Tag: Bertrand Russell

Predicting the Future with Bayes’ Theorem

In a recent podcast, we talked with professional poker player Annie Duke about thinking in probabilities, something good poker players do all the time. At the poker table or in life, it’s really useful to think in probabilities versus absolutes based on all the information you have available to you. You can improve your decisions and get better outcomes. Probabilistic thinking leads you to ask yourself, how confident am I in this prediction? What information would impact this confidence?

Bayes’ Theorem

Bayes’ theorem is an accessible way of integrating probability thinking into our lives. Thomas Bayes was an English minister in the 18th century, whose most famous work, “An Essay toward Solving a Problem in the Doctrine of Chances,” was brought to the attention of the Royal Society in 1763—two years after his death—by his friend Richard Price. The essay did not contain the theorem as we now know it, but had the seeds of the idea. It looked at how we should adjust our estimates of probabilities when we encounter new data that influence a situation. Later development by French scholar Pierre-Simon Laplace and others helped codify the theorem and develop it into a useful tool for thinking.

Knowing the exact math of probability calculations is not the key to understanding Bayesian thinking. More critical is your ability and desire to assign probabilities of truth and accuracy to anything you think you know, and then being willing to update those probabilities when new information comes in. Here is a short example, found in Investing: The Last Liberal Art, of how it works:

Let’s imagine that you and a friend have spent the afternoon playing your favorite board game, and now, at the end of the game, you are chatting about this and that. Something your friend says leads you to make a friendly wager: that with one roll of the die from the game, you will get a 6. Straight odds are one in six, a 16 percent probability. But then suppose your friend rolls the die, quickly covers it with her hand, and takes a peek. “I can tell you this much,” she says; “it’s an even number.” Now you have new information and your odds change dramatically to one in three, a 33 percent probability. While you are considering whether to change your bet, your friend teasingly adds: “And it’s not a 4.” With this additional bit of information, your odds have changed again, to one in two, a 50 percent probability. With this very simple example, you have performed a Bayesian analysis. Each new piece of information affected the original probability, and that is Bayesian [updating].

Both Nate Silver and Eliezer Yudkowsky have written about Bayes’ theorem in the context of medical testing, specifically mammograms. Imagine you live in a country with 100 million women under 40. Past trends have revealed that there is a 1.4% chance of a woman under 40 in this country getting breast cancer—so roughly 1.4 million women.

Mammograms will detect breast cancer 75% of the time. They will give out false positives—say a woman has breast cancer when she actually doesn’t—about 10% of the time. At first, you might focus just on the mammogram numbers and think that 75% success rate means that a positive is bad news. Let’s do the math.

If all the women under 40 get mammograms, then the false positive rate will give 10 million women under 40 the news that they have breast cancer. But because you know the first statistic, that only 1.4 women under 40 actually get breast cancer, you know that 8.6 million of the women who tested positive are not actually going to have breast cancer!
That’s a lot of needless worrying, which leads to a lot of needless medical care. In order to remedy this poor understanding and make better decisions about using mammograms, we absolutely must consider prior knowledge when we look at the results, and try to update our beliefs with that knowledge in mind.

Weigh the Evidence

Often we ignore prior information, simply called “priors” in Bayesian-speak. We can blame this habit in part on the availability heuristic—we focus on what’s readily available. In this case, we focus on the newest information and the bigger picture gets lost. We fail to adjust the probability of old information to reflect what we have learned.

The big idea behind Bayes’ theorem is that we must continuously update our probability estimates on an as-needed basis. In their book The Signal and the Noise, Nate Silver and Allen Lane give a contemporary example, reminding us that new information is often most useful when we put it in the larger context of what we already know:

Bayes’ theorem is an important reality check on our efforts to forecast the future. How, for instance, should we reconcile a large body of theory and evidence predicting global warming with the fact that there has been no warming trend over the last decade or so? Skeptics react with glee, while true believers dismiss the new information.

A better response is to use Bayes’ theorem: the lack of recent warming is evidence against recent global warming predictions, but it is weak evidence. This is because there is enough variability in global temperatures to make such an outcome unsurprising. The new information should reduce our confidence in our models of global warming—but only a little.

The same approach can be used in anything from an economic forecast to a hand of poker, and while Bayes’ theorem can be a formal affair, Bayesian reasoning also works as a rule of thumb. We tend to either dismiss new evidence, or embrace it as though nothing else matters. Bayesians try to weigh both the old hypothesis and the new evidence in a sensible way.

Limitations of the Bayesian

Don’t walk away thinking the Bayesian approach will enable you to predict everything! In addition to seeing the world as an ever-shifting array of probabilities, we must also remember the limitations of inductive reasoning. A high probability of something being true is not the same as saying it is true. A great example of this is from Bertrand Russell’s The Problems of Philosophy:

A horse which has been often driven along a certain road resists the attempt to drive him in a different direction. Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.

In the final analysis, though, picking up Bayesian reasoning can truly change your life, as observed in this Big Think video by Julia Galef of the Center for Applied Rationality:

After you’ve been steeped in Bayes’ rule for a little while, it starts to produce some fundamental changes to your thinking. For example, you become much more aware that your beliefs are grayscale. They’re not black and white and that you have levels of confidence in your beliefs about how the world works that are less than 100 percent but greater than zero percent and even more importantly as you go through the world and encounter new ideas and new evidence, that level of confidence fluctuates, as you encounter evidence for and against your beliefs.

So be okay with uncertainty, and use it to your advantage. Instead of holding on to outdated beliefs by rejecting new information, take in what comes your way through a system of evaluating probabilities.

Bayes’ Theorem is part of the Farnam Street latticework of mental models. Still Curious? Read Bayes and Deadweight: Using Statistics to Eject the Deadweight From Your Life next. 

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Bertrand Russell: Love is Wise, Hatred is Foolish

“Love is wise, hatred is foolish.”
— Bertrand Russell

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"Love is wise, hatred is foolish."

The British philosopher Bertrand Russell (1872-1970) gave us some of the more enduring developments in 20th-century philosophy. His 10 commandments of teaching and writing on avoiding foolish opinions demonstrate how Russell wanted philosophy to speak to ordinary people.

In this rare 1959 interview with BBC, Russell is asked to pass along advice to a later generation. In just under two minutes he articulates two things: one intellectual and one moral that still resonate today and cut through our noisy world.

 

Interviewer: Suppose Lord Russell that this film were to be looked at by our descendants, like a dead sea scroll in a thousand years time. What would you think it’s worth telling that generation about the life you’ve lived and the lessons you’ve learned from it?

Russell: I should like to say two things, one intellectual and one moral.

The intellectual thing I should want to say to them, is this: When you are studying any matter, or considering any philosophy, ask yourself only what are the facts and what is the truth that the facts bear out. Never let yourself be diverted, either by what you wish to believe, or by what you think would have beneficent social effects if it were believed. But look only, and solely, at what are the facts. That is the intellectual thing that I should wish to say.

The moral thing I should wish to say to them is very simple: I should say, love is wise, hatred is foolish. In this world, which is getting more and more closely interconnected, we have to learn to tolerate each other, we have to learn to put up with the fact that some people say things that we don’t like. We can only live together in that way—and if we are to live together and not die together—we must learn a kind of charity and a kind of tolerance, which is absolutely vital to the continuation of human life on this planet.

Ten Commandments For Living From Philosopher Bertrand Russell

bertrand-russell

The Ten Commandments that, as a teacher, I should wish to promulgate, might be set forth as follows:

1. Do not feel absolutely certain of anything.

2. Do not think it worthwhile to proceed by concealing evidence, for the evidence is sure to come to light.

3. Never try to discourage thinking for you are sure to succeed.

4. When you meet with opposition, even if it should be from your husband or your children, endeavor to overcome it by argument and not by authority, for a victory dependent upon authority is unreal and illusory.

5. Have no respect for the authority of others, for there are always contrary authorities to be found.

6. Do not use power to suppress opinions you think pernicious, for if you do the opinions will suppress you.

7. Do not fear to be eccentric in opinion, for every opinion now accepted was once eccentric.

8. Find more pleasure in intelligent dissent than in passive agreement, for, if you value intelligence as you should, the former implies a deeper agreement than the latter.

9. Be scrupulously truthful, even if the truth is inconvenient, for it is more inconvenient when you try to conceal it.

10. Do not feel envious of the happiness of those who live in a fool’s paradise, for only a fool will think that it is happiness.

Still curious? Russell is the author of many books including Why I Am Not a Christian, History of Western Philosophy, and The Problems of Philosophy.

Bertrand Russell: On Avoiding Foolish Opinions

bertrand russell avoiding foolish opinion

We’d all like to avoid folly, wouldn’t we?

Avoiding stupidity is easier than seeking brilliance. And it doesn’t take a genius. Only a few simple ideas.

Philosopher Bertrand Russell (1872-1970) offers some advice, which will not keep us from all error but will help us navigate away from obvious error.

On Avoiding Foolish Opinions

Via The Basic Writings of Bertrand Russell:

If the matter is one that can be settled by observation, make the observation yourself. Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted. He did not do so because he thought he knew. Thinking that you know when in fact you don’t is a fatal mistake, to which we are all prone. I believe myself that hedgehogs eat black beetles, because I have been told that they do; but if I were writing a book on the habits of hedgehogs, I should not commit myself until I had seen one enjoying this unappetizing diet. Aristotle, however, was less cautious. Ancient and medieval authors knew all about unicorns and salamanders; not one of them thought it necessary to avoid dogmatic statements about them because he had never seen one of them.

Many matters, however, are less easily brought to the test of experience. If, like most of mankind, you have passionate convictions on many such matters, there are ways in which you can make yourself aware of your own bias.

If an opinion contrary to your own makes you angry, that is a sign that you are subconsciously aware of having no good reason for thinking as you do. If some one maintains that two and two are five, or that Iceland is on the equator, you feel pity rather than anger, unless you know so little of arithmetic or geography that his opinion shakes your own contrary conviction. The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion. So whenever you find yourself getting angry about a difference of opinion, be on your guard; you will probably find, on examination, that your belief is going beyond what the evidence warrants.

A good way of ridding yourself of certain kinds of dogmatism is to become aware of opinions held in social circles different from your own. When I was young, I lived much outside my own country in France, Germany, Italy, and the United States. I found this very profitable in diminishing the intensity of insular prejudice. If you cannot travel, seek out people with whom you disagree, and read a newspaper belonging to a party that is not yours. If the people and the newspaper seem mad, perverse, and wicked, remind yourself that you seem so to them. In this opinion both parties may be right, but they cannot both be wrong. This reflection should generate a certain caution.

Becoming aware of foreign customs, however, does not always have a beneficial effect. In the seventeenth century, when the Manchus conquered China, it was the custom among the Chinese for the women to have small feet, and among the Manchus for the men to wear-pigtails. Instead of each dropping their own foolish custom, they each adopted the foolish custom of the other, and the Chinese continued to wear pigtails until they shook off the dominion of the Manchus in the revolution of 1911.

For those who have enough psychological imagination, it is a good plan to imagine an argument with a person having a different bias. This has one advantage, and only one, as compared with actual conversation with opponents; this one advantage is that the method is not subject to the same limitations of time or space. Mahatma Gandhi deplores railways and steamboats and machinery; he would like to undo the whole of the industrial revolution. You may never have an opportunity of actually meeting any one who holds this opinion, because in Western countries most people take the advantage of modern technique for granted. But if you want to make sure that you are right in agreeing with the prevailing opinion, you will find it a good plan to test the arguments that occur to you by considering what Gandhi might say in refutation of them. I have sometimes been led actually to change my mind as a result of this kind of imaginary dialogue, and, short of this, I have frequently found myself growing less dogmatic and cocksure through realizing the possible reasonableness of a hypothetical opponent.

Be very wary of opinions that flatter your self-esteem. Both men and women, nine times out of ten, are firmly convinced of the superior excellence of their own sex. There is abundant evidence on both sides. If you are a man, you can point out that most poets and men of science are male; if you are a woman, you can retort that so are most criminals. The question is inherently insoluble, but self esteem conceals this from most people. We are all, whatever part of the world we come from, persuaded that our own nation is superior to all others. Seeing that each nation has its characteristic merits and demerits, we adjust our standard of values so as to make out that the merits possessed by our nation are the really important ones, while its demerits are comparatively trivial. Here, again, the rational man will admit that the question is one to which there is no demonstrably right answer. It is more difficult to deal with the self esteem of man as man, because we cannot argue out the matter with some non-human mind. The only way I know of dealing with this general human conceit is to remind ourselves that man is a brief episode in the life of a small planet in a little corner of the universe, and that, for aught we know, other parts of the cosmos may contain beings as superior to ourselves as we are to jellyfish.

Still curious? Check out Bertrand Russell’s 10 Commandments of Teaching.