The Universe of Discourse

Wed, 25 Sep 2013

In which I revisit the pastimes of my misspent youth
Last weekend I was at a flea market and saw an HP-15C calculator for \$10. The HP-15C was the last pocket calculator I owned, some time before pocket calculators became ridiculous. It was a really nice calculator when I got it in 1986, one of my most prized possessions.

I lost my original one somewhere along the way, and also the spare I had bought from a friend against the day when I lost the original, and I was glad to get another one, even though I didn't have any idea what I was going to do with it. My phone has a perfectly serviceable scientific calculator in it, a very HP-ish one called RealCalc. (It's nice, you should check it out.) The 15C was sufficiently popular that someone actually brought it back a couple of years ago, in a new and improved version, with the same interface but 21st-century technology, and I thought hard about getting one, but decided I couldn't justify spending that much money on something so useless, even if it was charming. Finding a cheap replacement was a delightful surprise.

Then on Friday night I was sitting around thinking about which numbers n are such that !!10n^2+9!! a perfect square, and I couldn't think of any examples except for 0, 2, and 4. Normally I would just run and ask the computer, which would take about two minutes to write the program and one second to run it. But I was out in the courtyard, it was a really nice evening, my favorite time of the year, the fading light was beautiful, and I wasn't going to squander it by going inside to brute-force some number problem.

But I did have the HP-15C in my pocket, and the HP-15C is programmable, by mid-1980s programmable calculator standards. That is to say, it is just barely programmable, but just barely is all you need to implement linear search for solutions of !!10n^2+9 = m^2!!. So I wrote the program and discovered, to my surprise, that I still remember many of the fussy details of how to program an HP-15C. For example, the SST button single-steps through the listing, in program mode, but single-steps the execution in run mode. And instead of using the special test 5 to see if the x and y registers are equal you might as well subtract them and use the x=0 test; it uses the same amount of program memory and you won't have to flip the calculator over to remember what test 5 is. And the x2 and INT() operations are on the blue shift key.

Here's the program:

        001 - 42,21,11
002 -    43 11
003 -        1
004 -        0
005 -       20
006 -        9
007 -       40
008 -       36
009 -       11
010 -       36
011 -    43 44
012 -       30
013 -    43 20
014 -       31
015 -    43 32
016 - 42,21,12
017 -       40
018 -    45  0
019 -    32 11
020 -        2
021 - 44,40, 0
022 -    22 12

I see now that when I tested !!\sqrt{10n^2+9}!! for integrality, I did it the wrong way. My method used four steps:
        010 -       36   -- push stack
011 -    43 44   -- x ← INT(x)
012 -       30   -- subtract
013 -    43 20   -- test x=0 ?

but it would have been better to just test the fractional part of the value for zeroness:
                 42 44   -- x ← FRAC(x)
43 20   -- test x=0 ?

Saving two instructions might not seem like a big deal, but it takes the calculator a significant amount of time to execute two instructions. The original program takes 55.2 seconds to find n=80; with the shorter code, it takes only 49.2 seconds, a 10% improvement. And when your debugging tool can only display a single line of numeric operation codes, you really want to keep the program as simple as you can.

Besides, stuff should be done right. That's why it's called "right".

But I kind of wish I had that part of my brain back. Who knows what useful thing I would be able to remember if I wasn't wasting my precious few brain cells remembering that the back-step key ("BST") is on the blue shift, and that "42,21,12" is the code for "subroutine B starts here".

Anyway, the program worked, once I had debugged it, and in short order (by 1986 standards) produced the solutions n=18, 80, 154, which was enough to get my phone to search the OEIS and find the rest of the sequence. The OEIS entry mentioned that the solutions have the generating function

$$\frac{2x^2(1+2x+9x^2+2x^3+x^4)}{1-38x^3+x^6}$$

and when I saw that !!38x^3!! in the denominator, I laughed, really loudly. My new neighbor was in her back yard, which adjoins the courtyard, and heard me, and said that if I was going to laugh like that I had to explain what was so funny. I said “Do you really want to know?” and she said yes, but I think she was mistaken.

Sat, 18 Sep 2010

The coming singularity
A Wikipedia user asked on the Wikipedia reference desk page:

You know the idea that eventually we'll be able to download our brains/personalities to computer, to achieve physical immortality?
There is a big trouble with this version of the immortality thing that people rarely mention. You go to the scanning and uploading center one day and write them a check. They scan and upload your brain, and say "All done, time to go home!"

"That's it?" you say. "I don't feel any different."

"Well, of course not. You're no different. But the uploaded version is immortal."

Then you go home and grow old, and every once in a while you get an email:

	From: Mark Dominus (Immortal version) <mjd@forever.org>
Subject: Wish you were here

Having a great time here in paradise! Haven't aged a day.
Thanks!

Or maybe one like this:

	From: Mark Dominus (Immortal version) <mjd@forever.org>
Subject: Guess what I just did?

Today I had sex with Arthur C. Clarke while swimming in a
giant hot-fudge sundae. It was totally awesome! Too bad you
couldn't be here. I know exactly how much you would
have enjoyed it.

Sorry to hear you're sick.  Hope the chemo works out.

Then you die, and some computer program somewhere simulates the immortal version of you having a little ritual observance to mark your passing.

Sometimes the proponents of this scheme try to conceal this enormous drawback by suggesting that they obliterate the original version of you immediately after the upload. Consider carefully whether you believe this will improve the outcome.

Thu, 08 May 2008
 Order The Origin of Consciousness in the Breakdown of the Bicameral Mind with kickback no kickback
One of my favorite books is The Origin of Consciousness in the Breakdown of the Bicameral Mind, by Julian Jaynes, a psychologist at Princeton University. Nearly everyone seems to agree that this is either a work of profound genius, or of profound crackpottery, and also that they aren't sure which it is. Jaynes' theory, as nearly as I can summarize the book, is something like this:

Human consciousness (which Jaynes describes and defines in considerable detail) is a relatively recent development, dating back at most only about 3,000 years or so.

That is the shocking part of the theory. Most people probably imagine consciousness arising much, much earlier, perhaps before language. Jaynes disagrees. In his theory, language, and in particular its mediation of thought through the use of metaphors, is an essential prerequisite for consciousness. And his date for the development of consciousness means that human consciousness would postdate several other important developments, such as metalworking, large-scale agriculture, complex hierarchical social structures, and even writing. Jaynes thinks that the development of consciousness is a historical event and is attested to by written history. He tries to examine the historical record to find evidence not only of preconscious culture, but of the tremendous upheavals that both caused and were the result of the arrival of consciousness.

If preconscious humans farmed, built temples and granaries, and kept records, they must have had some sort of organizing behavior that sufficed in place of consciousness. Jaynes believes that prior to the development of consciousness, humans had a very different mentality. When you or I need to make a decision, we construct a mental narrative, in which we imagine ourselves trying several courses of action, and attempt to predict the possible consequences. Jaynes claims that Bronze Age humans did not do this. What then?

Instead, says Jaynes, the two halves of the brain were less well-integrated in preconscious humans than they are today. The preconscious mentality was "bicameral", with the two halves of the brain operating more independently, and sometimes at odds with each other. The left hemisphere, as today, was usually dominant. Faced with a difficult decision, preconscious human would wait, possibly undergoing (and perhaps even encouraging) an increasingly agitated physical state, until they heard the voice of a god directing them what to do. These hallucinated voices were generated by the right hemisphere of the brain, and projected internally into the left hemisphere.

For example, when the Iliad says that the goddess Athena spoke to Achilles, and commanded and physically restrained him from killing Agamemnon, it is not fabulating: Achilles' right brain hallucinated the voice of the Goddess and restrained him.

In Jaynes' view, there is a large amount of varied literary, anthropological, and neurological evidence supporting this admittedly bizarre hypothesis. For example, he compares the language used in the Biblical Book of Amos (bicameral) with that in Ecclesiastes (conscious). He finds many examples of records from the right period of history bewailing the loss of the guidance of the gods, the stilling of their voices, and the measures that people took, involving seers and prophets, to try to bring the guiding voices back.

Jaynes speculates that mental states such as schizophrenia, which are frequently accompanied by irresistible auditorily hallucinated commands, may be throwbacks to the older, "bicameral" mental state.

Whether you find the theory amazingly brilliant or amazingly stupid, I urge to to withhold judgment until you have read the book. It is a fat book, and there is a mass of fascinating detail. As I implied, it's either a work of profound genius or of profound crackpottery, and I'm not sure which. (Yaakov Sloman tells me that the response to Wittgenstein's Tractatus Logico-Philosophicus was similarly ambivalent when it was new. I think the consensus is now on the genius side.) Either way, it is quite fascinating. There needs to be some theory to account for the historical development of consciousness, and as far as I know, this is the only one on offer.

Anyway, I did not mean to get into this in so much detail. The reason I brought this up is that because of my continuing interest in Jaynes' theory, and how it is viewed by later scholars, I am reading Muses, Madmen, and Prophets: Rethinking the History, Science, and Meaning of Auditory Hallucination by Daniel B. Smith. I am not very far into it yet, but Smith has many interesting things to say about auditory hallucinations, their relationship to obsessive-compulsive disorder, and other matters.

On page 37 Smith mentions a paper, which as he says, has a wonderful title: "Involuntary Masturbation as a Manifestation of Stroke-Related Alien Hand Syndrome". Isn't that just awesome? It gets you coming and going, like a one-two punch. First there's the involuntary masturbation, and while you're still reeling from that it follows up with "alien hand syndrome".

To save you the trouble of reading the paper, I will summarize. The patient is a 72-year-old male. He has lesions in his right frontal lobe. He is experiencing "alien hand syndrome", where his hand seems to be under someone else's control, grabbing objects, like the TV remote control, or grabbing pieces of chicken off his plate and feeding them to him, when what he wanted to do was feed himself with the fork in his right hand. "During his hospital stay, the patient expressed frustration and dismay when he realized that he was masturbating publicly and with his inability to voluntarily release his grasp of objects in the left hand."

Reaction time tests of his hands revealed that when the left hand was under his conscious control, it suffered from a reaction time delay, but when it was under the alien's control, it didn't.

Whee, freaky.

Sun, 24 Jun 2007

Do you dream in color?
People have occasionally asked me whether I dreamt in color or on black-and-white, by which I suppose they meant grayscale. This question was strange to me the first time I heard it, because up to then it had not occurred to me that anyone did not dream in color. I still find it strange, and I had to do a Google search to verify that there really are people who claim not to dream in color.

One time, when I replied that I did dream in color, my interlocutor asked me if I was sure: perhaps I dreamt in black and white, but only remembered it as being in color later.

I am sure I dream in color, because on more than one occasion I have had discussions in dreams about colors of objects. I can't remember any examples right now, but it was something like this: "Give me the red apple." "Okay, here." "That is not the red apple, that is the green apple!" And then I looked and saw that the apple I had thought was red was really green.

One could still argue that I wasn't really dreaming in color, that it only seemed like that, or something. It's a delicate philosophical point. One could also argue that I didn't have any dream at all, I only thought I did after I woke up. I suppose the only refutations of such an argument either appeal to neurology or involve a swift kick in the pants.

And then suppose I have a dream in which I take LSD and have marvelous hallucinations. Did I really have hallucinations? Or did I only dream them? If I dream that I kill someone, we agree that it wasn't real, that a dream murder is not a real murder; it is only in your head. But hallucinations, by definition, are only in your head even when they are real, so don't dream hallucinations have as much claim to reality as waking hallucinations?

One might argue that dreamt LSD hallucinations are likely to be qualitatively very different from real LSD hallucinations—less like real LSD hallucinations, say, and more like, well, dreams. But this only refutes the claim that the dream hallucinations were LSD hallucinations. And nobody was going to claim that they were LSD hallucinations anyway, since no actual LSD was involved. So this doesn't address the right question.

Stickier versions of the same problem are possible. For example, suppose I give Bill a little piece of paper and tell him it is impregnated with LSD. It is not, but because of the placebo effect, Bill believes himself to be having an LSD trip and reports hallucinations. There was no LSD involved, so the hallucinations were only imaginary. But even real hallucinations are only imaginary. Are we really justified in saying that Bill is mistaken, that he did not actually hallucinate, but only imagined that he did? That seems like a very difficult position to defend.

I seem to have wandered from the main point, which is that I had another dream last night that supports my contention that I dream in color. I was showing my friend Peter some little homunculi that had been made long ago from colored pipe cleaners, shiny paper, and sequins by my grandmother's friend Kay Seiler. Originally there had been ten of these, but in the dream I had only five. When my grandmother had died, my sister and I had split the set, taking five each. In place of the five originals I was missing, I had five copies, which were identifiable as such because they were in grayscale. Presumably my sister had grayscale copies of the originals I retained. I explained this to Peter, drawing his attention to the five full-color homunculi and the five grayscale ones.

So yes, barring philosophical arguments that I think deserve a kick in the pants, I am sure that I dream in color.