Thursday, February 25, 2016

People in glass houses shouldn't call smart kids ignorant


So, an acquaintance forwarded another "kids these days can only take tests but don't know anything important" link; it included these questions as example of the problem:

"Who fought in the Peloponnesian war?  What was at stake at the Battle of Salamis?  Who taught Plato, and whom did Plato teach?  How did Socrates die?  Raise your hand if you have read both the Iliad and the Odyssey.  The Canterbury Tales?  Paradise Lost? The Inferno? 
Who was Saul of Tarsus?  What were the 95 theses, who wrote them, and what was their effect?  Why does the Magna Carta matter?  How and where did Thomas Becket die?  What happened to Charles I?  Who was Guy Fawkes, and why is there a day named after him?  What happened at Yorktown in 1781?  What did Lincoln say in his Second Inaugural?  His first Inaugural?  How about his third Inaugural? Who can tell me one or two of the arguments that are made in Federalist 10? Who has read Federalist 10?  What are the Federalist Papers?"

The funny thing, and I'm not the first one to notice this, is that the people who ask these questions in order to call others ignorant have little knowledge of the sciences, technologies, engineering, and math. (Or economics and business, for that matter.)

So, here's my response:

What happens when you drop metallic copper into sulfuric acid? What does it mean that the half-life of caffeine in the human body is approximately 2 hours? What is the main function of the kidneys and how does the heart work, namely what's connected to each part? Raise your hand if you can write the chemical equations for sodium hydroxide reacting with hydrochloric acid and for the combustion of propane. The quadratic equation solution formula? The equations of motion for a ballistic projectile? The complex conjugate of $(4 - 7i)\times (3+ 2i)$? 
What is discounted cash flow? How far are the Sun and the Moon from Earth? What is kinetic energy, and for a given moving object does it increase more when you double the mass or the speed? Why does the standard error for an estimate matter? How does a pressure cooker do its faster cooking? What's the difference in market outcomes for an increase in demand and an increase in supply, everything else being constant? What happens at Lagrange Points? What amino acids are essential, and why are they "essential"? What's Newton's first law of motion? His second law? What's an example of the difference in programming languages between a cycle and a conditional statement? Who can tell me one or two main differences between Newtonian physics and general relativity? Newtonian physics and quantum mechanics? What makes quantum mechanics "quantum"?

I contend that knowing the answers to my questions is a lot more important than to the first set of questions. Alas, many "educated" people don't think so. After all, most of the top questions lead to discussions where one can say more or less what one wants, but the bottom questions all have outside validators (the science, engineering, math, and economics or business).

The kids may well be ignorant, but the haughty superciliousness of most people whose knowledge base is the Humanities or Social Sciences is completely undeserved.

I'm going to start asking people who make big pronouncements about the ignorance of today's youth to calculate something like the missing value in the diagram above. It's basic Pythagorean theorem, applied twice, so everyone with a basic education should be able to do it, right? Right? RIGHT?

[Thoughts ruminate during the work day…]

The more I think about these two cultures, the more I see it's not just about different knowledge, it's about the focus of attention.

Compare the following question, from the original article:
Who taught Plato, and whom did Plato teach?  
with
What is kinetic energy, and for a given moving object does it increase more when you double the mass or the speed?
The answer the author was looking for, I think, is Socrates and Aristotle. Not the thoughts of Socrates and of Aristotle, but simply the persons. A lot of the questions in the original article are about people or events, not about concepts, ideas, or tools, which are what all my questions are about. (Kinetic energy is the energy of motion, $E_{K} = \frac{1}{2} m v^{2}$ so doubling the speed quadruples the kinetic energy, while doubling the mass only doubles the energy.)

Of course, some questions are out-and-out cultural virtue signaling. I'll see your
Raise your hand if you have read both the Iliad and the Odyssey.
And raise you a
Raise your hand if you have read both Molecular Biology of the Gene and Walter Rudin's Real and Complex Analysis and can answer the questions at the end of the chapters.
Game, set, and match, as they say in the Super Bowl.

One of the funniest things to see is the collision of these two focuses of attention, for example when people who don't like science try to pretend they "love" science by emphasizing people or events. That's when we see "science" questions like
  • Where was Einstein born? 
  • What Nobel Prizes did Marie Curie win?
These are, at best, history questions. Compare with
  • What is the energy of a 1kg mass going $99\%$ of the speed of light? 
  • If we start with 100g of Thorium-231 ($^{231}\mathrm{Th}$, an isotope in the decay chain of Uranium) and wait 51 hours (two half-lives), how much $^{231}\mathrm{Th}$ is left?
The answers to these don't depend on historic events or individual people. (They do relate to the people in the questions above by way of their work.) They require computation and thinking, for real. And that "for real" part is killer. For example, one can argue endlessly about the meaning of texts and the existence of "penumbras" in law or sticking to original intent, but there is no arguing with the technical questions.

That's one of the big issues that separates technical material from "soft" material: there's really an answer, and that answer can be shown to be right or tested with experiments that don't depend on feelings or whether Taul of Sarsus came up with it in the $94 \frac{1}{2}$ theses he nailed to the door of the Delicatessen in Wittenberg while he went in for a Schlagobers after the battle of the Salamis (pork against beef against chicken against vegan).

BTW, people who "love" science and haughty non-STEM professoriate: what's the answer to those two technical questions? Hint: don't forget the Lorenz correction.

"Won't someone rid us of these meddlesome quants?"

Saturday, February 20, 2016

Much ado about time preference

Today's José wants tomorrow's José to go on a diet, but when tomorrow arrives, the "new today" José will want the "new tomorrow" José to go on a diet, etc.

("My diet starts tomorrow" XXXL t-shirts available in the gift shop.)

As far as I know, Richard Thaler was the first economist to illustrate the inconsistency between choices in the short term and the long term with a simple pair of questions. First:

Q1: Do you prefer an apple in one year or two apples in one year and a day?

Most people choose the two apples. Then Thaler hit them with the second question:

Q2: Do you prefer an apple now, or two apples tomorrow?

And most people choose the one apple. This, trained economists and careful thinkers will say, is inconsistent. (This is one of the rare occasions when trained economists and careful thinkers will agree, so it's worth noting. :-)

Why is it inconsistent? For the same reason "my diet starts tomorrow" t-shirts are a good joke: because the decision is reversed simply by the passing of time. If instead of "in one year" and "in one year and a day" we had dates, say "on Feb 20th, 2017" and "on Feb 21st, 2017" and repeated the question every day, at some point the answer to Q1 would become "one apple," say on Feb 4, 2017.

Or maybe not. Maybe only on Feb 20th, 2017. Still, just the passing of time would reverse the choice, which is what "inconsistent over time" means.

Two common models of time preference that account for these inconsistencies are hyperbolic discounting, in which the exponential discounting used for finance (and for economics rational models) is replaced by an hyperbolic function; and a non-immediacy penalty for any delayed reward. In the second case, all future payoffs are discounted by a factor $\beta \times \delta(t)$, where $\delta(t)$ is the standard exponential discount factor and $\beta < 1$ is the non-immediacy penalty. The lower the $\beta$, the more now-oriented the decision-maker.

The reason why I've come to like the $(\beta,\delta(t))$ formulation is that it models a number of explanations that have little to do with time orientation and a lot to do with the actual circumstances of getting a reward.

For example, I give these choices to participants in one-day managerial decision-making exec-ed events:

Q3: Choose between $\$10$ now or $\$20$ tomorrow. (Nearly all choose the $\$10$.)
Q4: Choose between $\$10$ in a week or $\$20$ in eight days. (Nearly all choose the $\$20$.)

And when we discuss the "inconsistency" participants mostly bring up the mechanics of the transaction: how exactly are they going to get the money after the event is over? (It's hypothetical, of course, in these events money comes my way; but participants play along and take the decision seriously.) If it's now, they can just get the money and walk away. So the future is discounted not just because of the opportunity cost of having the money later but rather because it's associated with more hassle and uncertainty. Of course, when both payoffs are in the future, then participants prefer the larger payoff, as both payoffs have the same hassle and uncertainty.

Given the advantages of being temporally-consistent (which includes delaying gratification for bigger rewards), these non-opportunity cost reasons for now-preference are quite important. For example, in the case of people going on diets, their experience with bad diets may make them ask "what's the point? I might as well have that  second crème brûlée and a chocolate soufflé while I'm at it…"

I think that Scott Adams was right, the best think is to stop considering goals (that is making payoff-based choices) and adopt systems that work by bypassing the choice mechanisms. For me, the Paleo diet is one of them, strength training and rowing are another. YMMV, of course.

Another possibility is to practice delaying gratification as an exercise; it will be prophylactic against temporal inconsistency. There's a problem with this, of course, sometimes it's taken too far and leads to bad choices in itself. But in general, postponing a decision for a few days or considering whether a decision would change if the timing was shifted by a couple of days is a good idea.

Living for the now is a sure way to compromise the future.

--  --  --  --

For the quants…

The notion that the choice in Q3 could be due to standard discount (that is, a matter of opportunity cost of only having the money tomorrow instead of today) becomes ludicrous when we compute the discount rate associated: annualizing a $1/2$ one-day discount factor we get a yearly rate of (drumroll please…):

$\delta(\text{1 day}) = \frac{1}{(1+r)^{1/365}}= 1/2 \quad \Rightarrow \quad r = 2^{365}-1 = 7.515 \times 10^{109}$.

Choices like those captured by Q1-Q4 have to be driven by immediacy, as any attempt to find a discount mechanism that makes sense without a discontinuity at "now" quickly run into these ridiculously high discount rates.



References for the academically inclined:

✏︎ Thaler, Richard (1980): "Toward a positive theory of choice," Journal of Economic Behavior and Organization.
✏︎ Thaler, Richard (1981): "Some empirical evidence on dynamic inconsistency," Economic Letters

Wednesday, February 17, 2016

God, Religion, and Atheists

God


When someone asks me "do you believe in God?" I answer: that depends on what you mean by "believe" and by "God." To save time, let me answer the question that you thought you were asking, "Do you believe that my religion's God created the universe?" My answer is no, regardless of religion.

But, if we define "God" as an entity that created our universe by a deliberate act of will, then my answer is: I don't think we humans could know.

Consider a being, Steve, who says he's the creator of the universe. What test can I trust to tell me that Steve is indeed God? Obviously if Steve fails a test, then he can't be God, but the question is, what human-observable test can Steve pass only if he's the creator of the universe; a test that Steve will definitely fail if he's a very powerful alien of this universe, no matter how powerful?

Chew on that for a moment. (That test you just thought of doesn't work. Steve is a very powerful alien.) Repeat.


Religion


What about religion? Assuming for a moment that Steve's Godhood is still undetermined (and, I posit, indeterminable), shouldn't religion be irrelevant?

Religion qua word-of-God, yes. Religion as an important part of the human experience? No. Religion has inspired the greatest works of art in history. It has been used to justify war and genocide. It brought courage and solace to many in their hour of need. The powerful used it to cause hatred and division in service of their continued power. It has been the foundation of millenary civilizations. It has been the reason for multi-millenial clashes of civilizations. I could go on, but anyone who hasn't got the point by now won't get it at all.

Religion is too complex a topic for simplistic answers. Only the simpleminded think otherwise.

My approach is to treat religion as culture and ideology, where the specifics of a given religion and the acts of its adherents are what matters. Thus, a religion can be separated from belief in a higher being or acceptance of a higher purpose in life, and evaluated as a human construction.

Beyond that, I have the same position towards religion as Winston Churchill: a flying buttress, supporting [the good parts] from the outside.


God (II)


Ah, a mediocre mind says, Steve can prove he's God by bringing a dead person back to life.

Sigh! Steve is a really powerful alien who can read minds and obtain all recollections of the dead person from living ones, send a micro-drone to collect a sample of the dead person's DNA, create human clones with preprogrammed brains, and do it fast… shall we say three days, for tradition's sake? The clone will pass for the dead person in all tests devised by the living.

None of these powers makes Steve the creator of the universe.

In fact, Steve need not do anything beyond read and manipulate minds, and humans will not be able to tell with any test. Yes, Descartes figured this out first.

Things that only a creator of the universe could do, such as changing a universal physical constant or a mathematical truth would be hard for humans to measure, what with the universe instantly disintegrating, including us. That's what I mean by not being able to know whether God exists. It might just be Steve. Because, despite being very powerful, Steve is a mischievous alien:

"The arrogance of these barely sentient primates, believing that their paltry 'intelligence' is the pinnacle of achievement in the universe. I'll show them, and mess up their sex lives too." --Steve, circa 4004 BC.


Atheists


Speaking of mediocre minds, enter the contemporary internet-spawned "atheist." It considers itself vastly superior to everyone who professes a religion, simply by saying the words "I'm an atheist." That's the depth of its atheism.

Of course there are other atheists, real atheists, who typically do more interesting things than repeating ignorant internet memes about religion and the religious. On occasion, when asked about God, real atheists' answers are similar to the one above. They bristle at the use of God to justify political positions, even those they agree with, and to exploit the naïve. Most real atheists understand that some religions are an essential part of what built civilization, and respect that. And they understand that religions aren't all the same.

Many real atheists are embarrassed by the shenanigans of the "atheists." And, unlike "atheists," they accept that a religious person can be smart, knowledgeable, and a good individual; indeed, they know many like that.


God (III)


Meanwhile, Steve time-travels back to the 1960s and convinces Richard Feynman that hitting bongos at random makes him look cool, as a joke on future generations of physicists. And, especially, musicians.

Gwendolyn, an even more powerful 23-dimensional plasma collective, unimaginable by Steve, restructures the part of the human brain that recognizes rhythm and the associated DNA codons, in all humans, so that Feynman's randomness will appear as a high art form to all generations of humans hence. Thus Gwendolyn unwittingly creates late 20th-Century Earth music.

ZXKW-99, a dark energy sentience of varying dimensionality, with capabilities beyond what Gwendolyn can conceive, goes to Earth's Permian, finds the ancestor of all mammals and encodes 'Feynman bongo-playing sucks' in the genes for myelin, using an obscure 24th-Century Earth quaternary code. By accident, that makes the ion pumps in mammal neurons immune to diclorodiphenyltricloroethane.

[...]

God, outside the universe, observes the ongoing tomfoolery and considers changing the value of $\pi$ to reset the universe. Floods are so passé.


-- -- -- --


Bonus round - geeks only


What about a message inside a physical or mathematical constant? Say a message around the twenty-trillionth digit of $\pi$, encoded as a sequence of $p \times q$ ones and fives, where $p$ and $q$ are two large prime numbers, indicating that the ones and fives are to be arranged in a rectangle of sides $p$ and $q$. That message can only come from the creator of the universe.

So, Steve arrives on Earth, points the mathematicians towards the constant, the computers do their magic, and lo and behold, the $p \times q$ rectangle has a picture of Steve in it. That's proof that Steve is God, right?

Nope. At best, it proves is that Steve found the message and was able to change his appearance to look like it.

It also suggests that the creation of the universe was an act of will by an intelligent entity, and hints that there may be more messages, possibly using other numerical bases. Except that we're making a few unstated assumptions.

Ok, so it is possible for a creator of the universe to send us a message which will lead to the construction of a technology that would validate communication with that creator… if we could be sure that the numerical expansion, the interpretation of the message, and the construction of the apparatus were not being influenced by malfeasant aliens. Three big ifs.

The problem is, how could we be sure that our numerical analysis wasn't being hacked by Steve? That our interpretation wasn't being primed and guided by Steve? That our apparatus wasn't simply a Steve-detector, designed by Steve to create The Church of Steve?

Note that Steve doesn't really change $\pi$, he inserts that message in the computer, not the number. Only the creator of the universe can change $\pi$, but many human teenagers know how to crack into computers and change their code. And some of these human teenagers have read Carl Sagan and understand the use of prime numbers for creating rectangles and passing messages. So Steve recruits them with promises of Jolt Cola lakes and Pop-Tarts mountains.

Alas, the Church Of Steve is brought down when a Caltech student notices that "MIT Rulz!" is secretly embedded in every page of the Cosmic Encyclopedia used to build the God-detector.

God smiles and congratulates itself for creating nerds.

Saturday, February 6, 2016

Four bad messages from a Mythbusters episode

I had high hopes for the Mythbusters when they started, but these hopes were quickly squashed. Now in its last season, the Mythbusters have become a perfect representation of the 'people who "love" science, as long as they don't have to learn any.'

The recent episode "Driven to destruction" had four clear, though not explicit, messages; all of them were anti-science messages. Here they are:


I - Don't bother checking existing knowledge or consulting field experts

Adam wants to lift a car using only the suction of a vacuum cleaner to attach the car to the crane. He builds some suction cups and then places them on the car, without any consideration of the distribution of mass (and therefore of the lifting force necessary) in the car.

If Adam had consulted a mechanical engineer (or anyone with enough of an interest in mechanical structures to read a couple of books), he'd have learned that to lift an heterogeneous object using multiple attachment points to distribute the load, one needs to consider the distribution of mass and not just the total mass.

But here, like in most if not all episodes, the Mythbusters spurn extant knowledge and actual expertise and decide to pretend that science is 'make stuff up as you go.'


II - Calculations are boring, but show pretty charts (and formulas)

Adam's rig doesn't lift the car, it just creates attachment. Computing the attachment force is a simple matter: the total force is the maximum sustainable pressure of the system (vacuum cleaner motor fighting the atmospheric pressure on the output side, seals fighting it on the contact boundaries) times the surface of the attachment. This would be simple enough to measure and calculate (and then multiply by an engineering safety factor to account for faults).

Instead we get a chart about "linear relationship," which is true enough for the purposes of lifting the car, but doesn't even show what the calculation is. Also, because of the lack of expertise in how distributed lifting works, the calculations are actually quite dependent on where the attachment points go and therefore not linear at all.  (The point of saying "linear relationship" is to teach the audience yet another identity phrase.)

(There were no formulas in the show itself, but there are several, apparently randomly selected, during the opening credits.)

Note also that in the early part of the show pressure was measured in pounds per square inch, while in the last version of the experiment pressure was measured in millimeters of mercury. No effort was put into explaining how these relate to each other. Because the purpose of the gauge (and of the "measurement" for that matter) is to look and sound scientific without actually making any type of calculation.

"Math is hard," said Barbie the people who "love" science (as long as they don't have to learn any).


III - Experiments don't need controls or replication

As usual, Mythbusters experiments are made without a control condition and run only once. The lack of a control is less important in this episode, as they were really not testing any theories (unless one considers the quality of vacuum cleaner seals a theory), but the lack of replication is problematic.

Adam does make a lot of attempts to lift the car, eventually getting his rig to work. Once. Since there are all sorts of situation variables that aren't fixed, including the speed at which the crane operator lifts the load, that "experiment" needs replication.

Note that here we're not talking about the independent replication that is now debated in science (when team A publishes a result and team B checks that result by replicating the experiment). Independent replication has been the bane of the social sciences, for example. What we're talking about here is to make the car go up more than once.


IV - Change whatever elements of an experiment you want, no problem

When measuring the "force" (in fact the pressure) of the vacuum cleaner in the shop, and for the first few tests, Adam uses a home vacuum cleaner (looks like a Dyson), but later the experiments with the car use a shop vacuum cleaner, which in my experience creates a lot more pressure ("suction" is pressure). Jamie changes the explosive from a plastic explosive to ANFO (ammonia nitrate - fuel oil, a much slower explosive).

For the small-scale experiments to have any relevance to the large-scale experiments, all the elements other than scale should be unchanged. There could be a case for a different explosive if Jamie were trying to scale up the detonation speed, though that's hard to do correctly, but it would have gone in the other direction, using an explosive with higher detonation speed.

(The explosives are rigged by demolition experts, who could probably have taught Jamie how to do the detonation correctly, since it's their expertise; but that wouldn't work with the psychological premises of the show: that the Mythbusters are experts and experts don't ask for help -- both totally wrong.)


None of these things matter

To the audience, that is. Because their audience is full of people who "love" science, as long as they don't have to learn any. And they want explosions, words that they can use to impress equally ignorant friends (like stoichiometry), and the warm glow of looking down upon other people who don't profess "love" for science (but might actually know some).

And for those who believe that the Mythbusters might have some value as a motivator, consider the case of Planet Fitness: a gym where you pretend to work-out and people tell you how great you are doing, therefore preventing you from actually working out at a real gym.

The Mythbusters are the Planet Fitness of science education.