The physical dot becomes a mathematical point by losing all physical features, and vice versa." Except for the vice versa I agree.

You are arguing for a discovered rather than created mathematics. Again, I agree with the exception that Robinso(h)n's hyperreal numbers are perhaps a rather unphysical consequence of pragmatic, one could also say dirty, definition and use of infinity by Leibniz, Bernoulli, and Stevin. Cantor claimed the essence of mathematics its freedom.

Best regards,

Eckard

Dear Arved C. Huebler..........

I invite you and every physicist to read my work "TIME ORIGIN,DEFINITION AND EMPIRICAL MEANING FOR PHYSICISTS, Héctor Daniel Gianni ,I'm not a physicist.

How people interested in "Time" could feel about related things to the subject.

1) Intellectuals interested in Time issues usually have a nice and creative wander for the unknown.

2) They usually enjoy this wander of their searches around it.

3) For millenniums this wander has been shared by a lot of creative people around the world.

4) What if suddenly, something considered quasi impossible to be found or discovered such as "Time" definition and experimental meaning confronts them?

5) Their reaction would be like, something unbelievable,... a kind of disappointment, probably interpreted as a loss of wander.....

6) ....worst than that, if we say that what was found or discovered wasn't a viable theory, but a proved fact.

7) Then it would become offensive to be part of the millenary problem solution, instead of being a reason for happiness and satisfaction.

8) The reader approach to the news would be paradoxically adverse.

9) Instead, I think it should be a nice welcome to discovery, to be received with opened arms and considered to be read with full attention.

11)Time "existence" is exclusive as a "measuring system", its physical existence can't be proved by science, as the "time system" is. Experimentally "time" is "movement", we can prove that, showing that with clocks we measure "constant and uniform" movement and not "the so called Time".

12)The original "time manuscript" has 23 pages, my manuscript in this contest has only 9 pages.

I share this brief with people interested in "time" and with physicists who have been in sore need of this issue for the last 50 or 60 years.

Héctor

Dear Arved Huebler,

thanks for your comment. I think what HoTT does, is to facilitate a formal system which in its inner core states that without consistency there is no existence possible. If one assumes HoTT to be consistent itself, this leads to the impression that HoTT must capture and represent the fundamental truth. But not all consistent schemes do necessarily meet reality. Maybe HoTT does answer this question in the positive and says that all mathematically consistent formal systems are to be generated at some point (in time) and therefore indeed meet reality.

I think HoTT does state a triviality, namely that inconsistencies do not pave the path from the abstract to the concrete (especially physical reality). This path should symbolize the well known deductive principle in logics. Now, HoTT makes a huge leap by saying that if something suffices consistency, it must exist (somewhere, somehow). If one does understand HoTT as merely stating that consistency is necessary for existence, but not sufficient, i would wonder what the needed sufficient additional properties are to make something physically existent.

By assuming an entity of 'non-existence', and by stating that only consistent structures can come into existence, this 'non-existence' must be considered as existent - because within HoTT, it has the feature of consistency. Otherwise it could never produce the whole chain of events that led to our universe. Stated differently: the entity of 'non-existence' has a single property, namely the potential to produce something. This is a somewhat trivial logical conclusion based on our factual existence. Therefore one must understand your entity of 'non-existence' as existent. How can one and the same thing be existent and non-existent at the same instant? I really think that we cannot logically consistent assume such a non-existent entity being the first unmoved mover. And because this is logically inconsistent to me, i think, it must fail, although i nonetheless do not exclude that mathematics was generated by some other causes than itself.

Interesting essay. It has some overlap with the FQXi essay I wrote in 2015. I discuss HOTT there. This does seem to be a discrete structure that emerges from homotopy theory that is a digital-like system of types. My current essay does discuss some math foundation issues as well.

It is interesting to ponder the nature between the continuum with its infinitesimals and points with the finite and discrete. The continuum has no physical content as I see it, but is a convenient model system for a lot of physics. The physical dot or pixel (voxel) in quantum gravity is the Planck length, and this is the smallest length or region where a qubit of information can be localized. Anything smaller than this is the continuum that has a somewhat different physical meaning, and in the case of infinitesimals the physical meaning reduces to zero.

Cheers LC

Arved C. Huebler,

Quoting you, "The mathematical empty set is like a substrate, a carrier or a homogeneous background. The empty set is the precondition for the existence,"

The empty set (substrate) thus seems to be not of mathematical origin. Your analogy of 'pixels' creating dots on 'paper' using 'ink' is interesting. Here, there are three players. Which of these are of mathematical origin? In my opinion, the pixels alone are mathematical. The 'paper and ink' together create a 'black and white' substrate; if paper is white, ink is black, if paper is black ink is white. Only then can the pixels create dots. So logically 'ink' is also not of mathematical origin. So I argue that the substrate 'paper and ink' is of physical origin and 'pixels' is of mathematical origin. So what we see as 'dots' and 'complex patterns of dots' are just mathematical possibilities of the physical world. Physics provides the substrate, mathematics decides the structures.

Jose P Koshy

Dear Arved,

Your approach is interesting and I agree with some of your points. You talk about information but how do you give sense to that information ? Someone or something should to be observing it ? Information alone is just potential information, I believe that some sort of consciousness needs to be brought into the equation in order to transform that potential information into "real" information and eventually create a reality.

If you feel like it, please take a look at my essay and you will see more precisely what I mean. (A Universe of information and consciousness).

All the best,

Patrick

Dear Arved C. Huebler

I invite you and every physicist to read my work "TIME ORIGIN,DEFINITION AND EMPIRICAL MEANING FOR PHYSICISTS, Héctor Daniel Gianni ,I'm not a physicist.

How people interested in "Time" could feel about related things to the subject.

1) Intellectuals interested in Time issues usually have a nice and creative wander for the unknown.

2) They usually enjoy this wander of their searches around it.

3) For millenniums this wander has been shared by a lot of creative people around the world.

4) What if suddenly, something considered quasi impossible to be found or discovered such as "Time" definition and experimental meaning confronts them?

5) Their reaction would be like, something unbelievable,... a kind of disappointment, probably interpreted as a loss of wander.....

6) ....worst than that, if we say that what was found or discovered wasn't a viable theory, but a proved fact.

7) Then it would become offensive to be part of the millenary problem solution, instead of being a reason for happiness and satisfaction.

8) The reader approach to the news would be paradoxically adverse.

9) Instead, I think it should be a nice welcome to discovery, to be received with opened arms and considered to be read with full attention.

11)Time "existence" is exclusive as a "measuring system", its physical existence can't be proved by science, as the "time system" is. Experimentally "time" is "movement", we can prove that, showing that with clocks we measure "constant and uniform" movement and not "the so called Time".

12)The original "time manuscript" has 23 pages, my manuscript in this contest has only 9 pages.

I share this brief with people interested in "time" and with physicists who have been in sore need of this issue for the last 50 or 60 years.

Héctor

Arved C. Huebler

What are essential characteristics of a goal-directed system? A List?