These sections were prompted by occasions when I have been surprised at myself, or felt very stupid after speaking, writing, or doing. I hope that they will prove to be useful reminders, to myself and possibly to others.
Here are reasons for allowing somebody else to continue to speak, even when they are talking rubbish, and have denounced views that you believe are both true and useful as "vicious pernicious lies."
When you come up with a simple theory that explains somebody's actions you are probably wrong. There may be multiple such theories that fit the facts, so there could be a simple reason behind their actions - but not the one you have just thought of. Here are some situations where there is in fact no single simple reason at all.
This is explained by Benjamin Franklin in a 1772 letter to Priestley. He fills in two columns on a sheet of paper, one marked Pro and the other Con, with the arguments for and against a particular question, doing this over a period of time so that nothing is forgotten. Then he attempts to cross out reasons on each side, at each stage crossing out a similar weight of argument on each side, so that one counterbalances the other. The winning column is that left with reasons when all the reasons on the other column are crossed out. This useful and effective procedure cannot be summed with a simple short "He did X because Y."
A typical chess program considers the top of a vast tree of possible futures, where the nodes of the tree are chess positions and the lines joining nodes are single moves. The fringes of the tree it is considering are given scores. A best move at any particular time is one that can be made to lead down to a fringe node with highest possible score, assuming that the opponent makes the best possible choice (for them) at each stage. Usually a scheme called "Alpha-Beta Pruning" is used to find this best move without considering every possible future in the tree. For example, if you are considering a possible move and find that your opponent has at least one reply that forces this move to lead to a node with score worse than the best found so far, you can drop that idea without further consideration.
The explanation of the actions of, for example, the program Fritz 9, is not given by a simple "I did X because of Y". Instead, it displays the best several possible moves at the current stage, following each of them with the game that would lead us down to the fringe if each player made the best move at each stage. Even this is only a very short summary of the calculations behind the move, because there is nothing here to prove that in each such game each player does in fact make the best move at their disposal: that would require showing enough of the tree to replicate the alpha-beta prune (not all of the tree, but probably a fair chunk of it). For example, you can only be sure of checkmate when you know that no possible move by your opponent can get them out of it.
Where its assumptions hold, decision theory is the provably right way to make decisions. It is very rarely followed explicitly, but we might hope that sufficient practise (or natural ability) might, in some cases, lead to subconscious processes that at least produce the same best results as fully-fledged decision theory.
Under decision theory, we maximise an expected utility, u(x, t), where x is the action taken, and t represents the state of nature. We cannot observe t directly, but we are provided with a probability distribution p(t) that reflects the relative probabilities, before looking round, of the different possible values of t, an observation y, and the probability of this observation given t: p(y|t).
Given all of this mathematical infrastructure, we should choose the value of x associated with the maximum value of
Σtu(x, t)p(t)p(y | t)That is, we formulate a function u(x, t) that sums up the attractiveness, for each possible action x, of all the consequences of x in a particular state of nature t. Then we sum this over every possible t, weighting it by the probability of being in state t and observing y. Even u(x, t) on its own may summarise enough different consequences that "I like X because of Y" may be an over-simplification; in fact u(x, t) may summarise the results of many procedures similar to Franklin's Moral Algebra, one for each separate value of t. Then we sum the results of considering the different u(x, t) values produced by different states of nature t, weighted by probability that each particular t is the real t and so produced our observed y, so we get something more complex yet.
"No single point of failure," is often a goal of those building reliable computer systems: they try to build a system so that it can tolerate the failure of any single component. Ideally, we would calculate the exact reliability of a large number of possible designs and choose the best, but no single point of failure is a pretty good rule of thumb.
I have heard this applied to decision-making; in particular, I have heard the advice that you should never buy a house for just one reason (for example, because it provides a view of a particular piece of landscape). After all, you could be denied that view by somebody else building another house. Alternatively, you could lose interest in that view, for instance because commuting from that house to work leaves you without the opportunity to observe that view in daylight. Again, somebody who abides by this dictum will have no single simple reason for their actions.
Perhaps there is a good reason, but no short explanation of it: it turns out that there are theorems that you can prove (in theory) whose shortest proofs are unreasonably long. Godel proved that, for any computable function f(x), there are theorems of length x whose shortest proof is of length greater than f(x). Here computable definitely includes anything that you can write a computer program for, so f(x) can be very big indeed. See section 4.4, "lengths of proofs," in User:Likebox/Gödel modern proof. A hand-waving version of the proof there is as follows:
The famous Halting Problem shows that there is no computer program that can always be fed a computer program and an input, and determine whether that program, when fed that input, will ever finish. If there was a computer program that could always tell if a purported theorem has a proof at all, you could use this to test the purported theorem "Program X, given input Y, will finish." Therefore there is no computer program that can always tell if a purported theorem has a proof at all. But there is a computer program that can check a proof that somebody else supplies. If there was a computable f(x) such that any provable theorem of length x must have a shortest proof of length ≤ f(x) then we could write a computer program that checked all possible proofs of length ≤ f(x) and reported "no proof exists" if none of this huge but finite collection of purported proofs proved the target theorem. Therefore no such f(x) exists.
This really is penance! Apparently, this is the technical term for being sore a day or two after taking exercise, and there is still stuff to learn about it. Suggestions for avoiding this include warming up before exercise, keeping to a regular exercise schedule (e.g. every other day), and possibly eating a sensible meal after exercise.
There is more theory than experimental proof for warming up and warming down. One argument is that the lighter movements of warming up and down encourage blood flow (via one-way valves in the veins) to prepare the muscles, or to flush out waste products. If this is so, then the warm-up or warm-down exercise should be representative of the movements at times of full effort. Equestrians traditionally feel that allowing their horses to warm down is important.
I don't know what works for myself and what does not, so I can't help you, but at least now you have a term to web-search on, or look out for.