பட்டாம்பூச்சி விளைவு

பட்டாம்பூச்சி விளைவு (Butterfly effect) எனப்படுவது ஒரு கணித கருத்துரு. ஓர் இயங்கியல் அமைப்பில் (dynamical system) நுண்ணிய தொடக்கநிலை வேறுபாடுகளே (small variations of the initial condition) அமைப்பின் நீண்ட கால இயக்கத்தில் பெரிய வேறுபாடு கொண்ட விளைவுகளை ஏற்படுத்தலாம் என்பதுவே பட்டாம்பூச்சி விளைவின் சாரம்.

கருத்துருவின் எல்லைகள்

கணித எல்லைகள்

பட்டாம்பூச்சி விளைவு ஒரு குறிப்பிட்ட சில கணித பிரச்சினைகளிலேயே முக்கிய இடத்தைப் பெறுகிறது. எல்லா இடங்களிலும் இதை கருத்தில் கொண்டால் நடைமுறையாக தீர்வுகளை காண்பது சாத்தியமற்றதாகிவிடும். பல இடங்களில் கிட்ட தட்ட கணிப்பதே தேவை. இதை வில்லியம் ஜேம்சின் பின்வரும் கூற்றைக் கொண்டு மேலும் விளங்கிக் கொள்ளலாம்.

“ In mathematics we know how this method of ignoring and neglecting quantities lying outside a certain range has been adopted in the differential calculus. The calculator throws out all the "infinitesimals" of the quantities he is considering. He treats them (under certain rules) as if they did not exist. In themselves they exist perfectly all the while; but they are as if they did not exist for the purposes of his calculation. Just so an astronomer, dealing with the tidal movements of the ocean, takes no account of the waves made by the wind, or by the pressure of all the steamers which day upon night are moving their thousands of tons upon its surface. Just so the marksman, in sighting his rifle, allows for the motion of the wind, but not for the equally real motion of the earth and solar system. Just so a business man's punctuality may overlook an error of five minutes, while a physicist, measuring the velocity of light, must count each thousandth of a second. ”

- William James

மனித எல்லைகள்

இந்தக் கருத்துரு பொதுவாக தன்னிச்சை அல்லது சுய சிந்தனை, செயல் வல்மை அற்ற ஒரு அமைப்பை முன்வைத்தே முன்வைக்கப்படுகிறது. தன்னிச்சையாக சிந்தித்து இயங்கக்கூடிய சமூக சூழலுக்கு இந்த விளைவு எவ்வளவு பொருத்தம் என்பது கேள்விக்குரியதே.

வினை எது விளைவு எது

முதன்மைக் கட்டுரை: வினை விளைவுக் கோட்பாடு

“ We might say with perfect legitimacy that a friend of ours, who had slipped on the ice upon his door-step and cracked his skull, some months after dining with thirteen at the table, died because of that ominous feast. I know, in fact, one such instance; and I might, if I chose, contend with perfect logical propriety that the slip on the ice was no real accident. "There are no accidents," I might say, "for science. The whole history of the world converged to produce that slip. If anything had been left out, the slip would not have occurred just there and then. To say it would is to deny the relations of cause and effect throughout the universe. The real cause of the death was not the slip, but the conditions which engendered the slip, --- and among them his having sat at a table, six months previous, one among thirteen. That is truly the reason why he died within the year.................The human mind, however, is constituted on an entirely different plan. It has no such power of universal intuition. Its finiteness obliges it to see but two or three things at a time. If it wishes to take wider sweeps it has to use `general ideas,' as they are called, and in so doing to drop all concrete truths. Thus, in the present case, if we as men wish to feel the connection between the milky way and the boy and the dinner and the sparrow and the man's death, we can do so only by falling back on the enormous emptiness of what is called an abstract proposition. We must say, All things in the world are fatally predetermined, and hang together in the adamantine fixity of a system of natural law. But in the vagueness of this vast proposition we have lost all the concrete facts and links; and in all practical matters the concrete links are the only things of importance. The human mind is essentially partial. It can be efficient at all only by picking out what to attend to, and ignoring everything else, --- by narrowing its point of view. Otherwise, what little strength it has is dispersed, and it loses its way altogether. Man always wants his curiosity gratified for a particular purpose. And if, in the case of the unfortunate man, we lose ourselves in contemplation of the thirteen-at-table mystery, and fail to notice the ice on the step and cover it with ashes, some other poor fellow, who never dined out in his life, may slip on it in coming to the door, and fall and break his head too. ”

- William James.

இவற்றையும் பாக்க

• தசாவதாரம் (2008 திரைப்படம்)