The Power of Positive Ignorance, Part I

People often ask me “Jimbobboy, what do you think science is like, anyway?”

Or they would, if anyone who knew me gave a rat’s ass what I think science is like.

Fortunately, answering questions no one has asked is exactly what we have blogs for!

And today, the answer is that science is quantitative.

The text for today’s lesson is drawn from the book of Richard, with grateful acknowlegment of the demon squid.

This post is part of a kind of self-organizing series called “What I Think Science Is, Not That Anyone Cares.”  It’s sort of thematically related to the last one, but it is not about stupidity, exactly.
It’s more about two kinds of ignorance: the deficits we all have in various areas and to different degrees — the ones we can’t help, that is — and the ones we cherish and nourish and defend.
The test article today has both types in beautiful, illuminating display, but we will start with the first and deal with the second in a post to follow. It begins, as all good things do, with a blog flamewar.

The first dinner roll thrown in this food fight came during last year’s[1] election.   Libertarian yoyo (and now Senator) Rand Paul, at a Kentucky homeschoolers’ convention, declined to say how old he thought the earth is. Paul was mocked by PZ Myers as a craven weasel. A conservative Christian blogger rushed sarcastically to Paul’s defense, and was duly thrashed.

“So what?” I can hear you say, “Isn’t this just more of the childish raillery to be found in countless locations all over the intertubes, and rather lukewarm broth at that?”

You see, this is what happens when the common people are allowed access to computing machinery — you have become jaded. I’ll tell you what’s special about this exchange. It’s a springboard to a dual exploration of unintentional and intentional ignorance, that’s what it is. By the time we’re done exploring, you’ll thank me and ask for more, you will, so sit down and shut your pie-holes.

Where was I? Oh, yes, ignorance. Let’s address unintentional ignorance, and start with someone who was anything but ignorant.

Native ignorance about magnitudes

We would be reading, say, about dinosaurs. It would be talking about the Tyrannosaurus rex and it would say something like, “This dinosaur is twenty-five feet high and its head is six feet across.”  My dad would stop reading and say, “Now, let’s see what that means.  That would mean that if he stood in our front yard, he would be tall enough to put his head through our window up here.” (We were on the second floor.) “But his head would be too wide to fit in the window.” Everything he read me he would translate as best he  could into some reality.  It was very exciting and very, very interesting to think there were animals of such magnitude–and that they all died out, and that nobody knew why. I wasn’t frightened that there would be one coming in my window as a consequence of this. But I learned from my father to translate: everything I read I try to figure out what it really means, what it’s really saying.

Richard P. Feynman, What Do You Care What Other People Think?

Most everyone who reads these childhood stories of Feynman’s finds them irresistibly charming, and I’m no exception. I think the reason is that he is always looking for an early example of the process that made him such an extraordinary thinker. That process began with a child’s incandescent joy in discovery — a joy that Feynman experienced every moment of his life. In this case he is recalling how his father nurtured in him a sense of magnitude. It is noteworthy that Feynman learned as a wee sprout that when he heard “twenty-five feet” and “six feet” he should imagine the elevation and width of his bedroom window, because from that lesson, and others like it, one little boy grew to have a quick, powerful insight into aspects of our world most of us literally cannot imagine.

That insight is a special quality. It is essential to the successful pursuit of scientific discovery, and the greatest scientists have it to a degree that appears supernatural to the rest of us. Enrico Fermi’s ability to conjure with quantities was legendary, and hs name is now associated with a kind of estimation — the Fermi problem. The objective of a Fermi problem is to arrive at a reasonable answer to a complex question with limited  information. Accuracy in the usual sense is unimportant here, but understanding relationships is everything. In some cases, getting an answer  correct to within two orders of magnitude is considered pretty good.[3]

This is relevant to the present question because I think there is a spectrum of quantitative insight stretching from the truly extraordinary such as  Fermi and Feynman, through ordinary mortals like me and you, to those who have little or none of the magic juice. This is not a moral judgment. I would love to be able to grasp a difficult physical problem instantly, just as I would love to be able to dunk a basketball or have perfect pitch. That I am unathletic and musically untalented does not (I hope) reflect badly on me as a human being.  However, it does mean that I am unlikely to be tapped first at pickup concerts for the local string quartet, and that my audition for the Nuggets may go badly.

I don’t hold it against Martin Cothran that he has no sense of magnitude, but it must be admitted that he has none[4]. This is important because we live in a world where a sense of magnitude is increasingly valuable as one item in the toolbox of the everyday citizen. And the magnitudes of interest here are different enough that the everyday citizen should be able to distinguish between them. How different? For biblical literalists, often identified as Young Earth Creationists (YECs) the benchmark estimate for the age of the earth is that established by Archbishop James Ussher, who pegged  the date of the world’s creation at Sunday 23 October 4004 BC. In fairness to the Bish, we’ll cut him some slack on the dates. Any of the various  begats and begots could easily have been in error by a few years, leading to an honest error in his estimate of the earth’s age. It doesn’t matter,  because the best estimate for the earth’s age from the radiometric evidence is between 4.5 and 4.6 billion years. This staggering duration is so much greater than Ussher’s estimate that any simple error of estimation is overwhelmed. One of those two estimates is wrong: not just wrong, but wildly wrong, and wrong beyond any hope of correction by fine-tuning of methods. The ratio between those two numbers is 4.5 x 109/6000, or about[5] 750,000. Neither I nor anyone likely to be reading this is a Feynman or a Fermi, so an analogy may help us visualize this ratio. But what would be appropriate for the intended audience? Ah — I know.

An analogy

In Danny Leiner’s 2004 movie Harold & Kumar Go to White Castle, the eponymous restaurant was located in Montclair, New Jersey[6]. Now,  suppose for the sake of this analogy that the Montclair White Castle, befitting its significance as the symbolic object of all desire, is the only White Castle in the universe. And suppose further that Harold and Kumar, as good stoners, live not in New Jersey but in Monterey, California. The distance from Monterey to Montclair is about [7] 2600 miles. Imagine how the critical discussion might have gone[8] under these assumptions:

Kumar: Dude, I am so baked.

Harold: Tell me about it. Hey, you know what I could go for?

Kumar: Zat?

Harold: Some sliders, man. Let’s hoof it over to White Castle and get some sliders.

Kumar: Dude, White Castle is like three thousand miles away. You can’t walk there.

You take my point, I am sure. There is not enough dope in California to convince even Kumar that he could walk to New Jersey. And this conclusion is not affected by a large correction factor:

Harold: No, White Castle is only 2557 miles away.

Kumar: What are you, a geography major? It’s still too far to walk.

Let’s consider it established that no one, no matter how stoned, would consider walking from California to New Jersey for a slider, even without  precise information as to the distance. The magnitude is simply too great. Now, suppose we were to contract the Monterey-Montclair axis by the  factor of 750,000 discussed above. The distance from Harold and Kumar to the White Castle would shrink to eighteen feet, and Harold could march up and order sliders with little more effort than it takes to pass the bong. That is the difference between the generally accepted estimate of the earth’s age, and that embraced by creationists. You can’t walk there from here.

The next post will deal with willful ignorance about magnitudes.

Pointless Footnotes

[1] Yes; this all happened last year.  I’m a stonecutter, OK?  And I needed an example.

[2] This post will seem like an extended beating-up of Martin Cothran, because that is what it is. But what is the purpose of the Web, after all, if it is not to beat up on arrogant twits?

[3] I recall that there has been (and may still be) a Fermi Problem challenge held during MIT’s Independent Activities Period (IAP, also known as January) in which some problems had explicit success criteria of two or three orders of magnitude. Like “How many quarks in the universe? Full credit if your answer is greater than one-thousandth and less than one thousand times the correct number.” Anybody out there remember this? I’ll pay a bounty of $1000 for more information, up to a factor of 10E03.

[4] Cothran figures he can get away with this because he can claim agnosticism on any question of magnitude. Nice try.

[5] Keep in mind that two significant figures here are plenty. This will be on the quiz.

[6] Not, apparently, the location of any real-world White Castle, but birthplace of actor Kal Penn.

[7] It’s 2557 miles to be precise, but we’re not being precise here, now are we?

[8] Take all the colorful language as read.

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