24 Hours

Arnold Bennett, in an essay called “How to Live on Twenty-Four Hours a Day,” speaks of the use of time as though it were a kind of money:

You have to live on this twenty-four hours of daily time. Out of it you have to spin health, pleasure, money, content, respect, and the evolution of your immortal soul. Its right use, its most effective use, is a matter of the highest urgency and of the most thrilling actuality. All depends on that. Your happiness—the elusive prize that you are all clutching for, my friends!—depends on that. Strange that the newspapers, so enterprising and up-to-date as they are, are not full of “How to live on a given income of time,” instead of “How to live on a given income of money”! Money is far commoner than time. When one reflects, one perceives that money is just about the commonest thing there is. It encumbers the earth in gross heaps.

If one can’t contrive to live on a certain income of money, one earns a little more—or steals it, or advertises for it. One doesn’t necessarily muddle one’s life because one can’t quite manage on a thousand pounds a year; one braces the muscles and makes it guineas, and balances the budget. But if one cannot arrange that an income of twenty-four hours a day shall exactly cover all proper items of expenditure, one does muddle one’s life definitely. The supply of time, though gloriously regular, is cruelly restricted.

Which of us lives on twenty-four hours a day? And when I say “lives,” I do not mean exists, nor “muddles through.” Which of us is free from that uneasy feeling that the “great spending departments” of his daily life are not managed as they ought to be? Which of us is quite sure that his fine suit is not surmounted by a shameful hat, or that in attending to the crockery he has forgotten the quality of the food? Which of us is not saying to himself—which of us has not been saying to himself all his life: “I shall alter that when I have a little more time”?

We never shall have any more time. We have, and we have always had, all the time there is. It is the realization of this profound and neglected truth (which, by the way, I have not discovered) that has led me to the minute practical examination of daily time-expenditure.

“We shall never have any more time,” Bennett says, in the sense that we have 24 hours each day, never more and never less. The time is always the same; it is just a question of how that time is used. In principle, “balancing the budget” with respect to time should be just as easy as balancing the budget with respect to one’s income. Bennett illustrates this with an imaginary example:

“But,” someone may remark, with the English disregard of everything except the point, “what is he driving at with his twenty-four hours a day? I have no difficulty in living on twenty-four hours a day. I do all that I want to do, and still find time to go in for newspaper competitions. Surely it is a simple affair, knowing that one has only twenty-four hours a day, to content one’s self with twenty-four hours a day!”

To you, my dear sir, I present my excuses and apologies. You are precisely the man that I have been wishing to meet for about forty years. Will you kindly send me your name and address, and state your charge for telling me how you do it? Instead of me talking to you, you ought to be talking to me. Please come forward. That you exist, I am convinced, and that I have not yet encountered you is my loss. Meanwhile, until you appear, I will continue to chat with my companions in distress—that innumerable band of souls who are haunted, more or less painfully, by the feeling that the years slip by, and slip by, and slip by, and that they have not yet been able to get their lives into proper working order.

When someone says, “I cannot afford that,” typically this does not mean that it is literally impossible to buy it. He may have enough money in his wallet, or in his bank account. If he does not, he might easily save enough; or if even if this would be difficult, it might be possible to get a loan to manage the purchase. In the end, in most cases the person who says this really means that such actions would not be prudent, and that he would prefer to do other things with his money. The real issue is not the amount of money, but the person’s preferences, whether these be reasonable or unreasonable.

The same thing applies to time, but even more so, since everyone has the same amount of time. If we say, “I do not have time for that,” the real meaning is this: we prefer to do other things. And that preference must be rather strong, in fact, since the implication is that we prefer to do other things, not only sometimes, but all day, every day.

This does not necessarily imply anything blameworthy. A person can be quite reasonable in saying that he prefers to use his money for one thing rather than another, and he can be quite reasonable in saying that he prefers to use his time for one thing rather than another.

But what is not reasonable is to assert that we have a strong desire to do the thing that we say we do not have time for. If “we do not have time for that,” then our desire to do it must be relatively weak, in fact, since we let our desires to do other things take precedence over that desire, not only sometimes, but all day, every day.


Bias vs. Variance

Scott Fortmann-Roe explains the difference between error due to bias and error due to variance:

  • Error due to Bias: The error due to bias is taken as the difference between the expected (or average) prediction of our model and the correct value which we are trying to predict. Of course you only have one model so talking about expected or average prediction values might seem a little strange. However, imagine you could repeat the whole model building process more than once: each time you gather new data and run a new analysis creating a new model. Due to randomness in the underlying data sets, the resulting models will have a range of predictions. Bias measures how far off in general these models’ predictions are from the correct value.
  • Error due to Variance: The error due to variance is taken as the variability of a model prediction for a given data point. Again, imagine you can repeat the entire model building process multiple times. The variance is how much the predictions for a given point vary between different realizations of the model.

Later in the essay, he suggests that there is a natural tendency to overemphasize minimizing bias:

A gut feeling many people have is that they should minimize bias even at the expense of variance. Their thinking goes that the presence of bias indicates something basically wrong with their model and algorithm. Yes, they acknowledge, variance is also bad but a model with high variance could at least predict well on average, at least it is not fundamentally wrong.

This is mistaken logic. It is true that a high variance and low bias model can perform well in some sort of long-run average sense. However, in practice modelers are always dealing with a single realization of the data set. In these cases, long run averages are irrelevant, what is important is the performance of the model on the data you actually have and in this case bias and variance are equally important and one should not be improved at an excessive expense to the other.

Fortmann-Roe is concerned here with bias and variance in a precise mathematical sense, relative to the project of fitting a curve to a set of data points. However, his point could be generalized to apply much more generally, to interpreting and understanding the world overall. Tyler Cowen makes such a generalized point:

Arnold Kling summarizes Robin’s argument:

If you have a cause, then other people probably disagree with you (if nothing else, they don’t think your cause is as important as you do). When other people disagree with you, they are usually more right than you think they are. So you could be wrong. Before you go and attach yourself to this cause, shouldn’t you try to reduce the chances that you are wrong? Ergo, shouldn’t you work on trying to overcome bias? Therefore, shouldn’t overcoming bias be your number one cause?

Here is Robin’s very similar statement.  I believe these views are tautologically true and they simply boil down to saying that any complaint can be expressed as a concern about error of some kind or another.  I cannot disagree with this view, for if I do, I am accusing Robin of being too biased toward eliminating bias, thus reaffirming that bias is in fact the real problem.

I find it more useful to draw an analogy with statistics.  Biased estimators are one problem but not the only problem.  There is also insufficient data, lazy researchers, inefficient estimators, and so on.  Then I don’t see why we should be justified in holding a strong preference for overcoming bias, relative to other ends.

Tyler is arguing, for example, that someone may be in error because he is biased, but he can also be in error because he is too lazy to seek out the truth, and it may be more important in a particular case to overcome laziness than to overcome bias.

This is true, no doubt, but we can make a stronger point: In the mathematical discussion of bias and variance, insisting on a completely unbiased model will result in a very high degree of variance, with the nearly inevitable consequence of a higher overall error rate. Thus, for example, we can create a polynomial which will go through every point of the data exactly. Such a method of predicting data is completely unbiased. Nonetheless, such a model tends to be highly inaccurate in predicting new data due to its very high variance: the exact curve is simply too sensitive to the exact points found in the original data. In a similar way, even in the more general non-mathematical case, we will likely find that insisting on a completely unbiased method will result in greater error overall: the best way to find the truth may be to adopt a somewhat simplified model, just as in the mathematical case it is best not to try to fit the data exactly. Simplifying the model will introduce some bias, but it will also reduce variance.

To the best of my knowledge, no one has a demonstrably perfect method of adopting the best model, even in the mathematical case. Much less, therefore, can we come up with a perfect trade-off between bias and variance in the general case. We can simply use our best judgment. But we have some reason for thinking that there must be some such trade-off, just as there is in the mathematical case.


Logical consistency is important. If my positions fail to be consistent, this is clear proof that at least one of them is mistaken.

Nonetheless, logical consistency is not the supreme value. It would not be the supreme value even for someone who cared about truth alone. The reason for this is that someone may see that his position is inconsistent, and know that it follows that his position is partially mistaken, without knowing any concrete way to modify his position which will improve it. His best estimate of any particular modification may be that his position would end up containing a greater amount of error. In this case, caring about the truth will entail that he preserve his position without modification, despite recognizing that his position contains some falsity.

This happens to all of us, as we can see from one particular case. I would be foolish and arrogant if I believed, “All of my beliefs are true.” In order for that to be the case, I would have to be essentially infallible. So it is far more reasonable for me to believe that I am mistaken about some things. But then if we take all of my beliefs together, including the belief that “some of my beliefs are mistaken,” we can derive a contradiction.

And it is clear, in the general case, that I have no way to improve my position to eliminate the inconsistency. Believing that all of my beliefs are true would not improve it. It would add some consistency, but only by means of adding a definite falsity. Likewise, changing some other belief would not help, since even if some of my beliefs are mistaken, I do not know which ones those are. Changing a belief at random is likely to worsen my position overall. And if I examine my beliefs and come to the conclusion that I should modify one belief or another, this will not and should not change my conviction that some of my beliefs are mistaken.


Sola Me and Claiming Personal Infallibility

At his blog, P. Edmund Waldstein and myself have a discussion about this post about myself and his account of the certainty of faith, an account that I consider to be a variety of the doctrine of sola me.

In that discussion we consider various details of his position, as well as the teaching of the Church and of St. Thomas. Here, let me step out for a moment and consider the matter more generally.

It is evident that everything that he says could be reformulated and believed by the members of any religion whatsoever, in order to justify the claim that they should never change their religion, no matter how much evidence is brought against it. Thus, instead of,

But nor is such certitude based on an entirely incommunicable interior witness of the Spirit. Certainly it is impossible without such illumination, but what such illumination enables is an encounter with Christ, as a witness who is both external and internal.

a Muslim might say,

But nor is such certitude based on an entirely incommunicable interior witness of Allah. Certainly it is impossible without such illumination, but what such illumination enables is an encounter with Mohammed, as a witness who is both external and internal.

P. Edmund could argue against particular claims of the Muslim, and the Muslim could argue against P. Edmund’s particular claims. But neither would be listening seriously to the other, because each would assert, “It would be unserious in me to approach arguments based on natural evidence as though they could ever disprove the overwhelmingly powerful evidence of the [Catholic / Islamic] Faith.”

Regardless of details, each is claiming to be personally infallible in discerning the truth about religion.

It is possible to lock yourself into a box intellectually that you cannot escape from in any reasonable way. Descartes does this for example with his hypothesis of the Evil Demon. Logically, according to this hypothesis, he should suppose that he might be wrong about the fact that it is necessary to exist in order to think or to doubt things. Without accepting any premises, it is of course impossible to arrive at any conclusions. In a similar way, if someone believes himself infallible on some topic, logically there is no way for him to correct his errors in regard to that topic.

In practice in such cases it is possible to escape from the box, since belief is voluntary. The Cartesian may simply choose to stop doubting, and the believer may simply choose to accept the fact that he is not personally infallible. But there is no logical process of reasoning that could validly lead to these choices.

People construct theological bomb shelters for themselves in various ways. Fr. Brian Harrison does this by asserting a form of young earth creationism, and simply ignoring all the evidence opposed to this. Likewise, asserting that you are personally infallible in discerning the true religion is another way to construct such a shelter. But hear the words of St. Augustine:

Usually, even a non-Christian knows something about the earth, the heavens, and the other elements of this world, about the motion and orbit of the stars and even their size and relative positions, about the predictable eclipses of the sun and moon, the cycles of the years and the seasons, about the kinds of animals, shrubs, stones, and so forth, and this knowledge he holds to as being certain from reason and experience. Now, it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking non-sense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn. The shame is not so much that an ignorant individual is derided, but that people outside the household of the faith think our sacred writers held such opinions, and, to the great loss of those for whose salvation we toil, the writers of our Scripture are criticized and rejected as unlearned men. If they find a Christian mistaken in a field which they themselves know well and hear him maintaining his foolish opinions about our books, how are they going to believe those books in matters concerning the resurrection of the dead, the hope of eternal life, and the kingdom of heaven, when they think their pages are full of falsehoods on facts which they themselves have learnt from experience and the light of reason? Reckless and incompetent expounders of holy Scripture bring untold trouble and sorrow on their wiser brethren when they are caught in one of their mischievous false opinions and are taken to task by those who are not bound by the authority of our sacred books. For then, to defend their utterly foolish and obviously untrue statements, they will try to call upon Holy Scripture for proof and even recite from memory many passages which they think support their position, although “they understand neither what they say nor the things about which they make assertion.”

As Darwin Catholic points out, someone who argues that “either evolution is false or Christianity is false” does not make Christianity more credible, but less. In a similar way, someone who argues that their religion requires that they believe themselves personally infallible, is essentially saying, “Either my religion is false or I am personally infallible.” This does not make their religion more credible, but less, to whatever degree that one thinks they are right about the requirement.

(After some consideration, I will be posting at least on Sundays during February and March.)

The List of All True Statements

Earlier we noted that it is not possible to have a correct and an extremely detailed prediction of the future, if the prediction is known to people.

In a similar way, there are often restrictions on the possibility of bringing together all true statements of a certain form. This is frequently independent of whether people know of them or not.

For example, consider the library of Babel. A great deal is contained in it, including every sentence in this blog post, as you can discover by testing the site’s search function. Suppose someone were to go through these texts and make a list of all the true ones, avoiding meaningless, indeterminate, and false ones. In time, he would come upon this page, which has the sentence, “this sentence is not contained in your list of true sentences.” Should he include this sentence, or not?

If he does not include the sentence, he will have missed a true sentence. And if he does include it, he will have included a false one. So it is impossible in principle for his project to succeed: he cannot make a list of all the true sentences in the library.

This is related to the Paradox of the Liar, but it is not the same thing. Whether or not a sentence is contained in someone’s list is a perfectly objective fact. It is either there, or not, and there is no inconsistency in reality on this account. But the list maker still cannot succeed. In practice this is a case of the Liar Game.