In a high tech world the cure for the tragic shortcomings and perilous fallacies of human intuition is education, but education in economics, evolutionary biology, probability and statistics - unfortunately most High School and College curricula have barely changed since Medieval times!
Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as the result of animal spirits-a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.
First get a clear notion of what you desire to accomplish and then in all probability you will succeed in doing it.
My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.
I may finally call attention to the probability that the association of paternal and maternal chromosomes in pairs and their subsequent separation during the reducing division as indicated above may constitute the physical basis of the Mendelian law of heredity.
It is only through the psyche that we can establish that God acts upon us, but we are unable to distinguish whether these actions emanate from God or from the unconscious. We cannot tell whether God and the unconscious are two different entities. Both are border-line concepts for transcendental contents. But empirically it can be established, with a sufficient degree of probability, that there is in the unconscious an archetype of wholeness.
But the indeterminate future is somehow one in which probability and statistics are the dominant modality for making sense of the world. Bell curves and random walks define what the future is going to look like. The standard pedagogical argument is that high schools should get rid of calculus and replace it with statistics, which is really important and actually useful. There has been a powerful shift toward the idea that statistical ways of thinking are going to drive the future.
Not smoking enough will cause lung cancer! If anybody is getting a cancerous activity in the lung, the probabilities are that it's radiation dosage coupled with the fact that he smokes. And what it does is start to run out the radiation dosage, don't you see.
The belief in the probability of death with dignity is our, and society’s, attempt to deal with the reality of what is all too frequently a series of destructive events that involve by their very nature the disintegration of the dying person’s humanity. I have not often seen much dignity in the process by which we die.
Human intellectual progress, such as it has been, results from our long struggle to see things 'as they are,' or in the most universally comprehensible way, and not as projections of our own emotions. Thunder is not a tantrum in the sky, disease is not a divine punishment, and not every death or accident results from witchcraft. What we call the Enlightenment and hold on to only tenuously, by our fingernails, is the slow-dawning understanding that the world is unfolding according to its own inner algorithms of cause and effect, probability and chance, without any regard for human feelings.
Pi is not merely the ubiquitous factor in high school geometry problems; it is stitched across the whole tapestry of mathematics, not just geometry's little corner of it. Pi occupies a key place in trigonometry too. It is intimately related to e, and to imaginary numbers. Pi even shows up in the mathematics of probability
In corporation [corporate] religions as in others, the heretic must be cast out not because of the probability that he is wrong but because of the possibility that he is right.
Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.
It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset.
It is only by fidelity in little things that the grace of true love to God can be sustained, and distinguished from a passing fervor of spirit. . . . No one can well believe that our piety is sincere, when our behavior is lax and irregular in its little details. What probability is there that we should not hesitate to make the greatest sacrifices, when we shrink from the smallest?
Meanwhile, little people like you and me, if our prayers are sometimes granted, beyond all hope and probability, had better not draw hasty conclusions to our own advantage. If we were stronger, we might be less tenderly treated. If we were braver, we might be sent, with far less help, to defend far more desperate posts in the great battle.
As in the piling up of hypothetical alternatives, creative accidents follow the law of probabilities the more we fish, the more likely we are to get a strike.
All the politics in the world are nothing else but a kind of analysis of the quantity of probability in casual events, and a good politician signifies no more but one who is dexterous at such calculations.
I believe the calculation of the quantity of probability might be improved to a very useful and pleasant speculation, and applied to a great many events which are accidental, besides those of games; only these cases would be infinitely more confused, as depending on chances which the most part of men are ignorant of.
A point of great importance would be first to know: what is the capacity of the earth? And what charge does it contain if electrified? Though we have no positive evidence of a charged body existing in space without other oppositely electrified bodies being near, there is a fair probability that the earth is such a body, for by whatever process it was separated from other bodies - and this is the accepted view of its origin - it must have retained a charge, as occurs in all processes of mechanical separation.
Neither nature, experience, nor probability informs these lists of 'entitlements', which are subject to no constraints except those of the mind and appetite of their authors.
It is natural to men to judge of things less known, by some similitude they observe, or think they observe, between them and things more familiar or better known. In many cases, we have no better way of judging. And, where the things compared have really a great similitude in their nature, when there is reason to think that they are subject to the same laws, there may be a considerable degree of probability in conclusions drawn from analogy.
The first attempts to consider the behavior of so-called "random neural nets" in a systematic way have led to a series of problems concerned with relations between the "structure" and the "function" of such nets. The "structure" of a random net is not a clearly defined topological manifold such as could be used to describe a circuit with explicitly given connections. In a random neural net, one does not speak of "this" neuron synapsing on "that" one, but rather in terms of tendencies and probabilities associated with points or regions in the net.
Yet there seemed to be some truth in the law of probability, according to which the chance of success is directly proportionate to the number of repetitions.
One would appear ridiculous who would say, that it is only probable the sun will rise to-morrow, or that all men must die; thoughit is plain we have no further assurance of these facts than what experience affords us.
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