Dear Roy,
I'm glad you are trying to see what the relationships are between the conventional concept of set and that of the set of structs. However, it appears that you are simply *assuming* that one of the developed versions of set theory should fit the bill. Unfortunately or fortunately, this cannot be so, for a number of reasons: none of the known approaches deals with such temporally and finely structured entities as structs.
Hi Lev,
Yes I am *assuming* that set theory is a place to start - sort of. It is actually the methodology I have developed since encountering several formalisms (mostly in the computation context) which claim to be Foundational - and which then ask for comments. To make sense of such formalisms I have tried to develop a better understanding of the foundational classics: set theory, automata theory, lambda calculus - and then see what the new formalism offers.
Having now read a 96 page paper on ETS theory (only once though) I think that I would now describe the situation a little differently. There is a straw man argument that:
Set Theory is a foundation for Mathematics;
Mathematics is a foundation for Physics;
Physics and Mathematics is a foundation for Biology
implies that
Set Theory is a foundation for Physics and Biology. (ditto with Peano arithmetic)
Having studied Set theory for some time I have no idea whether Set Theory has anything to say about physics or biology, although it does have remarkable logical things to say.
The ETS theory seems to be challenging Set theory for this straw man role of "foundation of physics and biology" - except in ETS theory we might have a genuine candidate for that latter role. However this also assumes that a single framework can fullfill all the tasks ETS seems to have set itself:
1. Foundation for Quantum Processes
2. Foundation for Epigenesis and biology
3. Foundation for Space-Time and cosmic inflation
An earlier post asked to apply ETS theory to protein folding. For me, still trying to understand how much is in the theory, I would ask (for the biology case) "where is the DNA?" That is could ETS theory have predicted the need for DNA if we didnt already know about DNA - and if so where does the strut formalism "hide" the parameter that is DNA?
Also a video presentation of ETS theory would be helpful to make sure that we are grasping it propertly.
Roy,
Yes, indeed, Tom (T. H. Ray) also asked about protein folding.
The point is that the corresponding struct is supposed to store this (temporal) information about folding, so that the spatial instantiation of the protein struct relies on that representation.
As to "where is the DNA?" I would reply, that DNA is a part of the *particular hardware* implementation of the spatial instantiation process: on some other planet this hardware most likely would look different.
By the way, here is a simplified visual illustration (Windows Media Player) of the process of spatial instantiation of the struct representation for the Bubble Man example from Part III of main ETS paper.
Hi Lev,
Coming late to a forum like this involves a lot of catchup. I think that you were originally interested in discussion of the application of ETS-like ideas to "cosmic space expansion" in some generic sense. Unlike some other posters I dont have any alternative theory to propose, just try to understand the ETS formalism better and understand its limits (for now). For me this means digging into precisely what certain words mean. Some problem words are "implementation" and "instantiation" (when discussing a presumed Fundamental formalism).
The papers and your reply on protein folding and DNA suggests that there are two entities here:
(i) the ETS/struct represention/formulation - which encodes information
(ii) the "spacial instantiation" of the above
So the "real object" (as conventially understood) lives in the spacial instantiation space, but gets its information (on how to fold - or evolve) from the struct (framework(s))in ETS?
In the ETS model the structs are the "behind the scenes" dynamic source of all information and change?
One short comment made in the main paper on Quantum Entanglement (about a measurement affecting future and past events) suggests to me that the ETS structs are acting as "hidden variable"-type repository of information. If so then hopefully you can agree that it is necessary to do quite a bit of work to tease out what is really in this theory.
For now I shall also remark about the lack of discussion of a formal grammar within the papers I have seen. Earlier posts suggested that the number 11 contained no historical information. This isnt quite correct from a grammar perspective. So in a formal language an 11 instance would have a specific syntactic construction like:
11 = plus(5,6)
this shows how this 11 got (computationally) constructed. We would expand 5 to get maybe:
5 = plus (succ(0),4) etc.
So contrary to claims made about numbers even they naturally form part of a syntax tree, which contains a struct-like history. Hence the need for a clarification in this area too.
I hope these comments are of interest for now.
1.'So the "real object" (as conventially understood) lives in the spacial instantiation space, but gets its information (on how to fold - or evolve) from the struct (framework(s))in ETS?'
Yes.
2.'In the ETS model the structs are the "behind the scenes" dynamic source of all information and change?'
Yes.
3.'One short comment made in the main paper on Quantum Entanglement (about a measurement affecting future and past events) suggests to me that the ETS structs are acting as "hidden variable"-type repository of information. If so then hopefully you can agree that it is necessary to do quite a bit of work to tease out what is really in this theory.'
Yes, of course.
4.'So contrary to claims made about numbers even they naturally form part of a syntax tree, which contains a struct-like history. Hence the need for a clarification in this area too.'
Not quite!
When we write 11, we have no way of knowing how that 11 was obtained: '11' could have been obtained as '7' "followed" by '4', which is different from '2' "followed" by '9' (from my post of Aug. 26).
This is progress!
Just to return to the last point where we have an issue. My formal question here is something like:
G:"Does the struct formalism use syntactic structure (ie grammar) to encode temporal information?"
Furthermore if the answer to that question is "yes", then more needs to be said about what the link between ETS and syntactic structures is (I know that there is a commment about Chomsky somewhere, but that is not enough, nor quite what I mean!)
Finally if the answer is "yes" then the comments about numbers like 11 need to be reworded: it is here that some clarification is still called for.
If the answer to G is "no" then I have noticed that several grammatical structures do seem to be in use in ETS theory (forming classes, forming structs, susbstructs, etc) so it seems that grammatical structures are at work here all the same, even if they dont encode "temporal" information. So I would like to see a clarification of what is grammatical and separately what is temporal. Maybe sorting this out will even help you present this theory differently.
Just in case my remarks about number grammar are not clear, here is more analysis. Using Peano functions 0 and succ, there is only one representation of each number:
so 4 = succ(succ(succ(succ(0))).
I suspect that is what you mean by saying that there is no history to the numbers in Peano arithmetic.
However if we also introduce the Peano binary relation Plus, then we now have multiple methods of representing 4
4 = plus (succ(succ(0)),succ(succ(0))),
4 = plus (succ(0), succ(succ(succ(0)))), etc
These multiple representations of 4 (as they now are) have what physicists might call a "gauge freedom". The canonical representation is:
4 = succ(succ(succ(succ(0))))
This gauge freedom could be used for something, and it seems to me that ETS theory is using a similar idea to represent temporarily how the 4 got formed from its components.
"Does the struct formalism use syntactic structure (ie grammar) to encode temporal information?"
Roy, the answer is mainly "no".
You, for no fault of your own, are missing the issue of *representation*, the no man's scientific land. ;-)
In particular, a string is not a good representation because it does not contain its own formative history, and since there are exponentially many possibilities such formative history cannot be effectively recovered. (See also my paper.)
On the other hand, the issue of structural/temporal representation cannot be properly addressed outside the general scientific context, i.e.as it will be used in physics, for example.
In that sense, as a bonus suggesting the right direction, ETS possesses one critical property: its syntax and semantics are "congruent" (see my paper "Representational Formalism in Which Syntax and Semantics Are Congruent: Towards the Resolution of Searle's Chinese Room Challenge", which was written for cognitive scientists).
What this effectively means is that ETS representation of a process/object should be a direct copy of what is actually going on in nature, if the concept of structured event is indeed the right basis of the language of nature (and not triangles, circles, etc. as Galileo thought).
"Does the struct formalism use syntactic structure (ie grammar) to encode temporal information?"
To elaborate a bit more, I should mention that a struct simply records a stream of (observed) events, but it is postulated that the generation of such a stream is guided by the corresponding generative structure (class representation, a generalization of the grammar concept).
Even Stephen Hawking, in a moment of honest revelation ("The End of Physics"), acknowledged that any so-called final theory in cosmology cannot be proven to be ultimately the case, or it could always be eclipsed by new information. Why?
Godel's theorem.
In fact, this theorem places an unassailable boundary on any non-trivial mathematical axiom, etc., like those involving cosmology.
Many insightful and quasi-ultimate theories are still possible, but Godel's theorem puts a limit on mathematics that honest mathematicians and physicists would be wise to acknowledge.
Of course, accepting the reality of Godel's theorem also brings back the idea of contingency involving the universe, and since this is a philosophical concept that brings up the possibility of something outside the universe responsible for its creation, such honesty is not expected to come from those intent on disproving such a creation.
For those who cannot handle the limitation imposed by Godel's theorem, the best thing to do is ignore it as if it, too, doesn't exist. The second best thing to do is to deny the application of the theorem that even Hawking admitted applies to theories of physics. The third best thing to do is to simply claim that the theorem itself is limited to minor applications that Hawking did not realize.
There are indeed many ways to put your heads into the sand when confronted with a reality you just don't like.
But more is to be gained by just a little bit of humility as all good scientists should have, especially when trying to come up with ultimate mathematical theories that will never be and can never be completely ultimate.
DH
The ultimate limit of mathematics in cosmology is spelled out quite clearly by Gödel's theorem that even Stephen Hawking acknowledged in 2002.
Alas, it appears that only a small minority of honest physicists and mathematicians appreciate the ramifications of Gödel's theorem, which sets forth that no non-trivial system of arithmetic propositions can have proof of consistency within itself. As Hawking finally recognized (See his Gödel and the End of Physics speech/paper, 2002.), Gödel's theorem definitely applies to physics and the vain quest for an absolutely final TOE based on higher mathematics.
Hawking was, however, slightly in error in his "end of physics" lamentation. A total theory of all is still possible, but it will never contain the proof of it being necessarily true and absolutely final within itself since Gödel's theorem shows this to be impossible. Something else could always come into play to compel a change in a theory that could hold for thousands or even billions of years.
If all physicists/cosmologists would be a bit more honest as Hawking was(at least in 2002), greater insights into the nature of the universe and its creation/contingency would be readily apparent and open to greater discoveries, but even Hawking's latest collaborator Mlodinow simply dismisses Gödel's theorem as "not applicable to a TOE" (of course, he offers no evidence to support his bogus disdain, which is quite telling) in direct contradiction to what the theorem demonstrates, plus he ignores what his more accomplished co-author admitted about the theorem.
Such ignoring is definitely a most pernicious form of "ignor-ance" that does not want to accept the truth if it goes against an ideology of belief that should be absent in legitimate scientific inquiry.
So, to understand any limits of mathematics in cosmology, start with the ultimate (how ironic) limit as demonstrated by Gödel's Theorem.
Onward!
Dear All,
Everything in the universe is connected eternally in singularity, separability is an illusionary perception when one is in duality.
Relativity is the theory that best describes duality, where as singualrity is the absolute truth and several quantum mechanic observations are closer to this truth.
who am I? I am dualilty, I is the singualrity.
Please see the mathematical equation representing the absolute truth of
Love,
Sridattadev.
If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true
If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true
If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true
If 0 x i = 0 is true, then 0 / 0 = i is also true
If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true
It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~, where "i" can be any number from zero to infinity. We have been looking at only first half of the if true statements in the relative world. As we can see it is not complete with out the then true statements whic are equally true. As all numbers are equal mathematically, so is all creation equal "absolutely".
This proves that 0 = i = ~ or in words "absolutely" nothing = "relatively" everything or everything is absolutely equal. Singularity is not only relative infinity but also absolute equality. There is only one singularity or infinity in the relativistic universe and there is only singularity or equality in the absolute universe and we are all in it.
Love,
Sridattadev
Any (mathematical) cosmology theory that posits the a priori existence of highly complex mathematical structures prior to the creation of the universe is implicitly positing the existence of a mathematical world which is eternal. There are not theory of creation of the whole universe but instead explain how the mathematical eternal part of the universe at some point rules the evolution of our world from it. Nothing explain the existence of this relatively complex mathematical core, and nothing explain the connections between the mathematical world and reality.
Hi Lev,
In the 1990's I developed a theory of visual perception (Ph.D thesis: Perception of the image world") that developed a concept of image structure hierarchy corresponding to the ontogeny/phylogeny of objects.
"In light of this, the 'similarity' of objects should be understood as the 'similarity' of their formative
histories, and hence this formative history (or object's structure) must be captured in the object's
formal representation."
In my approach, the detection process of an image structure recapitulate in its sequence and structure the morphogenesis process. This is a modern version of the old aristotlean conception of the actualization of the object's form into human mind at it intellectual level. The platonic world in this model in implicitly built-in in the hiearchical structure of the vision system of animals.
Postulate 1: the universe is a family of evolving and interactive classes of (irreversible)
processes.
I would prefer:the universe is an evolving family of evolving and interactive classes of processes.
Notice that with the structural hiearchical representation, it is not necessary to represent time by a parameter, or a dimension of space. By the universal principle that STRUCTURAL HIERARCHY IS HISTORY, you get a Bergsonian duration built-in.
- Louis
All of mathematics is limited by Axiom of Choice. I propose that Axiom of Choice can be extended to include Relativity, and therefore define a model by which ALL of observable physics can be modeled.
Axiom of Choice extended to include Relativity
This model potentially describes the foundations under quantum entanglement and related decoherence, time independent photon interactions within fringe patterns, entropy, duality, time, gravity, subatomic particles, deformable space, ...
This is only a foundation for a cosmological model based upon quantum causality that allows for building evolving relativity upon a base of causal states. The system has the potential to model diverse physics environments different then our own; but our own as one set of non-relativistic singularities that moderate relativistic singularities (sub-atomic particles).
The remainder of the thought mapping that has accumulated is found at:
QESdunn
Until corruption can largely be eliminated, I do not want space-time manipulation to be developed. The reason is that then weapons will otherwise be developed to enslave the masses. Manipulating space-time allows for remote manipulation of subatomic particles. Which with advanced application can mean automatically detecting distraction, and causing pain. Not just in self, but in all those whom you care about. Ultimately causing death if acting outside of boundaries.
Eliminate ALL Corruption
retweet: Part of Civil Rights is that Representation is free of Treason http://tinyurl.com/lpqsur5
My theory on the limits of mathematics:
Theory of Everything using Leibniz, Kant and German Idealism
James,
The Axiom of Choice may be replaced by an Axiom of Exclusion that isolates a Natural Index of 12 numbers that index (by dimension) the mathematical structures encompassing physics. Incorporating this into proof theory leads to a proof of the Riemann Hypothesis. Of course, to get the $1,000,000 from the Clay Mathematics Institute requires that you also convince them that you are allowed to change the rules of proof.
My theory on the limits of mathematics:
http://www.academia.edu/8991727/Phenomenal_World_as_an_Output_of_Cognitive_Quantum_Grid_Theory_of_Everything_using_Leibniz_Kant_and_German_Idealism
