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 sI thought TSLA batteries started at 75 kWh?! 🤔 Possible explanations:
250 kW * 300 s = 75 MJ
75 MJ = (60%-19%) * Capacity, or
Capacity = 183 MJ = 51 kWh
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
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."
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
