Today’s error message of the day:

17:54:01,994 WARN [JBossASSecurityMetadataStore] WARNING! POTENTIAL SECURITY RISK. It has been detected that the MessageSucker component which sucks messages from one node to another has not had its password changed from the installation default. Please see the JBoss Messaging user guide for instructions on how to do this.

Say what you will about technology, but there’s something wonderfully sweet about a world where the term “mathematic attacks” can be taken seriously.

Ruby lets you do the strangest things.

  
  class NilClass
    def val
      @val||=0
      @val+=1
    end
  end
  
  Array.new(10).map{|x|x.val}   ## => [1,2,3,4,5,6,7,8,9,10]
  

$100 to anybody who can go to RubyConf and give a scheduled talk about hiding variables in nil under the pretense of security. $200 for talking for the entire designated time without getting thrown out.

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.

I 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:

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

• P₂(1) = P₁(P₁(1)) = 3
• P₂(2) = P₁(P₁(2)) = 5
• P₂(3) = P₁(P₁(3)) = 11

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:

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.

Inspired 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”.

By 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.

Right 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.

I enjoy anything that can give meaning to really large numbers. For example, the fractal program I recently started has generated the following image:

If we take this image to be roughly six inches across (an idea easier to accept if you click and view the enlarged version), and try to describe the size of the entire fractal at that scale, it turns out to be so large that if you start with some object whose length is the diameter of the observable universe, it would take ten million of these objects for every possible chess position (the Wikipedia puts the number of chess positions at approximately 10⁵⁰) laid end to end to span it.

And I only just started a couple weeks ago.

irb(main):001:0> “this is fun”.gsub("",“yep”).gsub("",“it is”) => “it isyit iseit ispit istit isyit iseit ispit ishit isyit iseit ispit isiit isyit iseit ispit issit isyit iseit ispit is it isyit iseit ispit isiit isyit iseit ispit issit isyit iseit ispit is it isyit iseit ispit isfit isyit iseit ispit isuit isyit iseit ispit isnit isyit iseit ispit is”