#fun with math

[spankymerve]

One of the fun things about the lag operator (applied to a vector space of infinite sequences) is that every element of the field over which the vector space is defined is an eigenvalue. All sequences of the form x_(n+1) = a*x_n are eigenvectors, and their corresponding eigenvalues are a^-1, where a^-1 is a's multiplicative inverse (unless a = 0, in which case the corresponding eigenvalue is 0). In other words, any time series with constant growth (or shrinkage) is an eigenvector, and the corresponding eigenvalue is the inverse of the growth factor.

You can extend this logic to double-lags, in which case the eigenvectors remain the same, and the corresponding eigenvalues are a^-2, or n-lags, in which case the corresponding eigenvalues are a^-n. You can even extend this to the n-forward-shift operator, in which case the eigenvalues are a^n.

[surreality51]

Some lovely recent interviews, in which Zhu Yilong shares his views on acting and continues to be as confused as we are about our Zhu Yilong problem (4:06 in vid #1 and 0:58 in vid #2).

Some interesting perspective on his sudden rise in popularity this year:

Number of shares of posts on his official Weibo account (aka Chinese Twitter), pre-Guardian:

Number of shares of photos on his Weibo account now:

Interesting to note that the kudos have increased roughly 100%-400%, comments have increased about 1,900%, but the shares have increased ~18,000% (if I understand what those icons mean). Holy mackerel. I guess people like the visuals.

[quoththemaiden]

I'm amused by the implication that 1) Inui doesn't consider a one-person increase to be within the margin of error, and 2) he's butchered his math because going from 48 to 49 is actually a 2.08% increase which is obviously incredibly different from 1.75%.

(His actual line was 1.75倍, which means it increased by a factor of 1.75, not by 1.75%. It must have previously been 28, and he was gleeful to be able to announce an increase of precisely 75% when the 49th person showed up. But that isn't as funny.)

((Or maybe it's actually funnier. Good for him finding the joy in round numbers!))

[nimblermortal]

How Unlikely Is It That the Audits of Comey and McCabe Were a Coincidence? A Statistical Exploration.

The chances are minuscule. But minuscule is not zero.

This article was exactly what I wanted it to be from start to finish. A review of basic statistics; an examination of bias in framing the problem; snide digs at how certain people use Twitter; an elaboration of the original problem into graph form; and a calculator that allows me to determine the exact size of group that switches the resulting probability from 99.999% to >99% (157,746)

[taperwolf]

When I was very young, I read an essay in a children's encyclopedia that illustrated exponential growth by giving it as a reason for why there aren't vampires.

Suppose, they said, that on a given night there's one vampire in the world. Each night, that vampire bites a human, turning them into a vampire as well, who must do the same. If you do the math on that, you get your basic exponential progression — 1, 2, 4, 8, 16, 32, and so on — so if n is the number of nights since that first vampire was alone, the total number of vampires is 2^n, yielding, at the end of 33 nights, 8.6 billion vampires. And since that's more vampires than there are people in the world, and since the world is not currently overflowing with vampires, there can't be any such thing as vampires.

Even at 5, I could spot the flaw in that argument — no, you haven't disproven the existence of vampires, you've proven that vampires can't work the way they do in your made-up thought experiment. Maybe they don't have to bite somebody every night, or maybe they don't always make everybody they bite into vampires, or maybe there's some other unknown factor limiting their reproduction.

So I guess my point is that I'm still kind of miffed that Childcraft set me up like that, and I then had to suffer through the next eleven years before learning about Buffy.

[author-james-raisanen]

If you clone a muse to become b muse and put them in a group, would that make them c muse? Or would you need to clone b muse to make a three-muse band to get c muse?

[publiusmaximum]

It's my dad's birthday today.

He's 210 times the age of my kid. This tickles me.

[magnanimousman]

Give a Man a Fish

Last year Jeff Bezos donated 00.1% of his wealth to charity. At median income if an average Joe donated one one thousandth of their wealth annually, it would amount to a tax deductible $30. Now while 10% of Amazon employees in Ohio are on food stamps I can’t help but wonder... If you can give a man a fish, and call it charity, or teach a man to fish, and call it charity, can you give a man the scraps of a fish you just ate and call it charity? I wonder, if I took the remains of a salmon I ate if the remaining meat still clinging to the bones would constitute a larger or smaller portion of that fish, than say Jeff Bezos’ charitable donations as it relates to his net wealth. I could cook a fish, weigh it, eat it, weigh the bones, clean the bones for a final third weigh in, subtract that total from the first two, and then divide the total boneless weight of the fish against the scrap meat. I could do that, but I feel like even the possibility of a comparison speaks strongly enough for it’s self.