Limits of mathematics in cosmology

Don, how would one go about designing an experiment to record the sound of one hand clapping?

Tom

"It is not a difficult extension of GR to say that time structures space."

Yes, you can say that, but only because we want to put a better face on the situation. The spacetime cannot be physical, simply because the underlying concept of the vector space is purely mathematical.

Numeric language is too plain or rather too far removed from 'reality'. One needs a richer symbolic language. To me, a more 'physical' formalism is the one which is structurally a 'copy' of the actual physical processes: events are represented as events, where their interconnections are preserved. That is why, for example, Feynman's diagrams took off so fast.

Hi Tom,

The experiment to detect what particles do when in isolation and at very low velocities will take some art and compromises. I think it is doable.

The experiment to detect one hand clapping is trickier but I think the result will be: The one hand makes a sound that is the universe. The trick is that you have to listen continuously.

Those who know the truth have no need to listen anymore all they have to do is recite what they already know.

I know Jessica Alba is hot, everything else is up for grabs.

Hi Lev,

It is interesting that Feynman diagrams have a beginning state that consists of real particles and a final state that consist of real particles. The in-between interactions are considered virtual. It makes it look like events consist of particle arrangements.

You gave me an idea, I was just browsing Feynman diagrams and came across a statement:

"an electron which quickly emits and reabsorbs a virtual photon, called a self-energy" This fits very well with wave-length hopping.

Thanks,

Don L.

Isn't the mathematics issue the tip of the iceburg here? The real substance of 'the problem' in mdern physics arises from ( dare I say it...) cognitive issues. All of the phenomina we witness in the physical world, regardless of the scale we are looking at, arise through acts of 'consciousness'. It would seem to me that the closer we look at 'reality' the closer we get to its 'assembly language' which is responsible for our being able to percieve the world in the first place. Anyone who had a BBC mocro knows the problems our high level languages ( views) can encounter if we start 'peeking and poking', around on this level. Its only reasonable that eventually a computer will discover electricity, which woll make a mockery out of everything it knows if it starts 'pinging' the supply to see what happens.

To discuss the idea of time as existing or not as a 'reality', is a very precarious activity in the sence that the physicality that supposedly defines what 'is real' is in itself totally undefined.

The accusation that view leads to philosophy and not science maybe an underestimation of the power of human thought. Perhaps we ought to take a break and look up from our instruments and ask not just 'what we want to know' but consider 'where also, we want to go'!

Ps. I love this stuff! Thanks for your replies, I will read all referencies.

It is unfortunately, aa novel idea I would like to put forward, about the solution to the short comings of mathematics and its ability to map onto the 'reality' which we intend it to describe.

My proposition is based upon the following logic.... @ Mathematics can only be meaningful to the extent that the axioms upon which it is based have neaning@

To date, the axioms of mathematics, the axioms of set theory, 'impose' a linear sequential meaning all phenomina upon which it is employed. The major effort in the mathematical sciences has been to extend the axiomatic model, and the point at which we begin to see this model fail is the point at which effort ought to be turned not to extend this model further, but to seek more meaningful fundamental axioms.

This line of inquiery is, by definition, pre mathematical, that is, the search for mathematical axioms canot be guided by existing mathematics,n neither is this axiomatic search necessarily a mathematical task.

The study and search for a more meaningful axiomatic system is a disipline in itself and the expectations of 'meaningful' set of axioms need to be put forward 'first' before the search is engaged in order to obtaain a 'goal set' of axioms. This can possibly be posed by the question ' what do we want'? and thewn set about phrasing a set of axioms based upon our requirements.

This is a bold step, for it implies that experience gained over the centuries using our supposed 'objective axioms' must be replaced by our hopefully informed subjective requirements, obtained during our experience of the shortcomings of the previous 'objective axioms'.

I cannot see any way around this issue. A transformation from objective to subjective axioms, for one issue is clear here and that is the admission that our supposedly objective axioms of set theory have been subjectve all along, in favour or a system of mathematics which favoured our 'linear and subjective experience' of reality.

Any suggestions?

I would just like to add here that 'everything', quite literally all advances we can possibly make do only one thing... They advance or attempt to advance the axioms of set theory. This is all that modern science is about, how could it be about anything else? Mathematics is, by definition, the imposition of a linear sequential view upon reality.... why we should expect it to be able to wrap itself around phenomina which do not suit this view is at best 'complicity', at worst, ignorance of the actual situation.

I know many professional scientists who are wholly unaware of this situation and who would be hard pressed to even give the notion that the spectacular gains of mathematics to date, are spectacularly 'one dimensional'!

I keep being drawn back to this issue.

I once saw some graffiti on a wall when I was a teen. It was a terrible message..

"The courage of your convictions"

was the message. Perhaps the time has come for science to get over the shock that 'it exists at all' and move on to the idea that we have to decide what it is we want from it!

Pretty scary stuff!

I have read some of the initial posts here, but I think that the status of Set Theory has been inappropriately stated. First of all set theory is not a single theory but a collection of Axiom systems of different strengths and types. As an initial example we have ZF set theory versus NBG set theory which introduces objects called Classes. The simple equation that a Set = Point is too simple also.

Perhaps the most relevant formulation of Set theory for the purposes of the process centric ideas discuessed here is the version of Set Theory from Axcel with the "Anti-Foundation Axiom". In this form of set theory we can have:

a member a

a member b member a

and so on. This has been used to model processes. Admittedly none of these forms of set theory are intended directly to model space-time or its components directly, but we need to be more general in our views of what Set theory (and hence Logic) actually is.

Also the attempt to formulate a system of axioms as a subset of Peano axioms is certainly possible. There are many simpler structures than Peano axioms which capture concepts of ordinal relations which can be formed. In doing so we are being "pre-number" in a sense.

In fact certain kinds of computer scientists use these formulations a lot for giving abstract descriptions of computation systems (which are not necessarily number based systems). There may be links here with the original question of the first post, although a I would need to see (or develop) an axiomisation of the "struct" concept or similar to see what the relationship was.

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).