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…

Fun with numbers for October 19, 2019

(Yes, yet another tweet-recycling post. When I unfroze the blog the reason was that I was tweetstorming blog posts, so now I'm refactoring ideas from twitter, with — one hopes — improvements.)

Negative [effect on carbon capture]

Via Thunderf00t, who manages to find the occasional bad product gem amongst the many non-bad products he "busts!" by not understanding engineering (or pretending not to), we learn of Negative, a captured-carbon bracelet.*

Enter basic math, illusion exits stage left.

Say Bay Area Bob commutes from San Francisco to Palo Alto (100 mi roundtrip), 5 days/week (500 mi/week) on a 25 MPG car; that's 20 gallons of gasoline burned per week.

Gasoline is a complicated mixture, but let's simplify by treating it as 100% iso-octane (2-2-4-trimethylpentane), C8H18; let's simplify further by assuming perfect stoichiometric burn, so 1 kg of iso-octane generates 3.1 kg of CO2.

Gasoline has a density of 0.7489 kg/l or 2.835 kg/gal; this generates 8.75 kg(CO2)/gal(gasoline), so a weekly commute creates 175 kg of CO2.

Say that bracelet is 25 g of pure carbon. That corresponds to 1/1910th of the carbon in a single one-week commute for Bob. (175 kg of CO2 contain 47.7 kg of carbon.)

I'm sure every Bay Area Bob will be sporting one of these Negative bracelets.

What about other hydrocarbons? Given the small mass differences between alkanes, alkenes, and alkynes, we can take a look at the CO2 per kg(hydrocarbon) with a simple calculation:

Note that the maximum CO2 per kg is when the fuel is pure carbon, at 3.67 kg (CO2)per kg (C). So the approximation above (for Bob) isn't too bad.

-- -- -- --

*Another annoying habit of TF is to gloss over the math, usually to the point where his approximations accumulate into nonsensical territory and occasionally even significant technical errors.

Much ado about Ruby Rose's petite physique.

One of the criticisms of Batwoman that might have some merit is that a petite person like Ruby Rose is not credible as an action hero; that a punch from her not-very-muscular arms would not knock out a 250-lb henchman. To which I reply: as opposed to not-exactly-Schwarzenegger Ben Affleck or Christian Bale throwing said 250-lb henchman clear across a parking lot with a single arm? Pah!

This scene, where Batwoman gets shot by a pistol led to some comments on how she would have been thrown in the air, backwards. Because "momentum," say the people who love science but can't do math (or actually bother to learn the science they profess to "love").

The batsuit is bulletproof (has been all along); assuming that it completely distributes the pressure of the impact over the 1/4 square meter of her torso front, there's little effect, as can be seen from the delta speed for the system:

Say Batwoman (Ruby Rose + suit) = 50 kg, bullet (looks like a .45 ACP) is 15g at a muzzle velocity of 250 m/s, so conservation of momentum shows the after-impact speed to be (0.015 * 250)/(50.015) = 0.075 m/s or less than 0.3 km/h, a very small change in velocity to Batwoman that can be easily countered by a braced position.

An alternative way to see the limited effect:

Consider that the bullet is stopped by the suit and loses all its velocity while pushing back 5cm. Assuming constant force, it takes t = 2 s/v = 2 (0.05)/250 = 0.0004 s to stop, for an acceleration of a = v/t = 625000 m/s^2 and a force F = 9375 Newton (almost 975 kgf, but just for 400 microseconds), which spread over 1/4 square meter of her torso is a pressure of 0.38 kgf/cm^2, which is the pressure of a light finger poke (again, for 400 microseconds).

And a tip of the hat to old-style scifi machinery (no labels on buttons or indicators):

Flexagons. Not the hexa ones.

A late entry: more battery nonsense.

Via eevblog, we learn of yet another life-changing momentous innovation by a lone inventor squashed by the Big Industry Conformance Bureau:

I didn't read the article, but from the photo we can see that the '1500-mile battery' volume is about 2 liters, so a little bit of arithmetic ensued:

1500 miles w/ better-than-current vehicles (say 200 Wh/mi): 300 kWh (1.08 GJ)
Volume of battery, from article photo let's say 2 l) so energy density = 504 MJ/l
Current Li-Ion battery energy density ~2.5 MJ/l to  5 MJ/l (experimental)

Home inventor creates something something 100 to 200 times more dense than
current technology (and about 15 times more energy-dense than gasoline)?!

Nope, not credible.

(Note: apparently the photo is deceptive, and the actual "1500 mile battery" is larger, only 9 times more energy-dense than current technology. Which is as non-credible, especially the idea that car manufacturers would be able to stop small electronics makers from adopting a technology that would allow for smaller batteries in laptops and longer times between charge in cell phones. Added Oct 21.)

Fun with numbers for Sep 27, 2019

Near-miss asteroid? Pah!

Asteroid 2017 KP27 just missed Earth on Sep 26th; well, missed by almost 1 1/2 million km, but considering how big space is, that's a close-ish call.

Whenever one of these close calls happens there's a lot of Tweeting and Facebooking and Instagramming, not to mention the ignorant bleating from the absurdly ignorant of science official voice of the establishment traditional media, about how we could have all died just-like-that. Where are Ben Affleck and Bruce Willis when we need them?

Not so fast. (Literally, that's the issue: velocity squared.)

Asteroid 2017 KP27 relative speed in this pass was 4,805 m/s and its diameter is between 19 and 42 meters. There's no estimate of its mass in the Nasa database, but we can make a few approximate calculations. Generally these asteroids fall into three types: carbonaceous (think giant snowball, only made of methane and carbon dioxide), silicate (big rock), or metallic.

Data from Krasinsky et al. (July 2002) "Hidden Mass in the Asteroid Belt," Icarus, 158 (1): 98–105, puts densities for these three types at 1.38, 2.71, and 5.32 g/cm$^3$ respectively.  (Source: Wikipedia for the reference and the actual article for the numbers, viva la public library proxy server.)

Assuming as reference cases the two extremes in diameter and using the geometry of a sphere (we're just doing order-of-magnitude calculations, really), we can compute the kinetic energy KE for both this close call and the next time we pass asteroid 2017 KP27 (Sep 15, 2020; closest approach will be 44 million km at a relative speed of 13,178 m/s):

As is clear from the table, even at its higher speed in 2020, this puny little pebble is at best a single city-buster, while at its recent speed it carried less energy than a theater-wide tactical nuke.

So, not the ELE some people feared. Still, could ruin your day if it landed within the same neighborhood.

Visible from space? Double Pah!

From Orson Scott Card's The Swarm:

Visible from space isn't really that distinctive, in fact it's positively common, as long as there's enough color and light contrast. For purposes of this analysis, space starts at an altitude of 100 km (could also be 80 km, but, what the hay, I like round numbers in metric).

I can see objects 1 m tall at a distance of 1 km, and I'm not exactly hawk-eyed, so an object more than 100 m along its smallest dimension should be visible from space by someone like me (possibly much smaller, for people with better vision who didn't spend most of their life reading, coding, writing, or doing math), as long as there's enough contrast with the surroundings.

My heavy-reader eyes have a resolution of at least 1/1000 radians per pixel (actually more, since I can see some detail in 1 m objects at 1 km, but let's keep it simple), which is 3 minutes and 26.3 seconds of angle [in degrees].

For comparison, the Cheyenne Tactical M200 Intervention marksmanship rifle has sub-MOA (Minute Of Angle) accuracy at over 2000 m. (A pair of these rifles are important in Red Metal by Mark Greaney, a [mostly] good piece of MilFic I recently read. And, no, it's not a Grey Man novel, it's a different storyline.)

Fun with numbers for Sep 9, 2019

So, this might become a thing, blogging augmented tweets.

Rotten Tomatoes is at it again

Dave Chappelle apparently has a Netflix special that has critics and audience at loggerheads. Being a little more quantitative, we can say that the critics are 862,712 times more likely to be using criteria opposite to those of the audience than the same criteria. The logic is in this post.

There are two differences between that blog post and this calculation that are worth mentioning:

1. Computing $c(12352,124)$ without loading special numerical packages that can handle large numbers is beyond the capabilities of most mathematical software, so we use a trick: as we're only interested in a likelihood ratio, and those combinations appear in the numerator and denominator, we know that in the end they'll cancel out, so we ignore them altogether.

2. Small probabilities raised to a large exponent quickly get to the precision limits of the floating point representations; to deal with that we make our calculations in log-space. So instead of computing $0.01^{124}$, which would be well below the 1E-99 ($10^{-99}$) limit for most numerical software, and be treated as zero, we compute $124 \times \log(0.01)$, do all the operations in this log space and at the end we exponentiate the result.

Used Apple Numbers (in lieu of RStudio) for this one, was surprised to learn that LOG is $\log_{10}(\cdot)$ despite Numbers also having a LOG10 function. Oh, well, no problem as long as one is careful:

Tesla bull tries to praise superchargers, arithmetic and hilarity ensue

Sooooo I tried the 250kW charger for the first time and I think I'm in loooooove 🥰 -- Went from 19% to 60% I kid you not in just 5 mins. Thanks @elonmusk @Tesla 🙏

Your battery capacity is 51 kWh?!

5 minutes = 300 s
250 kW * 300 s = 75 MJ
75 MJ = (60%-19%) * Capacity, or
Capacity = 183 MJ = 51 kWh

I thought TSLA batteries started at 75 kWh?! 🤔 Possible explanations:

1. Tesla bull is exaggerating; if it took 10 minutes, or the starting point was close to 40%, that would point to a 100 kWh battery.

2. Tesla software is lying to the car owner, making the numbers look rosier than they actually are.

3. Battery has lost capacity, which happens to batteries because of the underlying principles (two main chemical reactions, one exoelectric, one endoelectric; but secondary, parasitical reactions exist that lower the battery capacity over time). Even for a 75 kWh battery that would be a very big loss (1/3), unless his charging cycles are deep and irregular (that kills batteries faster).

Counting calories is like Enron accounting

Just thinking logically, here, if you were bailing water out of a boat, would you keep adding water in?

Okay, so if you're trying to lose weight by using body fat for energy, why would you eat carbs, whose sole nutrition value is as energy? Why eat when not hungry? *

(Most of the arguments I have about calories are with people who for some reason want others to eat carbs. Counting calories biases you towards choosing carbs over fat, since fat is more energy-dense.)

But more to the point, the whole foundation of calorie counting is Enron-like accounting, where some things are counted (more or less), some things are estimated, and many other things are sort-of, kind-of assumed away in some "basic metabolic energy needs" or other ways of saying "let's assume everyone has the same basic efficiency in chemical energy extraction and mechanical power production."

The lack of accounting for energy lost as heat, which anyone out of shape who's ever jogged with an athletic friend can tell you varies a lot with the person, is the most obvious Enron-like accounting.  Higher body effort for the same mechanical output is reflected in heat loss, and differences in that heat loss can be (as calculated in that figure) in the 100-200 kCal/hour range.

That's the same difference as the mechanical energy difference between jogging and walking.  One hour at the low end of that difference (remember, this is just heat, the mechanical energy is the same for both people) every other day is equivalent to 2 kg of fat extra per year if we believe in the basic model of calories-in calories-out.

Now,  how much difference can there be in unmeasured chemical energy output? Depends on the person and the diet, but note that on a 2500 kCal/day diet a systemic difference of 2%, that is 50 kCal/day, is equivalent to 2 kg of fat extra per year if we believe in the basic model of calories-in calories-out.

Can different people with the same general diet show a 2% difference? Yep. For example, a paper called "Energy content of stools in normal healthy controls and patients with cystic fibrosis," by Murphy, Wootton, Bond, and Jackson in Archives of Disease in Childhood (1991) [thanks PubMed], includes data about the controls' intake and stool. Here are the computations for the first 5 healthy controls:

Yeah, just like that, if CICO were true, these people, on the exact same diet, would show a 3 kg per year weight gain difference. 30 kg per decade.

So, whenever people start talking about calories, be aware that they might be looking for a way to say "you're overweight because of your moral failings; if only you were as virtuous as I am!"

- - - - -
* 1. Carbs are delicious, even addictive. Just be aware of the trade-off: they slow down body fat loss and make you hungrier faster. Because controlling appetite is key to fat loss, that second part is much more damaging than the first. Any "diet" that requires constant attention and self-control is going to fail for normal people with normal lives in normal society: just look around you.

2. There's a situation when I'll eat even though I'm not hungry: if I know I'll become hungry later when no high-protein food will be available and the hunger will be inconvenient or require iron will to avoid eating institutional carbs-and-fat food. Usually this situation can be avoided by taking high-protein foods like Biltong (no, it's not jerky; yes, it's worth the price) or hard-boiled eggs with you, but there are situations when that's socially unacceptable.

Nerding out with science fiction

The book is Dream of the Iron Dragon by Robert Kroese. Highly recommended science fiction.

At $c/3$, each kg of mass in the ship has kinetic energy of 607 TJ, the equivalent of a large tactical nuclear weapon (145 kiloton TNT), or about nine times the Hiroshima explosion. The relativistic increase in mass in small (around 6%, of course), but that velocity-squared, that's the big deal. (At these speeds we have to use the relativistic formula for KE, the one with $mc^2$ in the numerator.)

A table of temporal dilation (it's a highly non-linear transformation):

At 99.95% of the speed of the light, one hour of ship time would be 31 hours, 37 minutes, and 48 seconds in the resting frame. At that speed, each kilogram of mass in the ship would have 2.75 exajoule of kinetic energy or, in big boom terms, about 13 times the energy of the largest hydrogen bomb explosion (the Tsar Bomba at 210 PJ or 50 MtTNT).

Another excerpt of the same book, non-numeric, but very dear to anyone who's ever worked in a large bureaucratic organization:

#NerdWhoMe

Fun with numbers for Sep 1, 2019

Apple declines to burn 17 billion, Tesla boosters disappointed.

Ross Gerber, a Tesla booster who provides endless entertainment on TSLA twitter, had an interesting idea (the same idea he's had for the last 4-5 years), that Apple should burn 17 billion dollars instead of giving them to people who hold AAPL stock.

The first Tesla car that was targeted at the general public (as opposed to tech billionaires and centi-millionnaires who wanted to be thought as forward-thinking) was the Model S, introduced in 2012. So we'll use 2012 as the beginning of Tesla as a real car company.

As I write this it's Sunday, September 1st, 2019 and the last TSLA close was on Friday, August 31st at 225.61. We'll compare this number with the stock closing price for the closest date for all years 2012-2018 and compute the annualized growth. Then we use that growth to forecast the evolution of an hypothetical Apple stake of 17 billion.

Using a 5-year growth rate for that tweet was basically the textbook default, but looking at that table, the last two columns really tell an interesting story… didn't Ross suggest Apple buy Tesla in late 2017 and in late 2018? Because the numbers in that table say something about financial acumen.

Calories, calories, calories... What a bunch of nonsense!

This marvel of mechanical engineering is the Siemens STG5-9000HL gas turbine. Running in single-cycle mode at nominal power it takes in almost 59,000 kg of LNG per hour or around 900 MW (Calories in: 755 million kCal/hour) and delivers around 400 MW of spinning power to a generator, for about 360 MWe (Calories out: 310 million kCal/hour) of electrical power.

Wait, what? Isn’t it Calories-In-Calories-Out? Is the turbine getting fatter or something?

No. Running in single-cycle mode the system loses around 60% of its power to unrecovered heat.

This is the real problem with CICO and 'Just Get a Caloric Deficit' recommendations: because no one measures the energy lost in radiated, conducted, and convected heat, or the energy content of urine, feces, and ‘outgassing,’ and because those show large variation across people (and across different situations for the same person, including changes in diet), the whole thing is nothing more than pretend science: like astrology made with computers, adding the trappings of science to a flawed foundation yields nothing valuable.

Well, of no real value, but monetizable; and there’s also the moral posturing afforded by telling others that being fat is proof of their lack of willpower or moral failings. (And, of course, since it doesn’t work, leads to continuing supply of clients.)

Thermodynamics is not a magical incantation. But some people use as if it were.

(I'd be willing to bet that 90% of the people who invoke 'thermodynamics' as a magical incantation to ward off the evil spirits of low-carb diets couldn't have made the junior-high Physics computations in that first paragraph.)

More infrastructure

"How can you take photos of those ugly things when there are all these flowers and rocks?"

Me: because when you understand what these things are, you marvel at the detail, at the functionality, and at the fact that they work to begin with. Also, I photograph nature too.

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...

Learning, MOOCs, and production values

Some observations from binge-watching a Nuclear Engineering 101 course online.

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.

For example, there was a class experiment measuring the half-life of excited $^{137}\mathrm{Ba}$, with students measuring radioactivity of a sample of $^{137}\mathrm{Cs}$ and doing the calculations needed to get the half-life (very close to the actual number).

For the duration of the experiment (several minutes), this is all the online audience sees:

Learning = 1% lecture, 9% individual study, 90% practice.

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:

Kicking "Angels and Demons" while it's down

First, the ever entertaining Cinema Sins:

Now for some science. Let's assume that the stolen vial contained 1 gram of antimatter. Then, the explosion would release $E = mc^2 = (0.002) \times (3 \times 10^8)^2 = 1.8 \times 10^{14}$ Joule. At 4.184 petajoule per megaton of TNT equivalent, that is an explosion of roughly 43 kiloton.

(The more observant readers will notice that there's two grams in the energy computation. That's one gram each matter and antimatter.)

The operational ceiling of helicopters is around 25,000 ft, but the helicopter piloted by Ewan McObi-Wan Kenobi is nowhere close to that altitude when he jumps. An air burst of 43 kiloton even at say 10,000 ft would create a lot more damage than shown in the movie. (For comparison, Hiroshima's burst was at the yield-optimized height of 2,000 ft and with a yield of about 15 kt.)

So Ewan McThe Ghost Writer would probably be a carbonized carmelengo rather than a usurper to the Vatican throne. And probably so would the faithful in St. Peter's square and the Cardinals in Busch Stadium The Sistine Chapel.

- - - - Fait divers - - - -

Here's the page that CERN put up to address the errors in the movie.

Nikolaj Lie Kaas, who plays the assassin, plays the corrupt CEO of the energy company in the recent Danish series "Follow The Money." I guess he's typecast as the sociopathic type now.

I claim extra nerd points for using RStudio to do the computations (was already open; it's pretty much always open these days):

The strange case of the oscillating black hole at the gym

There's a micro-black hole at my gym, and it oscillates between a position under the squat cages and the deadlift platform, in synchrony with my powerlifting program.

It's the only possible explanation.

The data: following my not-very-demanding powerlifting program (which is very low volume, even for powerlifting), I should have gained $5\%$ in both the squat and the deadlift in the last six weeks. This is feasible because I'm recovering strength from the beginning of the year, not creating new strength. (Who said powerlifters have crazy superstitions?)

Clearly, what is happening is that the same mass (bar + weights) is exerting a larger force on my body, which means that there's a micro-black hole under the gym. Since I estimate that there's a 3-meter foundation, this being earthquake territory and all, I postulate that the black hole is below that:

Furthermore, it has to move, since it doesn't affect bench press (where, despite a damaged right rotator cuff, I'm recovering strength well above the program envelope) but it affects the other two lifts. Since it affects both lifts the same percentage, that black hole has to move diagonally, as seen above. It also oscillates back and forth between the squat and deadlift stations.

Two black holes, you say? Don't be ridiculous. Two back holes, indeed! Pah!

So, a little back-of-the-drawing calculation, the kind that drives OCD quants crazy...

(with three or four corrections along the way, including a slight ahem when I used $c = 3\times 10^{9}$ instead of the correct $c = 3\times 10^{8}$ m/s)

... and I have my micro-black hole. As small as the total gains of an entire continent's worth of CrossFitters, at a Schwarzchild radius of $3\times 10^{-16}$ meter and as heavy as a Planet Fitness personal trainer, at a mass of $2\times 10^{11}$ kilogram. That mass means that the black hole won't evaporate anytime soon, so my stalled gains will continue.

(The time to evaporate a black hole with a mass of $10^{11}$kg  is in the billions of years, about the time it would take for a CrossFitter to do one good chin-up or a Planet Fitness client to lose five ounces of fat.)

Clearly this is an important discovery. Hello, Nobel Committee? Got a pick for 2017 Physics yet?


Alternative explanation 1: weight gain on my part

First off, to cancel a $5\%$ increase in squat and deadlift, I'd have to have gained close to $15\%$ of my bodyweight over six weeks. That's not impossible (or even unheard of), but in reality I've been losing weight at about 1kg per week, mostly fat, hopefully more than 1.5kg of fat per week (muscle mass increasing at 0.5kg/week during a recovery is reasonable).

Also, weight gain wouldn't affect squat and deadlift in the same way, unless I gained all the weight above my sternum. (I continue to improve my mental skills, but that doesn't significantly increase the mass of the brain...)

In an ass-to-grass squat (my type of squat), the femur goes over a 110-120 degree arc, hence getting to the weakest part of the quads force curve. So, some more weight in the torso may affect the ability to squat heavy. But for the deadlift, the drive with the legs is only an arc of 60-70 degrees, well away from the weak part of the force curve for the quads, therefore the loss of deadlifting power given additional bodyweight should be much lower than the loss for the squat, not the same. But the same it is.

(In the squat my weakness is the quads, in the deadlift, the spinal erectors; never my glutes. Hip thrusts, baby, hip thrusts FTW! I do leg-extensions with the full stack for reps, but only an ass-to-grass squat hits the quads at their full extension...)

This explanation is therefore dismissed.


Alternative explanation 2: poor supplementation

A picture is worth a thousand words (and about two hundred dollars):

Of course, I eschew that marvelous "supplement" family, anabolic steroids, or if one wants to be a little more discreet, TRT, testosterone replacement therapy. I like my reproductive system to stay at manufacturer's specification. It's kind of a big deal for me, to have the theoretical capability for reproduction (Theoretical because the 3.75 billion women in the world took a vote and unanimously –minus my mother– decided that for the good of the universe I should not reproduce; who am I to question democracy?)

This explanation is therefore dismissed.


Alternative explanation 3: I'm no longer an 18-year-old kid.

Poppycock and balderdash! Balderdash, I say!

Age is but a number and you're as young as you feel. Besides I'm barely in my early middle age -- just a few months past 30.*

This explanation is dismissed with extreme prejudice and a SEAL Team 6 visit.


Conclusion

The only possible logical conclusion is that, like in the 1990 David Brin scifi novel Earth, there's a naughty micro-black hole oscillating between the space under the squat cages and the lifting platforms, and by enormous coincidence its period matches my powerlifting program.

Obviously the solution is to combine the Westside Barbell approach of growing a big belly with the Testosterone Nation recommendation of synergistic beard growing and head shaving so that, even with increasing gravity, gains will come:

It's Science!


-- -- -- --
* 236 months, to be precise.

Fun with numbers while walking

Yesterday I went for a walk in San Francisco. To pass the time and keep my mind off the Pokemon Go players making pedestrian traffic in Golden Gate Park hazardous, I decided to do a few approximate calculations about jet engines.

Let's say a jet engine used as a gas generator produces 22 000Lbs (= 10 000 kgf or 100 000 Newton, approximately) of thrust at a nozzle velocity of 720 km/h. How much air is it moving?

To generate thrust, a mass $m$ of air is accelerated from zero to 720 km/h (200 m/s) per second. The thrust is given by $F= ma$, so the flow, or mass/second, is 100 000/200 or 500kg/s. Since air density is about 1g/l at ground level, we need 500 cubic meters of air to go through the engine per second. That's the volume of a large room (20 by 10 meters surface, 2.5 meters ceiling) per second.

Just for fun, how much power is the engine generating? Considering only the kinetic energy imparted to the air (per second, since we're interested in power), we have $1/2 \times 500 \times (200)^2$, or 10  MW. Of course, since the air is very hot, some more power could be recovered using heat exchangers on the power turbine exhaust gases (making it a Brayton-Rankine combined cycle power plant).

Since a gas generator has an efficiency of around 1/3, this turbine will need about 30 megajoule of chemical energy per second entering the combustors, or about one liter of jet fuel every 1.2 seconds. (Looked up jet fuel energy density on my phone while walking --- ain’t living in the future grand? In the past I'd have to look that up in Perry's or Marks'.)

Yes, the numbers are very rough approximations; that's what you do when walking around. I also picked numbers that would be easy to divide in my head. Remember, I had to avoid Pokemon Go players who kept moving in unpredictable patterns in my path:

Edited (about 30 minutes after posting): During my walk I incorrectly computed the power as 1 MW instead of 10 MW, basically because keeping a lot of zeros in your head while avoiding the Pokemaniacs is difficult. The original post used that value; while rereading it after posting, I realized my order-of magnitude error and corrected it and the fuel calculation.