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.

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*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 October 9, 2019

Rotten Tomatoes and Batwoman

The day after the pilot, a familiar pattern emerges:

Using the same math as these two previous posts, it's 198,134,550 (almost 200 million) times more likely that the critics are using the opposite criteria to those of the audience than they both using the same criteria.

A couple of days later, more data is available:

This data makes the case even more stark: it's now 2,924,953,580,108 (almost three trillion!) times more likely that the critics are using the opposite criteria to those of the audience than they both using the same criteria.

And today (with a tip of the Homburg to local vlogging nerd Nerdrotics), it's even worse:

With this data (ah, the joys of reusable models, even if "model" is a bit of a stretch for something so simple, relatively speaking) we get that it's now 11,028,450,795,963,200 (eleven quadrillion!) times more likely that the critics are using the opposite criteria to those of the audience than they both using the same criteria.

For what it's worth, I liked the pilot, despite my nit-picking it on twitter:

Aerobics: The Paper that Started The Craze.

Here are three explanations that all match the data:

I. The official story: running develops cardiovascular endurance. This is the story that led to the aerobics explosion, to jogging, and to all sorts of "cardio" nonsense. Note that this story is isomorphic to "playing basketball makes people taller."

II. The selection effect story: people with good cardiovascular systems can run faster than those without. This is the "tall people are better at basketball than short people" version of the story.

III. The athletes are better at both story: people who have athletic builds (strong muscles, large thoracic capacity, low body fat) are better at both running and cardiovascular fitness because of that athleticism.

Most likely the result is a combination of these three effects, or in expensive words, the three variables (cardiovascular fitness, muscular development, and running ability) are jointly endogenous. Note also the big excerpt from Body By Science at the end of this post.

Let's take  a closer look at that table:

Not that I'm questioning Cooper's data (okay, I am), but isn't it strange that there are no cases when, say a runner with a distance of 1.27 mi had VO2max of 33.6? That the discrete categories on one side map into non-overlapping categories on the other? No boundary errors? That's an unlikely scenario.

Also, no data about the distribution of the 115 research subjects over the five categories. That would be interesting to know, since the bins for the distance categories are clearly selected at fixed distance intervals, not as representatives of the distribution of subjects. (It would be extremely suspicious if the same number of subjects happened to fall into each category. But if they don't, that's informative and important to the interpretation of the data.)

I know this was the 60s; on the other hand, the 60s were the first real golden age of large-scale data processing (with those "computer" things) and a market research explosion.

One of the factors that confounds these "cardio" results is that training for a specific test makes you better at that test. Another is that strengthening the muscles that are used in a specific motion makes that motion less demanding and therefore puts less strain on the cardiovascular system.

This excerpt from Body By Science illustrates both of these confounds:

Grant Sanderson (3 Blue 1 Brown) on prime number spirals

A late addition: Elon Musk promises PowerPacks for CA

Which brings up two thoughts:

a. Is "just waiting on permits" the new "funding secured"?

 

b. Each powerpack has 210 kWh capacity, so one charges ~3 Teslas, assuming they're low on charge but not zero. (Typical tank truck ~ 11,000 gal tops-up 733 x 15 gal gas tanks. Just FYI)