Tuesday, March 24, 2015

The danger of weak arguments

Weak arguments are not neutral, they are damaging for technical or scientific propositions.

There's overwhelming evidence for the proposition "Earth is much older than 6000 years." (It's about 4.54 billion years old, give or take fifty million.) Let's say that Bob, who likes science, as long has he doesn't have to learn any, is arguing with Alex, an open-minded young-Earth creationist:

Alex: Earth was created precisely on Saturday, October 22, 4004 B.C., at 6:00 PM, Greenwich Mean Time, no daylight savings.

Bob: That's ridiculous, we know from Science(TM) that the Earth is much older than that.

Alex: What science? I'm willing to listen, but not without details.

Bob: Well, scientists know exactly and it was in Popular Science the other day, too.

Alex: What did the Popular Science article say?

Bob: I forget, but it had two pretty diagrams, lots of numbers, and a photo of Neil DeGrasse Tyson in his office. He has a wood model of Saturn that he made when he was a kid.

Alex: So you don't really know how the age of the Earth is calculated by these scientists, you're just repeating the conclusion of an argument that you didn't follow. Maybe you didn't follow because it's a flawed argument.

Bob: I don't remember, it's very technical, but the scientists know and that's all I need. Why don't you believe in Science(TM)?

Alex: It appears to me that your argument is simply intimidation: basically "if you don't agree with me, I'll tag you with a fashionable insult." Perhaps that's also the argument of the scientists. They certainly sound smug on television, as if they're too good to explain themselves to us proles.

Alex, despite his nonsensical belief about the age of the Earth, is actually right about the form of argument; by presenting a weak argument for a truthful proposition, Bob weakens the case for that proposition. Note that this is purely a psychological or Public Relations issue; logic mandates that a bad argument for a proposition doesn't change the truth of that proposition. Too bad people's brains aren't logical inference machines.

(There's a Bayesian argument for downgrading a belief in a proposition when the case presented for that proposition is weak, but a rational person trying to learn in a Bayesian manner the truth of a proposition will do a systematic search over the space of arguments, not just process arguments collected by convenience sampling.)

This is one of the major problems with people who like science but don't learn any: because of the way normal people process arguments and evidence, having many Bobs around helps the case of the Alexes.

A weak argument for a true proposition weakens the public's acceptance of that proposition. People who like science without learning any are fountains of weak arguments.

Let's convince people who "like science" that they should really learn some.

Friday, March 20, 2015

Adventures in science-ing among the general public

I've been running an informal experiment in social situations, based on an example by physicist Eric Mazur:

A light car moving fast collides with a slow heavy truck. Which of the following options is true?

a) The force that the car exerts on the truck is smaller than the force that the truck exerts on the car.

b) The force that the car exerts on the truck is equal to the force that the truck exerts on the car.

c) The force that the car exerts on the truck is larger than the force that the truck exerts on the car.

d) To know which force is larger (that of the car on the truck or that of the truck on the car) we need to know more details, for example the speed and weight (mass, really) of each vehicle.

The majority in my convenience sample pick the last option, d. Included in this sample are people with science and engineering degrees. Most of the people I asked this question can quote Newton's third law of motion: when prompted with "every action has..." they complete it with "an equal and opposite reaction."

So far, my convenience sample replicates Mazur's results.

But unlike his measurement (which was made with those classroom clickers that universities use to avoid hiring more faculty and having smaller, more personalized class sessions), mine sometimes comes with arguments, explanations, and resistance.

And here's the interesting part: the farther the person's training or occupation is from science and technology, the stronger their objections and attempts to argue for d, even as they quote Newton. I don't think this is the Dunning-Kruger effect. It's more like a disconnect between concept, principle, meaning, and application.

It's not like linking concepts to principles and meaning and then applying those concepts is important, right? Especially in science and engineering...

Sunday, March 15, 2015

Discussing technical material ≠ arguing opinions

A problem of discussing [minimally] technical material with educated non-technical people is that they don't understand the difference between arguing opinions and discussing technical material.

This problem becomes much greater when the material is probability and when the example is something that the non-technical persons have been using for a while to assert their mastery of quantitative thinking.

Take, for example, the boy-girl problem: "one of two children is a boy, how likely is it that the other is also a boy?"

The right answer is one-half, though figuring that out requires some minimal understanding of probability, namely the difference between states and events and the mechanics of using prior and conditional probability to compute a posterior probability.

That computation is not the point.

The point is that even after this explanation, even in-person, some people think that they can argue for $1/3$. And that verb, "argue" is the problem.

Given a mathematical derivation yielding a result you don't like, the first step in a discussion of the result has to be pointing out the error in the derivation. My video does that for the $1/3$: the error is assigning "prior" probabilities after observing an event, in particular an informative event. (It's at the end of the computation because I need to introduce the basics of probability thinking first.)

But the people arguing for $1/3$ after that video never think they have to find the error; they either want both solutions to be valid (and don't understand why that's a problem, which is much more worrisome than not knowing how to think about probability) or appeal to some form of authority, like "I saw the $1/3$ on SciShow and they have millions of views" (which is an even bigger problem and one that is widespread, probably a consequence of how science is being popularized).

For a successful technological society, reality must take precedence over self-esteem, for nature cannot be fooled, paraphrasing a much smarter person (last sentence of report).

Software I use - part of a new computer decision process

Trying to decide whether to update (by buying a new one) my MacBook Pro, get a new MacBook Air, or switch platforms to Linux or even Windows. So I listed the software I use, and the first observation is that unless I'm willing to spend a lot of money on new programs, I'm hard-locked to the Mac platform...

TexShop. I write mostly in LaTeX. In the past I used LaTeX only for research but now I make almost all my handouts and discussion documents in LaTeX. (When I don't, they are almost always InDesign one- or two-page documents.) I know that there are WYSIWYG environments for people who want to write in a Word-like environment, but being a long-time programmer I prefer to edit LaTeX source code.

R. This is my main programming environment, having replaced Stata and MATLAB. I considered using Octave or Python, but in the end R is the best combination for my needs.

Mathematica. Every so often I need to do some tedious calculus, so I trust Mathematica for that. (When I do more than a few pages of calculus by hand, there's usually a missing sign or a transposed fraction somewhere.)

TextWrangler. Heir to the venerable BBEditLite, it's my mainstay text editor. I use it for all text that is not LaTeX, including programming, web posts, drafts of long emails, and outliner for talks. (I don't use a specialized outliner program for the reasons I gave in this post.)

Keynote. I used it as mostly a projector management system, with all content created on other tools, but now I use it for about one-quarter to one-third of all slides. Integration with iTouch and iPad allows for good control (which, I'm told, has existed in the Windoze ecosystem for several years now…).

Numbers. Not as good as Excel for most tasks that a manager would use a spreadsheet, but it's a simple way to mock-up quick models for class demonstrations. Anyone doing serious spreadsheet work must use Excel, though, since Apple seems intent on leaving the professionals behind. Really.

Pages. Although I don't use  Microsoft Word as a text editor, I occasionally work with people who do. It's hard to believe that a word processor in 2015 doesn't allow facing pages (odd/even pages); were I to use a word processor rather than LaTeX, this would mean Word, not Pages. Apparently Apple is intent on leaving even school reports to Microsoft...

Adobe Illustrator. My main drawing program, for diagrams and illustrations. Even though there are now some minimally acceptable drawing tools in Keynote, they are still very weak compared to Illustrator.

Adobe InDesign. When I need to make diagrams that include a lot of text and not a lot of drawing, I prefer InDesign to Illustrator. InDesign is also my program of choice for making compact handouts, of the type I send for remote discussions or distribute at speaking events. (In the old days, I used to make my teaching handouts with InDesign, but once I went for long handouts, I switched to LaTeX.)

Adobe Photoshop.
 I use it for final production on many slides, though a little less now as I move towards a simpler aesthetic. It also serves as my photo editor, not that I edit photos that often.

Magical number machine. A good calculator for quick arithmetic, which I used to do with an HP calculator, but gave that away in my last physical decluttering. I also use it to do arithmetic on the projection screen while using boards or flip charts.

LaTexIt. Quick LaTeX rendering for inclusion in diagrams or slides.

Voila. Page capture on steroids; can capture entire web pages as well. It has some minor editing affordances, but I do all image editing in Photoshop.

Screenflow. Captures screen, mic, and camera, for webinar-style videos. I use it for all sorts of video editing as well. Haven't opened iMovie since I got Screenflow.

VLC. Because Apple's video players are terrible.

NetNewsWire. My RSS feed reader. I could move to the cloud, and have considered that, but for now I'm happy with this. I only open it once a day, in the morning, to get a sense of what's going on.

Google Chrome. It's less of a background hog than Safari, which isn't saying much, really.

Skype. To communicate with people. Despite Microsoft's best efforts to make it unusable, the network I have on Skype is still strong enough for me to use it.

Kindle app. I have lots of Kindle books, so this is a no-brainer. (I replaced a lot of paper books with Kindle books in the 2013 declutter, using the rule that if I was likely to reread a book and its Kindle price was low, I'd rather have the electronic copy and the free physical space.)

iBooks. I also have a lot of ePubs and even some Apple iBooks, so this is again a no-brainer. I think iBooks manages multimedia content better than the Kindle.

iBooks Author. Maybe. I'm considering using this to release an interactive version of some of my teaching materials, but the limited platform (Apple only ecosystem) and the volatility of the eLearning technologies are a concern.

Simple comic. It reads comic book formats, of course, but also some other formats such as 7z which can be useful under certain circumstances. Also, I have a number of old comics in .cbr format, for nostalgia sake.

iTunes. For now my music player; it's acceptable when fed through a quality DAC. Its strong point is organization, thought that's just relative to competitors: as far as art music is concerned, no program works well, just passably.

iPhoto, soon to be replaced with Photos. To organize photos, not really a serious competitor to Photoshop when it comes to edit them.

That's it. No Handbrake for a new laptop since they no longer have optical drives (though I might install it for video file conversion, which it does very well); no email program, since I use web interfaces to keep email checking to a minimum; and no games, since I have the three I play on my phone, iTouch, and iPad (falling tiles, mahjong, and solitaire).

Sunday, February 8, 2015

Science popularization has an identity problem

Some influential science popularizers are doing a disservice to public understanding of science and possibly even to science education.

Yes, it's a strong statement. Alas, it's a demonstrable one.

With the caveats that I enjoy the Mythbusters show, especially the recent series with their back-to-origins style, and that this post is not specifically about them, the recent episode about The A-Team presented an almost-perfect example of the problem.

"Stoichiometry."

Midway through the episode Adam uses this word. It's an expensive way of saying "mass balancing of chemical equations" (not how it was described in the show). And then, well... and then Jamie proceeded to not use stoichiometry.

To be concrete: they were exploding propane. Jamie tried mixing it with pure oxygen and got a big explosion. Then they mention stoichiometry. At this point, what they should have done was to introduce some basic chemistry.

The propane molecule has 3 carbon and 8 hydrogen atoms, $\mathrm{C}_{3} \mathrm{H}_{8}$. It burns with molecular oxygen, $\mathrm{O}_{2}$, yielding carbon dioxide, $\mathrm{C} \mathrm{O}_{2}$, and water vapor, $\mathrm{H}_{2} \mathrm{O}$.

Chemists represent reactions with equations, like this:

$\mathrm{C}_{3} \mathrm{H}_{8} + \mathrm{O}_{2} \rightarrow \mathrm{C} \mathrm{O}_{2} + \mathrm{H}_{2} \mathrm{O}$

This equation is unbalanced: for example, there are three carbons on the left-hand side, but only one on the right-hand side. By changing the proportions of reagents, we can get both sides to match:

$\mathrm{C}_{3} \mathrm{H}_{8} + \mathbf{5} \, \mathrm{O}_{2} \rightarrow \mathbf{3} \, \mathrm{C} \mathrm{O}_{2} + \mathbf{4} \, \mathrm{H}_{2} \mathrm{O}$

Once we have this balance, we can determine that we need 160 grams of oxygen for each 44 grams of propane. For this we need to look up the atomic masses (to compute molar masses) of carbon (12 g/mol), hydrogen (1 g/mol) and oxygen (16 g/mol). (*)

Back on the Mythbusters, after mentioning stoichiometry, Jamie starts trying out different proportions of propane to oxygen. If he had actually used stoichiometry he'd already have the proportions calculated, as I did above, about four times more oxygen than propane by mass; no need to experiment with different proportions.

(Yes, there'a a lot of experimentation in engineering, but no engineer ignores the basic scientific foundations of her field. Chemical engineers don't figure out mass balances by trial and error; they use trial and error after exhausting the established science.)

This illustrates a major problem in the way science is being popularized: to a segment of the educated and interested audience, science is an identity product. Like a Prada bag or a sports franchise logo on a t-shirt, they see science as something that can signal membership in a desired group and exclusion from undesirable groups.

Hence the word "stoichiometry" inserted in a show that doesn't actually use stoichiometry.

"Stoichiometry" here is, like the sports franchise logo, purely a symbol. The audience learns the word, in the sense that they can repeat it, but not the concept, let alone the principles and the tools of stoichiometry. The audience gains a way to signal that they "like" science, but no actual knowledge. Like a sedentary person who wears "team colors" to watch televised games.

Some successful science popularizers pander to this "like, not learn, science" audience, instead of trying to use that audience's interest in science to educate them.

So what, most people will ask. It's the market working: you give the audience what they want. And there's no question that selling science as identity is good business. Shows like House MD, Bones, The Big Bang Theory, all take advantage of this trend. Gift shops at science museums cater to the identity much more than the education: a look at their sales typically finds much more logo-ed merchandize than chemistry sets or microscopes.

(Personal anecdote: despite having three science museums nearby, I had to use the web to get a real periodic table poster. A printable simple table from Los Alamos National Lab.)

"Liking" science without learning it is bad for society:

1. Crowds out opportunities for education. People have limited time (and money) for their hobbies and activities. If they spend their "science budget" on identity, they won't have any left for actual science learning. Many more people read Feynman's two autobiographies than his Lectures On Physics or his popular physics books.

2. Devalues the work of scientists and engineers, by presenting a view of science that excludes the hard work of learning and the value of the knowledge base (trial-and-error in lieu of mass balance calculations, for example). Some people end up thinking that science is just another type of institution credential (or celebrity worship) instead of being validated by physical reality.

3. Weakens science education. Some people who go into science expect it to be easy and entertaining (in the purely ludic sense), instead of hard but rewarding (deriving satisfaction from really understanding something), as that's what the popularization depicts. They then want schools to match those expectations. While colleges may not want to simplify science and engineering classes, they put pressure on faculty for more "engaging" teaching: less technical, more show. (**)

4. As science becomes more of an identity product to some people, and increasingly perceived as identity-only by others, it becomes more vulnerable to non-scientific identity threats, such as derailing a major scientific and technical achievement in space exploration by talking about sartorial choices and sociological forces in academia.


So, what can we do?

First, we should recognize that an interest in science, even if currently trending towards identity, can be channeled into support for science and science education. As societal trends go, a generalized liking for science is better than most alternatives.

Second, there are plenty of sources of information and education that can be used to learn science. There's a broad variety of online resources for science education at different levels of knowledge, free and accessible to anyone with an internet connection (or indeed a library card; books were the original MOOCs).

Third, current "science as identity" popularizers may be open to educating their audiences. Contacting them, offering feedback, and using social media to otherwise proselytize for science (as in scientific knowledge and thinking like a scientist) might induce them to change their approach.

The most important thing anyone can do, though, is to try to get people who "like" science to understand that they should really learn some.

(Final note on the A-Team episode: Adam should have played Murdock, not Hannibal.)

- - - -
(*) I learned to do this on my own as a kid, but the material was covered in ninth grade chemistry. (A long time ago in a country far away, in ninth grade you chose a technical or artistic area in school; mine was 'chemical technology' because my school didn't have electronics.) A side-effect of my early interest in chemistry is that I have quasi-Brezhnevian eyebrows: you burn them off five or six hundred times, they grow back with a vengeance.

(**) Some schools protect their main reputation-building degrees by creating non-technical versions of the technical courses and bundling them into subsidiary degrees. So, for example, they have information technology courses, which sound like computer science courses but are in fact nothing like them.
          Another approach is the encroachment of humanities, arts, and social sciences "breadth" requirements into science and engineering degrees. When I studied EECS in Europe, we had five years of math, physics, chemistry, and engineering courses. A similar degree in the US has four years and usually a minimum of one-year-equivalent of those "breadth" requirements, though some people can have more than two-year-equivalent by choosing "soft engineering" courses like "social impact of computers."

Monday, January 26, 2015

One of two children is a boy, how likely is it that the other is a boy?

One-half. Not one-third; one-half.

Since I work with probability and statistics, I sometimes endure someone trying to 'teach" me that it's one-third. Because I've tired of explaining why 1/3 is the wrong answer, one person at a time, I made a video:



Essentially the problem is foundational: people who get the wrong answer do so because they haven't learned to think in terms of states, events, and their probability implications.

Updated Feb 3rd, 2015: A colleague sent me another example of people assigning "prior" probabilities after observing an event. I made a short video about it:



Saturday, January 24, 2015

The easier it is to graduate college, the bigger the advantage of graduating


The easier it is to graduate college, the bigger the advantage of graduating. Obvious, no?

Wait, what?

"No, no, no, I hear you say. The harder it is to graduate college, the bigger the advantage of graduating." This sounds reasonable: if graduating college is very hard, then being a graduate signals high ability. But alas, that seems to forget the effect on the people who don't graduate.

First let's have a point of agreement: the easier it is to graduate college, the worse the average graduate will be. (Keeping the population constant, of course.) Any reasoning, or model, that doesn't capture this effect will be prima facie wrong.

Now to the point of disagreement: that the easier it is to graduate college, the more important it is to graduate.

Let's consider a job market choosing between a college graduate $G$ and a non-graduate $NG$, based solely on that fact. Then, what the job market should care about should be the average "quality" of these two groups of people.

(We'll assume that there's some "quality" $q$ that determines success in college that is correlated with what the job market wants.)

Let us study, then, the behavior of $E[q|G]$ relative to $E[q|NG]$ as a function of a threshold quality needed for graduation $T$. The definition of $T$ is that all members of the population with $q \ge T$ graduate college and all others do not. This is obviously an approximation.

First, let's consider a simple population, with quality uniformly distributed on a finite support (this is called a Hotelling model), which without loss of generality and significant gain in simplicity we assume to be the interval $[0,1]$.

We'll use as a measure of the advantage of college the ratio of expected quality,
\[ \frac{E[q | G]}{E[q | NG]} = \frac{E[q|q\ge T]}{E[q | q < T]} = \frac{(1+T)/2}{T/2}
\]
A few days ago I plotted this function while microwaving my lunch:


The chart also shows the average quality of a college graduate, and it does decrease as the fraction of people graduating (i.e. the ease of graduating) increases.

Later that day, having another food-related wait, I decided to do the same for a standard Normal distribution, $q \sim N(0,1)$.
\[
 \frac{E[q | G]}{E[q | NG]} = \frac{\frac{\frac{1}{\sqrt{2 \pi}} \,\int_{T}^{+\infty}  q \, e^{-q^2/2} dq}{1 - \Phi(T)}}{\frac{\frac{1}{\sqrt{2 \pi}} \, \int_{-\infty}^{T} q \, e^{-q^2/2} dq}{\Phi(T)}}
= \frac{\frac{e^{T^2/2}}{1 - \Phi(T)}}{\frac{- e^{T^2/2}}{\Phi(T)}} = - \frac{\Phi(T)}{1 - \Phi(T)}
\]
Note that this is always a negative number, an artifact of having the distribution centered at zero, so that $E[q|q < T] \le 0$. Since it could easily be shifted into positive values simply by adding a positive mean to the distribution (and making the formula above a bit unwieldy), it's irrelevant, only the relative positions on the plot matter. If you're uncomfortable with that, be my guest, add a $\mu >> 0$ to the formula and make your own plot.

Here's the plot for the normal distribution, with $T$ in the scale of standard deviations:


One simple way to see how this works is the following: if college is really easy to graduate (which includes access to college and financing, by the way), only very unmotivated people will not graduate college, as long as the job market expect you to.

Perhaps instead of getting more people into college, society should work towards not having an expectation of a college degree.