A modest proposal about uncertainty

Joan Roughgarden in Beyond Belief made a very astute observation of a problem, and then proposed a lousy solution to it. The problem she was addressing had to do with the public perception of evolution as something quite uncertain scientifically (“theory vs fact”). She observed that the public sees science changing its stance on many things, especially in medicine. One day, you should eat bran. The next, bran is bad for you. The next, bran is good for you again. As a result the public observes that some sciences are uncertain, and can’t distinguish one field from another or one type of claim from another, so they apply doubt to all of science even when it is not warranted by the science. Her solution involves using religious analogies, interpreting phrases in the Bible to explain things like natural selection and mutations, in order to communicate it to a group of people who share and value that vocabulary. Dawkins rightly chews her out for this approach, pointing out how far she is stretching the meaning of the phrases just to fit her philosophy.

The problem she is stating, however, is quite real. How can we expect the public to make decisions about medicine, global warming, evolution, the big bang, etc... when they (somewhat rightly, somewhat wrongly) observe that the scientists themselves are arguing about it? The Intelligent Design folks are currently using this observation to sow doubt with the public in their efforts to “teach the controversy” of evolution to inject creationism into the schools. It is a failure of the scientists, and the media that covers them, to communicate with the public. Can we do better?

I have a proposal, which I’ll sketch out in a toy example. The problem is not the communication of facts, or even of the procedures of science. The problem is with the communication of uncertainties. In day to day life, we easily handle claims with different levels of uncertainties. The sun rises in the east each morning has low uncertainty. The claims of the auto salesman or the politician have higher uncertainty. Quantifying it is, of course, more challenging but the qualitative features of uncertainty are known to nearly everyone. So scientists and journalists really need to take efforts to communicate the uncertainty of every claim, not just the fact of the claim or how the new observations differ from the old observations. How could this be done? I think, at least roughly, one should include a plot of the probability distribution with any claim. One doesn’t need to know advanced math to see the picture. If every claim is accompanied by a plot of the uncertainties, the public will get used to reading them. Let me demonstrate with a toy example.

Say, I am trying to determine the origin year of homo sapiens. I realize there isn’t just one year, and there is a process, but it is not much harder to include those in this simple analysis. I have several homo sapiens fossils where I’ve measured the age, which allows me to calculate my best guess of the age, and the distribution of my uncertainty shown here.

I’ve used a normal, Gaussian, distribution here although in fact it probably should be something skewed left and probably a lot flatter to reflect our greater uncertainty with age, and that we have other observations that put confident lower limits on the origin of homo sapiens. Again, the details aren’t important because all attempts at clarifying the distribution only further help with communicating the uncertainty to the public. A few observations are in order here:

1. there are many possible values for the origin that lie well outside of our data yet have non-zero probability
2. Our “best guess” is around the middle of this distribution, but it really can’t be interpreted as “homo sapiens originated 250,000 years ago” as it might read in a newspaper

Now, we have a new paper that adds another fossil much older than than the previous ones, around 340000 years ago. Newspapers may claim “origin of homo sapiens 150% older than originally thought”, or “estimates of the origin of humans overthrown by new data”. How might it look with the uncertainties plotted?

There are a number of lessons that can be read from this.

1. the new data updates our “best estimate” by only a little - the old data, combined with the new data, are used for the estimate
2. our uncertainties have widened - by having a larger range of data, our uncertainties may have increased with new data.

In reality, estimating an origin (first event) will update a bit differently than this example shows. For example, the uncertainties in the right-half of the distribution may not be affected at all by an older observation. If this data were in medicine, however, and we were estimating the effect of some new treatment, then the update would be very similar. A single result of a strong effect may not increase our best estimate for that effect by a huge amount. The uncertainties in many medical treatments, or dietary recommendations, straddle the origin: there is significant probability for no effect. It would be fruitful to see the plot of uncertainties, pushed a little this way and that, updated in perhaps a wiki style by scientists as new data come in. There would be many lessons, all of which would help the public understanding of science.

1. observations rarely overturn well-supported scientific understanding
2. not all topics have equal uncertainties - doubting everything the same amount is not rational
3. certainty is never an option, but sometimes the uncertainty is so low that there is a practical certainty
4. nature itself, not authority, determines our best guess and some of our uncertainty
5. if the thing you are measuring has a small effect, then you should expect a series of measurements of the effect to change sign: bran is good, bran is bad, bran is good, etc.... This doesn’t mean that the scientists are waffling, it only means that the effect is small and difficult to detect - and probably meaningless.

I think the public could learn to, at least qualitatively, understand and use plots like these. Perhaps there is a better way to display it that does not do violence to the truth, and I’d be open to that. I think getting in the habit of making plots like this would be good for the scientist as well, forcing them to address and communicate the actual uncertainties in their claims.

The Economics of Religion: More good than harm?

There are some that argue that religion should be eliminated because of all of the harm it does, such as the suicide bombings, honor killings, the Inquisition, etc... This includes the “New Atheists”, like Sam Harris and Richard Dawkins. Others counter that this one-sided perspective ignores all of the good that religion does, such as support for people when they are ill, the donations to natural disaster funds, etc... They argue that religion does more good than harm. This sort of argument is used in economics, and is similar (although not identical to) a cost-benefit analysis. One can focus on, for example, the harm that cars bring in pollution and pavement like environmentalists do or one can focus on the benefits of cars like the access to better health care, the allowance of critical population densities to support significant industries like the industry reps would do. An economist would then weigh both sides, benefits minus costs, and see which to prefer.

In order to do this with religion one cannot simply take the good of religion subtract the bad, come up with a positive number, and say that religion is a benefit to society. It’s like saying that the treatment for the measles is two aspirin and some juice resulting in more cases of recovery than death and saying that we shouldn’t replace this treatment with something else. As is turns out, for the measles, a vaccine will prevent nearly all contractions of the disease, and virtually all deaths.

If we replace religion with a rational perspective (as Sam Harris proposes), which includes a respect for spiritual experiences but not the supernatural explanations of them, then it may be that we essentially vaccinate people against such behavior as suicide bombings, honor killings and inquisitions.

Rounds in Australian Open

In a previous post, I included predictions for Round 1 of the Australian Open. I am posting the next Rounds' predictions here.

Round 2

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Round 3 - Given Jan 20, 2011

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Predictions for the Australian Open

I am not really into sports, but a student of mine is doing a project on developing an automated system for predicting professional tennis matches. We are posting his system's predictions for the Australian Open. I'll post more, before each round as the results come in. I just want the predictions to come before the events! (I'm a bit late for that, but I did receive the file two days ago. :) ). How well does it do? You'll have to stay tuned!

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Religion, Science, and Humility

I've been listening to the "Beyond Belief" workshop, where many very bright people discuss the role of science and religion in society.  I need to go back and re-listen to some of them, but I was struck by the attached clip from the very end of Session 4.

In this 5-minute audio clip, Darren Schreiber, UCSD Political Science, make the point that science shows little humility.  He continues to claim that his religion is what motivates him for humility, to face the unknown with a humble, searching perspective.

His comments are followed up by Ann Druyan, the wife of the late Carl Sagan, in which she essentially says that science and its methods promote the utmost humility.  We are not afforded absolute truths, and if whatever knowledge that we are most confident in gets disproved then science will give its highest honor to the person disproving it.  She points out that science brings us out of a childish narcissism, a key part of nearly all religions, which demands that we are central to the universe.

 

Francis Collins, Science and Religion: How Religion Halts Science

In reading Francis Collins' book, "The Language of God", I was struck by the way in which the religious claims enter into the scientific discussion.  There were three main arguments that he used:

1. The parameters of the universe (e.g. speed of light, gravitational constant, etc...) are extremely finely tuned for the support of living beings, and is unexplainable through science
2. Our sense of morality (especially pure altruism) is unexplainable from the perspective of evolution
3. Our universal longing for God is unexplainable from the perspective of evolution and rational thought

Each of the arguments has the same form: "I don't know how to currently explain something, therefore it is unexplainable in principle, therefore there must be a God."  Taken to its extreme, we can find Colbert's summary "There must be a God, because I don't know how things work." particularly appropriate.

It's really a bold religious statement, ironically full of the arrogance that religious people often attribute to scientists.  By saying that our current knowledge cannot explain something, therefore it can never be explained, is stating that you know better than all other future generations of people.

The problem with the statements, however, is not the arrogance.  It is that they are show-stoppers: once you make the claim that something is unexplainable, then you stop looking.  So-called Intelligence Design suffers from the same problem: by saying that a designer is needed to create the stated irreducibly complex mechanisms, then there is no use in searching for an explanation.  It stops science, stops curiosity, stops investigation.

These types of arguments, then, are not just wrong they are dangerous because they stop the types of inquiry that could possibly show that they are wrong.  In this way, they have a tendency to protect themselves in the world of memes.

I am not saying that we have answers to points 1-3 above (although I think we have some very good ideas at least for 2 and 3), but to go from ignorance to "God must have done it" is extremely sloppy logic, if it can be called logic at all.