The Packbats' Weblog

Does anyone know why, when a MacBook Core 2 Duo running 10.5.8 crashes hard - so hard that even a Vulcan nerve-pinch is ineffective - that the iTunes will keep playing until it finishes the song?

Question for the day: what's your favorite deleted scene from a movie?

For me, it's a tie between the bit that was edited out of the ending sequence in Dead Again and the alternate ending of The Sixth Sense.

Edit: Comments may contain spoilers. (Duh.)

Reposted from my Facebook:

Imagine the following scenario (a variation on the classic dilemma known as Newcomb's Problem):

About six months ago, a crack team of psychologists came up with a brilliant new device, and decided to run a curious experiment to test it. The experiment takes the following form:

1. Each subject, chosen by lottery, is provided with the money to purchase two identical plain manilla envelopes.
   
2. They and their envelopes are given free transportation to the lab, where they (but not the envelopes) fill out a survey.
   
3. They wait approximately one hour, and then are ushered into the experiment room.
   
4. In that room, they are permitted to examine three stacks - one containing twenty U.S. fifty-dollar bills, one containing twenty fifty-dollar-bill-sized pieces of blank U.S. fifty-dollar-bill stock, and one containing one thousand U.S. one-thousand-dollar bills.
   
5. An attendant removes the stack of thousand-dollar bills. They are instructed to privately place one of the remaining stacks in each of their manilla envelopes, so that they would have two apparently-identical envelopes, and then signal.
   
6. On the signal, the attendant returns with a case, which either does or does not contain the million dollars. The subject then gives either of their two envelopes in return for the case.

There is only one catch in this procedure: the case either contains blank bills or the million, as follows. If the psychologists predict the subject would return the envelope with the thousand dollars, the case contains the million. But if the psychologists predict that the subject will return the envelope with the blank paper, the case contains blank paper. And in each of the one hundred trials so far, the psychologists have always gotten it right. Everyone has either left with the thousand or left with the million.

(Edit: Well, not quite. A few clever people thought to randomize the envelopes so that they didn't know whether they lost the thousand or not. About half of them walked away with a thousand, the other half with nothing.)

The experiment is valid - it has been tested by dozens of experts in experimental protocol, sleight of hand, hypnotism, and every other relevant field. They neither coerce your choice nor switch out the million if you choose to keep the thousand.

You are in the room, with your two envelopes, and the attendant is before you with his case.

Do you give him the thousand dollars or the blank paper?

Surprisingly topical for a Sunday, the following question, reposted from thequestionclub:

Inspired by a thread on IIDB, a two-part question:

1. Do you believe that at least one god is real? (For purposes of this question, interpret the word "real" as per Eliezer Yudkowsky's The Simple Truth.)

2. a. (For those of you who answered "yes" to the above:) Describe this god (or a few of the most important gods, if you ascribe to a more-than-one-god theory) to the best of your ability. If you are unsure, say, "I'm not certain of this, but I believe [...] with X confidence". If you cannot find the words, say, "I don't know if I can express this properly, but it is something like [...]". If you are tempted to say nothing at all, please: say something, however incredibly hedged. I specifically promise not to judge anything you say in any comment I make on this post. Just say what you believe.

b. (For those of you who answered "no" to the above:) Describe the characteristics that something would have to have to be called a god. Does it need to be a person? (Would being a person help?) Does it need to be able to subvert the laws of physics? Does it need to be benevolent?

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Unlike on the post on thequestionclub (edit: which is here if you are curious), anonymous comments are allowed and unscreened, and I've temporarily disabled IP logging. Feel free to weigh in however you feel comfortable!

Because the question is too pressing to be left unasked.

[Poll #1157201]

In the comments on my artist-QOTD post, jfs gave a good definition of art: art occurs whenever a person creates something whilst trying to evoke an emotional reaction. I was just thinking about the specifics of that - why "emotional" reaction, what kinds of reactions can/does art make, what kind of moral value should we ascribe to the methods and contexts of these reactions ... I don't know if this will be coherent, but it might be interesting interest.

I guess I'll start with Dan Brown and Myst. No - I'll start with Agatha Christie and Myst; it's wrong to snipe at works you haven't perused.

Wait - no, the point doesn't really work with Agatha Christie. I'd better just start somewhere, and let the chips fall as they may.

One purported property of Dan Brown's writing is that it makes the reader feel clever. Specifically, The Da Vinci Code is accused of making its readers feel clever by showing them stupid puzzles. Assuming "feeling clever" is an emotional reaction (not much of a stretch, I think), I point out the following:

• Assuming it was on purpose, The Da Vinci Code is art.


• In addition, The Da Vinci Code is successful art in the evocative¹ sense, not merely in the financial sense.


• It is being criticized for the way it evokes these feelings - its critics say it should not make the reader feel clever in this way, presumably because the reader does not earn feeling clever.

"Hey," my brain said. "What about Myst? It does take a little cleverness to solve those puzzles - isn't feeling clever justified there?"

I'm not going to divert to the obvious moral, here. (I was tempted, mind - any excuse to plug Indigo Prophecy/Fahrenheit is welcome.) Instead, I think we should consider where this idea of justification of art, in this earned-emotion sense, leads. Is the emotional climax of Terminator 2 justified? What about the excitement and satisfaction of a good game of Grand Theft Auto: Vice City? Or of a good performance of Beethoven's Symphony No. 5 in C minor? Or, on a more abstract note: are we justified in evaluating these works and the reactions they evoke? Or, higher still: are we justified in rejecting such evaluations as unworthy, or unnecessary, or inappropriate?

Comments are open.

1. "Evocative of emotional reactions". Hey, I wanted something short and snappy. ^

So, first color version of a possible cover:



I have chosen the title as well – "The Device", no relation to the album or the band – and a masthead:



As for what the contents will be ... I have no idea*. Suggest something?

* Not strictly true. The first installment of Jeffrey 'Channing' Wells's "Chicken And Stars" might well be featured prominently.

Too little stuff for a complete update*, but a few funny things:

• The guy (vaguely African-seeming, but I wouldn't really know) who said he was 'good at math', but needed help with 'translations'. 'Translations', in this case, being along the lines of:
  

  Fill in the blank with the appropriate word phrase: "a - b" means b ______ a.

  
  I begged off, saying I had to finish my art assignment^†, and gave him directions to the mathematics building^‡.
  
• My ankles hurt so much afterwards, I could barely move.
  
• What does the question of whether you can know something absolutely as a truth have to do with abortion? No, I'm serious, I still can't figure that one out.
  
• If a bank can lend out 90% of the money deposited therein, adding $100 to the bank's lending stock adds $1000 to circulation by a simple geometric series (r = 0.9) ... if all the money in circulation is redeposited deposited in the bank. So, what is the point of this exercise, exactly? And why are the business students still being tested on it?
  
• "At schema yourself resemblant". There – now I've posted a nonsensical spam subject line too.

Ta!

* Says the guy who just posted a one-line update consisting of a single link.^§
† Which means this probably occurred Sunday afternoon.
‡ He'd actually started off asking for directions, then asked me if I could help him solve the problems. I carefully refused to sit in his car out of the cold while I looked at his stuff.
§ Which, incidentally, has both shown me a whole lot of tracks I might be interested in, and that I know nothing about electronic music at all. Neither of which surprised me. I was glad to see that "synth pop" was the correct category for Eurythmics, though.

I was lying in bed the other night thinking about bases of arithmetic....

You know, it's kinda odd that insomnia due to math isn't that rare, for me.

Anyway, I was thinking about bases of arithmetic, and Hal Clement's throwaway gag in Still River* about an ancient academic controversy over octal versus duodecimal at the School in his story, and the problem of factoring, and how weak the theoretic justifications for all those specific bases are.

You may be surprised at this claim. "But octal is clearly the most rational," you might be saying. "Binary is the most fundamental base of arithmetic, and octal is a logical extension of that."

Uh-huh. Logical extension how, exactly? If you've got an old 24-bit mainframe?

"That just implies hexadecimal is even better."

Yeah, okay, but that's still just one advantage – convenient relation to binary. Besides, larger bases get more and more inconvenient as you have to memorize more and more figures and (more importantly) bigger and bigger multiplication tables. So hex is great for computer scientists, and octal used to be great for computer scientists, but that doesn't translate to their being the best day-to-day radices. They've got one advantage – one huge advantage – but it's only a useful advantage in a few contexts.

And when we turn to duodecimal, base 12 (and its cousin, sexagesimal, base 60), we find a similar sole advantage: the base has many factors. Yeah, that's great if you're writing fractions – 1/3 becomes 0.4_duodecimal, 4/15 becomes [00].[16]_sexagesimal (each bracket is a decimal representation of one figure), etc. – but how often do you need to?

Actually, that gets to the key point: what do you need to do regularly with a number system? Really, it comes down to:

• Write.
  
• Add.
  
• Subtract.
  
• Multiply.
  
• Divide.
  

...pretty much in that order. I mention "write" because while messing with the basic principle of positional notation may be fun, standard positional notation is a pretty solid, intuitive way to write down how many books you have on the second shelf of your bookcase.** And while binary may be logically the simplest radix, 10101 takes up a lot more space than 21†. (Oh, and just coming up with symbols for a sexagesimal system is horrid, forgetting all its other disadvantages.)

So, what about these others? Well, we're only looking at standard positional systems, so whatever advantages balanced ternary systems have, we're ignoring them. Anyway, in standard positional systems, 'add' and 'subtract' pretty much make only one contribution to complexity: how many digits are in your basic addition tables. And since we humans have shown that we can handle base 10 pretty well, anything up to around that size is probably fine. Multiplication is almost the same, but there's an advantage for highly composite (and not-quite-highly composite) radices – all the rows with divisors of the base are simpler. (I guess that means duodecimal isn't quite as pointless as I thought.) Division – well, you're doing long division, so have to come up with a compromise between having fewer digits (higher radix) and fewer multiples of the denominator (lower radix). Oh, and having lots of divisors means fewer recurring 'decimals'.

This sounds like it's building up to sell duodecimal after all. No, it isn't.

I'm saying we should use senary. Base six.

The actual inspiration for this came that night, when I was comparing duodecimal and octal to decimal. Duodecimal, I had decided, had the advantage of many factors. Octal, of being a power of 2. But what about decimal?

Well, as it happens, I had already realized that decimal was unusually good at testing divisibility. As it happens, there are two types of numbers that are very easy to check divisibility of in a given base: factors of the base, and adjacent natural numbers to the base. In decimal, the first group consists of 2, 5, and 10. The latter group consists of 9 and 11. Divisibility by the first set can be checked through examining the final digit – an even digit means multiple of 2, 5 or 0 mean multiple of 5, 0 means multiple of 10. This is really easy – in big O notation, it's O(1), meaning it takes a constant length of time for any number. As for 9 and 11, it's easy to prove from modulo arithmetic that you need merely add all the digits (for 9 – 'casting out nines', basically) or alternately add and subtract (for 11) to check divisibility. These are both O(log n) – the time they take is proportional to the length of the number, written out.‡

Now, all bases get the benefits of these two effects. But because 9 is a power of 3, in base 10 this means that testing divisibility by 2, 3, 5, and 11 is easy. Four of the first five prime factors, accounting for 75.76% of all numbers. That's pretty good – only missing the seven. Duodecimal only gets 2 and 3 from its factors, and 11 and 13 from the casting-out methods, so it misses five and seven. Octal would get seven, of course (one less than the base), but it only has two as a prime factor and nine = three squared as one over the base, so it misses five.

But six doesn't. It misses eleven, but with seven it gets 77.14%, better than base 10, which beat bases 8 and 12. It's smaller than 10, which means only six symbols and 21 unique entries each on the addition and multiplication tables. (It would be 36, but since 2+3 = 3+2 and 2*3 = 3*2, a large fraction drop out.) Being smaller also makes long division easier – you need only write 5 multiples of the divisor, instead of 9. Against that, you've got longer numbers, but even when you get pretty large (e.g. the age of the universe, 13.7 billion years), it's not a big difference (13 senary figures as opposed to 11 decimal figures). Being divisible by 2 and 3 means 1/2, 1/3, and 1/4 are all easy (1/4 = 0.13_senary), and adds extra simplicity to two rows of the multiplication table (which has only six to start with, including the ones row).

Add these factors together, and I think that makes 6 the perfect base.^§


But hey, who cares what I think!

[Poll #924107]

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* Which is actually a pretty lame book, on rereading, but I still like it.
** Not that bijective numerations are that hard to count in – I just didn't want every link to be to Wikipedia.
† I'm not counting the Adobe Photoshop manual in this count.
‡ Which, you must note, is often much less than the number itself.
^§ Yes, I did in fact spent seven hours writing a long, technical discussion of the relative merits of five different systems of positional notation, combined with an a priori enumeration of the most important principles of a number system, just so I could conclude with that sentence. I regret nothing!

From active_apathy.

( First, a couple questions for demographic purposes... )