Yesterday, I purchased some books from a Walden book store that was having a "going out of business" sale. In case you don't know, the Walden chain was apparently bought some years ago by the Borders company, which is now going out of business and closing all of its stores, including the Waldens. They were offering discounts on books of 50% or 60% off―though there may have been a few marked down 70%, according to their advertisements, most were less. All of those I bought were 60% off, but they also had signs promising an additional 15% discount for Monday through Wednesday.
Now, I assumed that this meant that those books would be 75% off the original price, and I suspect that a lot of people would make the same assumption. It did occur to me that there was another possibility, namely, that the 60% discount would be applied to the original price and then the 15% discount applied, which would be less than 75% off. However, for some reason, this thought didn't stick in my mind, and I stuck with my original assumption.
So, when I took my books to the check out, I was rather annoyed to find that the discount was only 66%, instead of the 75% I was expecting―that is, if you first take 60% off the price, and then take an additional 15% off the discounted price, the result is only 66% off the original price. Though annoyed, I decided that the 9% difference wasn't enough to make a fuss about, so I went ahead with the purchase.
I expect that a lot of people would make the same mistake I made, and the possibility that the 15% discount would be taken off the already discounted price might not even occur to them. In fact, the cashiers immediately explained how the discount worked to me and seemed to be prepared to deal with just this confusion. However, after spending several minutes picking out books, many people will do what I did and spend the 9% rather than have wasted their time.
Now, I've checked Borders' ads for the sale, and they're not literally false advertising, since they say "60% off orig. price" and "15% off sale price". But the words "orig. price" and "sale price" are in a smaller type face than the rest. I'm tempted to call this "the small print fallacy", since it's a common way for ads to include legally required information without drawing attention to it. Also, there was the unusual abbreviation "orig.", presumably of "original", which makes the word shorter and less noticeable.
Why did they not just replace the "60% off" signs with "66% off" signs in order to avoid confusing the customer? Why did they advertise two separate discounts, one applied after the other, unless the goal is to lead people into making the mistake that I made?
I'm not sure why I was fooled by this, especially since the possibility of such a thing actually crossed my mind. I could have asked a clerk, or looked more carefully at the signs before selecting books, though it might not have affected my purchases. I think that one reason the idea didn't take hold in my mind is that I trusted the store not to pull such a trick. However, the store is closing, and no longer has the usual incentives not to alienate customers.
The 15% discount ends today, and will be over by the time you read this, but it's likely that the Borders and Walden book stores will have similar sales before they close their doors. Also, I've seen this same trick before in ads, though I don't think that I've ever fallen for it. In any case, I wanted to issue a warning about these specific sales, "going out of business" sales in general, and this particular trick of a percentage discount with an additional percentage off. Such a discount may not add up to as much as you think.
Michael Shermer's latest "Skeptic" column in Scientific American discusses the difference between science and pseudoscience:
The boundary problem between science and pseudoscience…is notoriously fraught with definitional disagreements because the categories are too broad and fuzzy on the edges, and the term “pseudoscience” is subject to adjectival abuse against any claim one happens to dislike for any reason. In his 2010 book Nonsense on Stilts…, philosopher of science Massimo Pigliucci concedes that there is “no litmus test,” because “the boundaries separating science, nonscience, and pseudoscience are much fuzzier and more permeable than Popper (or, for that matter, most scientists) would have us believe.”
Shermer offers a pragmatic definition of "science" as "what scientists do", but this doesn't really solve the "boundary problem", since it just changes it into the question of who are the scientists. Shermer quotes with apparent approval the historian Michael D. Gordin: "No one in the history of the world has ever self-identified as a pseudoscientist." So, in order to know what scientists do we need to know who the scientists are, and there's no Pseudoscientific American magazine to help us identify the pseuds.
However, I agree with Pigliucci that the concept of science is vague, so that we shouldn't expect an exact definition of "science"―or "pseudoscience", for that matter―but neither is one needed. The lack of a precise definition is not usually a problem for telling the difference between science and pseudoscience, any more than the fact that "bald" is vague means that we can't tell a bald man from one with a full head of hair. Of course, there are borderline cases―that's what it means to be vague―but the way to deal with them is to point out that they're problematic cases with characteristics of both science and pseudoscience.
Shermer is right to emphasize the importance of what scientists do, since it's what they do that sets them apart from pseudoscientists. As Bertrand Russell wrote:
[I]t is not what the man of science believes that distinguishes him, but how and why he believes it. His beliefs are tentative, not dogmatic; they are based on evidence, not on authority or intuition.
- Bertrand Russell, A History of Western Philosophy (Book-of-the-Month Club, 1995), p. 527
- Michael Shermer, "What is Pseudoscience? Distinguishing between science and pseudoscience is problematic", Scientific American, 9/15/2011
Even though the next presidential election is still over a year away, we're already seeing public opinion polling of potential voters' candidate preferences. In addition, we're also seeing the usual exaggeration of the significance of poll results by ignoring or downplaying the margin of error. Michael Rooney at the Critical Thinking Web Exchange analyzes a recent example of such ado about nothing (see the Source, below). Check it out.
At this point, even if a poll shows statistically significant differences between candidates, there's still so much time before the election that there would be little reason to expect such a difference to persist long enough to affect it. A lot can happen to change public opinion in a year.
Here's another thing to keep in mind: since we're already seeing polling at this early date, there are bound to be scores of polls before the election. Given the standard 95% confidence level, this means that we can expect 5% of these polls to be off by more than the usual margin of error.
Source: Michael Rooney, "Bogus Precision", Critical Thinking Web Exchange, 8/24/2011
Resource: How to Read a Poll, Fallacy Watch
No Confidence Interval
The latest "Bad Science" column by Ben Goldacre explains the role of confidence intervals in statistical studies, and gives an example from the British media of how reporters ignore them. I've discussed this issue previously (see, for instance, the Resource below), but mainly in the context of public opinion polling. However, any study that uses sampling to draw a conclusion about a population will have a confidence level and margin of error.
Reporting on polls, at least in the United States, is usually better in this respect than reporting on scientific studies, as there is a well-established rule that the margin of error be included in poll reports. In contrast, reports of statistical studies often do not mention the confidence interval. This is unfortunate, as Goldacre explains. Check it out.
Source: Ben Goldacre, "Unemployment is rising – or is that statistical noise?", Bad Science, 8/19/2011
Resource: How to Read a Poll, Fallacy Watch
A Big, Black Cloud of Contextomy
Continuing the theme begun in the previous entry, Ed Schultz on his television show on Monday quoted Texas Governor and Republican presidential candidate Rick Perry:
Schultz: I think there's an element of racism every time people claim the first black president doesn't love this country. Perry comes from the radical country club that loves to remind white America President Obama is other, not like you. Perry also wants you to know that he's pro-business.
Perry: I'm a pro-business governor. I don't make any apologies about it, and I will be a pro-business president. Getting America back to work is the most important issue that faces this country, being able to pay off $14.5 trillion or $16 trillion worth of debt. That big black cloud that hangs over America.
Schultz: That black cloud Perry is talking about is President Barack Obama.
To his credit, on his next show Schultz apologized for quoting Perry out of context, though it was probably unclear exactly what he was apologizing for unless you had seen the previous show.
Schultz: Last night we played a clip of Governor Perry talking about the debt being a black cloud over this country. We did not present the full context of those statements and we should have. Here's the full clip. Let's get it right.
Perry: I'm a probusiness governor. I don't make any apologies about it, and I will be a probusiness president. Getting America back to work is the most important issue that faces this country. Being able to pay off 14.5 or $16 trillion worth of debt. That big black cloud that hangs over America, that debt that is so monstrous. There's only one way you get rid of it that's practical, that makes sense. That is to free up America. Free up American entrepreneurs.
Schultz: No doubt about it, it was a mistake, and we regret the error. On this particular statement, we should not have included it on our coverage of his overheated rhetoric. That's our mistake.
I presume that the particular statement that Schultz should not have included was his claim that Perry referred to President Obama with the phrase "big, black cloud". The original clip also cut Perry off right before he said "that debt", making it clear that he was not referring to Obama. If the original clip had included the full statement, it would have been obvious that Schultz's innuendo that Perry was making a racist remark was unjustified.
Source: Burgess Everett, "Schultz regrets Perry remark about 'big black cloud'", Politico, 7/16/2011. Has a link to the video.
Name that Fallacy!
Via: Michael Koplow, "Virtual ellipsis", Ed Absurdum, 8/4/2011
One Universe is Enough!
The cover story of the current issue of Scientific American, by cosmologist George F. R. Ellis, deals with the multiverse theory in physics:
In the past decade an extraordinary claim has captivated cosmologists: that the expanding universe we see around us is not the only one; that billions of other universes are out there, too. There is not one universe—there is a multiverse. … In this view, not only is our planet one among many, but even our entire universe is insignificant on the cosmic scale of things. It is just one of countless universes, each doing its own thing. … I am skeptical about this claim. I do not believe the existence of those other universes has been proved―or ever could be. Proponents of the multiverse, as well as greatly enlarging our conception of physical reality, are implicitly redefining what is meant by "science".
Ellis' article answers one question I had about the multiverse idea, namely, whether physicists are using the term "universe" in some unfamiliar way. According to Ellis, there are different types of multiverse that―according to me―reflect different notions of "universe":
- Parts of space that are so far away that light has not had time to reach us since the Big Bang. In my view, these are simply distant parts of our own universe, though they may be forever inaccessible to us even in principle.
- Prior to the Big Bang there may have been another "universe"―perhaps even infinitely many, if each "universe" has a finite life-span. In my view, these would simply be earlier states of our own universe, even though they may be forever closed off to us if the Big Bang destroyed all evidence of their existence.
- More deserving of the term "universe" would be alternate "universes" each with its own separate spacetime.
My only objection to these types of "universe" is that they're purely speculative. They may well exist for all we know, but there doesn't appear to be any current evidence supporting their existence, and such evidence may be forever unobtainable.
I don't even object to calling them "universes" so long as we keep in mind what we mean by that. In fact, one consideration for calling them "universes" is that they are separate, self-contained areas of space or time, and causally isolated from our own "universe". However, this consideration mitigates against the possibility that we can ever have evidence of their existence. In other words, if we were ever able to get evidence of the existence of such a "universe", that fact would be evidence that it does not deserve to be called a "universe". The third type of "universe" best fits the definition of a "universe" as a self-contained spatial, temporal, and causal whole, but it is also for that very reason forever inaccessible to us. We would never be able to see such alternate universes, even if they exist, for they do not exist within the space of our own universe, and any light generated within such a universe can never leave it.
I've previously criticized the multiverse theory (see the Resources, below) for a couple of reasons: First of all, the so-called "fine-tuning" argument given in support of it is too weak to sustain such a strong conclusion. Of course, it would be a mistake (specifically, the Bad Reasons Fallacy) to conclude that the theory is false simply because a certain argument for it is bad. However, the fine-tuning argument is the main support usually given for the theory. Here's most of what Ellis has to say about this argument, with some of the physics omitted:
A remarkable fact about our universe is that physical constants have just the right values needed to allow for complex structures, including living things. …[A]n exotic multiverse provides a tidy explanation for this apparent coincidence: if all possible values occur in a large enough collection of universes, then viable ones for life will surely be found somewhere. … I agree that the multiverse is a possible valid explanation…; arguably, it is the only scientifically based option we have right now. But we have no hope of testing it observationally.
When Ellis writes that the multiverse theory "is the only scientifically based option we have right now", I suspect that he is alluding to the religiously based alternative that God fine-tuned the universe for us. If physicists think that the only possible explanations for the "fine-tuning" of the universe are a multiverse or God, then the only "scientific" alternative is the multiverse. However, if there is no hope of ever testing the theory, then in what sense is it a scientific alternative? Moreover, there is a missing alternative:
Proponents of the multiverse make one final argument: that there are no good alternatives. As distasteful as scientists might find the proliferation of parallel worlds, if it is the best explanation, we would be driven to accept it; conversely, if we are to give up the multiverse, we need a viable alternative. This exploration of alternatives depends on what kind of explanation we are prepared to accept. Physicists' hope has always been that the laws of nature are inevitable―that things are the way they are because there is no other way they might have been―but we have been unable to show that this is true. Other options exist, too. The universe might be pure happenstance―it just turned out that way. Or things might in some sense be meant to be the way they are―purpose or intent somehow underlies existence. Science cannot determine which is the case, because these are metaphysical issues.
Indeed. Which brings us to the second objection: the multiverse theory is really a metaphysical theory, rather than a scientific one, and in this respect is not one whit better than the theory that God did it. The physicists who advocate it are thereby doing metaphysics rather than physics.
A scientific theory must be, at least in principle, empirically testable, that is, there must be some conceivable way its existence will make an observable difference to the universe. Now, there's some slight hope for the multiverse theory so long as it posits only type 1 or type 2 "universes", which are really only spatially or temporally distant parts of our own universe. Type 3 universes, in contrast, are by definition "outside" our universe's space and time, and not part of its causal order. Whether such "universes" exist cannot possibly make any empirical difference to the actual universe, so that they belong to metaphysics as much as the God who fine-tuned the universe. I'll give Ellis the last word:
Nothing is wrong with scientifically based philosophical speculation, which is what multiverse proposals are. But we should name it for what it is.
Source: George F. R. Ellis, "Does the Multiverse Really Exist?", Scientific American, 7/19/11. You may need to subscribe to see the whole article.
- The Arguments that Failed, 3: The "Fine-Tuning" Argument, 1/20/2009
- New Book: The Fallacy of Fine-Tuning, 6/19/2011
- Fine-Tuning the Fine-Tuning Argument, 6/27/2011
A Self-Answering Question
What question contains the word "platypus" for no apparent reason?
Source: John Allen Paulos, Beyond Numeracy: Ruminations of a Numbers Man (1991), p. 114