Monthly Archives: February 2009

Probability, the Law of Large Numbers and |truth|

Below is a thought-provoking, if half-baked, non-dualistic take on the central principle of probability theory.

The Law of Large Numbers by Ramesh Balsekar.

Ramesh Balsekar

Creating Order Out of Disorder:

The Theory of Probability – The Law of Large Numbers

One of the best kept secrets of the universe relates to the question of how the sub-atomic, micro-world of particles which are at the same time wavicles, which defy strict determinism and mechanical causation – how this ambiguous “undulating carpet of foam” gives rise to the solid, orderly macro-world of everyday experience, of causality. The macro world, as we see it, is very determined, very clear, very precise, cause and effect, and yet the micro-world out of which this has come is, for the human mind, for the human intellect, total chaos.

Out of this chaos and disorder, how could the order of the macro world arise? The modern scientist’s answer is that this seemingly miraculous feat of creating order out of disorder must be seen in the light of the theory of probability or “law of large numbers.” But then, this “law” cannot be explained by physical forces. The human intellect says, “The natural law must have a certain physical basis.” It need not. It’s a wrong assumption. This law cannot be explained by physical forces. It hangs, so to speak, in the air.

It is, however, not difficult to see the point through a few examples. The first two examples are classic cases from Warren Weaver’s book on the theory of probability. One: The statistics of the New York Department of Health show that in 1955 the average number of dogs biting people reported per day was 75.3. In 1956, 73.6; in 1957, 73.5; in 1958, 74.5; in 1959, 72.4. How could the dogs know when they should start biting and when they should stop biting? A similar statistical reliability was shown by cavalry horses administering fatal kicks to soldiers in the German army in the last century. They were apparently guided by the so-called equation of probability. And then the murders in England and Wales, however different in character and motives, they displayed the same respect for the law of statistics. Since the end of the First World War, the average number of murders over successive decades was 1920-29, 3.8 per million of population; in the thirties, 3.7; the forties, 3.9; the fifties, 3.3; the sixties, 3.5. It’s there in statistics. Why? The human intellect by nature wants to know “Why?” The only answer is “Why not?”

These bizarre examples illustrate the paradoxical nature of probability which has puzzled philosophers ever since Pascal initiated that branch of mathematics, and which Von Neumann, perhaps the greatest mathematician of our century, called “black magic.” The paradox consists of the fact that the theory of probability is able to predict with uncanny precision, the overall result of a large number of individual events, each of which, in itself, is totally unpredictable. In other words, we are faced with a large number of uncertainties producing a certainty, a large number of random events creating a lawful, total outcome but paradoxically or not, the law of large numbers works!

The mystery is why and how it works. It has become an indispensable tool of physics and genetics, of economic planners, insurance companies, gambling casinos and opinion polls – so much so, that the “black magic” has been taken for granted. Basically, what the question boils down to is “By what agency is this controlling and correcting influence exerted?” How do dogs of New York know when to stop biting and when to make up the daily quota? How are murderers in England and Wales made to stop at four victims per million? By what mysterious power is a roulette ball induced after a time to restore the balance in the long run? By the law of probability, we are told. But that law has no physical powers to enforce itself. It is impotent and yet virtually omnipotent.

The purpose and design of this acausal agency is unknown and, more likely, unknowable to the human intellect. But somehow we feel intuitively that it is related to that striving towards higher forms of order and unity in diversity which we observe in the evolution of the universe at large. As Feynmann has concluded, the order from disorder principle seems to be irreducible, inexplicably, just there. To ask why is like asking why the universe is there, or why space has three dimensions? If indeed, it has! As Prof. David Bohm has put it, “Thus, one is led to a new notion of unbroken wholeness which denies the classical idea of the analyzability of the world into separately and independently existing parts.” One Tao master has put it very vividly, saying, “You pull out a blade of grass and you shake the universe.” There is no event which is not connected to everything else that happens in the universe. You think you have pulled the blade of grass out of the ground. The real point is that the blade of grass has been pulled. By what hands is immaterial. The metaphysical implications of this principle are fundamental.

It is a remarkable fact that in 1925, before he created his famous equation, Erwin Schrödinger stated in his My View Of The World, “This life of yours which you are living is not merely a piece of this entire existence, but is, in a certain sense, the whole. Only this whole is not so constituted that it can be surveyed in one single glance.” This, as we know, is what the Brahmans express in that sacred mystic formula which is so simple and yet so complete, “That thou art,” or again in such words as, “I am in the east and in the west. I am below and above. I am this whole universe.”

The problem for the human being arises because we seem to have some control over our daily lives and yet we cannot avoid feeling that we’re helpless victims to another Will, subject to some incredibly superior order, what Schopenhauer called a “metaphysical entity,” a kind of universal Consciousness compared to which individual Consciousness is but a dream. If we realize the wholeness of the universe and accept the fact that there is a miraculous order being brought out of apparent disorder, a kind of certainty out of the uncertainty of the probability theory, if we accept this without seeking an explanation, then it will not be difficult to accept that situation. It is just there and why not? It is a self-generated process in which the human being is a very, very small part.

We cannot make total order of our observations on the working of this world of paradox. There always appears to be something missing. There is paradox and yet there is an exquisite order to the paradox and utter confusion for the limited human intellect. We feel inadequate and helpless only because we attempt to observe and then discern the pattern. All we can really do is to go along with it. The human intellect likes order. It doesn’t like this theory of probability and uncertainty. I came across this next passage by a physicist: “Why should we not have security? Why should we not have certainty? We cannot have this world. It is unacceptable, it is unworkable. A world of certainty is unworkable.”

The alternative to this uncertain world is a certain world. In such a world particles will follow determined paths, with exact locations at each and every point. That is what the human intellect wants because that is something it can understand. But this alternative of a certain world is known to be unworkable. That tiny electron inside of every atom would have to radiate each and every instant in such a certain world. It would lose all of its energy and quickly fall into the nucleus. All atoms would disappear. All electromagnetic energy would vanish. All nervous systems would cease their activity. All life would stop, for life as we know it can only exist through the blessing of uncertainty. Security is a myth.

So, for the seeker to expect that he will follow such and such path, follow certain disciplines, meditate for such and such a time, and feel that he has a right to expect to be enlightened… That kind of certainty, that kind of expectation is a myth.

Out of the millions of people, how many have had their minds turned inwards? How many have given up their “happy life” to be miserable seekers? They had no choice.

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Sitting here, you and I | خنك آن دم كه نشستيم

A first attempt at translating the work of Mowlana Jalaluddin Mohammad Balkhi ‘Rumi’ (in memory of my late grandfather, who would not have understood, but who i loved, and who loved me, nonetheless):

خنك آن دم كه نشستيم در ايوان من و تو
به دو نقش و به دو صورت به يكى جان من و تو
رنگ باغ و دم مرغان بدهد آب حيات
آن زمانى كه در آييم به بستان من و تو
اختران فلک آیند به نظاره ما
مه خودرا بنماييم به ايشان من ه تو
من و تو بى من و تو جمع شويم از سر ذوق
خوش و فارغ ز خرافات پريشان من و تو
طوطيان فلكى جمله جگرخوار شوند
در مقامى كه بخنديم بر آن سان من و تو
اين عجبتر كه من و تو به يكى كنج اين جا
هم در اين دم به عراقيم و خراسان من و تو

khonak an dam keh neshastim dar eyvan, man o to

beh do naqsh, o beh do surat, beh yeki jan, man o to

rang-e-bagh o dam-e-morghan bedahad ab-e-hayyat

an zamani keh dar ayyim bebostan man o to

akhteran-e-falak ayand beh nazzareh-ye ma

mah-e-khod ra benemayyim beh ishan man o to

man o to, bi man o to, jam’ shavim az sar-e-zowq

khosh o faregh ze khorafat-e-parishan man o to

tutiyan-e-falaki jomleh jegarkhor shavand

dar maqami keh bekhandim bar an san man o to

in ‘ajabtar keh man o to beh yeki konj inja

ham dar in dam beh ‘eraqim o khorasan man o to

/cool/that/moment/when/we sit/on/the veranda/you and I/

/in two images/in two forms/in one soul/you and I/

/colours of the garden/and the breath of birds/give/the water of life/

/that time/that/we enter/the garden/you and I/

/the stars of heaven/arrive/to gaze upon/us/

/the moon/itself/we show/to them/you and I/

/you and I/without/you and I/join together/in delight/

/happy/and free/from/scattered extravagant stories/you and I/

/parrots of heaven/all together/liver-eaten/become/

/in a place/where/we laugh/in that manner/you and I/

/this/most strange/that/you and I/in/one/corner/here/

/at once/in/this moment/in/Iraq/we are/and Khorasan/you and I/

Sitting here, you and I, the courtyard breeze is cool

Two images, two forms, one thought, you and I

The orchard-shades, the songs of birds give up the world’s secrets

When we find ourselves here in this garden

The stars of distant galaxies come to gaze on us

You and I, together, we show them the moon

You and I, without ‘you’ and ‘I’, we are absolute joy

Happy, free from empty words, such are you and I

All those birds of paradise, full of childish envy

While in that same place, you and I, we cannot help but laugh

What’s truly strange is  you and I, here together, now

At once here in the west and at once here in the east

such we always were

You

and I

-translation by halewi

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Darwin’s unfinished revolution | The Economist

Cambridge paleontologist Simon Conway-Morris has interesting ideas about the tendency of evolution to follow certain overarching pathways. In a recent talk while visiting here on campus, he went on to make some oblique, but fascinating, conjectures about the immanence of phenomena such as complexity and intelligence. The Economist discusses him here:

… Simon Conway-Morris, a palaeontologist at Cambridge University, in England, is the champion of a new interpretation of evolution—one that challenges the view that it is largely governed by the accident of circumstances. Unlike Gould, he thinks that if evolution were replayed from the beginning, a lot of things would turn out the same.

Dr Conway-Morris has arrived at this view from a detailed study of what is known as convergent evolution. Darwin himself was intrigued by this phenomenon, in which different groups of organisms independently evolve similar solutions to similar problems, whether these solutions are teeth, eyes, brains, ecosystems or societies. Where other biologists have noted such convergences as “remarkable”, Dr Conway-Morris believes they actually tell a broader story.

His argument is that, given the nature of physics and chemistry, there may be only a limited number of ways in which things can work. Evolution will be channelled into these successful paths, and thus does have trends. Two of these, he thinks, are towards complexity and intelligence. He adds that things “don’t just happen in chemistry”. They happen because of pre-existing causes. Whether it is the molecules of crystallin that are used to build an eye or the haemoglobin that makes blood carry oxygen, the nature of molecules themselves means that evolution is more likely to follow a path determined by their basic structure. Evolution is a mechanism, and it works within rules.

Dr Conway-Morris’s view of the world may or may not turn out to be correct. If it is, it may prove more palatable to some people than the current interpretation of the biological world as ultimately materialist and purposeless.

Darwin himself was deeply troubled by his materialist thoughts and what they meant. He considered how thoughts and emotions were simply secretions of the brain. From his correspondence it seems his religious beliefs never reached a fixed position, but he was sensitive to the extent to which his ideas could upset others. He even devised a diplomatic answer that avoided challenging the existence of God. When asked about the origins of emotions, instincts and degrees of talent, he noted, “say only they are so because brain of child resembles parent’s stock”.

via Charles Darwin’s revolution is unfinished | Unfinished business | The Economist.

And in audio, here.

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Arab press increasingly numb to Israeli political rhetoric

“Conventional wisdom has it that Israeli Jewish voters are more likely to vote for candidates with a reputation of taking a tough stance vis-a-vis the Palestinians. In both the popular and political lexicon, this translates into spilling Palestinian blood, destroying Palestinian homes and further narrowing Palestinian horizons,” writes Khaled Amayreh in the English language Al-Ahram Weekly. …

An attempt to find an opinion piece about the upcoming elections in newspapers of the Persian Gulf states, Jordan or Syria came up blank. The outcome does not interest the Arab media, since whoever becomes Israel’s new prime minister is hardly any different from the other contenders. “Israel’s foreign policy agenda is no longer a mystery to us,” explains a Jordanian columnist writing in the Al Rai newspaper. “The interest in what is happening in Israel derived from the impression that different prime ministers can set different agendas – solve the Palestinian problem, withdraw from the Golan Heights, create regional opportunities. Today everyone is using the language of violence. Everyone wants deterrence against the Palestinians and no one is talking about peace agreements.”

via Haaretz – English language edition

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Israeli TV: government PR as coherent as zionist hip-hop

via YouTube – Eretz Nehedert – Israeli hasbarah

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