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Wandering Towards a Goal Essay Contest (2016-2017)
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The Dot, the Point, the Dot — the Intention by Arved C. Huebler
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Author Arved C. Huebler wrote on Mar. 8, 2017 @ 16:41 GMT
Essay AbstractMathematics is not a formalism made by humans, but the logical origin of our reality. In this essay a hypothesis will be investigated, how physical entities derive from the mathematics by an emergent leap. Inspired by HoTT mathematical induction is assumed as main impetus of the development. Finally the intention as an emergent capability for analyzing meta-information will be considered.
Author BioBorn in 1960, studying Physics in Heidelberg and Berlin, PhD as print engineer at Berlin University of Fine Arts, R&D director at Bertelsmann Group Gütersloh, since 1997 professor at the Institute for Print & Media Technology, Chemnitz University of Technology at Chemnitz/Germany
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Stefan Weckbach wrote on Mar. 8, 2017 @ 20:29 GMT
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...
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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
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Author Arved C. Huebler replied on Mar. 9, 2017 @ 13:14 GMT
Dear Stefan Weckbach,
Thanks for your intensive discussion on my thoughts. For sure, the essay may be classified under meta-physics. But I interpret this meta-physics solely as mathematics including logics, without anything else. This offers the fundamental option to calculate the next steps. The initial point is the entity of 'non-existence' combined with the mathematical induction, e.g. according to HoTT. Consciousness is not required. This is only part of the human understanding. The pattern of electrons in an atom shows a mathematical structure without any human consciousness.
My essay is only a hypothesis next to other conceivable hypotheses. We have to test, (1) whether the proposed singularity is evaluable, and whether (2) a link with emergent physical entities as e.g. the Minkowski space-time becomes possible. After that I dare talking about further philosophical implications.
Thanks
Arved
Stefan Weckbach replied on Mar. 9, 2017 @ 21:44 GMT
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...
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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.
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Author Arved C. Huebler replied on Mar. 12, 2017 @ 22:03 GMT
Dear Stefan Weckbach,
Thanks for your comprehensive reply, which helped me a lot.
To be frank, I am not in a position to judge HoTT and understand it in all aspects. Like a lot of other formal constructions, as you mentioned it shall consist of trivial elements, too. What I learned and where I was inspired is the idea of designing mathematics as a process instead of a steady...
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Dear Stefan Weckbach,
Thanks for your comprehensive reply, which helped me a lot.
To be frank, I am not in a position to judge HoTT and understand it in all aspects. Like a lot of other formal constructions, as you mentioned it shall consist of trivial elements, too. What I learned and where I was inspired is the idea of designing mathematics as a process instead of a steady structure, as the traditional understanding suggests. The motivation for their approach was, as I understood the story of HoTT, to receive the ability to verify mathematical statements automatically.
It is only a suggestion, a hypothesis. And if mathematics is a process, which is enfolding a mathematical universe, we can ask about possible effects. My result for this question is not a homogeneous mathematical universe, but a singularity, which has to become happen.
The other question is about the definition of mathematics itself, whether it is formulated as HoTT, as a set theory or what ever. I think, my argumentation in the essay is to short, and my explanation is not clear enough:
Most of the scientists follow Platon with his differentiation between idea and form, which means today: Only physics is true reality, mathematics is something else. If you can’t measure, it is not reality. As I understood, you argue in this way, too.
My hypothesis: Lets assume, there is no difference between idea and form. In this case, what mathematics might represent? It should be the „existence“ itself as a “pre-physical” entity.
You are right, my argument of logical induction from an initial point of non-existence towards an unfolding complex structure is simple, as the HoTT is simple in its basic foundation. But is it wrong? I have the vague hope, that it might be possible to generate a mathematical estimation for the parameters of the assumed singularity. And perhaps, at the end this might offer a link to physical entities like physical space and time.
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.
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Stefan Weckbach replied on Mar. 13, 2017 @ 17:33 GMT
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...
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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
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adel sadeq wrote on Mar. 8, 2017 @ 20:37 GMT
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
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Author Arved C. Huebler replied on Mar. 9, 2017 @ 13:17 GMT
Dear Adel,
I have read your earlier essay „Fundamental Theory of Reality“. Because there are a lot of related papers available, I decided not to fill my eight pages with a review-like essay. Sorry for the missing reference. I will read your article asap.
Thanks Arved
Vladimir F. Tamari wrote on Mar. 8, 2017 @ 22:54 GMT
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
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Author Arved C. Huebler replied on Mar. 9, 2017 @ 13:23 GMT
Dear Valdimir,
Thank you for your input. The printed dot guided me to the question on the smallest ever-possible information. From my point of view, this might be a simple change itself, as it also occurs in mathematics. But I do not believe in mathematics as an invention of man, as you stated. There is a logical, mathematical pattern behind everything independently from the human mind. And my hypothesis addresses the question, how it might be possible that this mathematical pattern with no physical dimension creates a first physical dimension.
Best regards
Arved
Conrad Dale Johnson wrote on Mar. 9, 2017 @ 12:45 GMT
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.
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 09:24 GMT
Dear Conrad,
thanks for your feedback and impetuses.
If I understand right, you feel mathematics is to simple to cover all the phenomena of physics, e.g. continuous fields. But I thing, it is possible to show mathematically a transition from a countable set of infinite entities to a continuous entity.
Perhaps my text was not sufficiently intelligible. The term pixel was defined as a basic element, which can be identified at a certain scale level. This pixel may consist of very complex substructures, based again on basic elements at a lower scale, and so on. So, an printed dot of ink is much more complex than one quantum dot, because it consists of an uncountable number of quantum dots in a very complex structure.
As you state very right, a ordinary logical (=: mathematical in my essay) structure itself has no effect in the physical word, it needs an entity with at least one physical parameter to effect something in the physical world.
But my hypothesis is: At a fare end of highly complex mathematical structures, an emergent creation of a first physical entity, e.g. a Minkowski cell, might happen. And the I look for a possible way, how this can work.
Regards
Arved
sridattadev kancharla wrote on Mar. 9, 2017 @ 13:42 GMT
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
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.
attachments:
10_zero__i__infinity.docx
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 09:47 GMT
Dear Sridattadev Kancharla,
thanks for your feedback, but I am to restricted to follow you argumentation. Fpr me it is difficult to find the link between your approach and my essay.
Good luck for you work
Regards
Arved Hübler
Eckard Blumschein wrote on Mar. 9, 2017 @ 17:37 GMT
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
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 10:18 GMT
Dear Eckard,
thanks for you statement. But what a pity, the vice versa is my approach.
Lets try to explain my understanding by and improve the weak explanation at my essay:
Assume elements, and assume these elements will assemble a pattern, a structure. You may be able to discover logical rules and regularities in this structures. If the elements have physical features, you will discover physical laws. If we think the elements without any physical properties as an abstract model, we will discover pure mathematics, logical patterns itself. That is, what you agree about.
Now the vice versa:
My 1st hypothesis: This pure mathematics may exist without any physics. They exist as logical pattern of the existence itself (I call it mathematical point). You do not agree, as you stated.
But it is only a hypothesis to see what happens, if we assume this. Is there a logically reason, why this assumption might be nonsense?
My 2nd hypothesis: At a moment when this pure mathematics becomes highly complex, an emergent step will create a first physical entity (e.g. a Minkowsky cell or something else).
Again: Is there a logically reason, why this assumption might be nonsense?
Rest of my essay is asking for A possible explanation, how and why such an emergent process works. I supposed a singularity.
My future task: To proof this hypothesis (and perhaps adjust it).
But if there are arguments showing that these hypotheses are impossible, I could save time.
Thanks for your time and regards
Arved
Eckard Blumschein replied on Mar. 31, 2017 @ 04:35 GMT
Dear Arved,
You should indeed use your mind better. Well, possibility obviously precedes actuality. Impossibility definitely belongs to the past. Isn't therefore a Minkowsky cell no physically real entity?
Your first hypothesis assumes that there is only one pure mathematics. This would contradict to G. Cantor's claim that the essence ...
Let's go into details. Inspired by Bedürftig, Katz, Mückenheim, and Spalt, I am distinguishing between the strictly logical Galilean notion "infinite" as the opposite of finite and the so called mathematical pragmatic notion of a relative infinity introduced by Leibniz/Bernoulli which led to counter-intuitive and evidently unnecessary in physics constructs including naive and axiomatic set theory, hyperreal numbers, etc.
I maintain that the lazy pragmatic neglect of the distinction between rational numbers and the continuum of genuine real numbers led to - as I found out - nonsensical physical singularities within IR instead of CQ.
Eckard
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Héctor Daniel Gianni wrote on Mar. 9, 2017 @ 18:53 GMT
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
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 10:22 GMT
Dear Héctor Daniel Gianni,
thank your for your long list of statements. Unfortunately I am not able to find a connection to my essay, so I am not in the position to comment it.
Thanks again and good luck.
Regards
Arved
Lawrence B. Crowell wrote on Mar. 10, 2017 @ 01:02 GMT
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
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 11:04 GMT
Dear Lawrence,
thanks for your statement. I have read your earlier paper "Mathematical Physics as Topological Numbers, Types and Quanta" and I found a lot of interesting ideas. But for this essay of mine, I decided not to review other papers because of the eight pages restriction. I am very sorry.
For sure, the question of the physical content of an continuum is interesting, as you discussed in your paper. But I believe, it is not such a big secret. Perhaps it is related to the emergent step from one scale to another.
Also interesting is the physical equivalent of the smallest physical dot, as you mentioned. I did not proceed as far as quantum information, because that is a very tricky discussion, which I want to avoid. What is a technical necessity at a qubit, and what is the real physically effective information content?
So, I restrict myself and talk only about bits in general, which also includes qubits. And in my essay I used the term "pixel", because that is a single parameter entity. Your suggestion to talk about voxels refers to three dimensions, but perhaps one dimension is the initial state.
Thanks again,
Regards
Arved
Jose P. Koshy wrote on Mar. 10, 2017 @ 06:53 GMT
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
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 11:28 GMT
Dear Jose,
thank you for your contribution. You highlight a very interesting question, which was the initial motivation of mine to enter this field between physics an information and mathematics.
But I do not agree with your way to distinguish mathematics from physics. All three „player“, as you called it, have an equivalent entity either in the mathematics and the physics:
name – physical entity, e.g.print – mathematical entity
existence – printed dot on paper – mathematical point/element
potential existence – unprinted paper – empty set
impossible existence – missing sheet – not defined
Acording to my hypothesis, mathematics describes only the existence itself and its logical relations (mathematical rules). But in physics we have the existence of at least one physical parameter, e.g. voltage or spin, or here in the case of printing the visual contrast, and its logical relations (physical laws).
Regards
Arved
Patrick Tonin wrote on Mar. 11, 2017 @ 13:59 GMT
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
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 11:45 GMT
Dear Patrick,
thanks for your comments.
Not I have to give sense to information, but something has to be able to sense a change, if this change should be information.
I known, there are a lot of very complex definitions of information available, e.g. the term of "potential information“ you have mentioned. But I want to start with the simplest definition of information, which is possible. And that is the "message of a change“ for the case, that this change has an effect.
But my essay was only able to address the way from the basic mathematical existence to the emergence point of physics. The way onwards to more complex forms of information like consciousness is not covered. A task for the future.
Thanks and regards
Arved
Héctor Daniel Gianni wrote on Mar. 12, 2017 @ 22:45 GMT
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...
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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
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Shaikh Raisuddin wrote on Mar. 13, 2017 @ 06:57 GMT
Arved C. Huebler
What are essential characteristics of a goal-directed system? A List?
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Author Arved C. Huebler replied on Mar. 13, 2017 @ 11:54 GMT
Dear Shaikh Raisuddin,
I see no relation to my essay, but from my point of view an answer to your question is: At least the system needs the capability to detect the direction of the goal.
Regards
Arved
Joe Fisher replied on Mar. 15, 2017 @ 16:06 GMT
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
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Satyavarapu Naga Parameswara Gupta wrote on Mar. 16, 2017 @ 18:34 GMT
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...
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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/
Be
st wishes to your essay.
For your blessings please…………….
=snp. gupta
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Jonathan J. Dickau wrote on Mar. 17, 2017 @ 03:16 GMT
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 (○). From this, real existence is derived (●), and then two existences are logically true (●●)." 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
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Jonathan J. Dickau replied on Mar. 17, 2017 @ 05:29 GMT
As it turns out..
I got to spend a lot of time hanging out with printing presses as well.
Warm Regards,
Jonathan
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Jonathan J. Dickau replied on Mar. 17, 2017 @ 16:01 GMT
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
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Jonathan J. Dickau replied on Mar. 17, 2017 @ 16:03 GMT
The word for Physics in Chinese is..
Wu Li
Regards, JJD
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Stefan Weckbach replied on Mar. 18, 2017 @ 10:01 GMT
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...
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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.
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Jonathan J. Dickau replied on Mar. 28, 2017 @ 02:19 GMT
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
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Rajiv K Singh wrote on Mar. 18, 2017 @ 12:10 GMT
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...
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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 (○)". 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.
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Dizhechko Boris Semyonovich wrote on Apr. 7, 2017 @ 04:06 GMT
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
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William Walker wrote on Apr. 8, 2017 @ 02:45 GMT
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