Tuesday, January 24, 2012

How it went?

Mark McWilliams requested some kind of summary about the development of TGD, and I decided to write an article about the the history of TGD. I could not avoid telling also about turning points of my personal life since my work and life are to high extent one and the same thing.

I have tried to represent the development chronologically but I must confess that I have forgotten precise dates so that the chronology is not exact. Very probably I have also forgotten many important ideas and many side tracks which led nowhere. Indeed, the study of the tables of contents of books and old blog postings and What's New articles at the homepage forces me to wonder how I can forget something so totally.

The article should help a novice to get an overall view about the basic ideas of TGD are their evolution during these 34 years. To myself a real surprise was to see how many deep ideas have emerged after 2005: one can really speak about a burst of new ideas. Most of them relate to the evolution of the mathematical aspects of TGD and to their physical interpretation but also the experimental input from LHC, Fermilab, and elsewhere has played a decisive role in stimulating ideas about the interpretation of the theory.

Unavoidably the emphasis is on the latest ideas and there is of course the risk that some of them are not here to stay. Even during writing process some ideas developed into more concrete form. A good example is the vision about what happens in quantum jump and what the unitarity of U-matrix really means, how M-matrices generalize to form Kac-Moody type algebra, and how the notion of quantum jump in zero energy ontology (ZEO) reproduces the basic aspects of quantum measurement theory. Also a slight generalization of quantum arithmetics suggested itself during the preparation of the article.

I gave to the article a title which is easy to guess: "Evolution of TGD". It can be found at my homepage which is now living at webhotel with address http://tgdtheory.com/.

Note: The links of old postings to my homepage do not work anymore. Apologies. To get to the link work one can replace "http://tgd.wippiespace.com/" with "http://tgdtheory.com/", and if this does not work, with "http://tgdtheory.com/public_html/".

13 Comments:

At 12:31 AM, Anonymous Anonymous said...

Matti:

Your work with p-adic numbers has me intrigued.

Would it be possible to calculate fractals (or fractal turning points) for a given price function using p-adic/adelic numbers?


Regards.

 
At 7:18 PM, Anonymous matpitka@luukku.com said...

Difficult to say. Suppose one asks for extrema, say maxima, for the p-adic counterpart of a cost function.

In purely p-adic context the notion of extremum does not make sense since p-adic numbers are not well ordered. One can only compare their norms and this variational principle is very rough too - rough to my opinion.

One can transform the problem to a purely algebraic one just by studying the p-adic counterparts of say partial differential equations associated with a real variational problem. In TGD framework this makes sense. [The general vision is that p-adic physics is algebraic physics: real physics is about magnitudes.]

On could consider the p-adic analog of differentiable cost function and map it to its real counterpart by canonical identification (I) which is continuous map. This function would be non-differentiable but continuous a a function of its p-adic argument.

One could also map reals to p-adics by the inverse of I. The inverse would be two-valued for integers with finite number of pinary digits (the analog for the nonuniqueness of decimal expansion: 1=.999999....) but one could choose branch with finite number of digits so that p-adic image would be unique. Altogether one would have

R--->Q_p by the inverse of canonical identification. Q_p--->Q_p by p-adic cost function and from Q_p to R by canonical identification.


I have represented some p-adic fractals at my homepage at

http://tgdtheory.com/figu.html .

 
At 9:05 PM, Anonymous Anonymous said...

Matti:

This:

http://tgdtheory.com/square.GIF

is the most relevant representation of what I am looking for.


From what I understand, there is a need to construct some type of mapping from p-adic numbers to real numbers. This will then yield results that can be compared with the price dynamics. Is a super-computer needed for the mapping?

Regards.

 
At 1:24 AM, Anonymous matpitka@luukku.com said...

Dear Anonymous,

Let us try to figure out what should one do.


a) One must construct modules for p-adic arithmetics. Sum, product, difference, division. I constructed them myself using MATLAB but they ar rather slow and primes must be rather small.

Mathematica very probably has packet for p-adic arithmetics. Probably this kind of packet gives the expression of p-adic number as the analog of decimal expansion

x= \sum x_np^n


b) The canonical identification is defines as the map

\sum x_np^n--> \sum_n x_n^(-n)

Canonical identification should be coded since it is certainly not in Mathematica.

c) In the construction of p-adic fractals I used the inverse of the canonical identification to map reals to p-adics: the form of inverse is same


This was about p-adics and reals and canonical identification.

Quantum rationals require more.

a) One should be able to construct auantum rationals r_q=m_q/n_q from rationals =m/n interpreted as ratios of p-adic integers.

a) One can write r= p^s*(m/n). p-Adic integers m and n have pinary expansions

m= SUM m_kp^k

and

n =SUM n_kp^k

m_k and n_k are not divisible by p and are smaller than p.

b) One must replace m_k (n_k) by the quantum counterpart by decomposing it into a product of powers of primes p_i and by replacing these prime factors by their quantum counterparts

p_i -->sin(2*pi *p_i/p)/sin(2*pi/p)

c) After this one must map the resulting p-adic quantum rational to real quantum rational by canonical identification taking p-->1/p for both m and n.

Calculations require of course cutoff in the highest power of p. When I did computations for almost two decades ago personal computer posed strong restrictions on the number of pinary digits and
only small p:s could be considered. Probably one can do more now. One must just try and see.

 
At 2:09 AM, Blogger Ulla said...

These were useful links. It would be as important that the old ideas were somewhere, so the errors don't have to be repeated. Say: Old TGD? A failure is often just as important as the right answer. This would also give TGD some more credibility. I have often heard that "when he never says he was wrong"...

And maybe those old pages have TGD easier explained, what I have often found from Mark's site.

And a search engine, thanks, if it is possible?

I would not have written like that, as I have said before. You was afraid of Orwin? No need to be after that.

Everyone have problems, exactly everyone, I think. You want to keep emotions out???

 
At 5:22 PM, Anonymous Anonymous said...

Matti:


Along with your replies, I have consulted this source to aid in my understanding:


http://arxiv.org/ftp/arxiv/papers/1102/1102.2515.pdf


Unfortunately, mathematics isn't my persuasion so I'm afraid a lot of this is beyond me.

After reading your replies (of which I am gracious for) and doing further research on my own I have come to the conclusion that I would not be able to program an indicator that interpolates p-adic fractals onto a price chart. Assuming it's even possible to create what I am looking for, it is obvious I do not possess the skillset for such an endeavor.

Regards.

 
At 3:48 PM, Anonymous Anonymous said...

This sounds quite familiar:
http://www.mdpi.com/2075-1729/2/1/1/

 
At 7:35 PM, Anonymous matpitka@luukku.com said...

To Anynymous:

While wandering in web yesterday I saw an article telling about the work of Andrulis, who has written the article in the link.

Our visions are very similar. For instance, we both realize that life and its origin are real and profound problems. Not just dance of quarks as one skeptic finnish colleague has been telling with a great success in his popular books! Even representatives of church have hastened to tell that they fully agree!

We seem also to share the vision that life and consciousness appear in all scales.

The difference is that our emphasis are very different. Andrulis is biologists, I am a physicst.

 
At 8:18 PM, Anonymous matpitka@luukku.com said...

Still to Anonymous:

During another web wandering I saw a popular article (New Scientists or some other journal) about the evidence for the evolutionary ladder.

It might sound surprising that evolutionary ladder would have been challenged. Most laymen have the feeling that Darwin's theory of evolution postulates it and that it has been very successful.

This is not however the case. In materialistic approach evolutionary arrow is in principle forbidden. Goal directed evolution would be Intelligent Design and even local direction of evolution is at odds with the second law of thermodynamics as we want to understand it.

Therefore evolution would be only apparent for a good skeptic and materialist. Evolutionary ladder would be illusion. We only tend to put ourselves to the top and to order life forms as lower ones near to us if they resemble us (say have language facility). Random change followed by choice selects as success makers those life forms which best suit to the existing environment. There is no evolutionary ladded, only more or less random environmental history faithfully reflected by the biopshere. Suddenly the arrogant skeptic has become infinitely humble and are forced to claim that they are at the same level as simple mono-cellulars (heh heh ;-))!

Stephen Jay Gould's "Wonderful Life" (also I had it but I loaned it;-)) discusses so called Burgess Shale fauna as a support for the illusionary character of evolutionary ladder. Precambrian Explosion led to a burst of what according to the usual standards look like highly developed life forms most of which then disappeared. Evolutionary ladder does not conform with this mass extinction.


The view in favor of real evolution is however to me quite convincing. Formation of multi-cellulars or animals able to communicate with language and behave socially is not to me a random adaptation to changing environment. We differ from monocellulars in some decisive manner. But I must be also able to explain the Cambrian explosion.

In TGD framework one can indeed find this kind of explanation. The basic vision is that in quantum cosmology cosmological evolution takes place as relatively fast expansions between steady situations without any cosmic expansion. This is true also for Earth. This explains the strange finding which is much stronger than that of Wegener. If the radius of Earth were 1/2 of its recent value, the continents would fit nicely together to form single super-continent covering the entire surface of Earth. The theory allows to get rid of so called snowball Earth theory developed to explain ancient climate at Earth, and having several difficulties. See this

http://tgdtheory.com/public_html/genememe/genememe.html#expearth .


Expanding Earth theory assumes that the life developed in the womb of Mother Gaia (being sheltered from meteorites and cosmic rays) in underground lakes, and when the radius of Earth grew by a factor of two around Cambrian explosion life bursted to the surface from under surface lakes and started to fight for survival. This explains Gould's realization without forcing to give up the evolutionary ladder.

This requires that the counterpart of photosynthetic machinery storing the energy of photons of visible light to metabolic energy existed already in underground lakes before the Great Event. It is a good home exercise to develop a theory for how this machinery might have worked;-).

 
At 11:20 PM, Blogger Ulla said...

I cannot hold back a small comment :)

It is a very hardmelted truth for these very intelligent scientists, that they in fact is made mostly of bacterias, with bacterial consciousness (protoconsciousness). The human add to it is maybe minor? We only COLLECT it from our cells, which in most cases are bacterias. So, we can say we are a colony of bacterias with superimposed fields. A superorganism.

My professor at school used to say we were a project of mitochondrias, which is a symbiotic bacteria, de facto. This view is only different, not any more wrong than our usual one.

I just thought of Lubos when I read that :) His intelligence as a result of bacterial minds. But so, he is also very humble :)

 
At 11:49 PM, Blogger Ulla said...

Yesterday I heard a great program at radio about the finnish physicist Rauno Lauhokangas and whale language. Whales use pictures transferred with voice, and they even have personal names. This requires memory and consciousness.

One picture can be so dense with information that it is all black, he said.

http://www.interspecies.com/pdf%20and%20styles/whale%20language.pdf 5 -160 Hz says this.
"It can not be overstated that these echoes are not precisely “pictures”, but something unique, closer to holograms displaying threedimensional, X-ray, and kinetic information. Because the original echoes are almost inconceivably dense with information, and because the same echolocation “images” may be altered by such attenuating factors as current, tide, and spatial distance, the actual communication of social echoes may not consist of simply mimicking the original sonar. One plausible idea is that whales encode the dense, overlapping beats of social echolocation, not within phonemes, but within the similarly dense, overlapping pulses of the harmonic progression."

Remember, light is also holographic. It just gives another kind of picture.

They also used the voice as tool in hunting, like bats. Ultrasound can go through almost 1 meter of soil or rock, so they see the animal in there. The can navigate by sound. I read about a blind boy that also had learned the skill some year ago.

How different is not their world from our. We often forget that we use a small area of the em-spectrum to sense our world, and it can be very different at other levels. The sensed world can even disappear totally.

We know it is there although all signals goes straight through. But if we would be at the other place in spectrum, would our science look like it does today? Certainly not.

 
At 9:13 PM, Anonymous matpitka@luukku.com said...

Thank you Ulla.

Very interesting article. Maybe some-one manages to invent code allowing humans to understand something about whale talk. First of all one should be able to guess about what whales would be talking about. Problems of everyday life, family problems, business affairs,..?;-)

Very probably the pioneers have already done all kinds of things to whale talk. For instance, when human speech is slowed down, it consists of sounds with pitch going down: somewhat like whale song. What happens if whale talk is fastened: how would we hear it? Could it sound more like human speech?

One old idea what comes into mind is that genetic code could be be the deep molecular structure behind speech so that phonemes would be analogs of amino-acids.

*The coding should be extremely flexible at "phenotype level" but fixed at the level of hardware - somewhat like high level computer language which is flexible but reduces to assembly language at bit level.

This is possible since arbitrary sequences of associations from symbol to its representation at molecular level is possible. One-one correspondence would however pose conditions on the number of phoneme-like basic symbols.

*The distributions of codons in intronic portions of DNA are claimed to resemble distributions of phonemes in language (Zipf's law).

* If computers learn to understand natural language by pattern recognition, one might consider this option seriously.

*The notion of phoneme is questioned in the article. Phoneme can be replaced with more general symbol: in the article coding based on rhythmic patterns is proposed.


The idea about sound hologram does not look attractive and is criticized in the article. The whole point of language is to replace huge formation packets with simple symbols representing classes of objects. Hologram like representation would be like visual representation and carry huge amount of un-necessary bits when creating a simple generating the desired association would be enough.

 
At 12:55 AM, Blogger Ulla said...

The fact that our bodies contains about the same amount of water as in the ocean (with a big varation within the phylas) is quite interesting, together with our screaming and singing cells. Water is electrically leading and em-waves of all frequencies are commuting and interacting. So, in principle a single cell in our body could experience the whole body? Just as whales? Our cells use another frequency than our senses, and so we don't hear them. Nerves also NEVER connects directly to cells.

A whale could experience all emotions, with so broad spectrum. Everything almost. Nobody can tell lies there? It only needs a scream or a song. Fascinating. Also the fact that the lower boundary is 5 Hz.

The em-spectra can also be seen as thermodynamic spectra? Entropy (low frequencies) to negentropy (all higher frequencies)? So in fact our bodies also strives to entropy. The difference is how we use the negentropic noise or information.

 

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