The solution of the Monty Hall problem hinges on the concept of information, and more specifically, on the relationship between added information and probability.
Tenderness is greater than love. I do not admire carnal love when it is by itself and bare. I do not admire its disorderly selfish paroxysms, so grossly short-lived. And yet without love the attachment of two human beings is always weak. Love must be added to affection. The things it contributes to a union are absolutely needed — exclusiveness, intimacy, and simplicity.
How much do you think it costs to go to college? Most people are likely to answer by adding together their expenditures on tuition, room and board, books, and the like, and then deducting any scholarship funds they may receive. Suppose that amount comes to $15,000.
Economists keep score differently. They first want to know how much you would be earning if you were not attending college. Suppose
that salary is $20,000 per year. This may seem irrelevant, but because you give up these earnings by attending college, they must be added to your tuition bill. You have that much less income because of your education. On the other side of the ledger, economists would not count all of the university’s bill for room and board as part of the costs of your education. They would want to know how
much more it costs you to live at school rather than at home. Economists would count only these extra costs as an educational expense because you would have incurred these costs whether or not you attend college. On balance, college is probably costing you much more than you think. And, as we will see later, taking opportunity cost into account in any personal planning will help you to make more
rational decisions.
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be
Lorentz invariant. Of course, the situation is different if the quantum mechanical predictions are of limited validity. Conceivably they might apply only to experiments in which the settings of the instruments are made sufficiently in advance to allow them to reach some mutual rapport by exchange of signals with velocity less than or equal to that of light. In that connection, experiments of the
type proposed by Bohm and Aharonov, in which the settings are changed during the flight of the particles, are crucial.
Structure is a primary element of experience and not something that is added by the mind. In this respect, it can be said that the techniques of understanding call for a drastic revision of the usual modes of thought that treat being and understanding as independent or at least as separable from one another.
We find amongst animals, as amongst men, power of feeling pleasure, power of feeling pain; we see them moved by love and by hate; we see them feeling terror and attraction; we recognize in them powers of sensation closely akin to our own, and while we transcend them immensely in intellect, yet, in mere passional characteristics our natures and the animals' are closely allied. We know that when
they feel terror, that terror means suffering. We know that when a wound is inflicted, that wound means pain to them. We know that threats bring to them suffering; they have a feeling of shrinking, of fear, of absence of friendly relations, and at once we begin to see that in our relations to the animal kingdom a duty arises which all thoughtful and compassionate minds should recognize - the duty
that because we are stronger in mind than the animals, we are or ought to be their guardians and helpers, not their tyrants and oppressors, and we have no right to cause them suffering and terror merely for the gratification of the palate, merely for an added luxury to our own lives.
Hell, any plan that added "and then we pray" is not a trip to Disneyland.