Slashdot Mirror
Traffic Jams In Your Brain
An anonymous reader writes "Carl Zimmer's latest foray into neuroscience examines why the brain can get jammed up by a simple math problem: 'Its trillions of connections let it carry out all sorts of sophisticated computations in very little time. You can scan a crowded lobby and pick out a familiar face in a fraction of a second, a task that pushes even today's best computers to their limit. Yet multiplying 357 by 289, a task that demands a puny amount of processing, leaves most of us struggling.' Some scientists think mental tasks can get stuck in bottlenecks because everything has to go through a certain neural network they call 'the router.'"
Have they tried unplugging it, waiting 30 seconds, and plugging it back in?
Couldn't it just be that we do not really have direct access to the raw computational capacity of the brain? There are savants and people who have trained themselves tremendously who can do arithmetric like this, using memory tricks and such. Wouldn't that be more like a hack to "reach down" to utilize the low-level capacity of the brain? The brain is nothing like a man-made computer, but doesn't the "layers of abstraction" still apply? The brain can calculate 357 by 289, but it does not naturally "understand" what 357 or 289 is, or for that matter what the high-level instruction from "me" to "multiply" is.
Emotions! In your brain!
How about 357 * 289 being hard is because 7 is the average size of the short term memory, and you need to remember more numbers than that to arrive at 103,173?
... the way math developed and was taught is not the only way to teach "math", this is one thing that I've learned as I've grown up. And I'm still doing much research in this area.
There are better ways to teach people how to do those computations but it requires a conceptual understanding that there is not a "Set" way of thinking about "numbers" (really our alphabet for communicating distinction and differences) linking the way we naturally think with foreign languages developed by a narrow set of minds. see: Mayan numerals.
http://en.wikipedia.org/wiki/Maya_numerals
Notice how mayan numerals rerepsent themelves as geometric objects that are easily discerned at a glance versus our our highly compressed representational notation (1,2,3,4). Mayans knew that all numbers are made of distinct geometric distinctions and hence they used simple uniform geometric objects as representation to communicate numbers "at a glance", representation _matters_ to how we think about concepts and how we can use them and map them between systems of thinking that only SEEM different on the surface.
You have to understand the numbers can be rethought as natural ratio of shape and size in the real world, when we measure things in the real world we use arbitrary ratios of an object in regards to our own visual system.
For instance 357 by 289 can be broken down to
3.57 x 2.89
What you're trying to do is limited the # of elements by changing the ratio you have to see "lots of things" as merely representations of smaller scale things and things get a lot easier once you understand this principle.
The whole way math is taught is really fucked up and made for a narrow range of particular minds that function and "Get" how our mathematical system developed. If you begin studying the history of math, you realize that representation and HOW YOU THINK about how we mathematize nature matters a hell of a lot more then just throwing stuff other people figured out at kids in a symbolic format developed for a narrow subset of human minds.
Math is just a symbolic language to communicate our observation of distinctions and differences in regards to space, matter and time in the world.
My grandmother, while she still was alive, could do these kinds of tricks in her head in a few seconds. She could multiply 2 and 3 and 4 and 5 digit numbers, divide and even take roots. All in her head. The day she finished high school the war started, so instead of becoming a teacher she was making tank gun rounds and then after the war worked as a food store clerk and then an accountant and the head accountant for a number of stores at the same time (this was the old USSR). Most of her life she was around numbers. So in the stores even until 1980s they didn't calculators or electronic machines, they used abacus. She calculated everything in her head in seconds and told the result, the buyers would not believe her and ask her to show them on the abacus, so she did. I cannot say that I ever heard her being wrong about calculations.
I believe she remembered a lot of the calcuations ahead of time, so she nearly knew the results (pre-cached the results) and then worked the small differences out. I don't have that cache of numbers, but 2 and 3 digit numbers I can do fairly quickly.
289 and 357 to me is (3570 - 357) + (35700 - 3570 * 2) + 35700 * 2. So the only difficulty here is making sure I don't screw up the subtractions, and those are just a matter of paying attention.
You can't handle the truth.
Here's an analogy to illustrate the category error people make when comparing the human brain to a computer:
"A Sony Walkman can record and play music in realtime, fast-forward and rewind, and store an hour's worth of music. These tasks require a 75 Mhz processor and 100 megabytes of memory on an iPod Shuffle. Therefore, a Sony Walkman has a 75 Mhz processor and 100 megabytes of memory."
We had a family friend (he has passed now) who could go to a railroad crossing with a train going 60 miles per hour down the track and correctly add the 7 digit (or more sometimes) numbers on each train car as the train passed.
He said that he would not "add" the numbers but allow for them thus coming up with a total more through allowing the right answer than by math manipulation like we would have to do consciously.
The whole thing was sort of spooky to behold... here we were writing down the numbers of each car and he effortlessly knew the running total. It was if he allowed his unconscious part of his brain to observe the number, add it to the running total without interfering with the process mentally and then his conscious mind would retrieve the answer from the unconscious mind at the end of the train or after 20 cars have passed or other terminating choice.
And in the end, the love you take is equal to the love you make
I think I saw the PBS special that covered what was mentioned. There is a school in Asia (Japan? China? India? Don't remember, it has been a while since I saw the special) where the students are started at a young age using an abacus. They learn to do complex calculations quickly. Once they read a high speed, they take away the abacus and let the students use an imaginary one. Stage 3? They begin limiting the finger twitching until the abacus exists only in the visuospacial sketchpad and "muscle memory". Although more challenging for an adult learner, with enough years even an adult could learn this method. The advantage of the abacus is manipulating larger numbers than some of the "finger" tricks - but essentially these schools reduce them to just that, minor finger twitches that trigger a mental image of an abacus.
Chunking to optimize usage of working memory is pretty impressive. Think about how we teach kids to decompose the problem of 289 * 357. We essentially tell them to break it into 4 problems x = 289 * 7, y = 289 * 5 * 10, z = 289 * 3 * 100, and x + y + z. However, we then teach student to do the same with each of the 3 subproblems of 4 calculations (289 * 7 is a = 9 * 7, b = 8 * 7 * 10, c = 2 * 7 * 100 and so on). Thus we have 13 problems to solve while the typical range of items in working memory is 5-9. By creating the mental abacus, the person conducting the calculation now has it fit inside the limits of the working memory.
I could not do the problem mentally. However, when I looked at it I said 289 * 357 is about 300 * 350, or just under 105000 ( 11 overestimation is greater than the 7 underestimation of two similarly sized numbers, so I would expect to be over slightly in my estimate). For most cases where mental calculation is needed, an approximate 3% error isn't too bad.