Let $f(x)$, $f \in \mathrm{C}^{\infty}$, be the following infinitely continuously differentiable function over the space of real numbers:
\[ f(x) \doteq \sum_{n=0}^{\infty} \frac{e^{-2} \, 2^n}{n!} + \frac{1}{\sqrt{2 \, \pi}}\int_{-\infty}^{+ \infty} x \, \exp(-y^2/2) \, dy; \] then, applying Taylor's theorem and the Newton–Leibniz axiom,
\[f(1) = 2.\]
Time out! What the Heck?!?!
Okay. Breathe.
Let's restate the above in non-pompous terms.
Let $f(x)$ be the following function \[f(x) = 1 + x\] then $f(1) = 2$.
All the words between "following" and "function" in the first paragraph mean "smooth," which this function certainly is; $f \in \mathrm{C}^{\infty}$ is the formal way to say all the words in that sentence, so it's redundant.
As for the complicated formula, it uses a series and an integral that each compute to one. Eagle-eyed readers will notice that the first is the Taylor series expansion of $e^2$ times the constant $e^{-2}$ and the second is $x$ times the integral of the p.d.f. for the Normal distribution for $y$, which by definition of a probability has to integrate to 1. Taylor's theorem and Newton–Leibniz axiom are used to get the values for the series and the integral from first principles, as is done in first-year mathematical analysis classes, and which no one would ever use in a practical calculation.
I took a trivially simple function and turned it into a complicated, nay, scary formula. With infinite sums, integrals, and theorems. Taylor is relatively unknown, but Newton and Leibniz? Didn't they invent calculus? (Yes.) So my nonsensical formula acquires immense gravitas. Newton! And Leibniz!!
And that's the problem with an increasing number of public intellectuals and technical material.
There are some genuinely complex things out there, and to even understand the problems in some of these complex things one needs serious grounding in the tools of the field. There's no question about that. But there's a lot of deliberate obfuscation of the clear and unnecessary complexification of the simple.
Why? And what can we do about it?
Why does this happen? Because, sadly, it works: many audiences incorrectly judge the competence of a speaker or writer by how hard it is to follow their logic. And many speakers and writers thus create a simulacrum of expertise by using jargon, dropping obscure references and provisos into the text, and avoiding simple, clear examples in favor of complex and hard-to-follow, "rich," examples.
What can we do about it? This is a systemic problem, so individual action will not solve it. But there's one thing we each can do: starve the pompous of the attention and recognition they so crave. In other words, and in a less pompous phrasing, when we realize someone is purposefully obfuscating the clear and complexifying the simple, we can stop paying attention to them.
Simplicity actually requires more competence than haphazard complexity; it requires the ability to separate what is essential from what's ancillary. To make things, as Einstein said, as simple as possible, but no simpler.
It's also a good thinking tool for general use. Feynman describes how he used to follow complicated topological proofs by thinking of balls, with hair growing on them, and changing colors:
As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)—disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!”
If it’s true, they get all excited, and I let them go on for a while. Then I point out my counterexample.
“Oh. We forgot to tell you that it’s Class 2 Hausdorff homomorphic.”
“Well, then,” I say, “It’s trivial! It’s trivial!” By that time I know which way it goes, even though I don’t know what Hausdorff homomorphic means.
Excerpt From: Richard Feynman, “Surely You’re Joking, Mr. Feynman: Adventures of a Curious Character.”
Let's strive to be like Einstein and Feynman.
- - - - - This post was inspired by an old paper that starts with $1+1=2$ and ends with a multi-line formula, but I've lost the reference; it might have been in the igNobel prizes collection.
But there's a disturbing trend in education (brought in from non-technical fields) and in the reporting of technical fields (done by people with minimal-to-none interest in the technical matters, and yes, that includes those with putative training in the technical fields whose work is now in the infotainment business) of moving away from technical knowledge even in those technical fields:
The answers to the type 2 questions, real technical questions, from the top:
First question: The combustion equation would be
CH$_4$ + 2 O$_2$ $\rightarrow$ CO$_2$ + 2 H$_2$O
but it's unnecessary; since each methane molecule will yield a CO$_2$ molecule we can simply calculate the ratio of the masses: m(CO$_2$)/m(CH$_4$) = (12+2*16)/(12+4) = 44/16 = 2.75, so a metric ton of methane will yield 2.75 metric tons of carbon dioxide.
Second question: The density of air at one standard atmosphere and 19°C is 1.225 kg/m$^3$, so a 25 m$^3$ room contains 30.625 kg of air. A 1000 W heating element releases 3.6 MJ of energy in one hour. The increase in temperature is therefore (3600 kJ)/(30.625 kg x 0.72 kJ/(kg °K)) = 163 °K, for a final temperature of 182°C.
(Assuming no losses to the outside and using a constant value for the isochoric specific heat for air throughout the temperature range 0-200°C to avoid computing an integral, a reasonable approximation given it varies between 0.70 and 0.74 in that range.)
Third question: At resonance frequency $wL = 1/(wC)$ so $w^2 = 1/(LC)$, $w = 57,735$ radian/s or f = 9189 Hz. At that frequency the capacitor and inductor cancel each other out (impedance is zero and power factor is 1), so peak power is $5^2/100 = 250$ mW and RMS power is $250/\sqrt{2}$ = 177 mW.
These are not "gotcha" questions: I learned to solve the second in 11th grade; I learned electronics and chemistry by myself as a kid, but the material to solve the first was taught in 9th grade and the third in 11th grade, for students taking a chemical or electronics track in high-school (9th-12th grades). All of this was assumed known for incoming EECS students in the early 80s in Portugal.
Tempora mutantur, nos et mutamur in illis
From a video of an event in 2016. Most of the weight loss happened in the last 12 months as the result of intermittent fasting and a focus on high-protein, low-energy foods.
Another growth industry in San Francisco
When authors want to be science-y, but don't want to do the science…
From a mil-fic book that we'll keep unnamed.
At 18 km altitude, the gravity is 99.4% of the gravity at sea level ($6378^2/(6378+18)^2$), so Colonel Z would need super-human perception to be able to separate that $0.006 g$ from the turbulence and change in aircraft acceleration due to atmospheric changes.
(The story itself makes little sense, it's a remake semi-update of Tom Clancy's "Red Storm Rising," but with several errors of logic and biased by the need to make Russians super-hyper-badissimo-evil idiots.)
Chocolate milk, the high Protein-to-Energy version
Geeky linkage
(Because work has gotten into the way of blogging, social media, and other things. Book is 90-95% complete.)
Claustrophobia-inducing video by Smarter Every Day crawling inside a torpedo tube in a submarine while it's under the Arctic Ice Cap.
Nasa makes Einstein-Bose condensates aboard the ISS.
Scott Manley showcases the ideal villain lair, complete with a rocket to take the villain to a secret space base. Or a smart way to use the oceans to position a launch pad precisely where one wants (on the Equator, for example, to minimize the energy necessary to change the inclination of the orbit for a GEO satellite).
Because a real geek needs some sci- fi in their life.
Yes, the first observation is that I am a science geek. Some people binge-watch Kim Cardassian, some people binge-watch Netflix, some people binge-watch sports; I binge-watch college lectures on subjects that excite me.
(This material has no applicability to my work. Learning this material is just a hobby, like hiking, but with expensive books instead of physical activity.)
To be fair, this course isn't a MOOC; these are lectures for a live audience, recorded for students who missed class or want to go over the material again.
The following is the first lecture of the course, and to complicate things, there are several different courses from UC-Stalingrad with the same exact name, which are different years of this course, taught by different people. So kudos for the laziness of not even using a playlist for each course. At least IHTFP does that.
(It starts with a bunch of class administrivia; skip to 7:20.)
Production values in 2013, University of California, Berkeley
To be fair: for this course. There are plenty of other UC-Leningrad courses online with pretty good production values. But they're usually on subjects I already know or have no interest in.
Powerpoint projections of scans of handwritten notes; maybe even acetate transparencies. In 2013, in a STEM department of a major research university. Because teaching is, er…, an annoyance?
The professor points out that there's an error in the slide, that the half-life of $^{232}\mathrm{Th}$ is actually $1.141 \times 10^{10}$ years, something that he could have corrected before the class (by editing the slide) but decided to say it in class instead, for reasons...?
The real problem with these slides isn't that handwriting is hard to read or that use of color can clarify things; it's the clear message to the students that preparing the class is a very low priority activity for the instructor.
A second irritating problem is that the video stream is a recording of the projection system, so when something is happening in the classroom there's no visual record.
As a former and sometimes educator, I don't believe in the power of lectures without practice, so when the instructor says something like "check at home to make sure that X," I stop the video and check the X.
For example, production of a radioactive species at a production rate $R$ and with radioactive decay with constant $\lambda$ is described by the equation at the top of the highlighted area in the slide above and the instructor presents the solution on the bottom "to be checked at home." So, I did:
Simple calculus, but makes for a better learning experience. (On a side note, using that envelope for calculations is the best value I've received from the United frequent flyer program in years.)
This, doing the work, is the defining difference between being a passive recipient of entertainment and an active participant in an educational experience.
Two tidbits from the early lectures (using materials from the web):
Binding energy per nucleon explains why heavy atoms can be fissioned and light atoms can be fused but not the opposite (because the move is towards higher binding energy per nucleon):
The decay chains of Uranium $^{235}\mathrm{U}$ and Thorium $^{232}\mathrm{Th}$:
(Vertical arrows are $\alpha$ decay, diagonals are $\beta$ decay.)
Unfair comparison: The Brachistochrone video
It's an unfair comparison because the level of detail is much smaller and the audience is much larger; but the production values are very high.
Or maybe not so unfair: before his shameful (for MIT) retconning out of the MIT MOOC universe, Walter Lewin had entire courses on the basics of Physics with high production values:
(I had the foresight to download all Lewin's courses well before the shameful retconning. Others have posted them to YouTube.)
Speaking of production values in education (particularly in Participant-Centered Learning), the use of physical props and audience movement brings a physicality that most instruction lacks and creates both more immersive experience and longer term retention of the material. From Lewin's lecture above:
Yes, yet another rant against the "I Effing Love Science" crowd.
Midway through a MOOC lecture on nuclear decay I decided to write a post about production values in MOOCs (in my case not really a MOOC, just University lectures made available online). Then, midway through that post, I started to refine my usual "people who love science" vs "people who learn science" taxonomy; this post, preempting the MOOC post, is the result. Apparently my blogging brain is a LIFO queue (a stack).
Nerd, who, me?
I've posted several criticisms of people who "love science" but never learn any (for example here, here, here, and here; there are many more); but there are several people who do love science and therefore learn it. So here's a diagram of several possibilities, including a few descriptors for the "love science but doesn't learn science" crowd:
The interesting parts are the areas designated by the letters A, B, and C. There's a sliver of area where people who really love science don't learn science to capture the fact that some people don't have the time, resources, or access necessary to learn science, even these days. (In the US and EU, I mean; for the rest of the world that sliver would be the majority of the diagram, as many people who would love science have no access to water, electricity, food, let alone libraries and the internet.)
Area A is that of people who love science and learn it but don't make that a big part of their identity. That would have been the vast majority of people with an interest in science in the past; with the rise of social media, some of us decided to share our excitement with science and technology with the rest of the world, leading to area B.
People in area B aren't the usual "I effing love science" crowd. First, they actually learn science; second, their sharing of the excitement of science is geared towards getting other people to learn science, while the IFLS crowd is virtue signaling.
People in area C are those who learn science for goal-oriented reasons. They want to have a productive education and career, so they choose science (and engineering) in order to have marketable skills. They might have preferred to study art or practice sports, but they pragmatically de-prioritize these true loves in favor of market-valued skills.
As for the rest, the big blob of IFLS people, I've given them enough posts (for now).
- - - - -
Note 1: the reason to follow real scientists and research labs on Twitter and Facebook is that they post about ongoing research (theirs and others'), unlike professional popularizers who post "memes" and self-promotion. Or complete nonsense --- only to be corrected by much smarter and incredibly nice Destin "Smarter Every Day" Sandlin:
Note 2: For people who still think that if one of two children is a boy, then the probability of two boys is 1/3 (it's not, it's 1/2):
and the frequentist answer is in this post. Remember: if you think a math result is incorrect, you need to point out the error in the derivation. (There are no errors.)
This particular math problem is one favorite of the IFLS crowd, as it makes them feel superior to the "rubes" who say 1/2, whereas in fact that is the right answer. The IFLS crowd, in general, cannot follow the rationales above, though some may slog through the frequentist computation.
Early on in the movie Interstellar there are two important lessons about what makes a society fail (or succeed), both delivered in the parent-teacher conference that Cooper attends.
Lesson one: don't underestimate the power of engineering (and science)
Lesson two: beware of those who would rewrite the truth
(Excerpts from the novelization of the movie by Greg Keyes. No, I'm not a nerd. Ok, I am.)
Andrew Rader points out some problems with the movie:
The main problem was also pointed out by Kip Thorne in The Science of Interstellar: that fighting the blight on Earth would make a lot more sense than going to a different planet.
Thorne also raises the problem of orbital mechanics in chapter 7 of the book:
and proposes a few speculative mechanisms to get the necessary changes in velocity from gravity assists. Note that there are two decelerations one of $c/3$ and one of $c/4$ for a total speed change of $7c/12$ or $1.75\times 10^{8}$ m/s. Returning to the Endurance requires an increase in speed of $1.75\times 10^{8}$ m/s as well.
To see the size of the problem, let's say they take 500 seconds (8 minutes and 20 seconds) to do each maneuver (while the rest of the Universe ages significantly) and the Ranger's mass is 2 metric tons (for simplicity, we'll assume that the water taken in on the planet makes up for the loss of Dr. Doyle to stupidity, indiscipline, and lack of planning). If we assume constant thrust for simplicity, assume away all friction and ignore the propellant mass loss (yay, infinite specific impulse!), the thrust needed for each maneuver is $7 \times 10^8$ Newton or about the same as 1077 SpaceX Merlin engines (averaging their atmosphere and vacuum thrust to 650 kN). Since there's propellant mass loss, let's say we "only" need the equivalent of 900 Merlin engines. So, yes, only a gravity assist would do.
Yes, it's an oversimplification, but didn't feel like solving the Tsiolkovsky equation. Hence the drop from 1077 to 900 engines. (That's still equivalent to 100 Falcon 9 rockets.) By the way, Thorne appears unconvinced of the feasibility of those gravity assists and hence of the feasibility of whole expedition to Miller's planet. But at least they tried to be accurate with some science in the movie.
There are growing complaints that Silicon Valley companies discriminate against middle-aged engineers. But it might not be just ageism, it might just be aggregation error.
Engineering comprises mainly two things: a body of knowledge and a problem-solving mindset. To be a good engineer one needs an up-to-date body of knowledge in the relevant field and a facility with different problem-solving approaches used in the field (and possibly outside it as well).
(For the moment let's leave aside the problem-solving mindset; its dynamics are complicated and very situation-dependent: while some engineers acquire and develop problem-solving skills with experience, other fossilize their thinking, for example due to organizational practices.)
As part of what I do is continuing education, I have observed the dynamics of the body of knowledge as engineers' careers progress.
The largest group by far (sadly), makes little attempt to keep up-to-date with their field after formal education ends. In conversation, after a corporate training event, a member of this group told me that keeping up-to-date was "very nice in theory, but we don't have the time." All of us would like more time; but this person spent tens of hours per week watching TV. One of those hours per week spent updating their skill set would mean 52 hours per year, which would be more than enough (most of the participants in that event had fewer than 20h/year of training or study, and self-paced learning can be much more effective than group events.)
Most of the remaining engineers realized their technical obsolescence would become a problem and were retooling themselves for a management job. The main problem with this attitude is that there will always be fewer management jobs than engineers who plan to go into management. Secondarily, firms have both partially replaced management jobs with consultancy engagements and started prioritizing management-trained applicants over engineers.
A few engineers fell into a third category: those who keep up-to-date either because they realize the job implications of doing so or because they really love their engineering field. The problem, for those in this group, is that their small number makes them liable to be categorized into one of the other groups.
Placing ourselves in the position of Google, for example, the decision to consider a candidate who's been out of formal education for several years versus considering one that's just graduated --- even if Google believes that the energy of youth can be balanced by the temper of experience --- comes down to which of the three groups above the older candidate will fall into.
In the absence of good information, statistically the older candidate will be in the first group, in other words, aged, not experienced, a distinction that most of the engineers can but will not make (as it defeats their case).
(The younger candidate's type is irrelevant, because being fresh from school means an up-to-date skill set, at least for the near future.)
There are obviously many confounds: consider a choice between a newly minted computer engineer from Idaho State - Tubertown with no code to show (not even from school projects) versus a 45-year-old Caltech graduate class of '95 who has code on GitHub that is particularly relevant to the job, for example.
For the other engineers, who have been lax in their updating of skills, there's a solution: it's never too late to learn. And then: show, don't tell.
Science identity products like t-shirts, mugs, posters, and computer wallpapers are used to signal that the owner has an interest in science; unfortunately, because this interest in science has become fashionable -- at least in some segments of the population -- poseurs also buy these objects, lowering the quality of the signal.
I've written often (one, two, three, four, five times at least) about the problems with using science as an identity product, as with the people who "love science" as long as they don't have to learn any.
These products aren't necessarily only appealing to poseurs, though. People with a real interest in science and in science education also like them for, among other reasons,
1. Identity signaling. Like the poseurs, except it this case it's a real signal. People want to communicate their interest in science and the beauty of some scientific results and natural phenomena. (I own quite a few science identity products myself.)
2. Recruitment. These products can be useful motivators for bringing newcomers into an appreciation of science. By showing that there are other nerdsgeeks people interested in science, they create social conditions for others to come out as nerdsgeeks people interested in science.
3. Mere exposure. People like or at least feel more comfortable with things that appear familiar. The more exposure people have to scientific concepts and images, even if as part of jokes or background material in sitcoms like The Big Bang Theory, the less aversion they may feel when science content is presented to them.
There's one possible disconnect undermining these three points, though: that people who are influenced by exposure to the science identity products only like the aesthetics:
The big problem with the poseurs, which is a real problem not just my "I liked that band before it was cool" complaint, is not that they use the products to pretend to like science, though that would be bad enough. The real problem is that poseurs know that they don't actually like (or know) real science, so they feel threatened by those who do and take action to counter that threat, usually distracting from the science.
As my previous post showed, many poseurs in the media try to be "sciencey" but they fail miserably because in the end they don't understand that science is not like literature or art where the judgment of some other people is what matters. In science, reality is what matters. Poseurs don't get that, because to them reality is whether others buy into their pose.
Popular science content
Making science accessible to the general public is one of the most effective ways to improve society: it allows more people to partake of the benefits of knowledge (for example, avoiding junk science and quackery), it helps garner support for scientific enterprises that require public funding, and it creates the foundations for new generations with more and better scientists.
The problem is that popularizers can be real science popularizers or they too can be poseurs. And the poseur popularizers tend to be more popular. The glaring exception is Carl Sagan, but that's because he was both a pioneer in popularization and a real research scientist prior to that.
The most obvious difference is that Carl Sagan's Cosmos was designed to impress people with the power of science, while many current popularizers design their programs to impress upon the audience (a) how special they, the audience, are; and (b) how smart, knowledgeable, and suave the popularizer is. There are some exceptions, but they aren't the most successful popularizers, at least not on TV.
A rule-of-thumb that works for me is to ask whether the popularizer is an active researcher (or was until recently active) in the field. People whose job is some variation of "science popularizer" tout-court, even if they have some scientific training (which many of them don't), tend to focus on people and events rather than concepts and principles. In other words, they popularize the story of science rather than the actual science. (In many cases they either avoid the science completely, or they get most of it wrong.)
This rule works for two reasons:
First, an active researcher will know the science better than a non-researcher popularizer. This IMNSHO more than balances any communication advantages the non-researcher might have. One of the hilarious examples of this advantage is The Igon Value Problem, where active researcher Steven Pinker takes on the intellectual lightweight Malcolm Gladwell. (But supporting my observation above, Gladwell is more popular than Pinker.)
Second, an active researcher has to protect his/her reputation in the field. This adds motivation to get things right to the knowledge (the ability to do things right). When no one in Astrophysics takes you seriously (because you call yourself a scientist but your career total citations of 150 mark you as a museum manager), you can say ignorant things on twitter about planes and helicopters. An engineer who wrote nonsense like this would be mocked at any future technical conferences he/she attended:
Personally I decided to read textbooks in lieu of popularization books,* but there are some popular books I've read that I found worthy of recommendation, so here are two for now:
Deep science (or other technical) content
Leaning technical material is something that requires audience (perhaps in this case "student" would be the better term) participation.
Lectures can motivate study and are a good introduction to the material, but only self-paced study and practice exercises can make technical material stick.
There's a qualitative difference between (to quote again from my old post about Heisenberg) understanding that this is a joke, i.e. popularizer-level understanding:
Police officer: "Sir, do you realize you were going 67.58 MPH?
Werner Heisenberg: "Oh great. Now I'm lost."
and being able to completely spoil the joke by computing the actual uncertainty (deep understanding):
A simplified form of Heisenberg's inequality, good enough for our purposes, is
$\qquad \Delta p \, \Delta x \ge h $
Going by orders of magnitude alone, assuming that the mass of Heisenberg plus car is in the order of 1000 kg, and noting that the speed is given to a precision of 0.01 mi/h, an order of magnitude of 10 m/s, with $h \approx 10^{-34}$ Js, we get a $\Delta x$ of the order of
$\qquad \Delta x \approx \frac{ 10^{-34} }{10 000} = 10^{-38}$ m.
Only practice and study can create the kind of deep understanding that allows you to spoil people's fun at parties with numerical sidebars like this. Certainly something to aspire to...
That's not to say that lectures don't have value; I think of them as the warm-up sets you do before actually exercising. In that sense, they are very important, since they provide a passive experience that gets the material into context, setting up the active experiences of self-paced study and practice exercises.
Walter Lewin, shamefully retconned out of OCW and their official YouTube channels by MIT for undisclosed non-scientific transgressions, was one of the best Physics instructors online; even better than Feynman, since Lewin used actual in-class demonstrations and calculations matched to the examples. Here's a great class on standing waves:
1. MOOCs have economies of scale in production and diffusion, but the difficult parts of education, personalized attention, for example, don't scale.
2. MOOCs can derive brand equity from the institutions associated with the teaching, but whether that brand equity is deserved is an open question: there are many components to education beyond what most MOOCs offer. I made some observations about that regarding the Kenan-Flagler Online MBA.
3. MOOCs built out of classroom teaching and associated materials are audience-targeted; a course like Lewin's works well at MIT and possibly CalTech, but the speed of exposition and the amount of off-classroom work that Lewin expected from his students will not work for most other universities. Other materials, like textbooks, may partially make up for this, but even so most students would probably prefer better match between materials and audiences.
4. The major weakness of MOOCs as they exist now is the lack of evaluation and, in many cases, of ways to check your exercises. Since audiences (students) learn from these exercises, done individually and then corrected by a knowledgeable instructor, this is actually a much bigger weakness than I noted on the "MOOC-rize this" post.
In conclusion
There's nothing wrong about being out and proud as a nerdgeek someone who likes science; take care to avoid poseurs, both individuals and media darlings who don't have a track record of research; and if you want to learn more (kudos to you), there are plenty of MOOCs and other free resources to help you. One of those resources is called a Public Library and for the effort of getting a library card you can get a good education because in the end what matters is that you want to learn.
In the end what matters is that you want to learn. Poseurs don't want to.
-- -- -- -- -- -- FOOTNOTE -- -- -- -- -- --
* I find textbooks to do a better job than popularization books since I want to learn things at a more proficient level than a passing understanding. This requires time and effort, but I like it. (Hey, I lift heavy weights for no reason other than I like lifting heavy weights, so this isn't that different.)
The one enormous barrier to this approach is the ridiculous cost of textbooks in the US. I was interested in molecular biology, so I got Molecular Biology of the Gene, I believe for its weight in gold. There's now a new edition which costs its weight in diamonds, so I won't get that. Note that this is a personal interest in molecular biology; this is not work-related or anything monetizable, so the $\$200$ are a hobby expenditure. Which is fine, but still could discourage others from buying such an expensive book for a hobby.
I rationalize the cost by reminding myself of an old business associate who spent $\$150$ on a date with someone who, according to his later report, made Lady Macbeth sound warm and cuddly. So, that's about 3/4 of a textbook he could have bought there...
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.
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?"
If you cook, you control what goes in your food. That's reason enough to do it.
As for all the bad things in food that isn't prepared by you or your family, I recommend the book Salt Sugar and Fat. It describes how the processed food industry, and to a smaller extent restaurants, make choices that are good for business, good for taste, and bad for your health.
Cooking your own food allows for better control of what is ingested, a lesson that should be cultivated in children as early as possible. It also serves as a mechanism for avoiding excesses. For example, making your own french fries reduces the amount of french fries consumed, because of all the trouble it is to make them at home, from scratch, and clean up afterwards.
Cooking is educational
It's a great way to introduce science. Physics, chemistry, arithmetic, measuring, biology, nutrition (duh). Something as simple as making a vinaigrette illustrates different densities (vinegar and oil), solutions (salt in vinegar), immiscible liquids, emulsifiers (mustard), the importance of measuring quantities , acids (vinegar), fats (lipids), salts.
Cooking teaches production engineering. (Well, it is production engineering. Think about it.) Planning, organizing, executing, measuring, controlling, failing and recovering (when in doubt add butter), scaling recipes up and down, dealing with spoilage and leftovers, balancing choices (making baklava takes a lot of time, but sometimes you really want baklava). It can also be used to bring up the matters of cost management. Never too soon to teach kids fiscal prudence.
Cooking creates opportunities to talk about history, culture, and geography. Yes, food itself could be used to introduce these topics, but if you do it in the preparation (and the purchasing) it will be better remembered, and it fills up the time when things are in the oven or fermenting.
(As a side benefit, cooking also educates the parents, as they need to be prepared for teaching the children.)
Cooking develops important traits
Discipline. Like most interactions with the real world, cooking utensils and ingredients are very hard to emotionally blackmail or bargain with.
Patience, carefulness, study habits, observation skills. Because there's a clear payoff at the end, the food, cooking can be used to develop these important life skills. Baking and sauce reductions, for example, teach patience and carefulness. Analyzing recipes and procuring fresh ingredients develop study habits and observation skills.
Plan, Prepare, Work, Clean-up. Many intellectual experiences or intellectual descriptions of physical experiences are too circumscribed. Cooking provides a teaching laboratory for thinking about interaction with the real world: plan the work (and the shopping trip); organize the resources into a mise-en-place; do the work (this is the part that matches most intellectual tasks, the carefully circumscribed activity); clean-up and deal with the consequences.
Rule-following and creativity in balance. This is a very important life lesson, that many people get wrong. There are times when following the rules (the recipe) is essential, especially for beginners. And there are times, usually after a long period of following the recipes so that their rationale is well understood, for deviating and being creative. Creativity is not randomness borne of ignorance, it's willful deviation from rules borne of deep understanding of those rules.
Respect for manual work. Many educated people have a latent bigotry against manual work. Cooking, by integrating the intellectual, the creative, and a lot of physical work, acts as prophylaxis against that bigotry. (Lifting weights and playing a musical instrument partially remove this bigotry as well.)
Cooking is a bonding experience
Humans are, or so I'm told, social animals; apparently, you people like to do things in groups. Cooking presents many opportunities to develop teamwork and leadership skills. And it's extremely meritocratic, as the taste of food doesn't depend on the personal characteristics of those preparing it, other than through the actual cooking.
Family time is good, shared family work much better. Cooperating towards a shared goal creates a stronger bond than just spending time together. Teaching your children to cook is an act of love. It's a lot of work, of course, but that's part of the whole "love" thing.
Also, for small children, cooking provides both opportunity and motivation for developing dexterity and sensory skills. Dragging a finger across the screen of an iPad is not adequate activity to develop motor skills and there are more senses than vision and audition.
Cooking is an important skill to have
Even if all the above benefits were unimportant, which they aren't, cooking is an important skill to have.
You don't have to be a prepper to understand the value of being able to turn ingredients into a meal; you don't have to be a food critic (better yet, a gourmet) to appreciate that a little bit of knowledge about flavor creation and combination can make a lot of difference; and you don't have to be an hypochondriac control freak to be suspicious of the quality of ready-to-eat meals.
Most of all, cooking has a smooth learning curve which makes it one of the easier skills to acquire and maintain, and the results are often delicious and almost always edible.
The future needs people who really understand technical material, but I fear what now passes for technical education (including self-education) lacks depth.
Police officer: "Sir, do you realize you were going 67.58 MPH?
Werner Heisenberg: "Oh great. Now I'm lost."
there's a number of levels at which we can understand it.
At the recognition level, Alex associates "Heisenberg" with "science reference" and decides to laugh to appear educated. I find that most people who "love" science are like Alex. I also find people like this in my field of work, effectively LARPing at being experts.
At the knowing level, Blake has some idea that Heisenberg said that you can't measure speed and position together with arbitrary precision. Blake also knows that Heisenberg was talking about electrons or other particles, so applying his "rule" to a car must be hilarious.
At the understanding level, Chris can do what I did and spoil a joke by making calculations. From the linked post:
A simplified form of Heisenberg's inequality, good enough for our purposes, is
$\qquad \Delta p \, \Delta x \ge h $
Going by orders of magnitude alone, assuming that the mass of Heisenberg plus car is in the order of 1000 kg, and noting that the speed is given to a precision of 0.01 mi/h, an order of magnitude of 10 m/s, with $h \approx 10^{-34}$ Js, we get a $\Delta x$ of the order of
$\qquad \Delta x \approx \frac{ 10^{-34} }{10 000} = 10^{-38}$ m.
There are degrees of understanding, from the ability to make use of the uncertainty principle, as above, to deeper understanding of what that means for what the universe is like. But at the most basic level of understanding, you should be able to operationalize knowledge into decision, calculation, program, etc.
I think that there's some merit in trying to improve from recognition to knowledge and from knowledge to understanting. So here are a couple of observations on that:
Recognition to knowledge
The main problem in most cases, as I see it, is not of ability or opportunity but rather of motivation: if Alex gets social cachet for "loving" science just by recognizing a "science situation," why put in the effort to learn some science (or other technical material)?
There's a trap, however, for people who decide that they want knowledge: because of the identity problem in science popularization, most of the more popular sources are designed for recognition only, not understanding.
I find that books, lectures, etc. from active researchers or practitioners in the technical field (say Leonard Susskind instead of Neil deGrasse Tyson) generally mean better chance of knowledge rather than recognition. Even when non-researchers and non-practitioners are better at showmanship (mistaken for communication skils), it's worth a little effort to get real knowledge from those who understand it and don't treat their readers or audiences as an echo chamber.
(As for television shows, except for a few that are based on books by active researchers, they are to be avoided: they are not reliable sources, not even for the recognition level.)
Knowledge to understanding
Problem sets. That's the solution.
Well, to be precise, the step from basic knowledge to understanding has two parts: first, learn the concepts, principles, and tools of the field; second, practice them with incrementally difficult problems.
For the Heisenberg example, some of the elements needed for understanding are:
My rule-of-thumb for learning technical material is $1\%$ from being a passive member of an audience (to a lecture or a video) or a passive reader (reading but not thinking); $9\%$ from actively studying the material (say, working through solved problems, making sure you understand all the steps in an example); and $90\%$ is practicing, in the lingo of academe solving problem sets.
It then becomes a matter of how much practice and how much effort you're willing to put in: at this level, the difference between amateurs and professionals is that amateurs practice something until they get it right, professionals practice until they can't get it wrong.
Understanding something is so much better than just knowing it, and knowing it so much better than just recognizing it. It worth the effort and the change in attitude required. At least for me it is.
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:
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:
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 threesciencemuseums 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 twoautobiographies than his Lectures On Physics or his popularphysicsbooks.
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.
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."
Participant-centered learning is not scalable, so it's MOOC-resistant.
A couple of colleagues (in different fields) have shared MOOC-related worries with me. The logic goes, our research jobs are funded to a large extent by teaching, and if the need for teachers disappears, many schools will stop hiring expensive research faculty. Cathy "Mathbabe" O'Neil suspects MOOCs will have tragic consequences for mathematics research.
I'm not convinced.
As I see it, there are three main MOOC threats to traditional higher education: cost-effectiveness, brand equity of the schools offering the MOOCs, and quality of content. There's also one main visible weakness, certification.
Cost-effectiveness. The cost-effectiveness of MOOCs is the main argument I hear for "the end of universities as we know them," to which I say: if you can replace class X with videos of lectures and computer-graded problems sets, good riddance to class X.
Distance learning is an old proposition, it started with something called "a book." MOOCs add better media, the possibility of computer graded problem sets (for some fields, and requiring a significant investment in problem set design), and tutoring or discussion affordances.
But here's the crux: the scalable parts of MOOCs are the easy part of education. The hard part is motivating students, interacting with them and being responsive to their questions, taking the time to understand the reason for their incomprehension, and reacting in real time to information they bring into the class or developments in the field.
So, while MOOCs will work really well for highly motivated, studious students (nerds like me), the average student will need more personalized attention than is cost-effective to offer in large scale.
Repeat after me: Personalized attention doesn't scale.
True, many classes in many institutions of higher learning don't deliver anything more than the scalable parts of the MOOCs; no personalized attention or significant interaction with the students at all. Those classes are ripe for replacement by MOOCs, and that's good.
This is what gets me steamed about Mathbabe's post: if the professors don't add value to a student reading the textbook and solving the problem sets (that in many cases are straight off teachers' manuals from the textbook publisher and graded by teaching assistants), then what is the purpose of hiring someone with a deep understanding of the field a/k/a a research faculty member?
The answer to that lies in the value of an instructor with a deep understanding of the field to manage participant-centered learning (now called "flipped classroom" but in fact the only way anyone ever really learned any technical material was by practicing it).
Brand equity. Who wouldn't rather say "I took the Caltech Machine Learning course" rather than "I took the Cal State-Moraga Machine Learning course"? This is indeed a problem, but to a large extent it's a matter of brand credibility footprint, not a technological issue.
With prestigious schools creating extension campuses and joint ventures with other universities, MOOCs are only a small part of the problem. And let's remember that brand extensions are not one-way propositions; MOOC-rizing courses may dilute a school's brand equity. (So may having extension campuses, of course. Armani Exchange doesn't help the brand equity of Armani.)
Talking to some Hahvahd B.S. colleagues, I got the distinct impression that they believe the student physical presence in their Cambridge (Allston, really) campus is an essential part of the brand identity, one that they are not willing to compromise on. I'd venture that at Hahvahd B.S. they know a thing or two about the network and identity dimensions of brand equity.
So, I agree that the brand equity is an issue, but more because of extension campuses and joint ventures than MOOCs, since the brand credibility footprint is much more likely to encompass the former than the latter. (Says the visiting professor at TheLisbonMBA, a joint venture of UCP, UNL, and MIT.)
Quality. Obviously there's a difference between the quality of the classes taught at Caltech and at [the fictional] Cal State-Moraga; and that is part of the brand equity of Caltech. But the real question is whether the students of CS-Moraga are going to benefit from a class that was designed for Caltech students more than from one that was designed specifically for them.
Note that this immediately raises the question of whether CS-Moraga classes are customized to their student population (that is now, before being MOOC-rized). And that's again the issue of what faculty are doing at CS-Moraga: if they rely on the textbook and the teachers' materials provided by the textbook publisher in order to save themselves the trouble of actually preparing a class, then as I said above, good riddance.
On the other hand, in participant-centered learning the instruction follows from the participants' needs and skills, moving at their pace, therefore for good quality the instructor must have a broad training in the general field and a deep understanding of the materials of the class.
It's incumbent upon the faculty to make itself more valuable than a cost-effective MOOC, or a textbook for that matter. Otherwise, it's their own fault if they're MOOC-rized
Certification. Certification of knowledge is the weak point of MOOCs as they currently exist, but it's important to note two issues with this.
First, certification cannot be the only function of universities or research faculty, as certification alone doesn't require the large infrastructure and cost of a university or the need for broad research programs.
Second, and much more critical, if the MOOC certification weakness is part of the advantage of a traditional university, that weakness ends if universities stop taking their certification responsibilities seriously. When some schools graduate computer engineers who never wrote a program that passed a compiler's syntax check, let alone run, let alone run correctly or efficiently — to choose an example I heard from someone I trust — then the credibility of universities as certification mechanisms comes into question, and their advantage vis-a-vis MOOCs in this regard evaporates.
(Yes, there's a third possible issue, that of MOOCs adding some sort of credible certification. I believe that that's a long way off, given how it would require (a) an infrastructure to prevent fraud; (b) some sort of long-term evaluation, since not everything can be certified with a short test; and (c) legal protection in case of unacceptable demographic results in aggregate, which universities seem to have had grandfathered in, but other institutions have found themselves liable to.)
I for one welcome our new MOOC multimedia limited-interaction e-textbooks for the 21st Century. As a complement to real instruction: customized, personal, and responsive. And as a mechanism for making universities take certification seriously.
Binding energy per nucleon explains why heavy atoms can be fissioned and light atoms can be fused but not the opposite (because the move is towards higher binding energy per nucleon):
