(More) random stuff
Can’t let the blog die so I sort of have to at least post something from time to time. So here goes…
1. Global sex ratios:
At birth: 1.07 male(s)/female
Under 15 years: 1.07 male(s)/female
15-64 years: 1.02 male(s)/female
65 years and over: 0.79 male(s)/female
Total population: 1.01 male(s)/female (2011 est.)
Here’s one for the whole population, image credit: Wikipedia (much larger version at the link):
I’ve from time to time read about the Chinese gender ratio problem, I didn’t know there were much going on on that score in India. The clustering of gender ratio frequencies seems in my opinion sufficiently non-random to merit some explanation or other, especially when it comes to the northern provinces (Punjab, Haryana & Kashmir). Here’s a pic dealing with more countries:
2. Gambler’s ruin. I remember having read about this before, but you forget that kind of stuff over time so worth rehashing. I think the version of the idea I’ve seen before is the first of the four in the article; ‘a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet.’ I assume all readers of this blog already know about the Gambler’s fallacy but in case one or two of you don’t already do click the link (and go here afterwards, lots of good stuff at that link and I shall quote from it below as well) – that one is likely far more important in terms of ‘useful stuff to know’ because we’re so prone to committing this error; basically the important thing to note there is that random and independent events are actually random and independent.
A couple of statistics quotes from the tvtropes link:
“The Science Of Discworld books have an arguably accurate but somewhat twisted take on statistics: the chances of anything at all happening are so remote that it doesn’t make sense to be surprised at specific unlikely things.”
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.” (Mark Twain. Maybe it’s more of a science quote really – or perhaps a ‘science’ quote?)
“People (especially TV or movie characters who are against the idea of marriage) often like to cite the “50 percent of marriages end in divorce” statistic as the reason they won’t risk getting hitched. That is actually a misleading statistic as it seems to imply that half of all people who get married will wind up divorced. What it doesn’t take into account is the fact that a single person could be married and divorced more than once in a single lifetime. Thus the number of marriages will exceed the number of people and skew the statistics. The likelihood that any one person chosen at random will be divorced during their lifetime is closer to 35 percent (the rate fluctuates wildly for males, females, educated and uneducated populations). It’s still a huge chunk of people, but not as high a failure rate for marriage for an individual as the oft-cited “50 percent of all marriages” statistic would leave you to believe.” (comment after this: “How can you give that setup and not deliver the punchline. “But the other half end in death!””)
“Black Mage: 2 + 2 = 4
Fighter: You can’t transform numbers into other numbers like that. It’d just go on forever. That’s like Witchcraft! “
3. Messier 87. Interesting stuff, ‘good article’, lots of links.
4. Substitution cipher. I’d guess most people think of codes and codebreaking within this context:
“In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the “units” may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the text by performing an inverse substitution.
Substitution ciphers can be compared with transposition ciphers. In a transposition cipher, the units of the plaintext are rearranged in a different and usually quite complex order, but the units themselves are left unchanged. By contrast, in a substitution cipher, the units of the plaintext are retained in the same sequence in the ciphertext, but the units themselves are altered.
There are a number of different types of substitution cipher. If the cipher operates on single letters, it is termed a simple substitution cipher; a cipher that operates on larger groups of letters is termed polygraphic. A monoalphabetic cipher uses fixed substitution over the entire message, whereas a polyalphabetic cipher uses a number of substitutions at different times in the message, where a unit from the plaintext is mapped to one of several possibilities in the ciphertext and vice-versa.”
The one-time-pad stuff related is quite fascinating; that encryption mechanism is literally proven unbreakable if applied correctly (it has other shortcomings though..).
“there’s only so much a human female pelvis can increase in terms of width before serious functional problems in locomotion make change in that direction unfeasible. [...] If the pelvis was prevented from getting any wider due to biomechanics, and a large adult brain was a necessary condition of high fitness value for humans, then one had to accelerate the timing of childbirth so that the neonate exited while the cranium was manageable in circumference.”
6. Random walk. The article actually has some stuff related to the previous remarks on gambler’s ruin.