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?
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?
I don't think it's processing power or inability at all. I thnk it's lack of working memory. We can all work out 357 multiplied by 289 easily with pencil and paper. Very easily. And we could do it in our heads just as well if we could casually remember all the intermediary stages: e.g. 9 times 7 is 63, 9 times 50 is 450, 9 times 300 is 2,700, sum all three numbers and remember the result, now begin with 80 times... etc. But it's not easy for most people to do that. The computation is easy. But we need more registers.
Aide-toi, le Ciel t'aidera - Jeanne D'Arc.
Probably. You can scan a crowd because you have a hardware-level implementation for that; you can't multiply efficiently because that has to go through multiple levels of emulation, at least one of which has a severe lack of reliable memory.
We shouldn't forget that abstract thought is actually a very new evolutionary hack; we've only had a real culture for a 10,000 years or so. Before that, it was cave paintings for a 100,000 years. You can't expect a very experimental feature to be thoroughly optimized, yet.
Forget magic. Any technology distinguishable from divine power is insufficiently advanced.
The brain arguably is man-made.
I think you'll find there's usually a woman involved in the process too. :)
Aide-toi, le Ciel t'aidera - Jeanne D'Arc.
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."
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.
Try being a Canadian. We're caught between you guys and the rest of the world. So while my drivers license has my height in metres and my weight in kilograms, I honestly can't think of anyone (myself included) who uses those units in real life. When the newscasts give reports on a person of interest, it's always given in feet and pounds, because most people have no clue what a 1.75m, 80kg man looks like (but they can quite quickly imagine someone 5 foot 9, 176lbs). Yet small measurements of weight (for example, at any grocery store i've ever seen in Canada) are typically in grams or kilograms. Speed and distance are usually given in kilometres (/per hour), but older and/or rural folk still use miles because the entire township/rangeroad grid is still based on miles. So you have to know that driving 6 miles down the road is going to read as 10km on your odometer. But go to the drag strip and trap speeds are all given in mph. Volume is usually in litres, but due to the US being our largest trading partner, many industries still use gallons too (especially in bulk). When I worked for an oil distributor this was always something we had to watch out for, because our holding tanks were marked in litres, but everything we ordered from the US came in gallons. It was an important concept to understand when trying to calculate how many 20,000 gallon rail-cars of oil were needed to fill three 50,000 litre storage tanks. Oh and temperatures are mostly in celcius, but a good portion of the population (especially older people) have something of a working knowledge of fahrenheit. Typically, people know room temperature is about 72 (~23C) and that anything over 100 is "damn hot" (38C), usually from/for travel. Interestingly, one of the places this all gets REALLY frustrating is in cooking. While I just stated that temperature is usually in celcius, almost everyone I know gives oven temperatures in fahrenheit, which is funny because cooking always sounds really-really-hot: a 300 degree oven sounds like a LOT, but in celcius its only 150 - actually fairly cold to cook with. This is because so much of our media (like cooking shows, books, magazines, etc) is shared. Yet so few of our small measurements are, so many recipes are given in units people don't always have a lot of experience with. I cannot count how many times i've been at the grocery store looking for an 8fl-oz can of something, and I have to stand there and scratch my head to rough it in mililitres. Oh, and a quarter-pounder here is still a quarter-pounder - come to think of it, all the burger commercials i've ever seen have been in pounds. So much for small measurements in kilo/grams.
Anyways, the TLDR version is that Canada has the most screwed up measurement conventions of any country on the planet, hands down. ;)
The day the US switches to metric will be a very, very happy one for all Canadians. Not that i'm holding my breath.