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Columns > David Steinberg - Some Are Mathematicians

Published: 1999/02/15
by David Steinberg

The Wheel is Turing

Grand Master Turing once dreamed that he was a machine. When he awoke he exclaimed:

“I don’t know whether I am Turing dreaming that I am a machine, or a machine dreaming that I am Turing!.”

-The Tao of Progamming

What separates people from machines? Artificial Intelligence projects have been going on for decades, and yet they still haven’t produced anything that can pass a Turing Test1. The best that programmers have managed is to vaguely simulate the thought process in extremely limited environments. Douglas R. Hofstadter in Gödel, Escher, Bach: an Eternal Golden Braid wrote about a program that can interact with shapes. Hofstadter is a mechanist; he feels that intelligence ultimately can be defined by a collection of rules and algorithms. I have a mystic streak that makes me think that we are more than that. Guess which one of us thought that the program actually simulated intelligence?

Despite having serious doubts about the ability to write a program that would be intelligent, I am fascinated by the concept. When you think about how powerful the brute force of a modern processor is (A Pentium II 400 in theory can perform 467 million calculations per second.), one would think that there would be little that the human mind could do that a computer couldn’t. Everything that can’t be programmed is one more demonstration of how impressive the human mind is. Anything that a Turing Test can’t reproduce is what separates us from machines. Today, one thing that computers can’t simulate is the way we listen to music.

About a month ago, I listened to the Phish Bomb Factory show for the first time in two years. Despite that length of time, I could remember vast detail about the jams; I could kind of hum along with them. Think about how much music you can remember without even thinking about it or wanting to. Just mentioning “It’s a Small World After All,” “I’m Too Sexy,” or “Welcome to Our World of Toys,” should be enough to get the songs stuck in your head for a day or two. If you wrote up all of the music that you knew by heart, you would fill a rather thick book.

Now if we only had a large collection of musical knowledge, it wouldn’t be that impressive. What is so amazing is that we can use it on the fly. Not only do we have the ability to keep a stunning amount of music in our heads, but, to use a computer analogy, it’s like we are constantly cross referencing everything we ever hear against it. The speed at which we can go from hearing an opening chord of a song, to identifying it, to reacting to it is outstanding. I tested some of my audience recordings to see how quickly a crowd reacts. Songs that were in heavy rotation – “You Enjoy Myself,” “Mike’s Song,” and “Weekapaug Groove” were some Phish examples – were identified by the crowd in under a second. Think about that last one. Weekapaug just starts with a drum beat. In about one second, thousands of people were able to identify a song just from a rhythm.

Now it could be argued that people were expecting to hear those songs; those are very common songs, and at least in the case of “Weekapaug Groove,” the anal set list fans were expecting it somewhere in the set since there was a “Mike’s Song” earlier. (The show I was listening to was 11/21/98; there was enough separation between the two that I suspect most fans had forgotten about the “Mike’s Song.”) Fair enough. I tried a few rarities to spice up the mix. I put in for the Grateful Dead “Help on the Way” from 9/19/90 and the 10/9/89 “Dark Star.” The test for the Phish crowd was the “1999” New Year’s show opener and the most unexpected song of the year – 8/9/98’s encore of “Terrapin Station.” It didn’t make a difference. Only the Terrapin took anytime at all to digest- an entire 4 seconds. The other responses were close to instantaneous.

One of the problems with many subjects is that it’s not enough to read about it to learn. You have to do experiments to truly understand. As a teacher, I hated to give a lot of homework, but I knew that was the only way my students would learn. In that spirit, I would suggest that anyone who wants to be really impressed by the human mind try this game. Walk over to your CD’s. Close your eyes and grab 8 or 9 from different parts of your collection. Put them in a bag and mix them up so you won’t have any visual clues to where each CD came from (important if, like me, you keep your collection in alphabetical order). One by one, again with your eyes closed, put them in your CD player. Before it can play the CD, hit pause. Fast forward to track 3. Randomly fast forward a minute or two in the track. Hit play. You might be surprised at how quickly you can identify each track. Two seconds of music is frequently more than sufficient.

At this point, I’m sure that some of my readers are objecting. Many CD players let you give your CD’s a name that comes up whenever you put them in. There are even some programs that, whenever you put in a CD, go out on the net, download the title and artist information, and display it. How is that any different than the little fast forward test? To answer that, you need to know how those CD players work. Any music CD has a 2 second lead-in track where the table of contents is stored. In addition to letting the CD player know where the tracks begin and end, some identification information is encoded. How do I know this? I put the Velvet Underground CD “Loaded” into my automated CD player. It came up with the title and tracks. I burned two copies of this CD. One of them I kept the lead in and the other one I didn’t. The two CD’s were musically identical; no Velvet Underground fan would have been fooled for a second. However, the CD player could recognize the first CD, but not the second.

What separates people from machines? Some people might claim that only living beings have souls. Sure that spark of consciousness is important, but finally the real difference has been explained. Humans can recognize their favorite song…. played by a cover band…. off key…. recorded on a Fisher Price tape deck… while having a screaming fight… during an earthquake. Computers can’t identify a CD without a cheat sheet. Sometimes it’s the smallest things that are the most impressive.

Personal Notes:

I realized last month that I have yet to thank Sarah Bruner for her help with this column. Every month she reads it, edits it, and makes it much better than it otherwise would be. On a more serious note, I would like to dedicate this column to the memory of Jenn Carswell. I’ve known a lot of people who have wrestled with darkness; for the first time someone lost.

[1] The Turing Test – created by Alan Turing (1912-1954) – gave one way of describing a machine as being intelligent. A computer program passes the Turing Test if someone can’t tell if they are communicating with a computer program or a person when they are using it. While some programs can claim to pass a Turing Test in limited contexts (like “Eliza” programs which mimic a really annoying Freudian psychologist), usually all you have to do to make a program fail is give non-standard input. If you tell Eliza, “I want to fork the banana tree eggplant with the bucket,” the likely output is “Why do you want to fork the banana tree eggplant with the bucket?” There is an interesting Alan Turing biography site that has more information on both the Turing Test. The information about Turing himself is pretty interesting too – persecuted for being out about his homosexuality, he was jailed, given special treatments designed to kill his sex drive, removed from the interesting work he was doing, and ultimately committed suicide. For a lighter touch, check out The Twinkies Turing Test in which the question of whether Twinkies are intelligent is addressed.

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