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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.'"
So the claim is that our brain is a field-programmable gate array (for economy and flexibility and performance) that takes time to re-arrange to accommodate different sorts of tasks.
Sounds entirely sensible to me.
But distracted me too long to get first post.
Rgds
Damon
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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.
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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.
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I've seen some people claim that you get a small abacus in your head once you've learnt it (and got some experience with it, I assume). Any chance your grandmother was claiming something similar?
I wonder if idiot savants' routers are just fewer hops from the backbone? ;P
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I am not expert, and this is just from a brief conversation I had in an elective class many years ago with a neural science professor but I asked how it is the brain does things in an instant that would likely take a powerful micro computer most of a day, while simple multiplication is often quite difficult for me to do in my head.
The reason he gave is that the brain works usually in a in precise manor. You have lots of different groups of neurons that your relatively plastic brain has wired up to do things like recognize certain patterns. If enough of those go high other parts of your brain proceed as if there was certainty. That works well for evaluating how hard the sterling wheel is pushing back and deciding how much more to stimulate muscles to contract. When you doing something like math though there is only a very specific correct symbol. They parallelism of the voting system breaks down and your brain how to check that all or almost all of those networks agree.
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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.
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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.
Look for a book called "FingerMath." It teaches how to use your fingers like an abacus. After you get used to it you can stop moving your fingers and just kind of "feel" the calculations. No, I never practiced it enough to get good at it. But it is a pretty good book.
The real problem is that the internal representation of numbers is logarithmic. It has exact resolution only for a limited range. With practice or talent, you can make small numbers into sparse matrices of these exact numbers in different digit positions, and work those out (probably the auditory cortex will do the job) at far higher speeds. You will still be limited to 4-7 ops per sec while relaxed, possibly being able to strain yourselv to reach 15-25 ops per sec if you really concentrate to the point of forgetting to breathe.
We can easily add two logarithmic numbers and get a new logarithmic number. Precision in a problem, though.
See, with concrete numbers, we are working in the wrong radix (8 or "e" would be better, by far) and really messing things up badly because we need to construct representational objects in short term memory. These are exact, but cannot be parsed any faster than spoken words, and there are problems in using them for calculations, which will require slow lookups and step by step processes for most people. With proper training, you will refactor the problem in parallell with solving it, which speeds it up a great deal. With repeated use, you will form circuits that are going to accelerate processing. But you will still probably not get much faster than 10-30 digits per second and 3-4 ops per second.
Hacks that give you access to the representation can solve the problem as noted above.
Hacks that give you access to the wetware can probably overload some brain regions into doing the math for you with parallell computing. I would hazard a guess at a temporal or insular location for such processing, but wouldn't know, as I haven't seen any fMRI studies on where savants put the circuitry to do it.
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