Wednesday, March 22, 2017

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. 😎

Thursday, March 9, 2017

Collected early March geekery

😎 Two talks by Edward Tufte (I read Tufte's notebooks regularly):




😎 The end of modern medicine (rise of the superbugs):


Be afraid. Be very afraid. Ok, moderately cautious.


😎 Don't let Dave Jones borrow your pre-release not-yet-for-sale oscilloscope:


(The electrolytic capacitors in the power supply led to a big argument in the EEVBlog forum.)


😎 A digital clock coded using the Conway "game of life." From twitter user Abraham (click that link for an animated version, or get the code and run it on any of the many simulators):


Behold this example of "my code-fu is bigger than your code-fu." Nerds, nerds everywhere (on Stack Exchange, that is):
http://codegolf.stackexchange.com/questions/88783/build-a-digital-clock-in-conways-game-of-life/111932#111932
It's a French coder... I expect the clock to end the cycle with a "Ich gebe auf!" πŸ˜‰


😎 Interesting paper on molten salt reactors, works as a good introduction (non-technical) to them. MSRs are the future of nuclear (at least for now).



😎 Nice to see physicists addressing the really important problems (not really):



πŸ˜‹ Two-ingredient (plus salt and spices) tomato soup: 6oz tomato paste, 24oz milk.

Two ingredient tomato soup.

And the final product (3 hours in the slow cooker), dressed with fresh basil and parmesan:

Two ingredient tomato soup dressed up with fresh basil and grated Parmesan.


πŸ€„️ Easy puzzle from a repository of Martin Gardner puzzles: Which of the two dots is the center of the circle? Can you prove it?
(More of an optical illusion than a puzzle, since there's enough information in the picture to make a determination without guessing.)

I have a complete collection of Martin Gardner puzzle books and partly trace my interest in computation and information manipulation systems to the "Mathematical Games" columns in Scientific American. (And to their successor, "Metamagical Themas," which is an anagram of "Mathematical Games.")

Tuesday, March 7, 2017

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...

Sunday, February 26, 2017

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.

Friday, February 24, 2017

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!

Thursday, February 16, 2017

Practicing information presentation design

All skills need practice, and designing ways to present information is a skill.

Since I can't show work-related materials for legal reasons, and also I don't make as many presentations as I used to when it was, well basically my job, I keep my information-design skills in top shape by applying them to more entertaining matters.

(Click the images to magnify.)


Augmenting quotes: South Australia power woes.

In this case the quote is a tweet, but it works with longer quotes too.


I admit that there are elements of chartjunk in my design: the background of wind turbines and the Australian flag in an Australia outline. But those serve as additional cues to what really happened (and where): reliance on non-dispatchable capacity has made the South Australia grid a joke among electrical engineers.

South Australia has been featured on this blog before, for a worse case of the same problem.


A larger version of augmenting a quote: Popular Science shills for WaterSeer


In this case, it's an augmentation to critique, not to support. Thunderf00t has a science-accurate, still very snarky video about the WaterSeer:


(Added on Feb 19, 2017.)

Why, some ask, be so harsh on those promoting the WaterSeer, when equally stupid products like the Fontus Water Bottle and Solar Roadways, not to mention out-and-out con jobs like the Triton Artificial Gills exist?

The answer is that those products take money from people who are both relatively well-off and ignorant. The WaterSeer diverts money that would help the poorest of the poorest, and they have no say in the matter.

The Fontus Water Bottle takes money from people who buy multi-thousand-dollar bicycles and hundred-dollar socks; Solar Roadways fleeces taxpayers a little bit for a product that is stupid on its statement (put solar panels in the shade of moving vehicles).

The WaterSeer, by diverting money from solutions that could actually work, leads to more poor people dying. Clear enough?


Annotated photos: Oroville Dam repairs.

Engineering, that neverending fight between Nature and Man! In the case of the Oroville Dam, Nature's side got a lot of help from Man, or maybe one should say from politics, incompetence, bad design, and bad luck.


There were two points I wanted to make: the scale of the problem (which is nicely contextualized by the size of those dump trucks) and the misclassification of soft soil as a spillway. This one photo from the California Department of Water Resources, with minimal annotation, makes the case quite clearly. All that was needed was to make the points more salient for less attentive audiences.


Contrasting visual narratives with data: The California Drought

While photos (and videos) are great tools to support a narrative, much more so than text and massively preferable to data, sometimes contrasting the narrative (the two photos) with the actual data (the graphs from the California Department of Water Resources) can illustrate how the prevailing narrative is actually stretching the truth.



(Added 2/22/2017.)


Property maps: Science-adjacent television shows.

Recently I found myself binge-watching Numb3rs (from the DVDs, since Netflix has dropped them); it's one of the few fiction shows that actually included teaching vignettes. Charles Eppes would explain real mathematical concepts with simple illustrations and computer graphics.

Pondering that, I realized that The Big Bang Theory also does a little bit of that, much less of course, but there's one major difference: Charles Eppes is cool and well-accepted by the non-mathematicians on the show (and dating Navi Rawat, a/k/a Amita), while the scientists in TBBT are portrayed as total nerds.

The other TV show that portrayed a science-y person as cool was MacGyver (the original, the new one might as well be called McBourne); but in that show the science was terrible. But MacGyver was cool and more importantly, his approach to solving problems was "use your brain, not your fists."

Having been exposed to MacGyver early on, I started carrying around a Swiss Army knife, duct tape, and a lighter (I don't smoke, but MacGyver carried around strike-anywhere matches which were difficult to find in Portugal). I currently own eleven SAKs, from a small keychain model to one of the largest ones that's still practical to use. I don't own the ludicrously fat one.

So, there are two dimensions, goodness of science and coolness of scientists, which my MBA training says necessitates a two-by-two matrix:


But I'm a quant too, so I can do numbers and graphs. Using multi-dimensional scaling on similarity ratings (my own, so there's a clear researcher effect) on a number of television shows, we find more granularity:


House MD and Bones have better science than MacGyver and the vast majority of TV science fiction, but they don't discuss the science much. There are some times when Brennan introduces some real science in the discussion or House points out something accurate, so they aren't "teching the tech," but unlike TBBT or Numb3rs, there's never elaboration.

The scientists are portrayed as less nerdy than those in TBBT (and the general portrayal of people with technical skills in other shows); both Brennan and House have social foibles, but they are highly functioning and comfortable with themselves. They don't make science "cool" per se, but they make scientists central to society (curing people, solving crimes), rather than ivory tower researchers with no connection to the real world.

Numb3rs had a lot of support in the math community; a few links:

Side-by-side comparisons: EEVblog versus Thunderf00t.

Most data only becomes information when adequate context and knowledge are applied. In many cases, a contrast table (a side-by-side comparison) along appropriate variables can make the relevant points more salient. Behold:


This table was inspired by the coincidence that both EEVblog and Thunderf00t made debunking videos recently, one a good video with technical demonstrations and a clear analysis of what was shown, the other a snark-filled collection of fallacies, namely guilt-by-association (with Solar Roadways) and distraction (the video keeps talking about PET as if that was the plastic to be used).



(Yes, I know Thunderf00t's real name is known, but since he was doxxed, I don't use his real name.)


Note: someone asked what's suspicious about Thunderf00t's recent increase in the rate of video releases and the change in topic mix. When a male of the species increases money-making activities and starts avoiding topics like feminism, that's a strong indication that his mind has gone under the control of a female woman of the opposite sex, or what Millennials call "hooking up." Should the hypothesis be correct, we should see indications of more direct female oppression soon, like button-down shirts and a haircut.

(The obvious suspiciousness of an alleged Australian who's that pale is unquestioned.)

Sunday, February 12, 2017

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 aperΓ§us, 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.

- - - - - - - - - -

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.