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imairfanの日記

2011-08-20

Fibonacci Sequence

Leonardo Fibonacci, the great 13th century Italian mathematician (1175–1250) created the “Fibonacci sequence” to explain behavior in nature mathematically. History has it that the first question he posed was how many rabbits would be created in one year starting with one pair.


Etching of Leonardo Fibonacci
The sequence is actually quite simple. Start with "1" and add the previous number to create the next. So, 1 + 0= 1, 1 + 1 =2, 2 +1 =3, 3 + 2=5, 5 +3 =8….and so on…so the sequence is…0,1,1,2,3,5,8,13,21,34,55,89,144,233 and so on. Mathematicians have been enamored with the sequence ever since. It not only predicted rabbits' explosive reproduction numbers, but accurately measures a wide array of activity and behavior in nature.

Over time, this sequence was used by the master painters to define the dimensions of their paintings. There is something “pleasing” to humans about the proportions defined by the sequence. Think of 3x5 index cards, or how many times most people knock on a door, or ring the phone….3 is the most common, 5 is second. Humans have 5 senses, five fingers. The patterns of the spiral of sunflowers seeds also can be explained using the sequence.

The Fibonacci sequence also gives us the “golden mean” used in many mathematical calculations. The golden mean is 1.61—which is arrived at by dividing a Fibonacci number by the previous number. For example 89/55=1.61. Going the other direction 55/89=.61—which is how market technicians come up with Fibonacci retracements. Skip a number, 55/144=.38, the next retracement. I could go on with the many combinations used by market technicians. Suffice it to say the harmony of these numbers in nature was the cornerstone of much of W.D. Gann’s work to explain grain markets' pricing behaviors.

The other application of the sequence by Gann was with respect to time. Consider how 21- and 55-day moving averages are a favorite of purist technicians. It was this aspect of time when applied to the “birth dates” of markets that I wish to concentrate on—specifically for the Treasury market.

On August 22, l977, the Chicago Board of Trade started trading 30-year bond futures. This year, August 22 falls on a Monday. It will be the THIRTY-FOURTH ANNIVERSARY (34 is a Fibonacci number). My goal is not to make a market prediction as much as to share a fascinating possibility.



The next Fibonacci number is 55, it's a difference of 21, which could determine the length of the next cycle. If this Gann cycle is accurate, it may mean a cycle high in price, a cycle low in rates in the Treasury complex could occur possibly on August 22, or thereabouts. Another way to look at this would be, that it may be the BEGINNING OF A 21-YEAR CYCLE in lower prices, higher rates.

Simply stated, if this measure were truly predictive, it could mean the end of a bull cycle and the beginning of a bear cycle in Treasury prices. This may not mean that once the cycle's low yield is reached, the market will immediately reverse. Yet, if you were to look back , over time it could show up as an important turning point in the market.

There have been several large changes over the years in the bond contract, like a coupon change 11 years ago from an 8-percent coupon to the current 6-percent coupon. I can’t say if that would distort Gann’s theories. At the margins I hope readers find this interesting. Yet for those of you out there that believe in a higher order to human behavior, this could prove to be a prediction that W.D Gann might have mailed into CNBC if he was alive today.

Man vs Machine


A computer can quickly answer trivia questions in the form of a question. How is that a break through in intelligence? Computers have always been able to quickly recall random bits of information. I think IBM has confused pedantry and rote, their speciality, with intelligence, something their culture is remarkably free from, as we all do when we confuse test scores and memorizaton with intelligence.



Their computers win chess games not through intelligence, but by brute force. Its pretty much like pitting a man with a theodlite against a steam roller. If the man is not quick and intelligent, the steam roller will crush him.

To quote a dictionary, "intelligence is the capacity for learning, reasoning, understanding, and similar forms of mental activity;
aptitude in grasping truths, relationships, facts, meanings, etc."

I'll believe that the pedant who wins a Jeopardy prize is intelligent when he can explain quantum mechanics and how it relates to the structure of an orange and create a new something. Alan Turing and John McCarthy may be eminently quotable, truly great minds, but they and their followers seem to have confused rote with intelligence, mechanics with essence.

I do not pretend to be as intelligent as Alan Turing. He is certainly one of the greatest minds in computing and the theory of computatility. Turing's ideas and theories are the very stuff of computing 101. Every mainframe or 'PC' or laptop is defined to be "Turing complete"* (I might add "Turing complete Van Neumann machines"). A million of the machines are manufacted every day and are in every office and more and more homes all over the world, almost pervasive as coffee pots and tea pots; a single example of a Turing complete machine's application is the animation in our movies! If nothing else, Turing complete machines are amalgamating our world and making it more and more free.


But I have to disagree with him about the measure of computer intelligence. He proposes what he calls the "imitation game" as a measure of the question, "Can computers think". Among other arguments and measures, he rejects the argument from consiousness that Professor Jefferson Lister expresses. "Not until a machine can write a sonnet or compose a concerto because of thoughts and emotions felt, and not by the chance fall of symbols, could we agree that machine equals brain-that is, not only write it but know that it had written it." And I might add, knows what it means. Turing dimisses such an argument as mere slopisism. Turing goes on to say, "But I do not think these mysteries necessarily need to be solved before we can answer the question with which we are concerned in this paper." The implications are concerns extend beyond his paper; his is a mere quibble when he talks about substituting summer for spring; their are differences in both their actual environment and their essence, not mere substitiions from a list of seasons; the choice of words convey different meanings. I think the scope of his paper is too limited because the philosophical questions and the enigmas they present are the essence of man and his intelligence. Computing Machinery and Intelligence, A.M. Turningebner/Turing Article


I think the Turing Test fails because the definition of intelligence is too narrow. He "forces" the answer he wants, rather than explore the realm of intelligence. Playing a game per se is not a measure of intelligence. It only a simple question/answer game. It is only a measure of the ability to play a game. Turing_test*


My todo is to review the paper and the work of John McCarthy John McCarthy*.


The thread in the various definitions of the part and parcel of Artificial Intelligence* is artificial. I know minds better than mine are trying to solve theses problems.But I think bypass the notion that intelligence includes the notion of sentience and original thought, not just "creativity".


I use computers daily, I read the read, I listen to music, and talk with people. I can even, within my limited abilities, understand the ideas of others, synthesize my own ideas, express them orally and by writing them, relate them to other ideas, and discuss them.


Put simply, I am a sentient being, with a modicum of intelligence.


I'll will consider that computers have made a real breakthrough in intellence when, rather than playing chess and playing games (something computers have always been able to do), the computer can read the linked article about them and tell me what's it about, not just rotely spew it back. Rather than rotely quoting and modifying Shakspeare, or Plato, or Euclid, or Turing, or Christina Anapour, they can understand, look beyond their understanding and synthesize new ideas.


IMNSMO, robots are mere bumper cars with less intelligence than the village idiot. At least the village idiot is aware of his surrondings, hunger, thirst, heat and cold, other beings and his relation to them, and can learn from this mistakes (not to put his hand in burning embers?) Robot, write me a love note for my precious? Until they are sensitive to the differnces of gollum's, fine gems, and humans, I would not think them to be intelligent.


Will computers be able to discourse on my rhetorical question I began with?


(Please forgive me my misspellings. The supposedly smart program "Spell Check" seems to have only a 10th grade education, cannot understand context, and gives the most inane alternate spellings. Typically, they can't even recognize that syntesize is a mispelling!).


Before I get off my high horse, though computers are Turing complete, software manufacturers (do I hear the echo, Microsoft) subvert this at every chance.

2011-05-20

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