The funny behavior of the "oomph"

From a very enjoyable Richard Feyman lecture, "The Meaning of It All":

[S]cience can be understood directly when we understand that observation is the ultimate and final judge of the truth of an idea. . . . If there is an exception to any rule, and if it can be proved by observation, that rule is wrong. The exceptions to any rule are most interesting in themselves, for they show us that the old rule is wrong. [The scientist] does not try to avoid showing that the rules are wrong; there is progress and excitement in the exact opposite. He tries to prove himself wrong as quickly as possible. . . . There are ways to try it and see. Questions like, “Should I do this?” and “What is the value of this?” are not of the same kind.

. . . [T]here is a famous joke about a man who complains to a friend of a mysterious phenomenon. The white horses on his farm eat more than the black horses. He worries about this and cannot understand it, until his friend suggests that maybe he has more white horses than black ones. It sounds ridiculous, but think how many times similar mistakes are made in judgments of various kinds. . . . Another very important technical point is that the more specific a rule is, the more interesting it is. The more definite the statement, the more interesting it is to test. If someone were to propose that the planets go around the sun because all planet matter has a kind of tendency for movement, a kind of motility, let us call it an “oomph,” this theory could explain a number of other phenomena as well. So this is a good theory, is it not? No. It is nowhere near as good as a proposition that the planets move around the sun under the influence of a central force which varies exactly inversely as the square of the distance from the center. The second theory is better because it is so specific; it is so obviously unlikely to be the result of chance. It is so definite that the barest error in the movement can show that it is wrong; but the planets could wobble all over the place, and, according to the first theory, you could say, “Well, that is the funny behavior of the ‘oomph.’”

. . . We have a way of checking whether an idea is correct or not that has nothing to do with where it came from. We simply test it against observation. . . . We have lost the need to go to an authority to find out whether an idea is true or not. We can read an authority and let him suggest something; we can try it out and find out if it is true or not. . . . In that sense it makes no difference where the ideas come from. Their real origin is unknown; we call it the imagination of the human brain, the creative imagination—it is known; it is just one of those “oomphs.” . . . Incidentally, the fact that there are rules at all to be checked is a kind of miracle; that it is possible to find a rule, like the inverse square law of gravitation, is some sort of miracle. It is not understood at all, but it leads to the possibility of prediction—that means it tells you what you would expect to happen in an experiment you have not yet done.

The rules that describe nature seem to be mathematical. This is not a result of the fact that observation is the judge, and it is not a characteristic necessity of science that it be mathematical. It just turns out that you can state mathematical laws, in physics at least, which work to make powerful predictions. Why nature is mathematical is, again, a mystery.

. . . The laws are guessed laws, extrapolations, not something that the observations insist upon. They are just good guesses that have gone through the sieve so far. And it turns out later that the sieve now has smaller holes than the sieves that were used before, and this time the law is caught. . . . [Scientific k]nowledge is of no real value if all you can tell me is what happened yesterday. It is necessary to tell what will happen tomorrow if you do something—not only necessary, but fun. Only you must be willing to stick your neck out. . . . It is better to say something and not be sure than not to say anything at all.

Nicomachean Ethics IX.10

How many friends should one keep? 

Should we, then, make as many friends as possible, or-as in the case of hospitality it is thought to be suitable advice, that one should be 'neither a man of many guests nor a man with none'-will that apply to friendship as well; should a man neither be friendless nor have an excessive number of friends?

To friends made with a view to utility this saying would seem thoroughly applicable; for to do services to many people in return is a laborious task and life is not long enough for its performance. Therefore friends in excess of those who are sufficient for our own life are superfluous, and hindrances to the noble life; so that we have no need of them. Of friends made with a view to pleasure, also, few are enough, as a little seasoning in food is enough. 

Favors to the useful have to be repaid, so you don't want too many of that sort; and those you keep around only for fun can be few in number, since who has time for much fun? The world is full of work to do. 

But as regards good friends, should we have as many as possible, or is there a limit to the number of one's friends, as there is to the size of a city? You cannot make a city of ten men, and if there are a hundred thousand it is a city no longer.

There's an interesting question: are our cities not cities in Aristotle's sense, some of them containing millions? They remain polities of a sort -- a few of them, like Singapore, almost in Aristotle's sense. Hong Kong, perhaps, until the Communists took it back. Have we lost something essential to human community by becoming too many?

In ancient Athens, though it was a great city in its era, at least the key people could all know each other. To some degree that's true in small towns today. It seems as if a better community ought to be possible when we can all get to know one another and, therefore, make adjustments for each other. Yet of course it was that very city that put Socrates to death.

Famously we now have Dunbar's number, which suggests that the average person can maintain not more than about 150 relationships. Presumably Aristotle was trying to work out something similar here.

But the proper number is presumably not a single number, but anything that falls between certain fixed points. So for friends too there is a fixed number perhaps the largest number with whom one can live together (for that, we found, thought to be very characteristic of friendship); and that one cannot live with many people and divide oneself up among them is plain.

How many people can live together? We tend to think of two or three or five, but when we were younger and lived in barracks or dormitories the number was much larger.  

Further, they too must be friends of one another, if they are all to spend their days together; and it is a hard business for this condition to be fulfilled with a large number. It is found difficult, too, to rejoice and to grieve in an intimate way with many people, for it may likely happen that one has at once to be happy with one friend and to mourn with another. Presumably, then, it is well not to seek to have as many friends as possible, but as many as are enough for the purpose of living together; for it would seem actually impossible to be a great friend to many people.

Now another argument for monogamy:  

This is why one cannot love several people; love is ideally a sort of excess of friendship, and that can only be felt towards one person; therefore great friendship too can only be felt towards a few people. This seems to be confirmed in practice; for we do not find many people who are friends in the comradely way of friendship, and the famous friendships of this sort are always between two people. Those who have many friends and mix intimately with them all are thought to be no one's friend, except in the way proper to fellow-citizens, and such people are also called obsequious.

Fafhrd and the Grey Mouser, I suppose; but against that, the Rat Pack as a famous group of friends.  

In the way proper to fellow-citizens, indeed, it is possible to be the friend of many and yet not be obsequious but a genuinely good man; but one cannot have with many people the friendship based on virtue and on the character of our friends themselves, and we must be content if we find even a few such.

Indeed, even a few virtuous friends are a great wealth if one can find them. That is, however, a pragmatic difficulty rather than an answer to the question: shouldn't one want more if one could find them? 

It may be that only pragmatic answers are possible to this question; we are in fact limited by something like Dunbar's number; we can't in fact find very many virtuous friends in any human environ. It may be a limit to us rather than a proof about what ought to be wanted.

Yet that is in keeping with what we were told to expect in I.3: not proofs, which belong to mathematics and strict logic, but arguments about what is most probably true. Ethics often admits of no better than this; it is what we were warned the wise would seek from it, this and no more.

Nicomachean Ethics IX.9

Today's is a longer chapter; it is on the subject of whether people who are already happy need friends or not. There is not much to comment on here, other than to draw out the argument; the conclusion, that the supremely happy man will need virtuous friends or he'll be deficient in something important (and thus not supremely happy) is obvious.

It is also disputed whether the happy man will need friends or not. It is said that those who are supremely happy and self-sufficient have no need of friends; for they have the things that are good, and therefore being self-sufficient they need nothing further, while a friend, being another self, furnishes what a man cannot provide by his own effort; whence the saying 'when fortune is kind, what need of friends?' But it seems strange, when one assigns all good things to the happy man, not to assign friends, who are thought the greatest of external goods. And if it is more characteristic of a friend to do well by another than to be well done by, and to confer benefits is characteristic of the good man and of virtue, and it is nobler to do well by friends than by strangers, the good man will need people to do well by. This is why the question is asked whether we need friends more in prosperity or in adversity, on the assumption that not only does a man in adversity need people to confer benefits on him, but also those who are prospering need people to do well by. Surely it is strange, too, to make the supremely happy man a solitary; for no one would choose the whole world on condition of being alone, since man is a political creature and one whose nature is to live with others. Therefore even the happy man lives with others; for he has the things that are by nature good. And plainly it is better to spend his days with friends and good men than with strangers or any chance persons. Therefore the happy man needs friends.

What then is it that the first school means, and in what respect is it right? Is it that most identify friends with useful people? Of such friends indeed the supremely happy man will have no need, since he already has the things that are good; nor will he need those whom one makes one's friends because of their pleasantness, or he will need them only to a small extent (for his life, being pleasant, has no need of adventitious pleasure); and because he does not need such friends he is thought not to need friends.

But that is surely not true. For we have said at the outset that happiness is an activity; and activity plainly comes into being and is not present at the start like a piece of property. If (1) happiness lies in living and being active, and the good man's activity is virtuous and pleasant in itself, as we have said at the outset, and (2) a thing's being one's own is one of the attributes that make it pleasant, and (3) we can contemplate our neighbours better than ourselves and their actions better than our own, and if the actions of virtuous men who are their friends are pleasant to good men (since these have both the attributes that are naturally pleasant),-if this be so, the supremely happy man will need friends of this sort, since his purpose is to contemplate worthy actions and actions that are his own, and the actions of a good man who is his friend have both these qualities.

The chain of logic here is as follows: 

1) Happiness is an activity, a state that has to be made by action rather than something one inherits like property;
2) The particular activity that is happiness consists in using your vital powers to pursue virtue;
3) Virtuous friends will pursue virtue together, which is the happiness activity.
∴ To be supremely happy, one needs virtuous friends.

Notice the point about observation, though, which becomes important by the end of this chapter. 

After the jump, some further explanation of the mechanism and proof by Aristotle; and an important point buried in the argument that scholars often miss.