"probability"タグの名言

All statistics have outliers.

Statistics, likelihoods, and probabilities mean everything to men, nothing to God.

In practical life we are compelled to follow what is most probable ; in speculative thought we are compelled to follow truth.

Statistically, the probability of any one of us being here is so small that the mere fact of our existence should keep us all in a state of contented dazzlement.

You, dear reader, have now two accounts to choose between and there can be no doubt which is most probable.

He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.

4. Religion. Your reason is now mature enough to examine this object. In the first place, divest yourself of all bias in favor of novelty & singularity of opinion... shake off all the fears & servile prejudices, under which weak minds are servilely crouched. Fix reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason, than that of blindfolded fear. You will naturally examine first, the religion of your own country. Read the Bible, then as you would read Livy or Tacitus. The facts which are within the ordinary course of nature, you will believe on the authority of the writer, as you do those of the same kind in Livy and Tacitus. The testimony of the writer weighs in their favor, in one scale, and their not being against the laws of nature, does not weigh against them. But those facts in the Bible which contradict the laws of nature, must be examined with more care, and under a variety of faces. Here you must recur to the pretensions of the writer to inspiration from God. Examine upon what evidence his pretensions are founded, and whether that evidence is so strong, as that its falsehood would be more improbable than a change in the laws of nature, in the case he relates. For example in the book of Joshua we are told the sun stood still several hours. Were we to read that fact in Livy or Tacitus we should class it with their showers of blood, speaking of statues, beasts, &c. But it is said that the writer of that book was inspired. Examine therefore candidly what evidence there is of his having been inspired. The pretension is entitled to your inquiry, because millions believe it. On the other hand you are astronomer enough to know how contrary it is to the law of nature that a body revolving on its axis as the earth does, should have stopped, should not by that sudden stoppage have prostrated animals, trees, buildings, and should after a certain time have resumed its revolution, & that without a second general prostration. Is this arrest of the earth's motion, or the evidence which affirms it, most within the law of probabilities? You will next read the New Testament. It is the history of a personage called Jesus. Keep in your eye the opposite pretensions: 1, of those who say he was begotten by God, born of a virgin, suspended & reversed the laws of nature at will, & ascended bodily into heaven; and 2, of those who say he was a man of illegitimate birth, of a benevolent heart, enthusiastic mind, who set out without pretensions to divinity, ended in believing them, and was punished capitally for sedition, by being gibbeted, according to the Roman law, which punished the first commission of that offence by whipping, & the second by exile, or death in fureâ. ...Do not be frightened from this inquiry by any fear of its consequences. If it ends in a belief that there is no God, you will find incitements to virtue in the comfort and pleasantness you feel in its exercise, and the love of others which it will procure you... In fine, I repeat, you must lay aside all prejudice on both sides, and neither believe nor reject anything, because any other persons, or description of persons, have rejected or believed it... I forgot to observe, when speaking of the New Testament, that you should read all the histories of Christ, as well of those whom a council of ecclesiastics have decided for us, to be Pseudo-evangelists, as those they named Evangelists. Because these Pseudo-evangelists pretended to inspiration, as much as the others, and you are to judge their pretensions by your own reason, and not by the reason of those ecclesiastics. Most of these are lost... [Letter to his nephew, Peter Carr, advising him in matters of religion, 1787]

You were born a winner, a warrior, one who defied the odds by surviving the most gruesome battle of them all - the race to the egg. And now that you are a giant, why do you even doubt victory against smaller numbers and wider margins? The only walls that exist are those you have placed in your mind. And whatever obstacles you conceive, exist only because you have forgotten what you have already achieved.

I do not pretend to be able to prove that there is no God. I equally cannot prove that Satan is a fiction. The Christian god may exist; so may the gods of Olympus, or of ancient Egypt, or of Babylon. But no one of these hypotheses is more probable than any other: they lie outside the region of even probable knowledge, and therefore there is no reason to consider any of them.

I believe that we do not know anything for certain, but everything probably.

anything is possible but probably not that

Every time you understand something, religion becomes less likely. Only with the discovery of the double helix and the ensuing genetic revolution have we had grounds for thinking that the powers held traditionally to be the exclusive property of the gods might one day be ours. . . .

Among all the occurrences possible in the universe the a priori probability of any particular one of them verges upon zero. Yet the universe exists; particular events must take place in it, the probability of which (before the event) was infinitesimal. At the present time we have no legitimate grounds for either asserting or denying that life got off to but a single start on earth, and that, as a consequence, before it appeared its chances of occurring were next to nil. ... Destiny is written concurrently with the event, not prior to it... The universe was not pregnant with life nor the biosphere with man. Our number came up in the Monte Carlo game. Is it surprising that, like the person who has just made a million at the casino, we should feel strange and a little unreal?

Critical thinking is an active and ongoing process. It requires that we all think like Bayesians, updating our knowledge as new information comes in.

The wavefunction of superposed states doesn’t say anything about what the photon is ‘like’. It is a tool for letting you predict what you will measure. And what you will measure for a superposed state like this is that sometimes the measurement device registers a photon with a vertical polarization, and sometimes with a horizontal one. If the superposed state is described by a wavefunction that has an equal weighting of the vertical and horizontal wavefunctions, then 50% of your measurements will give the result ‘vertical’ and 50% will indicate ‘horizontal’. If you accept Bohr’s rigour/complacency (delete to taste), we don’t need to worry what the superposed state ‘is’ before making a measurement, but can just accept that such a state will sometimes give us one result and sometimes another, with a probability defined by the weightings of the superposed wavefunctions in the Schrödinger equation. It all adds up to a consistent picture.

The probability of apocalypse soon cannot be realistically estimated, but it is surely too high for any sane person to contemplate with equanimity.

Psychology helps to measure the probability that an aim is attainable.

The United States can pay any debt it has because we can always print money to do that. So there is zero probability of default.

The fact that we don't keep repeating tests in the same arena is not because the probability of the hypothesis showing its falsity in other arenas goes up after it has passed tests in one arena.

We didn't push the Russians to intervene, but we knowingly increased the probability that they would.