Preface to a Blog Series on Bostrom’s Anthropic Bias
I’ve started reading Nick Bostrom‘s 2002 book, Anthropic Bias: Observation Selection Effects in Science and Philosophy. I thought it’d be fun and productive to write a series of posts about the book as I go through it. Though I will hit the main points of each chapter to maintain context, my aim is not to give a summary of the book, but rather to contemplate the ideas in it that strike me as most compelling. I’ll survey Chapter 1 in a moment. First, some prefatory notes:
–The goal is one 1500- to 2500-word post per chapter, published weekly or so. We’ll see how that goes.
— The book isn’t math or logic heavy, though I can easily imagine many interested readers who happen to not be well versed in those areas asking stuff like, “How did we get from step 3 to step 4??” and “Where did that 2/3 come from??” and “What does that squiggly thing mean??” I’ll try to clarify such things when appropriate. Frankly, I’ll do this in many cases to check my own understanding.
–I can’t promise I’ll always correctly explain or even fully understand the book’s arguments. I’ll put in a good effort, but keep an eye on me, eh?
–Again, these posts aren’t meant to replace reading the book, particularly if you’re interested in exploring topics typically associated with anthropic reasoning (e.g., multiverse theories). For whatever reason, concerns about cosmology lack immediacy for me, so I’m unlikely to spend much time on that. However, the tools Bostrom aims to develop for thinking about those concerns seem to also be applicable to other concerns in which I am extremely interested. For example, how we do or should deal—mathematically, philosophically, psychologically, and in our daily lives as social beings—with the highly improbable (especially retrospectively) and the probabilistically subjective.
As I go along, the precise forms these interests take will become clearer and, I hope, further developed. (But, as so often happens with sustained philosophical adventures, I’ll probably end up even more confused than when I started.)
–These posts aren’t meant to constitute a critical response to Bostrom’s book. Rather, I see the book as a springboard. Bostrom is a wealth of information, clever arguments, and examples. I’ll of course question things when the mood so strikes, but my goal is by no means to look for problems. Philosophy, as I most enjoy it, is collaboration, not sword fight. Again, we’ll see how that goes.
–The final and eleventh chapter is called “Observation Selection Theory Applied.” Among the problems it visits is the Sleeping Beauty Problem, about which I currently enjoy a kind of confused agnosticism.* I’m curious to see whether working through the book takes me to a firmer opinion; and, if so or if not, whether this implies anything more generally about my views on the connection between probability (or at least subjective probability) and objective reality (i.e., “the real world”). To deepen this exploration, I’ll also consider some other thought-provoking discussions of the Sleeping Beauty problem, such as Bostrom’s 2006 paper on the topic and recent discussions over at lesswrong.com.
(*More specifically: my intuition currently tells me that the best answer is 1/3 when asking “What probability to assign to the question “Monday-Heads, Monday-Tails, Tuesday-Tails?”; and 1/2 when simply asking “What is the probability of Heads?”—though I give a little more weight to the 1/3 position, given that, in context, full consideration of the latter question seems to involve factoring in one’s degrees of belief about what day it is. If this doesn’t make sense to you because you’re new to the problem, no worries—it’ll make sense by Chapter 11.)
–Corrections, elaborations, and other forms of collaboration are of course encouraged.
Chapter 1: Introduction
Now for a quick survey of the first chapter, in which Bostrom sets the stage for discussion. He begins with an illustration of selection bias, borrowed from Sir Arthur Eddington1:
How big is the smallest fish in the pond? You catch one hundred fishes, all of which are greater than six inches. Does this evidence support the hypothesis that no fish in the pond is much less than six inches long? Not if your net can’t catch smaller fish. (Page 1)
The selection effect there is obvious: the net is only sampling big fish. Bostrom then cites a real-world example2:
In 1936, the Literary Digest conducted a poll to forecast the result of the upcoming presidential election. They predicted that Alf Landon, the Republican candidate, would win by a large margin. In the actual election, the incumbent Franklin D. Roosevelt won a landslide victory. The Literary Digest had harvested the addresses of the people they sent the survey to mainly from telephone books and motor vehicle registries, thereby introducing an important selection effect. The poor of the depression era, a group where support for Roosevelt was especially strong, often did not have a phone or a car. (Page 1)
Bostrom’s next example is that of a young investor deciding whether to invest in stocks or bonds. Once again, only a biased subset of data is collected from the domain of interest; in this case, the biased source is trading records preserved by “successful” countries, thus leading to an overestimation of the historical performance of stocks—the unlucky countries that had their stock exchanges obliterated by war, revolution, and currency collapses did not have preserved records for the young investor to review.
These three examples are used to set up an analogy in which the selection effect arises “not from the limitations of some measuring device but from the fact that all observations require the existence of an appropriately positioned observer” (page 2)—in other words, an “observation selection effect.” Bostrom notes that this phenomenon is “the subject matter of this book” (page 2), and seems to use the term more or less interchangeably with “anthropic reasoning” and “anthropic bias.” He also points out that, while the word “anthropic” seems to imply human, the bias effects in question merely require any sort of observer in possession of the cognitive tools that make observation selection effects possible.
The first example Bostrom offers for demonstrating observation selection effect:
We find that intelligent life evolved on Earth. Naively, one might think that this piece of evidence suggests that life is likely to evolve on most Earth-like planets. But that would be to overlook an observation selection effect. For no matter how small the proportion of all Earth-like planets that evolve intelligent life, we will find ourselves on a planet that did (or we will trace our origin to a planet where intelligent life evolved, in case we are born in a space colony). Our data point—that intelligent life arose on our planet—is predicted equally well by the hypothesis that intelligent life is very improbable even on Earth-like planets as by the hypothesis that intelligent life is highly probable on Earth-like planets. (Pages 2–3)
Bostrom unpacks this more, but I think this gets the point across. We’ll also see more about this in coming chapters. For now, I’ll include just a few more notes for setting the stage of the discussion.
Bostrom points out that “our primary objective here is to construct a theory of observation selection effects. We shall seek to develop a methodology for how to reason when we suspect that our evidence is contaminated with anthropic biases. Our secondary objective is to apply the theory to answer some interesting scientific and philosophical questions” (page 4).
He also notes that, while a Bayesian framework will be used, this shouldn’t deter interested readers. Results will be conveyed verbally: “The topic of observation selection effect is extremely difficult. Yet the difficulty is not in the math, but in grasping and analyzing the underlying principles and in selecting appropriate models” (page 5).
Then, in a section called “A Brief history of Anthropic Reasoning,” Bostrom includes a classic selection effect example from Francis Bacon; especially useful here is Bostrom’s commentary on why the example isn’t one of observation selection effect:
It was a good answer that was made by one who when they showed him hanging in a temple a picture of those who had paid their vows as having escaped shipwreck, and would have him say whether he did not now acknowledge the power of the gods,—‘Aye,’ asked he again, ‘but where are they painted that were drowned after their vows?’ And such is the way of all superstition, whether in astrology, dreams, omens, divine judgments, or the like; wherein men, having a delight in such vanities, mark the events where they are fulfilled, but where they fail, though this happens much oftener, neglect and pass them by. (Page 5)3
Bostrom notes (see footnote #2, page 5) that this isn’t an observational bias because one could have observed that sailors had gone missing. This seems correct. For instance, someone could have painted (or at least documented the names of) sailers as they paid their vows, then noted whether those sailers returned or went missing.
Before closing the chapter with a synopsis of the book, Bostrom points out that, though anthropic reasoning has its precursors (e.g., Hume, Kant, and, for the first clear instance in science, Ludwig Boltzmann), its modern era began with a series of papers by cosmologist Brandon Carter, who “coined the term ‘anthropic principle’ in 1974, clearly intending it to convey some useful guidance about how to reason under observation selection effects,” and that,”while Carter himself evidently knew how to apply his principle to get interesting results, he unfortunately did not manage to explain it well enough to enable all his followers to do the same” (page 6). Carter also originated the Doomsday argument, which will be discussed later in the book.
Ok, I think this sufficiently sets the stage. Next up is Chapter 2: Fine-Tuning in Cosmology. I foresee more discussion coming out of that one.
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- See Chapter 2 (titled “Selective Subjectivism”) of Eddington’s 1939 book The Philosophy of Physical Science—available here in paperback and here for Kindle.
- For a more detailed account, see “Why the 1936 Literary Digest Poll Failed” by Peverill Squire, The Public Opinion Quarterly, Vol. 52, No. 1 (Spring, 1988), pp. 125-133. Available at JSTOR.
- From Bacon’s Novum Organum, 1620.