Si Tacuisses, Philosophus Mansisses: Fun With Numbers for Boxing Day, 2019

Some collected numerical fun from twitter to end the year.

As an amuse-bouche, if you're going to mock other people for their lack of intelligence, perhaps don't make trivial arithmetic errors…

(In accordance with my recent resolution to be more positive by not posting negative content, I didn't post this to twitter and I obscured the author.)

Geometry and trigonometry to the rescue

Scott Manley likes For All Mankind, but would like the producers to get the science right a bit more often:

Trust but verify, as they said in the Soviet Union:

In case the trigonometry isn't obvious, the angle (call it $\alpha$) is important to translate the horizontal measurements (say $l_1$ measured at $h_1$) into vertical distance via the magic of tangents: $\tan(\alpha/2) = l_1/(2 h_1)$ from where we get $h_1 = l_1/(2 \tan(\alpha/2))$.

The calculation above is actually for a FoV of 60° (camera), not 120° (eyes) as said in the text, because I used a hand calculator and post-its and transcribed the result from the wrong post-it; this result is about twice the correct result; for more accuracy, here are the different altitudes calculated [using a spreadsheet, like a proper responsible adult] as a function of what the angle taken by the big ship (around 50 m linear dimension) is:

(There are many approximations and precision trade-offs in the measurement, but SM's point holds: these are clearly different orbits and no one in the production or writing team seems to have noticed.)

It's only the equivalent of one to five .50-cal bullets...

The Hacksmith made one of those "how much dangerous nonsense can we post before YouTube throttles our channel" videos:

and I checked their Physics:

They replied on twitter that the maximum speed was over 2000 RPM, at which point I calculated that the kinetic energy was close to that of five .50-cal bullets.

What could go wrong, amirite?

(I like how the producers of Nikita [with Maggie Q, not La Femme Nikita with Peta Wilson] thought that the Styer HS .50 was an appropriate rifle for a shot through a window across a city street. Spoiler alert: it isn't; it's too much gun, in the words of Mike Ermentraut. The rifle looks gigantic next to Maggie Q, which is probably why they chose that caliber instead of something in .223 or .308 either of which would be more appropriate --- he said with all his marksmanship expertise acquired on the training fields of the xbox.)

Et tu, Arthur C. Clarke?

Usually A.C. Clarke's science is spot-on (excerpt from The Songs of Distant Earth),

but in this case, no:

(We could say that it's the captain of the Magellan that's wrong, perhaps exaggerating for effect, not A.C. Clarke, but that's a cop-out.)

Here's an example of A.C. Clarke getting much harder science right, from Rendezvouz with Rama (an old tweet, from the era when I wasn't blogging):

(I mean, what kind of nerd does numerical integration to check on the feasibility of a scifi author's solution to a minor plot point just to post it on twitter? This guy! 🤓 [Pointing both thumbs at self.])

Tidal turbines and bad interpretation of statistics

Real Engineering had an interesting video about tidal turbines:

But I had an issue with the conclusions from the impact study, because they repeat a common error: mistaking statistical significance (or lack thereof) for effect size. This point deserves a better treatment, but for now here's a simple example:

The energy density of the ocean, like other renewables, is still a bit on the low side. Compared to Canadian actinides, it's certainly lacking:

Carbon capture wonky accounting

The XPrize has a video on "Everyday Products Made Out of Thin Air":

I like the Xprize and the ideas behind it, but most of these 'carbon capture products' are complete nonsense. The CO2 footprint for the processes that make and market the product is much larger than captured CO2. In other words, these products harm the environment by increasing the total CO2 output.

(Yes, I've covered this before, on one of the rare occasions I agreed with Thunderf00t.)

If you create say 1000 tonnes of CO2 building a factory to make a product that captures 100 g of carbon per unit, you need to make over 2.7 million units just to capture the CO2 created by building the factory alone! (If the product has 100 g of carbon, that came from 44/12*100 = 367 g of CO2.) Not counting the footprint of packaging, delivery, etc.

(This is the same accounting problem that people have comparing the CO2 footprints in production of wind turbines and gas turbines. If the gas turbines already exist and the wind turbines don't, the CO2 footprint of building them has to enter the calculation [but never does…].)

Note also that the products aren't made of 100% carbon, so the correct accounting for how much CO2 they capture would necessitate accounting for the CO2 footprint of the other components and their delivery — usually to a net creation of CO2 by these 'capture' products just in this manner.

Let us not forget delivery; even if we just consider local delivery with a city van (like those that are always blocking traffic in San Francisco by being double-parked in awkward places, not that traffic moves in San Francisco, vans or no vans), the numbers aren't encouraging:

A Ford Transit cargo van is rated for 25 MPG in the city. Assuming that gasoline is 100% trimethylpentane for simplicity, burning 1 kg of gasoline yields 3.1 kg of CO2. One gallon of gasoline is 2.86 kg (3.79 l * 0.755 kg/l) so 100 miles of delivery route has a 35.5 kg CO2 footprint. If each product unit has 100 g of carbon captured (367 g of CO2), it takes 97 units in that delivery route just to make up for the delivery itself.

Here are some real carbon capture products: first some really big ones a little bit south of the Bay Area