Thomas Theorem Quotes

The future is the result of actions, and actions are the result of behavior, and behavior is the result of prediction.

These dictates of Reason, men use to call by the name of Lawes; but improperly: for they are but Conclusions, or Theoremes concerning what conduceth to the conservation and defence of themselves; whereas Law, properly is the word of him, that by right hath command over others. But yet if we consider the same Theoremes, as delivered in the word of God, that by right commandeth all things; then are they properly called Lawes.

If men define situations as real, they are real in their consequences.

The combination of Bayes and Markov Chain Monte Carlo has been called "arguably the most powerful mechanism ever created for processing data and knowledge." Almost instantaneously MCMC and Gibbs sampling changed statisticians' entire method of attacking problems. In the words of Thomas Kuhn, it was a paradigm shift. MCMC solved real problems, used computer algorithms instead of theorems, and led statisticians and scientists into a worked where "exact" meant "simulated" and repetitive computer operations replaced mathematical equations. It was a quantum leap in statistics.

One Washington axiom, proved more times than the Pythagorean theorem, states that in the presence of oxygen, one loud fart with an obvious culprit will cover many small emissions in the same room, provided they are nearly simultaneous.

Experience has convinced me that an assumption, though false, if persisted in, will harden into fact, that continuous imagination is sufficient for all things, and all my reasonable plans and actions will never make up for my lack of continuous imagination. [or my over use of imagination....This quote is referencing The Thomas theorem : a theory of sociology which was formulated in 1928 by William Isaac - "if men define situations as real, they are real in their consequences” and this is because they will behave in a way that might bring the situation about. - If I think John Doe hates and is against me, and then I behave and treat him like an enemy, he will most likely actually become one due to my behavior towards him. ]

After hovering in the ethereal world of mathematics and geometry, economics was forced to crash-land and take its place in the real world of political debate. Do economists wish to pursue the Good Society in the spirit of the social contract tradition which started some time in ancient Greece, reasserted itself in Europe with J.-J.Rousseau and found its apotheosis in John Rawls? Or do they wish for a social contract which effectively rules the State out as anything other than a provider of order and security—a tradition which began with Thomas Hobbes and culminated in Robert Nozick’s theory? Or, indeed can economists think of something in between? Thus economics is back into the mire courtesy of Arrow’s third theorem, which dispels any hopes of a Rational Society springing from some form of advanced utility maximisation. Economics can no longer escape the political, philosophical debates which resonate across the humanities—from literature to sociology and from politics to moral philosophy. This is a good thing. At last, economics can become interesting again after a century of continuous pedantry.

Every mental activity—contemplating a theorem, savoring a hot fudge sundae, dreaming of the boy next door—consists of neurons firing in a certain sequence.

Evans-Pritchard’s confession reveals the way the power advantage of the subject whose definition of a situation prevails in the larger social context (in this case the majority of the Azande) shapes the environment and behavioral constraints that impact the subject who, although does not define the situation the same way, has to behave according to the former subject’s definition in order to obtain the needed resources (in this case Evans-Pritchard, who is interested in gaining knowledge of the social organization of the Azande). For Evans-Pritchard, while living among the Azande, the actual world is as if there were magical forces around, true oracles and evil witches, as his whole daily life is structured around those nonexistent entities.

We sit as in a boundless Phantasmagoria and Dream-grotto; boundless, for the faintest star, the remotest century, lies not even nearer the verge thereof: sounds and many-coloured visions flit round our sense; but Him, the Unslumbering, whose work both Dream and Dreamer are, we see not; except in rare half-waking moments, suspect not. Creation, says one, lies before us, like a glorious Rainbow; but the Sun that made it lies behind us, hidden from us. Then, in that strange Dream, how we clutch at shadows as if they were substances; and sleep deepest while fancying ourselves most awake! Which of your Philosophical Systems is other than a dream-theorem; a net quotient, confidently given out, where divisor and dividend are both unknown? What are all your national Wars, with their Moscow Retreats, and sanguinary hate-filled Revolutions, but the Somnambulism of uneasy Sleepers? This Dreaming, this Somnambulism is what we on Earth call Life; wherein the most indeed undoubtingly wander, as if they knew right hand from left; yet they only are wise who know that they know nothing.

The Bayesian Invisible Hand … free-market capitalism and Bayes’ theorem come out of something of the same intellectual tradition. Adam Smith and Thomas Bayes were contemporaries, and both were educated in Scotland and were heavily influenced by the philosopher David Hume. Smith’s 'Invisible hand' might be thought of as a Bayesian process, in which prices are gradually updated in response to changes in supply and demand, eventually reaching some equilibrium. Or, Bayesian reasoning might be thought of as an 'invisible hand' wherein we gradually update and improve our beliefs as we debate our ideas, sometimes placing bets on them when we can’t agree. Both are consensus-seeking processes that take advantage of the wisdom of crowds. It might follow, then, that markets are an especially good way to make predictions. That’s really what the stock market is: a series of predictions about the future earnings and dividends of a company. My view is that this notion is 'mostly' right 'most' of the time. I advocate the use of betting markets for forecasting economic variables like GDP, for instance. One might expect these markets to improve predictions for the simple reason that they force us to put our money where our mouth is, and create an incentive for our forecasts to be accurate. Another viewpoint, the efficient-market hypothesis, makes this point much more forcefully: it holds that it is 'impossible' under certain conditions to outpredict markets. This view, which was the orthodoxy in economics departments for several decades, has become unpopular given the recent bubbles and busts in the market, some of which seemed predictable after the fact. But, the theory is more robust than you might think. And yet, a central premise of this book is that we must accept the fallibility of our judgment if we want to come to more accurate predictions. To the extent that markets are reflections of our collective judgment, they are fallible too. In fact, a market that makes perfect predictions is a logical impossibility.

The PSR is reflected in points traveling in complex-numbered Euler circles where no point is privileged over any other. From this motion, we get sine and cosine waves, even and odd functions, symmetry and antisymmetry, orthogonality and non-orthogonality, phase, straight-line radii, right-angled triangles, Pythagoras’ theorem, the speed of mathematics (c), π, e, i, Fourier mathematics … and from all of that we get the whole of mathematics (eternal, necessary and mental; Being), and thus the whole of science (temporal, contingent and material; Becoming). And that is the whole universe explained. Nothing else is required. The PSR gives us mathematics, mathematics gives us science, and that’s all we need for the universe: science with a mathematical and rational core rather than with a material and observable core. What could be more rational and logical?

The Thomas theorem, a sociological staple, says: 'If men define situations as real, they are real in their consequences.

In any event, Socrates’ proof of prenatal immortality is that one of Meno’s uneducated slave boys actually comes up with the Pythagorean theorem without ever having studied geometry! Therefore, he must be remembering it. You recall that theorem: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Huh? We can barely remember that from tenth grade, let alone from before we were born.