I was recently required to choose between a handful of retirement-plan vendors, so I’ve had some information booklets lying around. One day on a stroke of pure reckless abandon, I decided to read a couple of the privacy policies, just to see what it said. Of the two I read, MetLife’s struck me as most interesting.
For instance, one of the reasons they list for why they might have to share information is to “help us prevent […] terrorism […] by verifying what we know about you.” Not to mention the all-inclusive reason: “Help us run our business”.
Then there’s “How We Get Information”. I may as well quote verbatim here:
What we know about you we get mostly from you. But we may also have to find out more from other sources to make sure that what we know is correct and complete. Those sources may include adult relatives, employers, consumer reporting agencies and others. Some sources may give us reports and may disclose what they know to others.
(emphasis mine)
As a software engineer, I’m particularly struck by the specificity of their method for protecting computer data: “We also take steps to make our computer data bases secure and to safeguard the information we have.” Good. I’m glad they’ve taken steps. The other privacy policy I read listed five specific techniques they use to protect computer data.
I didn’t choose MetLife.
This makes me want to start a Privacy-Wiki where people can read privacy policies and EULAs and create summaries for mass consumption. That’d make it harder for companies to hide things.
Very Prime Primes
2010-02-08I just finished the Math Book, which means I've done a lot of reading about various mathematical discoveries, which means I'm feeling terribly jealous that I couldn't have discovered any of them myself (since of course half of them look obvious in hindsight).
So to help myself cope I'm going to pretend I discovered something interesting. Here's how it goes:
This sequence isn't in the Encyclopedia of Integer Sequences, so that must mean that I've discovered something interesting. Couldn't possibly mean anything else. I'm sure it's just been overlooked up till now.Define a sequence of numbers called P1, which are simply the prime numbers (so P1(1) = 2, P1(2) = 3, P1(3) = 5, etc.). Then define a second sequence P2 which simply indexes P1 into itself, so
These are the prime-primes - the primes whose indices are also prime (i.e., the 2nd prime, the 3rd prime, the 5th prime, the 7th prime, the 11th prime, etc.). Of course the next step is to do this again. And again. Which gives us the following infinite sequence of infinite sequences:
- P2(1) = P1(P1(1)) = 3
- P2(2) = P1(P1(2)) = 5
- P2(3) = P1(P1(3)) = 11
P1 2 3 5 7 11 13 17 19 ... P2 3 5 11 17 31 41 59 67 P3 5 11 31 59 127 179 277 331 P4 11 31 127 277 709 1063 1787 2221 P5 31 127 709 1787 5381 8527 15299 19577 P6 127 709 5381 15299 52711 87803 167449 219613 P7 709 5381 52711 167449 648391 1128889 2269733 3042161 P8 5381 52711 648391 2269733 9737333 17624813 37139213 50728129 ... Finally we define a new sequence by taking the sum of the top-right to bottom-left diagonals (which I striped colorfully for your convenience):
2, 6, 15, 40, 121, 484, 2589, 18896, 180243, 2176090, 32236017, 571516348
Anyways, if you factor the numbers, it looks like it might be mildly interesting:
- 2 = 2
- 6 = 2·3
- 15 = 3·5
- 40 = 2·2·2·5
- 121 = 11·11
- 484 = 2·2·11·11
- 2589 = 3·863
- 18896 = 2·2·2·2·1181
- 180243 = 3·3·7·2861
- 2176090 = 2·5·7·7·4441
- 32236017 = 3·11·976849
- 571516348 = 2·2·13·89·123491
Stupid math.
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Self-Describing
2010-01-30Inspired by a recent xkcd, I’ve constructed a self-describing blog post. This post has seven hundred and seventy-two characters, six hundred and three of which are letters. Three hundred and ninety-one of those are consonants, and the other two hundred and twelve are vowels. There are thirty-three ’d’s, forty-four ’h’s, thirty-one ’i’s, and fifty-four ’n’s. The fifth sentence has thirteen fewer vowels than the third sentence. The seventy-first word is “frenzy”, and the five hundred and sixteenth character is ‘%’. The next sentence has eighty-six letters. The previous sentence has thirty-four letters, and the first comment has one hundred and twenty letters. The letters ‘j’ and ‘q’ only appear once in the entire post. The first and last words are both “inspired”.
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Venn Diagram for Real Numbers
2010-01-20By popular demand, I’m posting a Venn Diagram illustrating the relationship between the commonly-named subsets of real numbers:
The two rectangles are merely labels for the similarly shaded parts of the ovals. So the two green sections are the irrational numbers, and the gridded section is the transcendental numbers. Irrational could be defined as “not rational” and transcendental could be defined as “not algebraic”. If anybody knows of a clearer way to venn-diagram these sets, I’d be interested to see it.
Note that as far as infinite cardinalities go, the six terms fall into two different sizes: Integers, Rationals and Algebraic numbers are the same size, and are each smaller than the Irrationals, Transcendentals, and Reals, which are the same size as each other.
Remind me to write a post about how there are as many points on an inch-long line segment as there are in the entire universe.
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Tetris Tile Trees
2009-12-26Right when I was about to start working on a major improvement to the Mandelbrot program, I was struck with an itch to write a JavaScript applet that takes an arbitrarily shaped grid and tries to tile it with tetris pieces, using standard techniques for traversing search trees. So here it is.
I think it turned out pretty well for the amount of time I put into it. There’s at least one more significant optimization I hope to make, which takes advantage of the fact that connected components are independent.
So that’s all.
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