|The Boy With The Incredible Brain -- Critiqued
||[Jan. 25th, 2008|11:27 pm]
The Adventures of a Confounded Spinning Ball
Lately I've been encouraged to make more of my posts unlocked. I only do that under certain circumstances, but I feel this is an important occasion because I believe I have spotted a hoax and that I am unusually qualified to unmask it.|
I just watched The Boy With the Incredible Brain, a video that spoonless posted in his journal. Given the buildup, I was expecting to see something I'd never seen before, but I was very surprised -- the "savant" Daniel is much slower than I am at all the computations. Not a little slower. A lot.
That's fine. I know I'm an oddball as a "lightning calculator", so I'm not all that disappointed that Daniel can't beat me at a calculating contest. What I'm disappointed with is my perception of the whole video -- with both him and the scientists who are studying him. I smell grant money at the end of somebody's rainbow.
Before I go any further, I need to debunk the spectacular nature of the computations he was given. They are, to build an analogy, lightly tossed softballs, meant to be hit out of the park by somebody who spends a lot of time swinging at softballs.
He's given 37 to the power of 4. Here's how it's done: 37 squared is 1369. Somebody like Daniel (and me) knows this much by heart. I knew the squares of all two-digit numbers by heart when I was 11 just because I had practiced the process so much, looking for simpler and simpler methods for working with numbers.
37 to the 4th is 1369 squared. Well, that's not all that bad actually. I taught an 11 year old how to do it in just a few minutes that other day. That very number in fact. There are several ways to go about it, but one is to square 1370, then note that
1370^2 - 1369^2 = (1370 + 1369)(1370 - 1369) = 2739.
Squaring 137 is not that hard:
137^2 = (100 + 37)^2 = 100^2 + 2*37*100 + 37^2 = 10000 + 7400 + 1369 = 18769.
The next problem is dividing 13 by 97. This is a trick that I developed in middle school, and I loved it so much that I included it in my first book. I'll show 1/97, which will best demonstrate the effect:
1/97 = 1/100 + 3/100^2 + 3^2/100^3 + 3^3/100^4 + ...
Since 97 = 100 - 3, I was able to cleverly rewrite 1/97 as an infinite geometric series. Now the computations are simple:
1/97 = 0.01030927835051546391752577319587...
I can spit those digits out as fast I can pronounce them, which is much faster than Daniel did it. The key is to work with the digits in pairs, multiply each pair by 3, then adding 1 for each 1/3 of 100 we result surpasses. For instance, 13/97, we start with 13*3 = 39 and add 1 because 39 is more than 1/3 of 100:
0. 13 40
Now, we multiply 40*3 to get 120. We already used the 1 to add to 39, so we ignore it. So, we now have
0. 13 40 20
Next, 20*3 = 60, plus 1 because 60 is between 1/3 and 2/3 of 100:
0. 13 40 20 61
Next, 61*3 = 183. We ignore the 1 in front and add 2:
Once you have the hang of the method, producing more digits is quite simple. Daniel says he might be able to go up to 100 digits. I can go up to infinity digits, discounting time constraints. I could spit 100 out before the first minute was up.
But it does sound more dramatic to say 100, and it keeps the cards hidden if you're playing the game that I'm playing -- computing using a convenient series. You can't say you can spit out infinitely many, or somebody will catch on.
That's okay, I think I caught on anyway.
27 to the power of 7? Well, that's 3 to the power of 21. I knew the powers of 3 by heart back when I worked so many contest problems. No big deal. But, I don't remember 3^21 now, though I'm confident I can compute it quickly for several reasons, the biggest being that I still remember 3^10, which is 59049. That's an easy number to square:
3^20 = (59000 + 49)^2 = 59000^2 + 2*59000*49 + 49^2
Multiplication by another power of 3 is in fact the hardest part by far, but still not so bad. After all, we're not all that impressed by people who can multiply by 3, even if it's by ten digit numbers, right?
Even if I didn't recall 59049, it's not hard to get there. I could square 3^5 = 243. I could just multiply by 9 several times over. After all, 9 = 10 - 1:
6561*9 = 6561(10 - 1) = 65610 - 6561.
31 to the power of 6? Not that hard. 31 squared is 961. Now we can use binomial expansion on (100 - 39) to dramatically simplify the computation. The calculation is no harder than cubing 39 ultimately.
There might be methods for any of the above problems that I did not explore. Each of these methods came to mind literally within the first second that I heard each problem, which should display that they are just a matter of training. Just reflexes.
And they don't involve shapes and colors.
Note that they never once asked Daniel to multiply 7139 times 41562. Why did I pick a problem like that? Because there's very little special about the numbers, except that they don't contain the shortcuts inherent in every one of the problems Daniel worked in the documentary. They’re not even particularly easy to factor, so there’s no quick reconstruction to save the day.
It seems to me that the only reason not to test Daniel with such computations is that he is using methods like mine -- not seeing shapes and colors or whatever weird method he claims.
I also noticed that during the very first problem in the video, Daniel moves his fingers in a useful way. I don't believe he's "playing with shapes and colors" or something like that. I recognize those finger movements. Not precisely, but back when I was learning mental arithmetic (when I was only about as good at it as Daniel is), I would move my hands more than I need to now. It's a lot like what the Chinese kids working on the mental abacus. It's a mental image of real calculation. Those finger movements give the game away. Perhaps not alone, but along with everything I saw in that video, I have to conclude that Daniel's explanation of "spontaneous computation" from "shapes and colors" is a sham.
Note that the hard-drilled Chinese children can multiply any two four-digit numbers. So why is Daniel hailed, at the end of the video, as "one of 50" such high level savants in the world?
Perhaps because somebody wants a research grant?
So the guy memorizes digits of pi. That's just what he puts his mind to doing. Lots of people do it. Memorize 7 digits a day, which is just a phone number, and in ten years you'll know as many digits of pi as he does. Particularly if people pat you on the head a lot along the way. It is, after all, mostly a matter of motivation. Since more people started paying attention to the record, the record has grown very very quickly. I know just a couple of years ago a Japanese guy hit 100,000 digits. Oddly, it's a common obsession, and all kinds of people from around the world have shown an ability to memorize thousands of digits of pi.
I did find it impressive that he could learn a new language in a week, but I remember studying for the first semester exam during my first year of German. I learned hundreds of words in a couple of days, including verb conjugations and noun genders. German was the first language in which I learned a several hundred word vocabulary outside of English. I imagine that if I'd learned several languages, I would better be able to learn a new one. Particularly if I could clear my mind and focus on nothing else. I feel quite confident that were I focused more on languages, I could teach children to learn languages quickly -- particularly while immersed in the country that speaks the language, walking around with a trained tutor.
Also, 10 minutes to memorize a chess board?! That's a whole lot of time. I bet I know plenty of people who can do that. I'll bet that I can do it. I bet when I was 12 I could do it in under a minute. In fact, I suspect I could have trained myself to do it in 10 seconds.
Once, when I was in middle school, the drama teacher, Mrs. McCord (sp?) asked everyone in class their birth date. When she was done, she asked everyone to name the birth date of the last person who spoke. Around half the class remembered the birth date of the person before them. When it came my turn, I recited every one of them, which was 24 total birth dates.
I can't do that anymore, but I have plenty of witnesses to similar events. I think that the primary reason my memory no longer works that way is that I've trained myself to focus on other things. I focus on processing information, not storing it. Information is cheap after all -- why focus my brainpower on it?
I don't think such feats of memorization are particularly spectacular. I was one of eight players in an exhibition against Vivek Rao in which he played us blindfolded and beat us all. Most of us were pretty good players too (tournament players). Granted, I told him beforehand what opening I planned to play, but still. Isn't that a lot more impressive?
I found an a discussion of Daniel's Pi memorization process:
Daniel studied the sequence – a thousand numbers to a page.
"And I would sit and I would gorge on them. And I would just absorb hundreds and hundreds at a time," he tells Safer.
This strikes me as exaggeration. He doesn't "aborb hundreds and hundreds" of digit in the sense of memorizing them all at once. If he could do that, his 22k+ digit memorization display would be small change. The constant sense of exaggeration in Daniel's story erodes an enormous amount of credibility in my mind to his explanations of his ability.
That junk about the blackjack -- pure quackery. That's an experiment that can be repeated and he'll lose with those split 7's -- over and over again for each win. That seals the deal on my opinion that he's overstating his abilities. What's happened is that he's given up on trying to count numbers. He hasn't practiced, and the conditions are not ideal. So he just starts bullshitting. Who knows what didn't get filmed or didn't make the final cut.
He'd need to train to count cards, just like any other person with some number skills. The researchers or documentary makers were reaching on this one. They fell flat and probably don't realize how flimsy the rest of his abilities appear at this point, at least in regards to what Daniel is claiming about "shapes and colors".
This is where the story goes from silly to insulting my intelligence. There is nothing scientific about what's going on in that test. Daniel clearly has a good memory, that's all. They'd have gotten the same result from me and many others. It's insulting because they present this test as if it should be regarded as some kind of "final proof" of Daniel's ability to see numbers as shapes and colors.
Notice that Daniel never said, "Um, 242 isn't just one color, and it's cobalt blue, with streaks of silver and green polka dots." Amazingly, all the numbers happen to be single colors that are all represented in a standard play-doh kit.
Now, I'm not going to say that's "an intentionally sham experiment designed to reach for research dollars." I won't say it. It...just...might...be...that...God made the universe so that Daniel's brain sees in play-doh-vision.
It also strikes me that the way I tend to memorize numbers has a lot to do with context. If somebody gave me play-doh and told me to build numbers, I bet I'd come up with a method using prime factorizations. You could ask me five years later, and I'd recall that method. So it's not even an amazing feat of memory. It's just matter of the fact that understanding prime factorizations -- one of the truly obvious methods for organizing values of integers that is just beyond the mental reach of observers -- turns the problem into swinging at another big softball. Pow!
Anxiety Over Pi
And so what that he has anxiety when shown a pattern that deviates from his familiar mental picture of pi? That's not a "mean" test -- it's at best meaningless beyond the fact that Daniel has great affinity for pi, and at worst a softball served up to make Daniel look really mathy.
Here are my takes on a few choice quotes in the piece:
"His childhood holds a dramatic clue." (7:53)
I love this line. The drama is not the clue, but the effect of buildup the line itself has on an audience, talking the audience into believing whatever conclusions are conjured by the end. But really, Daniel's childhood betrays the real story -- that a kid who focuses on numbers develops special abilities for working with them.
That is in fact the premise of my career as a math teacher. It's that simple. I know because I've taught the methods I used above to dozens of children.
"By most measures, Daniel is autistic, but he's also picked up enough social skills to blend in." (14:41)
This quote really struck me. It's true that Daniel is interesting in some regard. While I've bashed his computational abilities, that's mostly because I think his "shapes and colors" story is nothing more than a cheap grab at attention (for which I feel only pity). Daniel's social skills are not horrible, but they're not par either.
Although I am more social than Daniel is, I see a great deal of similarity between our social abilities. I think mine are more well-developed due to necessity, but that’s another story. I post this quote partially because I am still unsure as to whether or not I am a high functioning autistic. I blend in well, and always have, but if Daniel is autistic, that makes me think that I probably am too.
"…his symptoms are not really interfering, currently, with his life."
My opinion on the matter of my own autism goes back and forth. By checklist, I am certainly high functioning autistic, but I feel like autism is particularly poorly described by symptom (as disorders are defined) – we need to find a way to describe how the clockwork in us is different.
I believe my clockwork is much like Daniel's. I can see it in his every move. If he is autistic, then I am autistic.
"One day you'll be as great as I am." (28:12)
Superb line, and probably helps with the charade that Daniel and Kim are alike in some way. But I don't buy it at all.
The greatest similarity between Kim and Daniel is intense memory. but Kim's is far more intense. He concentrates more wholly on his savant abilities. Of course, Daniel is more social, which may itself explain some of the difference. But overall, it's not clear that Kim is capable of less intensity, though Daniel certainly is.
”I’m very much a big skeptic of this.” (32:30)
Azoulai stuck me as one of the least skeptical scientists I’ve ever witnessed. His body language is of a person who wants to be impressed. But truthfully, I’m taking my shot at him here because the tests I saw in this documentary were so flimsy that I can’t respect him as a scientist.
"It was something that you just can't fake. These are the things specifically that are showing me that he's not bullshitting and he's not scamming. Even the mistakes that Daniel makes are the mistakes that are telling me 'you know what? This is legit. A faker wouldn't be doing this.'" (39:39)
A faker wouldn't do this? That's a scientific opinion? I thought science was about testing a hypothesis. I can test the hypothesis. I have. I've taught middle schoolers to do nearly all the "amazing" things Daniel did in the video.
But I have a strong opinion about this quote. I can't prove it, but it's the kind of quote that comes out of somebody's mouth when they're staging something. The whole video seems to have this defensive quality to it. This fits of course with my opinion that the computations are staged.
Don’t get me wrong, I am not accusing the researchers of staging the actual moments of computation. They’re just throwing him softballs.
"This could be the linchpin that spawns a whole new field of research. (40:56)
I find it utterly amazing that Daniel's shapes weren't put to any rigorous testing. I bet I could debunk them in 5 minutes. A researcher just says, "Wow, I'm blown away" as Daniel looks away, looking anxious.
This line, with lack of all credible backing, does nothing but support my case.
"The line between profound talent...and profound disability seems really a surprisingly thin one." (46:18)
That sounds to me like something somebody might say if they've gone through life playing mental games, never doing anything productive, finally deciding to play their cards in hoax, hoping for something good to happen. Hoping perhaps for a little fame.
"The bigger question is whether we all have some of those abilities within us. And that is what I refer to as the little rainman within us." (46:43)
Wow, that's so warm and fuzzy it makes me want to puke.
It is an interesting question, but the answer is plain: there are far more than 50 people with the abilities described in the documentary. There aren't a lot of people like "the real rain man", but Daniel isn't like that either, even if he wants to act like he is. Daniel is just a guy with a pretty high IQ who claims to squash shapes and sizes together to computer numbers.
Further Evidence and Questions
I would be interested in knowing how all these shapes and sizes mash together when Daniel divides one integer by another.
If Daniel's abilities are so abnormal -- if he uses shapes and sizes to compute in ways he can't explain...why is his primary profession as a tutor?
In the Wikipedia article on Daniel Tammet, his synaesthesia is explained as such:
In his mind, he says, each number up to 10,000 has its own unique shape, color, texture and feel. He can intuitively "see" results of calculations as synesthesic landscapes without using conscious mental effort, and that he can "sense" whether a number is prime or composite. He has described his visual image of 289 as particularly ugly, 333 as particularly attractive, and pi as beautiful. 6 apparently has no distinct image.
If you’re doing mental computation, 17 is an ugly number to work with. Unless you couple it with another number, like 6 (to make 6*17 = 102), it’s hard to find a nice way to multiply by 17. 17 squared is 289. Now, when doing large computations, you have to pair 17 with “nice” numbers twice to perform well. So, if 289 is involved, the computations are “ugly” to try to do mentally. It makes for a nice excuse if you miss those problems: “The squiggles in my head were ugly this time – hard to read.”
On the other hand, multiplication by 333 is extraordinarily easy because 3*333 = 999 = 1000 – 1.
Powers of 10 are, as I have alluded to already, the key to quick mental computation. It strikes me as convenient for Daniel to have picked a power of 10 to stop at for “seeing” numbers as shapes, colors, and textures. If I wanted to script a story like his, that’s exactly what I would do. It would make all the crap I made up easier to remember anyway.
Edit: I just came across post 463 in which somebody points out that the "Pi landscape" story contradicts Daniel's stated method of memorizing sequences of digits.