Reality vs nonsensical products (part 688 of Aleph-null)

Via Thunderf00t, I found this Waterseer-wannabe, which is about as feasible as the original Waterseer, that is not at all.

Obviously it's very important that the product is 3D-printed, rather than CNC-machined or heat-molded. 3D-printers, like the Internet Of Things, are magical incantations that can get around the laws of Physics. Or so one would think, given how credulous people become at the sound of these incantations.

Alas, as is usual with engineering, ugly numbers murder beautiful illusions:

Since the battery voltage is 12V, a 12kW Peltier effect cooler will require a 1000A current, which is likely to make Li-ion battery a bit... well, just watch what happens:

Engineering rule: when an electronic device starts outgassing, that's generally not a good thing.

The power of "equations"

If a picture is worth a thousand words, an equation is worth a thousand pages of text.

This was inspired by a livestream about free trade based on criticism of "original texts." (Basically Ricardo and Schumpeter.) The quotes aren't a diss on the texts themselves, but rather a way to emphasize that this is a type of scholarly pursuit in itself, though not the type used in modern economics, STEM, or pragmatic professional fields like business analytics or medicine.

What's the problem with the argumentation from these original texts? Simply put, the texts are long and convoluted, with many unnecessary diversions and some logical problems in the presentation. The valid arguments in these texts can be condensed in about one page of stated assumptions and two results about specialization.

It's not just that math's an efficient way to communicate, math has precise meaning and an inference process. It brings discipline and clarity to the texts and the inference process isn't open to debate. (Checks and corrections, yes; debate, no.)

Unfortunately, without math, the speaker's argument was essentially a sequence of variations on "Schumpeter points out that this assumption of Ricardo doesn't hold true," without the extra step of determining whether those assumptions are important to the final result or not. (We'll come back to this problem.)

Word-thinking about quantitative fields is generally to be avoided.

That was the inspiration, and this post isn't about free trade or the particular mode of thought of that speaker, but rather about the power of mathematical modeling, which I'm calling "equations" in the title.

Here's a reasonably robust statement: when the price of a commodity goes up, people buy less of that commodity. (Sometimes this is put as "demand goes down," which is incorrect, it's the demand quantity that goes down. Changes in demand are movements of an entire function.)

So, quantity is a decreasing function of price (and first-time readers of economics textbooks get confused because the charts have quantity in the $x$ axis and price in the $y$ axis). This has been known for a long time; what's the problem with that formulation, simplified to "when price rises, quantity falls"?

The problem, of course, is that there are many different types of decreasing function. Here are a few, for example (click for bigger):

Functions 1 to 4 represent four common behaviors of decreasing functions: the linear function has similar changes leading to similar effects; the convex function has decreasing effect of similar change (like most natural decay processes); the concave function has increasing effect of similar change (like the accelerating effect of a bank run on bank reserves); and the s-shaped function shows up in many diffusion processes (and is a commonly used price response function in marketing).

Functions 5 to 8 are variations on the convex function, showing increasing curvature. (Function 2 would fit between 5 and 6.) They're here to make the point that even knowing the general shape isn't enough: one must know the parameters of that shape.

That figure does have 2000 data points, since each function has 250 points plotted. (When talking about math, some people use drawing tools to make their "functions," I prefer to plot them from the mathematical formula; it's a habit of mine, not lying to the audience.) To describe them in text would take a long time (unless the text is a description of mathematical formulation), while they can be written simply as formulas; for example, the convex functions are all exponentials:

$\qquad y = 100 \, \exp(-\kappa \, x) $

with different values of $\kappa$. They are the type of exponential decay found in many processes, for example, where $x$ is time and $y(x) = \alpha \, y(x-1)$ with $y(0)>0$ models a process of decay with discrete-time rate $0 < \alpha < 1$. In case it's not obvious, $\kappa = -\log_{e}(\alpha)$.*

So, what does this have to do with reasoning?

Here we go back to the problem with arguments like "Schumpeter showed that Ricardo's assumption X was wrong." When a model is written out in equations, we have a sequence of steps leading to the result, each step tagged with either a know result, rules of math inference (say "$a \times b = a \times c$ simplifies to $b = c$ unless $a = 0$"), or an assumption of the model. This allows a reader to quickly see where a failed assumption will lead to problems and determine whether the assumption can be replaced with something true (or, as is the case with many of the assumptions made by Ricardo, is unnecessary for the result).

The main power, however, is that mathematical notation forces the speaker to be precise, and inferences from mathematical models can be checked independently of subject matter expertise. A mathematician may not understand any of the economics involved, but will merrily check that a decay process of the kind $y(n)= \alpha \, y(n-1)$ can be described by an equation $y(n) = y(0) \, \exp(-\kappa \, n)$ and determine the relationship between $\kappa$ and $\alpha$.

From those precise models, one can make inferences that take into account details hidden by language. Consider the "price rises, quantity falls" text and compare it with the different decreasing functions in the figure above. The shape of the function, its slope and its curvature have different implications for how price changes affect a market, differences that are lost in the "price rises, quantity falls" formulation.

It bears repeating the first mentioned advantage: that hundreds of pages can be condensed in one page of equations. Once one's mind is used to processing equations, this is a very efficient way to learn new things. Stories about Port wineries in Portugal and textile factories in England may be entertaining, but they aren't necessary to understand specialization (which is what comparative advantage really is).

Math. It's a superpower mostly anyone can acquire. Sadly, most opt not to.


- - - - - Addendum - - - - -

No self-respecting economist would use the Ricardo comparative advantage argument for international trade now, particularly because it's so simple it can be understood by anyone. Most likely they'd use some variation of the magic factory example:

"Let's say a new technology that converts corn into cars is discovered and a factory is built in Iowa that can take ~ $\$20,000$ of corn and convert it into a car that costs $\$30,000$ to make in Michigan. Can we agree that this technology makes the US richer?

Now, move the factory to Long Beach, CA. Maybe there's a little more cost in moving the corn there, but we're still making the US richer, right?

Now, someone goes into the magic factory and discovers that it's really a depot: stores grain until it's sent to China on bulk carriers and receives cars made in China from RoRos during the night. The effect is the same as the magic factory, so it makes the US richer, right?"

There are many cons to this example, but it does make one issue clear: trade is in many respects just like a different technology.


- - - - - Footnote - - - - -

* It's obvious to me, because after decades of playing around with mathematical models, I grok most of these simple things. There are some people who mistake this well-developed and highly available knowledge (from practice) for ultra-high intelligence (rather than regular very high intelligence), a mistake I elaborate upon in this post. 😎

Deep understanding and problem solving

There's value in deep understanding.

Nope, I don't mean the difference between word thinkers and quantitative thinkers. Been there, done that. Nor the difference between different levels of expertise on technical matters; again, been there, done that.

No, we're talking the crème de la crème, experts that can adapt to changing situations or comprehend complexity across different fields, by being deep understanders.

Because any opportunity to mock those who purport to educate the masses by passing along material they don't understand, let us talk about Igon Values... ahem, eigenvalues and eigenvectors.

Taught in AP math classes or freshman linear algebra, the eigenvectors $\mathbf{x}_{i}$ and associated eigenvalues $\lambda_{i}$ of a square matrix $\mathbf{A}$ are defined as the solutions to $\mathbf{A} \, \mathbf{x}_{i} = \lambda_{i} \, \mathbf{x}_{i}$.

Undergrads learn that these represent something about the structure of the matrix, learn that the matrix can be diagonalized using them, how they appear in other places (principal components analysis and network centrality, for example).

But those who get to use these and other math concepts on a day-to-day basis, who get to really understand them, develop a deeper understanding of the meaning of the concepts. There's something important about how these objects relate to each other.

After a while, one realizes that there are structures and meta-structures that repeat across different problems, even across different fields. Someone said that after a lot of experience in one engineering (say, electrical), adapting to another (say, mechanical) revealed that while the nouns changed, the verbs were very similar.

This is what deep understanding affords: a quasi-intuitive grokking of a field, based on the regularities of knowledge across different fields.

For example: while many who have taken a linear algebra in college may vaguely recall what an eigenvalue is, those who understand the meaning of eigenvalues and eigenvectors for matrices will have a much easier time understanding the eigenfunctions of linear operators:

The structure [something that operates] [something operated upon] = [constant] [something operated upon] is common, and what it means is that the [something operated upon] is in some sense invariant with the [something that operates], other than the proportionality constant. That suggests that there's a hidden meaning or structure to the [something that operates] that can be elicited by studying the [something operated upon].

And this structure, mathematical as it might be, has a lot of applications outside of mathematics (and not just as a mathematical tool for formalizing technical problems). It's a basic principle of undestanding: what is invariant to a transformation tells us something deep about that transformation. (Again, invariant in "direction," so to speak, possibly a change of size or even sign.)

And this is itself a meta-principle: that the study of what changes and what's invariant in a particular set of problems gives some indications about latent structure to that set of problems. That latent structure may be a good point to start when trying to solve problems from this set.

Yep, really dumbing down this blog, pandering to the public...

Deepwater Horizon: Movie not-a-review

Even though this is not a review, but rather a description of how to enjoy a movie through advanced nerditude knowledge, there are some noteworthy points:

- The beginning gives an idea of how much infrastructure supports offshore exploration and the number of different companies and support industries involved. Maybe this will reduce the "nuclear energy needs a lot of additional infrastructure" comments; I'm not optimistic, though, because those comments are born of ignorance and fear.

- Casting is phenomenal and the actors portray accurately the type of worker one finds in dangerous, rough, hard jobs. Props to John Malkovich who plays the quintessential John Malkovich villain, with additional villainy and a southern accent.

- A scene I thought was "too Hollywood," when Wahlberg runs across a burning rig to start the emergency generators and save the day (well, within possible), is actually true. It actually happened, pretty much the way they showed in the movie.

- Kudos for the minimal "character development," a disease that has made many other movies unwatchable. There was some, obviously, but the movie kept to the story and focussed on the main action (first the decisions leading up to the accident, then the evacuation of the rig).

- Instead of "you should really care about this person because they have a family and lost their dog when they were little"-type "character development," we get credible interactions among human beings (which humanize them a lot more than that usual pap) and an accurate depiction of the culture in heavy industry, epitomized by: Wahlberg (about the skipped cement test): "Is that stupid?" Roughneck: "I don't know if that's stupid... but it ain't smart."

- The class demonstration that Wahlberg's daughter is preparing in the kitchen foreshadows the blowout, but it's a bit Hollywood: the complexity of what happened is beyond the movie and in fact the movie has a lot of situations where it's clear the writers decided to move forward without trying to explain what was happening (it's a movie, after all, not a training film for petroleum engineers).

- For all the entertainment value of the movie, and the educational points one may take away from it, there were 11 fatalities, a large number of injuries, and an ecological disaster involved. So, it was nice of the producers to include the final vignettes commemorating the losses.

Now, to the hard nerditude.

I heard of the incident at the Macondo well (that's the correct name for the location, the Deepwater Horizon is the drilling rig) when it happened and for a while the news were, as usual, full of uninformed speculation, name-calling, mentions of Halliburton (always a good villain for certain parts of the population) and greed, and attacks on fossil fuels.

Not being a petroleum engineer, I assumed that (a) everything the media said was either wrong or very wrong; (b) at some point there would be smart and knowledgeable people looking at this; and (c) reports from these smart and knowledgeable people would be put online, as a prelude to the many many many lawsuits to come.

So, when a friend bought the movie (friends with kids are great: they buy movies that I can borrow), I borrowed it and in a moment of extra nerdiness decided to learn something about the Macondo/Deepwater Horizon incident before watching the movie.

I struck gold with Stanford University:

I had a general idea about how drilling works, but the details are quite important. This video was very helpful:

Being an engineer, I went to the reports too. The easiest to read is the report to the President. Having read the report helped situate the movie, since a few of the important events are not in it (some are referred to in passing):

Halliburton simulated a specific cementing plan for the well, but the actual cementing did not follow that plan. In particular, because of the tight window of usable pressures for the cementing, the cementing pipe had to be centered accurately in the hole using more spacers than were actually used. Halliburton isn't mentioned in the movie because (a) they are scary and have lots of lawyers; or (b) they didn't do what they had simulated, on orders from BP, which makes it BP's responsibility.

Schlumberger (Sch-loom-bear-g-heh, which a roustabout calls Schlam-burger to mock Wahlberg's correct pronunciation) was on site to conduct a test of the cement and see if it had set, but as the action on the movie arrives on the rig, the testing team is leaving without running the test (what happened in reality). There's no doubt that the cementing failed, since that's where the oil and gas got into the pipe and eventually the riser to the surface, so in retrospect that test would have saved the rig and well.

Unmentioned in the movie is the large quantity of highly viscous plugging fluid used as a spacer between the cement and the drilling mud, which might have blocked the narrow pipes of the kill line and shown the zero pressure when there was in fact pressure. This is the part in the movie when the writers gave up, decided that giving an impromptu course in deep-water drilling to the audience was not their job, and moved forward into the actual action.

The most unbelievable scene in the movie, when Wahlberg runs across essentially a field of giant exploding flamethrowers (the burning rig) to start the backup diesel generators, is actually true. The rig was all electrically-operated, including the thrusters; without electricity they had no lights, no PA, and lost control of the rig (it moved off-station enough that it pulled the drill string through the blowout preventer and possibly disabled parts of the blowout preventer that would have cut the pipe and sealed the well).

Watching the movie, I found it difficult to believe that Transocean management, especially HR, was okay with 1 woman and 125 men on a 21-day rotation on a drilling rig, but that is apparently accurate (maybe a few more women, but overwhelming majority of people on the rig were men). The potential for lawsuit-inducing behavior just seemed too high.

All in all, I think that the movie was much more fun to watch having read the report and watched the videos beforehand than it would have been otherwise. I would have been thinking about the discrepancy between the drill pipe and kill line pressure and the blowout preventer failure till the end of the movie, so I would have missed the emotional and action-loaded last thirty minutes.

The Wahlberg/Rodriguez jump was all Hollywood, though.



Update April 5, 2017: the problems in the blowout preventer.

If it's a math problem... do the math

Or, The Monty Hall problem: redux.

I recently posted a new video, addressing the Monty Hall problem. The problem is not the puzzle itself, which has been solved ad nauseam by everyone and their vlogbrother.

The video is about what information is. By working through the details of the Monty Hall puzzle, we can learn where information is revealed and how. That is the reason for the video; that and a plea for something so simple and yet so ignored that I'll repeat it again:

If it's a math problem, do the math.

Now, this may seem trivial, but math (and to some extent science, technology, and engineering, to say nothing of business, management, and economics) makes people uncomfortable, even people who say they "love math."

Hence the attempt to solve the problem with anything but computation. By waving hands and verbalizing (very error prone) or by creating similar problems that might be insightful (but mostly convince only those who already know the solution and understand it).

If all you're interested is the computations for the solution, they're here:

The point of the video is not this particular table; it's the insights about information on the path to it: how constraints to actions change probabilities and how those relate to information.

For example, from the viewpoint of the contestant, once she picks door 1 (thus giving Monty Hall a choice of door 2 and door 3 to open), the probability that Monty picks either door 2 or door 3 is precisely 1/2; that's calculated in the video, not assumed and not hand-waved. But, as the video then explains, that 50-50 probability isn't equally distributed across different states:

A final remark, from the video as well, is that by having computations one can avoid many time-wasters, who --- not having done any computations themselves and generally having a limited understanding of the whole state-event difference, which is essential to reasoning with conditional probabilities --- are now required to point out where they disagree with the computation, before moving forward with new "ideas."

If it's a math problem... do the math!

Word Thinkers and the Igon Value Problem

Nassim Nicholas Taleb did it again: "word thinkers," now a synonym for his previous coinage IYI (Intellectuals Yet Idiots).

I often say that a mathematician thinks in numbers, a lawyer in laws, and an idiot thinks in words. These words don’t amount to anything. 

A little unfair, though I've often cringed at the use of technical words by people who don't seem to know the meaning of those words. This sometimes leads to never-ending words-only arguments about things that can be determined in minutes with basic arithmetic or with a spreadsheet.

To not rehash the Heisenberg traffic stop example, here's one from a recent discussion of the putative California secession from the US (and already mentioned in this blog): people discussed California's need for electricity, with the pro-Calexit people assuming that appropriate capacity could be added in a jiffy, while the con-Calexit people assumed the state would instantly be blacked out.

No one thought of actually looking up the numbers and checking out the needs. Using 2015 numbers, California would need to add about 15GW of new dispatchable generation for energy independence, assuming no demand growth. (Computations in this post.) So, that's a lot, but not unsurmountable in, say, a decade with no regulatory interference. Maybe even less time, with newer technologies (yes, all nuclear; call it a French connection).

There was no advanced math in that calculation: literally add and divide. And the data was available online. But the "word thinkers" didn't think about their words as having meaning.

And that's it: the problem is not so much that they think in words, but rather that they don't associate any meaning to the words. They are just words, and all that matters is their aesthetic and signaling value.

Few things exemplify the problem of these words-without-meaning as well as The Igon Value Problem.

In a review of Malcolm Gladwell's collection of essays "What the dog saw and other adventures" for The New York Times, Steven Pinker coined that phrase, picking on a problem of Gladwell that is common to the words-without-meaning thinkers:

An eclectic essayist is necessarily a dilettante, which is not in itself a bad thing. But Gladwell frequently holds forth about statistics and psychology, and his lack of technical grounding in these subjects can be jarring. He provides misleading definitions of “homology,” “sagittal plane” and “power law” and quotes an expert speaking about an “igon value” (that’s eigenvalue, a basic concept in linear algebra). In the spirit of Gladwell, who likes to give portentous names to his aperçus, I will call this the Igon Value Problem: when a writer’s education on a topic consists in interviewing an expert, he is apt to offer generalizations that are banal, obtuse or flat wrong. [Emphasis added]

Educational interlude:

Eigenvalues of a square $[n\times n]$ matrix $M$ are the constants $\lambda_i$ associated with vectors $x_i$ such that $M \, x_i = \lambda_i \, x_i$. In other words, these vectors, called eigenvectors, are along the directions in $n$-dimensional space that are unchanged when operated upon by $M$; the $\lambda_i$ are proportionality constants that show how the vectors stretch in that direction. Because of this $n$-dimensional geometric interpretation, the $x_i$ are the matrix's "own vectors" (in German, eigenvectors) and by association the $\lambda_i$ are the "own values" (in German, you guessed it, eigenvalues). 

Eigenvectors and eigenvalues reveal the deep structure of the information content of whatever the matrix represents. For example: if $M$ is a matrix of covariances among statistical variables, the eigenvectors represent the underlying principal components of the variables; if $M$ is an incidence matrix representing network connections, the eigenvector with the highest eigenvalue ranks the centrality of the nodes in the network.

This educational interlude is a demonstration of the use of words (note that there's no actual derivation or computation in it) with deep meaning, in this case mathematical.

Being a purveyor of "generalizations that are banal, obtuse or flat wrong" hasn't harmed Gladwell; in fact, his success has spawned a cottage industry of what Taleb is calling word-thinkers, which apparently are now facing an impending rebellion.

Taleb talks about 'skin in the game,' which is a way to say, having an outside validator: not popularity, not social signaling; money, physical results, a verifiable mathematical proof. All of these come with the one thing word-thinkers avoid:

A clear succeed/fail criterion.

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Added 2/16/2017: An example of word-thinking over quantitative matters.

From a discussion about Twitter, motivated by their filtering policies:

Person A: "I wonder how long Twitter can burn money, billions/yr.  Who is funding this nonsense?"

My response: "Actually, from latest available financials, TWTR had a $\$ 77$ million positive cash flow last year. Even if its revenue were to dry up, the operational cash outflow is only $\$ 220$ million/year; with a $\$ 3.8$ billion cash-in-hand reserve, it can last around 17 years at zero inflow."

Numbers are easy to obtain and the only necessary computation is a division. But Person A didn't bother to (a) look up the TWTR financials, (b) search for the appropriate entries, and (c) do a simple computation.

That's the problem with word thinking about quantitative matters: those who take the extra quant step will always have the advantage. As far as truth and logic are concerned, of course.

Schrödinger's Cat Litter

"Quantum mechanics means that affirmations change the reality of the universe."

Really, there are people who believe in that nonsense. I don't know whether affirmations work as a psychological tool (ex: to deal with depression or addiction), though I've been told that they might have a placebo effect. But I do know that quantum mechanics has nothing to do with this New Age nonsense.


The most misunderstood example: Schrödinger's cat

A common thread of the nonsense uses Schrödinger's cat example and goes something like this:

"There's a cat in a box and it might be alive or dead due to a machine that depends on a radioactive decay. Because of quantum mechanics, the cat is really alive and dead at the same time; it's the observer looking at the cat that makes the cat become dead or alive. The observer creates the reality."

No, really, this is a pretty good summary of how the argument goes in most discussions. It's also complete nonsense. The real Schrödinger's cat example is quite the opposite (note the highlighted parts):

(Source: translation of Schrödinger's "Die gegenwärtige Situation in der Quantenmechanik," or "The current situation in quantum mechanics.")

As the excerpt shows, Schrödinger himself described applying quantum uncertainty to macroscopic objects as "ridiculous." In fact, in the original paper, Schrödinger calls it burlesque:

In other words, this New Age nonsense takes Schrödinger's example of misuse of a quantum concept and uses it as the foundation for some complete nonsense, doing precisely the opposite of the point of that example.

Sometimes "nonsense" isn't strong enough a descriptor, and references to bovine effluvium would be more appropriate. In honor of the hypothetical cat, I'll refer to this as Schrödinger's cat litter.


Say his name: Heisenberg (physics, not crystal meth)

Schrödinger isn't the only victim of these cat litter purveyors: the Heisenberg Uncertainty Principle also gets distorted into nonsense like:

"You can't observe the position and the momentum of an object at the same time. If you're observing momentum, you're in the flow. If you're observing position, you're no longer in the flow."

As I've mentioned before, when over-analyzing a Heisenberg joke, the uncertainty created by Heisenberg's inequality ($\Delta p \times \Delta x \ge h$) for macroscopic objects is many orders of magnitude smaller than the instruments available to measure it. TL;DR:

Police officer: "Sir, do you realize you were going 67.58 MPH?
Werner Heisenberg: "Oh great. Now I'm lost." 

Heisenberg's uncertainty re: his position is of the order of $10^{-38}$ meters, or about 1,000,000,000,000,000,000,000,000,000,000,000,000 times smaller than an inch.

And yet, these New Age cat litter purveyors use the Heisenberg uncertainty principle to talk about human actions and decisions, as if it was applicable to that domain.


What are the "defenders of science" doing while this goes on?

Ignorance, masquerading as erudition, sold to rubes who believe they're enlightened. Hey, I'm sure many of the rubes "love science" (as long as they don't have to learn any).

Meanwhile, "science popularizers" spend their time arguing politics. Because that's what science is now, apparently...