Fun with geekage for August 2020

Technical fields aren't like other fields.

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.

Fun with geekage for July 4th, 2020

Been busy with book writing (another short book in the works while I wait for advance readers feedback on the numbers book; less math more management), so no time to blog. Some images from my Twitter for now.

When someone putatively supports one side (free markets) but uses such a flawed and weak argument, I recommend they wholeheartedly join the other side. This level of fail almost suggests it's a false flag.

A bit steep for me.

I find myself agreeing with and extending Yanis Varoufakis.

While getting some of YV's books in audible form for travel and rowing, I realized that maybe Audible's search engine has some pathologies...

Trying a new yogurt I found at Whole Paycheck, ahem, Foods. Those live cultures help with 'le transit intestinal' as the French say. Obs: 1. very pricey; 2. P:E ratio 2/3 (low for yogurt); and 3. Inconsistent message. Taste: 7/10, will buy again.

From a site that has "engineering" in its title. Apparently not engineering enough for its writers to do basic (middle-school) physics. Relying on the NYT for physics is like using a chocolate frying pan. Behold:

Note that at Mach 15, around 5 km/s the energy density of a projectile is 12.5 MJ/kg (~ 3 times that of TNT), so the first sentence only makes sense for a impactor of around 1 to 3 tons. (More feasible that 100 tons, at least.)

Audiophiles aren't, in general, audiophools. There's some foolishness in the wings, but mostly what people who criticize us don't like is that we have taste and discernment. 

Fun with numbers for November 1, 2019

Fast-charging batteries

From the web site that hangs off of the brand equity of the very prestigious journal Science: "New charging technique could power an electric car battery in 10 minutes" 

Congratulations to the team improving battery technology. But:

I. According to the news, this is a technology demonstration, though that might be inaccurate (the original report makes it a testing rig, which is one step farther back from a final product). There's a lot of work to do (and many avenues for failure) before this becomes a deployable product, much less at scale.

II. Charging a 75 kWh battery (AFAIK, the smallest battery in a Tesla car) in 10 minutes requires a charging power of 450 kW. Even using 480 V as the charging voltage, that's still a 937.5 A current; those cables will need some serious heft, and any impurities in the contacts will be a serious fire hazard.

III. A typical gas pump moves about 3 l of gasoline per second. Gasoline has around 34 MJ/l energy density, so that pump has a power rating of 102 MW, 227 times higher energy throughput than the new battery. Even if the distance/energy efficiency of internal combustion engines is lower than electric motors, that's a big difference. Also, you can buy Reese's peanut butter cups at gas stations.

More fun with Rotten Tomatoes

Watchmen (HBO series) shows that sometimes when data changes, the conclusions change.

Despite the caterwauling of many in the comic-book nerd community (not that I would know, as I don't belong… okay, I occasionally might take a look, but I'm not a comic book nerd… not since the early 70s…), data show that it's much more likely that the critics and the audience are using similar criteria for their evaluation of Joker than opposite criteria.

How much more likely? Glad you asked:

210,565,169,600,721,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times more likely.

Ah, the power of parameterized models: you set them once, you can nerd out on them till the end of time. (I haven't watched either the show or the movie. Maybe when they get to Netflix or Amazon Prime.)

Added Nov 3: Haven't watched it yet, but Rotten Tomatoes data shows that critics are 1,361,188 times more likely to be using the same criteria as the audience than opposite criteria to evaluate "For All Mankind."

Some progress in nuclear fusion?

Some simple physics:

1 kg mass = 9E16 J of energy ($E = mc^2$)
Coal has 30 MJ/kg specific energy
10E6 kg coal have 3E14 J (assuming Bloomberg meant using combustion)

Fusion is to have 1/300 efficiency relative to pure mass-energy conversion?

Kudos. Now, get to it!

Shredded Sports Science eats an apple

Shredded Sports Science has a video making fun of people who know even less about fitness and nutrition than the "experts" in those "sciences," where he takes a bite of an apple and says "one rep," another bite, "two reps," the joke being on Chris Heria of Thenx.

Huh, the quant says, I wonder how the numbers will go…

Let's say a warm-up set of 100 kg squats and the total vertical path is 1 m. How much energy does one rep use, just for the mechanical work?

Naïve physics neophyte: huh, zero, the rep starts and ends at the same point.

No. The mechanics of the rep are different on the way down and on the way up: assuming that the weight moves at constant speed most of the time, the down movement requires the body provide work to counteract acceleration, so we can approximate the total work by 2 * 100 * 9.8 * 1 = 1960 J.

Note that this is just the mechanical part. Muscles have less than 100% efficiency and that efficiency changes as fatigue increases, hence the heat (heat, and to a smaller degree, changes to the mix of waste products of muscle contraction, represent losses in efficiency).

The other side of the coin is the chemical energy in that apple, which is measured by the magic ['delusion' or 'deception' also work here] of mistaking the simple process of combustion for the very complex processes of digestion and respiration. But let's pretend…

Apples are basically 1/3 sugar and 2/3 water, with some esters and ester aldehydes for taste and aroma, so for a small bite let's say 15g of apple we get 5 g of sugar; that's 20 kCal or ~ 84,000 J.

Shredded Sport Science's little joke would point to a combined digestion, respiration, and muscle contraction efficiency of 2.33%.

Evolution would have selected this biochemical parameterization right out of the gene pool.

Fun with energy

Talk about counting calories in a way that matters. (From the BP energy stats 2019; and yes, their tables are in MtOE, not calories, but unit changes are trivial, except maybe for gymbros.)

Bay Area versus Europe

With the return of Silicon Valley on HBO, there's a lot of hating on the Bay Area going around, so here's a thought in numbers…

When nutrition and fitness studies attempt science with naive statistics

A little statistics knowledge is a dangerous thing.

(Inspired by an argument on Twitter about a paper on intermittent fasting, which exposes the problem of blind trust in "studies" when such studies are done to lower statistical standards than market research since at least the 70s.)

Given an hypothesis, say "people using intermittent fasting lose weight faster than controls even when calories are equated," any market researcher worth their bonus and company Maserati would design a within-subjects experiment. (For what it's worth, here's a doctor suggesting within-subject experiments on muscle development.)

Alas, market researchers aren't doing fitness and nutrition studies, mostly because market researchers like money and marketing is where the market research money is (also, politics, which is basically marketing).

So, these fitness and nutrition studies tend to be between-subjects: take a bunch of people, assign them to control and treatment groups, track some variables, do some first-year undergraduate statistics, publish paper, get into fights on Twitter.

What's wrong with that?

People's responses to treatments aren't all the same, so the variance of those responses, alone, can make effects that exist at the individual level disappear when aggregated by naive statistics.

Huh?

If everyone loses weight faster on intermittent fasting, but some people just lose it a little bit faster and some people lose it a lot faster, that difference in response (to fasting) will end up making the statistics look like there's no effect. And what's worse, the bigger the differences between different people in the treatment group, the more likely the result is to be non-significant.

Warning: minor math ahead.

Let's say there are two conditions, control and treatment, $C$ and $T$. For simplicity there are two segments of the population: those who have a strong response $S$ and those who have a weak response $W$ to the treatment. Let the fraction of $W$ be represented by $w \in [0,1]$.

Our effect is measured by a random variable $x$, which is a function of the type and the condition. We start with the simplest case, no effect for anyone in the control condition:

$x_i(S,C) = x_i(W,C) = 0$.

By doing this our statistical test becomes a simple t-test of the treatment condition and we can safely ignore the control subsample.

For the treatment conditions, we'll consider that the $W$ part of the population has a baseline effect normalized to 1,

$x_i(W,T) = 1$.

Yes, no randomness. We're building the most favorable case to detect the effect and will show that population heterogeneity alone can hide that effect.

We'll consider that the $S$ part of the population has an effect size that is a multiple of the baseline, $M$,

$x_i(S,T) = M$.

Note that with any number of test subjects, if the populations were tested separately the effect would be significant, as there's no error. We could add some random factors, but that would only complicate the point, which is that even in the most favorable case (no error, both populations show a positive effect), the heterogeneity in the population hides the effect.

(If you slept through your probability course in college, skip to the picture.)

If our experiment has $N$ subjects in the treatment condition, the expected effect size is

$\bar x = w + (1-w) M$

with a standard error (the standard deviation of the sample mean) of

$\sigma_{\bar x} =  (M-1) \,\sqrt{\frac{w(1-w)}{N}} $.

(Note that because we actually know the mean, this being a probabilistic model rather than a statistical estimation, we see $N$ where most people would expect $N-1$.)

So, the test statistic is

$t = \bar x/\sigma_{\bar x} = \frac{w + (1-w) M}{(M-1) \,\sqrt{\frac{w(1-w)}{N}}}$.

It may look complicated, but it's basically a three parameter analytical function, so we can easily see what happens to significance with different $w,M,N$, which is our objective.

Because we're using a probabilistic model where all quantities are known, the test statistic is distributed Normal(0,1), so the critical value for, say, 0.95 confidence, single-sided, is given by $\Phi^{-1}(0.95) = 1.645$.

To start simply, let's fix $N= 20$ (say a convenience sample of undergraduates, assuming a class size of 40 and half of them in the control group). Now we can plot $t$ as a function of $M$ and $w$:

(The seemingly-high magnitudes of $M$ and $w$ are an artifact of not having any randomness in the model. We wanted this to be simple, so that's the trade-off.)

Recall that in our model both sub-populations respond to the treatment and there's no randomness in that response. And yet, for a small enough fraction of the $S$ population and a large enough multiplier effect $M$, our super-simple, extremely-favorable model shows non-significant effects using a single-sided test (the most favorable test, and we're using the lowest acceptable significance for most journals, 95%, also most favorable choice).

Let's be clear what that "non-significant effects" means: it means that a naive statistician would look at the results and say that the treatment shows no difference from the control, in the words of our example, that people using intermittent fasting don't lose weight faster than the controls.

This, even though everyone in our model loses weight faster when intermittent fasting.

Worse, the results are less and less significant the stronger the effect on the $S$ population relative to the $W$ population. In other words, the faster the weight loss of the highly-responsive subpopulation relative to the less-responsive subpopulation, when both are losing weight with intermittent fasting, the more the naive statistics shows intermittent fasting to be ineffectual at producing weight loss.

Market researchers have known about this problem for a very long time. Nutrition and fitness practices (can't bring myself to call them sciences) are now repeating errors from the 50s-60s.

That's not groovy!