Continued Fraction and the Market

M

martys

I think about the technical aspects of the market all the time. Recently a voice in my dream told me to look at Continued Fraction. (I know I've finally gone over the edge. :( )

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html

I looked up Google and only find http://www.smdstock.com Harry told me that he has some proprietary continued fraction counting system used in conjunction with Point & Figure Charting. He published it once some 15 years ago in the newsletter but now it is a secret. So that is one dead end. Does anyone know what he is talking about?

Any suggestion on other directions of research? I am greatly appreciated your help.

I found some mentioning of good old Golden ratio and chaos on the web... Still can't connect the dots. :confused:
 
Quote from martys:

I think about the technical aspects of the market all the time. Recently a voice in my dream told me to look at Continued Fraction. (I know I've finally gone over the edge. :( )

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html

I looked up Google and only find http://www.smdstock.com Harry told me that he has some proprietary continued fraction counting system used in conjunction with Point & Figure Charting. He published it once some 15 years ago in the newsletter but now it is a secret. So that is one dead end. Does anyone know what he is talking about?

Any suggestion on other directions of research? I am greatly appreciated your help.

I found some mentioning of good old Golden ratio and chaos on the web... Still can't connect the dots. :confused:
More...
martys, do I have the film for you...

http://www.imdb.com/title/tt0138704/

:D
 
It is almost certain that a deeper understanding of continued fractions, or their consequences in dynamical systems, will play a large part in understanding at least the qualitative aspects of market dynamics.

The point is that any mathematics that is deep shows up in many places in nature, whether it be in the Riemann Hypotheses, Grand Unified Field/String theories, or markets:

http://en.wikipedia.org/wiki/Continued_fraction

Go down to the section "Continued fractions and chaos" and follow all the links - it will probably take you a full week of reading and will take you down the entire path of ancient to modern mathematics.

What is really interesting to me is - if it turns out that markets in fact are generated by some subset of these systems on some deep level, what and how does the human brain of [some] winning traders captures/intuit this deep structure, and how does that relate to what appears to be a KISS method employed by many traders?

People say that KISS is the way to approach trading the markets and that therefore these complicated attempts at understanding the markets are false. What many do not understand is that one of the most powerful conclusions of modern mathematics and highly abstract physics is Duality. I alluded to this starting with this post in this thread where I use the term "Covariant" instead of "Dual":

http://www.elitetrader.com/vb/showt...&perpage=6&highlight=misbehavior&pagenumber=3

An example of this is in the duality of light as both a particle and a wave in Quantum Mechanics. Both are needed for a complete understanding of nature. But there are modern abstract dualities that have been found in String Theories that are showing amazing connections between different ways of viewing apparently different theories:

http://en.wikipedia.org/wiki/T-duality

Physics is guiding mathematics in finding these deep structures. The current SciAm has a great article on how duality is being used to get a quantum theory of Gravity. I highly recommend it:

http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0002B59B-5B5C-1359-9B5C83414B7F0119

I am nearly certain that to any valid "simple" working theory of a market, there is a dual theory in some abstract [mathematical] space that explains the same thing. The key to dual theories is you almost always want to work in the dual space that is "easier", but like in the wave-particle duality of light you often need to work in both simultaneously for a complete understanding.

nitro
Quote from martys:

I think about the technical aspects of the market all the time. Recently a voice in my dream told me to look at Continued Fraction. (I know I've finally gone over the edge. :( )

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html

I looked up Google and only find http://www.smdstock.com Harry told me that he has some proprietary continued fraction counting system used in conjunction with Point & Figure Charting. He published it once some 15 years ago in the newsletter but now it is a secret. So that is one dead end. Does anyone know what he is talking about?

Any suggestion on other directions of research? I am greatly appreciated your help.

I found some mentioning of good old Golden ratio and chaos on the web... Still can't connect the dots. :confused:
More...
 
Thanks nitro. Actually I am not a math person (I was OK once but it's all downhill after college). This is what makes the dream interesting because I actually saw a continued fraction written out on some rock wall in the dream. Anyway I must admit it could be some subconscious garbage.

Sorry sciencetrader... you have to get my money some other way because I am too dumb to figure this one out.

KISS makes sense to me as stress management because:

Mental concepts -> conceptual fixation = stress (information overload??)

I also encounter duality in looking at price actions. Sometimes I see price movements as channels and sometimes I see them as volatility projection.

People would yell the market is going up... the market is going down... but I swear sometimes I see it setting itself up PHYSICALLY like a living orgainism for both up and down move simultaneously.

Things are not that newtonian.

P.S. I've never quite finished the PI movie from the beginning to the end... It does give me the comfort that maybe I am not that crazy.
 
Quote from martys:

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Things are not that newtonian.
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Some would say Cartesian.

I'm sure that neither Newton or Descartes would agree with this. They both had too much common sense for this.
 
Quote from martys:

Thanks nitro. Actually I am not a math person (I was OK once but it's all downhill after college). This is what makes the dream interesting because I actually saw a continued fraction written out on some rock wall in the dream. Anyway I must admit it could be some subconscious garbage.
...
More...
YW.

Think of it this way. People often say that computers were always sort of dumb and that they would never beat the world chess champion. Now that he has been defeated, people don't think about it anymore. But they should be thinking about it in this way: How is it, that a human being, being capable of calculating very few variations during the game, able to compete with a moster like Deep Blue or Hydra that are calculating 200 million plus positions a second? The point is people are in awe of the computer, when they should be in awe of the human being capable of keeping up with these monsters!

In a sense, we get a "complexity-measure" of chess in this way, and the extraordinary power of what humans do through intuition and pattern recoginition. Similar things probably occur in [some] humans grasping markets.

Take the oriental games of Go, or Shogi (the Chinese form of Chess). In those games, even the most powerful computers are trashed even by good amateurs. When we figure out these oriental games in the sense of having computers play them well, we will probably be that much closer to understanding a great deal more things, not only markets, but ourselves.

We should always be striving for the mathematical model explanations of anything worth studying, but in some sense, the human brain and it's "intuition" is able to grasp these things already. How it does that and how it errs in the same is the most powerful lesson to take from all of this.

nitro
 
i always pictured guys with lots of math smarts as guys that never could get laid. Maybe it was the cute beanie with the propeller on top........................:p
 
KISS is most applicable to futures, where there is a limited number of futures and a complicated model runs into the danger of over-fitting.

In equities, a more complicated model is feasible simply because there are so many data which leaves a lot of room to do out-sample testing.
 
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