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Traffic Jams In Your Brain

timothy posted more than 3 years ago | from the call-mine-the-concentrator dept.

Math 250

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.'"

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Router eh? (5, Funny)

MrQuacker (1938262) | more than 3 years ago | (#34290328)

Have they tried unplugging it, waiting 30 seconds, and plugging it back in?

Re:Router eh? (2, Funny)

fyngyrz (762201) | more than 3 years ago | (#34290334)

Yes, hello sir, my name is Rasheed. I understand your router is down. Can you tell me what lights are on on your modem? No Modem? Hmm. Let me call my supervisor.

Re:Router eh? (3, Interesting)

orangesquid (79734) | more than 3 years ago | (#34290542)

I wonder if idiot savants' routers are just fewer hops from the backbone? ;P

Re:Router eh? (0)

Anonymous Coward | more than 3 years ago | (#34290512)

Yeah, we call that "weekend".

Didn't help (1)

Wrexs0ul (515885) | more than 3 years ago | (#34290570)

It's worse than you think. I got the 825 instead of the 655 and now I can't get voice to work.

And don't get me started about where to put the USB key for a firmware upgrade.

-Matt

Re:Router eh? (1)

Pharmboy (216950) | more than 3 years ago | (#34290744)

Have they tried unplugging it, waiting 30 seconds, and plugging it back in?

Everyone knows you can't go back to the matrix. Worse yet, you end up on a decrepit ship eating food that looks like runny eggs and taking orders from some asshole named Morpheus.

Quick enough for this... (0)

Anonymous Coward | more than 3 years ago | (#34290330)

First!

That was easy! (2, Insightful)

anss123 (985305) | more than 3 years ago | (#34290350)

103173

I don't see what so hard about opening a calculator and typing some numbers.

Kids these days!

Re:That was easy! (5, Interesting)

roman_mir (125474) | more than 3 years ago | (#34290494)

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.

Re:That was easy! (3, Interesting)

tenchikaibyaku (1847212) | more than 3 years ago | (#34290526)

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?

Re:That was easy! (2, Insightful)

roman_mir (125474) | more than 3 years ago | (#34290600)

I don't know about that, it's does make some sense, it allows us to use visual memory to do calculations (like when we play chess without the board). I actually can imagine an abacus, it's nearly the same as imagining hands and fingers, it's easy to use that to do binary by the way.

But in case of my grandmother, she remembered a LOT of numbers just like that, because you know, decades of experience all around numbers.

Re:That was easy! (5, Interesting)

MDillenbeck (1739920) | more than 3 years ago | (#34290906)

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.

Re:That was easy! (1)

anss123 (985305) | more than 3 years ago | (#34290552)

Had a math teacher that could do stuff like that in his head. It was a little eerie when we struggled to get the result out of our fancy $150 programmable Casio calculators with color screens.

And USSR let women join the army?

Re:That was easy! (1)

roman_mir (125474) | more than 3 years ago | (#34290602)

Well, during the war there were plenty women in armed forces, you couldn't really tell them 'no', but she wasn't in the army, she was working like most women and children at a factory, building weapons.

Re:That was easy! (2, Informative)

vadim_t (324782) | more than 3 years ago | (#34290664)

He said making tank gun rounds. That was pretty common during the war, the US had Rosie the Riveter as propaganda of that kind of role.

In the USSR they served in combat, too. It was accepted somewhat reluctantly, but quite a few volunteered, and initial losses gave a reason for giving it a try. They turned out to make really awesome snipers [wikipedia.org] .

Draft service (0)

Anonymous Coward | more than 3 years ago | (#34290846)

In the USSR, the army joined you.

Re:That was easy! (2, Informative)

TheLuggage2008 (1199251) | more than 3 years ago | (#34290780)

While your grandmother may have had her own way of doing this, complex calculations can be done very quickly using the Trachtenberg system of mathematics [wikipedia.org] .

I actually have the book and swore to myself that (while I didn't need those computational skills) my kids would be taught it... my first is on the way now so I guess it's time to dust it off (the book... not the child).

For anyone interested in learning these skills, here is the Amazon search result page [amazon.com]

Re:That was easy! (0)

Anonymous Coward | more than 3 years ago | (#34290788)

I do these in the following way:
357 * 200 (which to me is: 357 * 100 * 2)
+
357 * 80 (which to me is: 357 * 20 * 4) (or 357 * 10 * 2 * 2 * 2)
+
357 * 9 (which is: (357 * 10) - 357), but 3570 - 357 isn't easy for me, I'd now do this: (3570 - 300, 3270 - 50, 3220 - 7)

As you say, it's now just a case of adding them up. Which given I've been filling my short term memory with the above calculations leaves me hoping I remembered the first resultant....
So normally I go over it again but this time I don't have to "work" out the answer of each mini calculation as that's there in the back of my mind but need "recaching" (or moving back out of PF) lol, sorry for the nerd joke!

   

Re:That was easy! (3, Funny)

RoverDaddy (869116) | more than 3 years ago | (#34290824)

Opening a calculator? I remember when calculators were physical things that you could flip upside down so they read '8008135'.

Re:That was easy! (1)

JustOK (667959) | more than 3 years ago | (#34290870)

773440

Re:That was easy! (0)

Anonymous Coward | more than 3 years ago | (#34291164)

There was 1 girl : 1
She was 16 : 116
She got "F"ed 69 times : 11669
3 Times a day : 11669 x 3 = 35007

What was she? (Turn the calculator upside-down for the answer!)

Re:That was easy! (1)

August_zero (654282) | more than 3 years ago | (#34290952)

People that think the brain works like a computer, don't understand either of them.

FPGA (2, Interesting)

DamonHD (794830) | more than 3 years ago | (#34290346)

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

Re:FPGA (1)

TheLink (130905) | more than 3 years ago | (#34290484)

It doesn't that much like an FPGA.

I can give a rough estimate of the multiplication answer quite quickly. If I keep needing similar or better estimates, after lots of practice I'd get better at doing it assuming appropriate feedback and training.

I haven't seen an FPGA adjust itself when you tell it "bad boy, that's not what I want".

As for picking out a familiar face so quickly. That's because there's a neuron or more in your brain that do the equivalent of yelling "Bingo!" every time you see or think of that face.

Human brains create models of the world. So in your brain there's a model of that familiar person - face, rough expected behaviour etc. Same for objects, and environments.

In the old days of slow computers when people wanted to simulate hydro stuff, they'd build scale models and pour water and see what happens.

Once the model is built, you could get good enough answers very quickly.

Re:FPGA (0)

Anonymous Coward | more than 3 years ago | (#34290678)

I haven't seen an FPGA adjust itself when you tell it "bad boy, that's not what I want".

To be fair I have not seen a human do that either.

Re:FPGA (1)

DamonHD (794830) | more than 3 years ago | (#34290692)

Nothing says that you can't have a separate route for getting approximate answers quickly in parallel with exact answers slowly. Indeed 'emotional' reasoning seems to be an example of the former: "That's not fair!" vs "That leaves me 6.8% out of pocket!"

Rgds

Damon

Re:FPGA (1)

baffled (1034554) | more than 3 years ago | (#34290578)

To me, if a thought process isn't innate, then I must consciously traverse it, step-wise. I suppose processes that I haven't been rigorously taught may consist of a set of steps which are only somewhat dependent on order, and I stumble my way through fulfilling requirements as necessary. Either way, I must consciously make my way from one part of a sequence to another.

This involves calling up the next step, which can be fast if the steps have been rigorously learned, or slower if I must analyze the process and determine (perhaps through logic) what the next step should be. At the same time I must temporarily save any data pertinent to the current stage of the entire process, to be utilized either immediately or further down the "processing pipeline."

I believe that makes a decent generalization of conscious thought processes for me, and it probably applies to most people. The act of performing this process in itself is a conscious decision, which the mind's eye must also keep itself aware of. Otherwise, it could get distracted, and lose itself in some tangent during a step in a thought process and either hamper the efficiency of the process or never finish it altogether.. All of that can also waste considerable processing power ;)

Pulling it between layers of abstraction. (4, Interesting)

Securityemo (1407943) | more than 3 years ago | (#34290348)

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.

Re:Pulling it between layers of abstraction. (5, Insightful)

h4rm0ny (722443) | more than 3 years ago | (#34290372)

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.

Re:Pulling it between layers of abstraction. (1)

Securityemo (1407943) | more than 3 years ago | (#34290382)

As I understand it, "living calculators" have learned to use their long-term memory to store values quickly.

Re:Pulling it between layers of abstraction. (1)

hedwards (940851) | more than 3 years ago | (#34291132)

Indeed, and I suspect that they've learned to use the rules of math as well. I'm far better than most and it often times takes less time for me to do it in my head than it does to pull out the calculator, even if it is right in front of me. The trick is to use the properties to make things simpler.

For instance 12*17=204 it's also 12*12 + 12*5=204. Most people can without much trouble do the latter, but the former is much more difficult for folks to do. Mathematically the result is the same.

Now, the reason why triple digits is typically much harder is that most folks don't know their times tables that high and you start running into the problem of how many times you can use the same portion of the brain at the same time. In general you can only use a portion of the brain once at a time plus whatever you can remember without starting over. Otherwise you end up with problems of consistency and reliability.

Re:Pulling it between layers of abstraction. (1)

Jarik C-Bol (894741) | more than 3 years ago | (#34290472)

I think you may actually be on to something here. Because intellectually, i know how to multiply those two numbers, but in practice, without paper, i'm going to drop digits at some stage and foul it up. I can do it perfectly on paper, and if i devote a large amount of my focus to hand waving and writing numbers in the air, I *may* be able to crank through it without paper, but there is still a decent chance of a computational error. Its like I need to output the results somewhere besides my short term memory, and 'writing' the numbers in the air helps send them to longer term memory somehow. physical output of the data and all that.

Re:Pulling it between layers of abstraction. (2, Insightful)

icebraining (1313345) | more than 3 years ago | (#34290762)

and 'writing' the numbers in the air helps send them to longer term memory somehow

Sure, it turns them into visual memories.

Re:Pulling it between layers of abstraction. (1)

cb88 (1410145) | more than 3 years ago | (#34291086)

Interesting that the brain must be able to reroute previous memories as input into unrelated areas... visualizing things for instance.

Re:Pulling it between layers of abstraction. (5, Insightful)

ultranova (717540) | more than 3 years ago | (#34290402)

Couldn't it just be that we do not really have direct access to the raw computational capacity of the brain?

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.

Re:Pulling it between layers of abstraction. (3, Insightful)

mr_mischief (456295) | more than 3 years ago | (#34291018)

We also haven't been worried so much about exact numbers of things for much of that time, and matching faces against memories isn't that exact of an example.

You're likely to recognize someone who grew a mustache or cut their hair, or to ask someone familiar to you where they got a fresh scar rather than walking right past them.

You are also not likely to care exactly how many bushels of barley you raised until you start selling the grain for currency or protecting it from known thieves. So long as your granary doesn't run out before the next harvest, you have enough grain. Even when bartering or selling for currency, unless you do a lot of it you can estimate your reserves of unsold stock. Once you move to a mercantile economy rather than being your own producer of sustenance, though, knowing how much of something you have and what you can get in exchange becomes more important.

Building things takes a similar route to economics. If you're building small houses with a central hearth, the construction skills are much more important than anything numeric. Once you're building grand temples and fortifications, engineering kicks in.

Now for the car analogy. I'll hit both engineering and economics. Once you have the materials and power sources to make automobiles and airplanes, engineering and trial-and-error still play a role. If you build custom buggies or roadsters on the weekends, you can utilize hard engineering but you probably don't need to. If you're meeting specific crash safety, fuel economy, and profit margin goals for the design of a car model and its highly automated production process for a big mass-market car manufacturer, your numbers had better be right.

Re:Pulling it between layers of abstraction. (1)

anss123 (985305) | more than 3 years ago | (#34290404)

Do we have any idea how the brain goes about calculating stuff, and at what precision?

I would be surprised if it has a general purpose math unit. It's more likely that there are some operations that has to be done, and it can do those very fast - e.g. sin(x)*y - but it can't suddenly switch to using another formula without major rewiring... and it might even be using table lookups instead of proper math.

Re:Pulling it between layers of abstraction. (2, Insightful)

mr_mischief (456295) | more than 3 years ago | (#34291050)

I don't recall a proper citation, but I seem to remember that even identifying quantities at a glance goes something like "none, one, two, three, four, five or six, some, a dozen, a score, a few score, oh my that's a lot". The specific levels at which those change over can vary, of course. Some people probably would say "about ten" before they'd say "about a dozen", too.

One thing I've always liked about the Imperial measurement system, in fact, is that although the math is a little harder the units and their ratios really seem to be more relevant. An inch, a hand, a foot, and a yard seem to be more reasonably compared to one another than a millimeter, a centimeter, and a meter. There's the decimeter which seems it would be a very reasonable length for measuring everyday things, but the meter is too long for many things and the centimeter is too short. I'm not sure why the decimeter is almost never used. The cubed decimeter is even the definition of the (surprisingly non-SI) liter. The official SI unit of volume is the cubic meter. Who the hell drinks a cubic meter of anything at one go? I'd drink a liter or a quart, or maybe a cup or a pint. Maybe even a half gallon or two liters Maybe several pints if you'd kindly agree to drive me home. ;-)

Re:Pulling it between layers of abstraction. (1)

anss123 (985305) | more than 3 years ago | (#34291186)

As European the Imperial system is pretty Greek to me. For length we do indeed use those "unwieldy" meters/centimeters, but for the few measurements (like a person's height) where it doesn't quite fit we use fractions of a meter. Before today I had never rely thought about it so I don't think it's much of a problem.

My exposure to imperial units is entirely through movies. I honestly can't say how far 5 feet are, or how heavy 5 stones are. I can guess that five feet is 1.2 meters and that five stones is half a kilogram, but while that would make sense to me it's probably very wrong.

I think it simply comes down to what you grew up with.

Re:Pulling it between layers of abstraction. (1)

hedwards (940851) | more than 3 years ago | (#34291178)

It depends whether you're talking about fuzzy math as in Fermi problems or more accurate stuff. Because it's two different processes that happen. The more accurate stuff is more taxing because it requires more attention, memory and care. You can round things at points when you just need a ball park.

11*56= 560+56 or 616. But, if you don't need exact precision, you can let 11 = 10 and add 60ish to the end product. It's not the correct answer of course, however as you add decimal places rounding like that often gets you close enough and it's a hell of a lot faster. And for some applications getting close fast is more important than getting exact later on. A lot of probability theory is like that.

For 2 digit numbers such a short cut makes little sense, but as you get larger numbers involved the difference in time gets to be pretty significant after awhile.

Re:Pulling it between layers of abstraction. (4, Insightful)

satuon (1822492) | more than 3 years ago | (#34290424)

I think it is because the brain is at heart an analog instead of digital machine. Multiplying integer numbers however isn't a task well suited for analog machines.

Re:Pulling it between layers of abstraction. (3, Insightful)

goodmanj (234846) | more than 3 years ago | (#34290848)

2 corrections:

1. "I think it is because the brain is at heart an analog instead of digital machine. Multiplying integer numbers however isn't a task well suited for analog machines."

The humble slide rule is a beautiful analog computer whose primary job is doing multiplication. A skilled user can do multiplication with one faster than he can use a digital calculator.

2. The brain isn't a digital computer, but it isn't really "analog" either. Individual synapses are either off (not firing) or on (firing), never something in between. But the *rate* at which they fire encodes information in a way that's not analogous to either analog calculating machines or digital computers.

Comparing the human brain to *any* human technology, be it a digital computer or an analog calculator, is a massive category error.

Re:Pulling it between layers of abstraction. (1)

JustOK (667959) | more than 3 years ago | (#34290892)

but there's a difference between being able to fire, and not able to refire right now because of reuptake

Re:Pulling it between layers of abstraction. (1, Interesting)

Anonymous Coward | more than 3 years ago | (#34291082)

What?? An analog machine multiplies number _much_faster_ than a digital one.
And, yes, they can also be very accurate about it. The accuracy only depends on the accuracy of the inputs, and the measurement of the output.

Re:Pulling it between layers of abstraction. (3, Interesting)

mr_mischief (456295) | more than 3 years ago | (#34291170)

I don't think the distinction is so much between analog and digital as between synchronous and asynchronous. The brain doesn't have a quartz crystal or a cesium atom telling it when a thought is over. It settles on a result, then sets a flag letting you know it's ready to read another input. In the mean time, some tasks take longer than others. Think of it as a CISC machine with no clock pulse and some bus contention maybe rather than a tightly clocked synchronous RISC machine.

Also, it's pretty clear that certain parts of the brain tend to act as special coprocessors or at least NUMA general purpose processors. Your data is moving from one place to another with different locality.

Add to that the fact that to get precision you must let the data circuits settle before relying on them (the purpose of latches and a clock in most traditional computer processors) but that most of our lives are lead in approximations, and it's easy to see why we're poorly constructed to do precise calculations as quickly as approximations.

We can build computers to be much faster at rough approximations and with good accuracy but poor precision than at precise answers, too. We usually don't, except for Non-P and NP problems, because having exact answers quickly is often the main advantage to using a computer.

Getting approximate answers even faster from the computer is only useful in certain situations. Oddly enough, many (but not all by any means) of these situations are things humans are already really good at on our own. The facial recognition used as an example in TFA is one. Maneuvering over rough ground, identifying close to optimal paths for the Traveling Salesman problem for a small number of inputs, or translating speech into text are all things most humans do pretty easily any time. They happen to be really difficult to do quickly with precision whether using a computer or not.

Luckily, we don't have to calculate the force of every footfall when we walk. Getting a close to optimal travelling route is much better than getting one of the worst options. For larger numbers of stops, a computer will do better faster than most humans on this problem, but that's because we know how to make the computer estimate, too. We tend to work with phonemes and with local context when working out the meaning of a sentence, and the best computer dictation and language translation systems (which are still lacking) do a lot of guessing and inferring based on context, too.

We live in a sloppy world. We get mostly sloppy inputs and produce mostly sloppy outputs. Things work out fine most of the time that way, but we need precision for some of our own non-natural projects. Getting precise answers when you don't need them is wasteful of resources. It's no wonder that to survive we're very good at getting sloppy answers quickly. It's no use to wait and figure out which exact angle you need to run away from danger. Close to 180 degrees is pretty good.

Re:Pulling it between layers of abstraction. (1)

ProfessionalCookie (673314) | more than 3 years ago | (#34290464)

The brain arguably is man-made.

Re:Pulling it between layers of abstraction. (5, Funny)

h4rm0ny (722443) | more than 3 years ago | (#34290492)

The brain arguably is man-made.

I think you'll find there's usually a woman involved in the process too. :)

Re:Pulling it between layers of abstraction. (-1, Troll)

Anonymous Coward | more than 3 years ago | (#34290970)

No wonder it can't do math.

Re:Pulling it between layers of abstraction. (0)

Anonymous Coward | more than 3 years ago | (#34291020)

Must be why guys are sometimes involved in car accidents as well...

Re: Pulling it between layers of abstraction. (2, Interesting)

A1rmanCha1rman (885378) | more than 3 years ago | (#34290478)

Yep. India's Shakuntala Devi (known in those days as The Human Computer) as a girl used to challenge the mainframes of the 70s with such prodigious feats as multiplication of 2 massive numbers, and frequently pointed out correctly that the computer was wrong after assessing its answer.

As usual, nothing was made of this ability aside from its sideshow value, and no studies made of her brain capacity or computational methods.

Last I heard, she's reduced to making a living selling horoscopes and the like, if she's still alive.

Question is, do we really want to know what our capabilities are as human beings, or do we just want to keep selling big iron to governments and corporations at great profit?

Re: Pulling it between layers of abstraction. (1)

Securityemo (1407943) | more than 3 years ago | (#34290500)

Why not both?

Re: Pulling it between layers of abstraction. (2, Informative)

mwvdlee (775178) | more than 3 years ago | (#34290682)

Last I heard, she's reduced to making a living selling horoscopes and the like, if she's still alive.

Tt seems she's doing quite well and is still active: http://en.wikipedia.org/wiki/Shakuntala_Devi [wikipedia.org]

Re: Pulling it between layers of abstraction. (1)

icebraining (1313345) | more than 3 years ago | (#34290772)

Real life mentats...

Re: Pulling it between layers of abstraction. (1)

A1rmanCha1rman (885378) | more than 3 years ago | (#34290916)

Real life mentats...

Glad to hear it, I checked the same Wikipedia article just after I posted this comment and also Googled her name for articles and pictures.

What struck me was that there are no pictures of her when she was carrying out her wondrous exploits at the age of 8, and precious little analysis of her abilities outside of documents posted in India.

That's a crying shame for such a prodigious talent.

Re: Pulling it between layers of abstraction. (1)

demonlapin (527802) | more than 3 years ago | (#34291022)

frequently pointed out correctly that the computer was wrong after assessing its answer.

What morons built a "mainframe" that couldn't multiply? Sounds like an urban legend.

Re:Pulling it between layers of abstraction. (2, Interesting)

goodmanj (234846) | more than 3 years ago | (#34290554)

The brain is not a digital computer in any useful sense. It has no clock, no real concept of "bits", either for data transmission or storage. Its elemental operations are best described in terms of message passing over a network, not in terms of math.

Yes, you can say that it can do tasks that only a powerful computer could perform, but that doesn't mean it's a powerful computer any more than a shark is a very powerful jet-ski. It's not a matter of "not having access" to "low level capability": at a low level, the brain is a totally different thing than a computer.

Re:Pulling it between layers of abstraction. (1)

Securityemo (1407943) | more than 3 years ago | (#34290594)

Yes, the underlying constructs are very different. But again, doesn't the concept of abstraction between high and low layers of processing still apply to any system that is made up of any form of discrete operations?

Re:Pulling it between layers of abstraction. (3, Insightful)

MDillenbeck (1739920) | more than 3 years ago | (#34290954)

Neurobiology is a fascinating topic. Of course a brain is not a digital. Neurons often have multiple connections (dendrites) and emit more than one type of neurochemical signal and often has more than one type of receptor. However, I can see the point that these neurochemicals are sent out in specific quanta and that a threshold needs to be exceeded to initiate a response. Thus instead of using a neuron as the basic unit but the receptor type as the unit, we can see neurology in a digital aspect. I would take it a step further that the brain would then be a series of parallel digital computers (based on receptors) that are networked to produce a series of responses, both when considering a network of neurons and within the neuron itself.

Essentially, what we are looking at is emergent behavior. On the receptor level we see digital activity. However, once we get to the neuron or brain level, the emergent behavior of the system appears analog.

Re:Pulling it between layers of abstraction. (0)

Anonymous Coward | more than 3 years ago | (#34290924)

The brain evolved to be able to recognise people who are familiar to you. Being able to pick out people you know from a crowd of unfamiliar apes is somewhat useful. Safety in numbers and solidarity and somesuch eh? Also somewhat useful being able to pick your enemies from a distance so you could avoid/destroy them, preferably before they recognised you.

Homonids never really needed the ability to multiply large and therefore abstract numbers.

Re:Pulling it between layers of abstraction. (1)

mikael (484) | more than 3 years ago | (#34291032)

I'd say it's more that we just need practise to build up the connections to all the different areas of the brain. Much like when solving a mathematics problem, there are so many different ways of looking at the problem. Sometimes it helps to use algebra or to draw a picture or diagram. That makes use of the visual areas of the brain - around 30% in mammalian brains. For simple arithmetic we usually learn times-tables (1x1 = 1, 2x2=2, 3x2=6, ... 12x12 = 144). Doing this for certain larger numbers is easy (350x200, 400x250), but the extra digits requires practise in remembering the intermediate results and performing the final addition. If you look as silicon design papers, they would have papers on how multiplication and division could be optimized with fewer transistors.

The brain has an architecture like a super-computer, with a data-flow design. If you look at the diffusion MRI/CAT scan images [weblogsky.com] which look at the directional bias of the fibres in the white matter of the brain (the long-distance communication network), there is definitely a tree-like network. Then all the different areas of the brain have separate purposes, like object image->name, or object image->orientation, sound->object name, objects images->distance (stereoscopic vision). Rehabilitation clinics with stroke and brain injury patients have diagnostic tests that are to measure impairment in these areas. Some patients could tell that there was an apple in front of them, but not whether it was upside down or not. Others would know there was an object in front of them, but not know what is was, or even how far away it was.

Pseudoscience? (5, Interesting)

contra_mundi (1362297) | more than 3 years ago | (#34290358)

How about 357 * 289 being hard is because 7 is the average size of the short term memory [wikipedia.org] , and you need to remember more numbers than that to arrive at 103,173?

Re:Pseudoscience? (1)

DamonHD (794830) | more than 3 years ago | (#34290412)

That's wouldn't contradict TFA, it might simply compound the problem for example.

Rgds

Damon

Re:Pseudoscience? (0)

Anonymous Coward | more than 3 years ago | (#34290426)

How about it being hard because they require ridiculous levels of accuracy (6 digits)? I can calculate the answer to 2 digits accuracy in a second or two and 3 digits in about 5-10 seconds. Good enough for most real life applications.

It's still a little unsettling that I'm beaten by a $2 calculator, I admit.

Re:Pseudoscience? (1)

goodmanj (234846) | more than 3 years ago | (#34290446)

The parent post has it exactly right. There's nothing new here, wild theories about "routers" and "traffic jams" aside. You can only keep 7 things in your head simultaneously, and multiplying 3-digit numbers takes more memory slots than that.

Exact values vary depending on how you think about the multiplication algorithm, but roughly:
1 digit x 1 digit : max 2 digits to remember at any point, easy task
1 digit x 2 digit : max 3 digits to remember, pretty easy
2 digit x 2 digit : up to 7 digits to remember, difficult but doable for most people
2 digit x 3 digit : up to 9 digits to remember: very difficult
3 digit x 3 digit : up to 14 digits to remember, nearly impossible

Multiplication starts getting difficult right at the point you'd expect based on the age-old "7 items in short-term memory" hypothesis. For confirmation, try doing *subtraction* in your head. It's easy to subtract two 2-digit numbers, because you only need to keep 6 numbers in your head at once. Two 3-digit numbers requires 9 digits of memory: it's difficult but barely doable. Two 4-digit numbers suddenly becomes nearly impossible. Being able to write down *any* of the numbers, either the inputs or the output, for multiplication or subtraction, makes the task drastically easier because it reduces the necessary short-term memory storage.

As you do mental arithmetic and start screwing up, you can *see* what the problem is: it's not a problem of neural bandwidth, it's just that you start forgetting some of the digits you're juggling.

Re:Pseudoscience? (2, Interesting)

Jarik C-Bol (894741) | more than 3 years ago | (#34290474)

which results in the weird memory tricks people have developed for doing large number math in your head. breaking down the problem into small chunks, so that you can operate the problem in 7 number chunks and whatnot is what the majority of them end up doing, they just get there by different paths.

Re:Pseudoscience? (1)

BananaBender (958326) | more than 3 years ago | (#34290510)

I think this line of reasoning is not convincing.
The brain masters computations (e.g. visual recognition tasks, speech recognition etc.) that require enourmous amounts of memory when implemented in a conventional computer system. Under the assumption that those recogntition tasks are inherently memory-intensive, the brain has to have similar amounts of memory at its disposal.
So, obviously, the brain is not lacking memory to execute complex calculations, but it seems to disallow the conscious control of brain structures to execute multiplications. Each single neuron could execute such multiplications with ease.

Re:Pseudoscience? (2, Insightful)

goodmanj (234846) | more than 3 years ago | (#34290712)

Under the assumption that those recogntition tasks are inherently memory-intensive, the brain has to have similar amounts of memory at its disposal.

I question the assumption you're making. The nervous system is not a computer in any useful sense: its elemental storage is not in bits, and its elemental operations are not bit logic. To compare its "specs" with a digital computer is to compare apples and oranges.

Example: pitch recognition. How does a computer recognize the pitch of a sound? An incoming audio signal is converted by an analog-to-digital converter and stored as a long string of numbers in memory. A Fourier transformation algorithm is performed to transform this into pitch-vs-amplitude data. The human ear can do the same thing: can we draw conclusions about the ear's memory storage, CPU speed, and analog-to-digital converter specs by the comparison? No, because the human ear doesn't work that way. It does frequency detection "in analog hardware", as a consequence of resonant structures in the cochlea: the signals coming out of the cochlea encode pitch information, yet the cochlea has no memory or CPU at all.

And that's just one tiny simple structure in the human nervous system. Multiply that category error by a million or so to see how false comparing brain processes to computing processes is.

Back to my original point: while at a neurons-and-ganglia level you can't compare the brain to a computer, the *conscious mind* *can* emulate a computer, among other things. But the mind can only emulate a computer with a short-term memory of 7 items, regardless of what you think the "memory" of the underlying substructure is.

And the fact that our conscious short-term memory holds 7 "items", not bits -- the items can be digits, words, names, faces, or objects -- continues to show just how un-like a computer the brain really is.

Re:Pseudoscience? (1)

MDillenbeck (1739920) | more than 3 years ago | (#34291010)

Good point. The "brain as a computer" is just a model, and over-simplification.

Also, there is an over-emphasis on the brain as a "CPU". For example, when learning a sport we put a lot of memory into the various techniques. How do you hold a basketball? What motion do you need to dribble or shoot? Where do you aim, how much force do you apply? Eventually, however, the athlete's body soon "learns" the motions - it is not something that needs to be loaded into working memory, but something that becomes automatic. The body "knows" how to respond based on a quick sensory input.

If I were to go with the computer analogy, the 5-9 pointers is a good one. Another one is to think of working memory as your registers - the easily and rapidly accessible storage slots. Once those are filled, you need to start swapping those out if you need to access more data. This slows you down in the calculations, or worse it prevents the calculation because you are faced with storing the results and loading new input will overwrite those stored results.

Re:Pseudoscience? (2, Insightful)

hedwards (940851) | more than 3 years ago | (#34291206)

Actually, you're not entirely correct, the human brain is much more like old console hardware than a modern computer. Because a lot of that stuff was done on consoles via registers. The programmer didn't have to do anything in particular other than write to or read from the appropriate register to have whatever done.

Such as on the GBA, if you wanted to write to the screen you would select the correct register and give it the correct value, the hardware would do the rest.

Re:Pseudoscience? (0)

Anonymous Coward | more than 3 years ago | (#34290782)

Let's just put it this way: a human brain's STM is an array of 7 void pointers, that can point to any type of object, be it a digit, a facial feature description, a sound pattern or whatever. The point is that there's just 7 pointers and that's it.

or it could be because... (1, Insightful)

Anonymous Coward | more than 3 years ago | (#34290360)

doing complex multiplication isn't inherently necessary to staying alive. being able to discern who is who is.

Here you go: 357 x 289 = 103173 (0)

Anonymous Coward | more than 3 years ago | (#34290390)

289 x 357 is surprisingly the same result.

Perhaps a Firmware update is needed? (1)

Froggels (1724218) | more than 3 years ago | (#34290396)

If it works for the Borg why not us?

The way math is taught... (4, Interesting)

blahplusplus (757119) | more than 3 years ago | (#34290414)

... 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 [wikipedia.org]

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.

Re:The way math is taught... (0)

Anonymous Coward | more than 3 years ago | (#34290508)

fascinating, i always thought the limiting factor was our crappy base 10 instead of binary derivated base 32 (5 fingers) or the ever awesome sexagesimal

Re:The way math is taught... (3, Insightful)

Rich0 (548339) | more than 3 years ago | (#34290522)

Uh, when I was taught math in elementary school, concepts similar to the Mayan depiction were often used. The only difference I see is that this was all done in base 10 and not in a hybrid of base-5 embedded in base-20.

I'm not really sure what you're getting at. Sure, you can represent numbers as shapes and sizes, but I don't see how this really helps mental math except when it comes to order-of-magnitude calculations.

If I want to multiply 357x289, I can already tell you that the answer is somewhere around 90000. The challenge comes if I want to know the answer to more than 1-2 significant figures. I don't see how using something like the Mayan system or any other system is going to accomplish this.

In any case, I'm not even sure what the problem that you're trying to solve is. The average person can do math well enough to get by in the real world. Sure, it would be nice to be able to walk down the aisle at the grocery store and figure out the per-unit prices in my head to 3 sig figs, but I don't see anything you're offering as accomplishing this. If I'm going to do a model simulation run I'm going to use a computer, and that requires almost zero mental effort around performing calculations - just a TON of creativity and analysis creating the mode/etc.

Re:The way math is taught... (1)

blahplusplus (757119) | more than 3 years ago | (#34290796)

"I'm not really sure what you're getting at."

If you're serious about understanding what I said ... It's not something that can possibly be communicated easily without book length treatment and requisite reading of a lot of literature.

Without which, you won't get it because you won't be able to see the relationships because you don't have the requisite conceptual framework in your head to see how different areas link to one another.

But It has to do with how human languages and mathematics basically use a more basic language in the mind - see: cognitive linguistics, and how our mind are able to map any arbitrary system onto any other arbitrary system of things. To be able to interpret one thing in terms of other things, which is very powerful the implications of which you will understand if you read enough.

Some good books for you to read:

http://www.amazon.com/Philosophy-Flesh-Embodied-Challenge-Western/dp/0465056741/ [amazon.com]

http://www.press.uchicago.edu/presssite/metadata.epl?mode=synopsis&bookkey=3637992 [uchicago.edu]

http://www.amazon.com/Where-Mathematics-Comes-Embodied-Brings/dp/0465037712/ [amazon.com]

Re:The way math is taught... (1, Insightful)

khallow (566160) | more than 3 years ago | (#34291088)

While math is a genuinely complex subject, I still think you should try to briefly elaborate on what you're talking about rather than just dumping links to books. I recently argued with someone about an economics subject. After making many unsubstantiated claims and accusing me of being "conditioned", his side eventually boiled to "watch my ridiculously long video for my argument" (I scrolled through the video, it had some psychedelic stuff, movie outtakes, etc, but not anything I'd consider related to the stuff he was talking about, except in some sort of weird brainwashing way). No offense, but I don't think it's fair to the reader (especially when you consider that your post may be read by hundreds of people) to acquire and read three books when they don't even know yet what you are talking about.

After all, the internet is the living embodiment of the letdown. If I breathlessly tell everyone "there's this paper that will change your life", odds are much better that it's something crazy, like Hollow Earth or Electrical Universe, than something that would actually be beneficial to you.

I'm not looking for a copy/paste of the book or anything like that. But it would be nice to describe briefly what goes on and how the method you describe addresses the grandparent's concern.

Re:The way math is taught... (1)

dcollins (135727) | more than 3 years ago | (#34290722)

"... 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..."

My argument: Math is not these computations (arithmetic). Math is communicating patterns; it's abstraction, use of variables, theorems and proofs. So frankly, spending any time at all on improved numerical computations is a total waste in the modern era. We really do have computers for that nowadays.

Care to explain exactly what your "research in this area" is?

Brain != Computer (1)

SigmundFloyd (994648) | more than 3 years ago | (#34290450)

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.

Exactly. That's why I've always been baffled by the commonplace brain-computer comparison, when it's so very clear that what goes on under the respective hoods is completely different.

Re:Brain != Computer (1)

MDillenbeck (1739920) | more than 3 years ago | (#34291034)

Is is a model, a simplification for understanding. Since the human mind is capable of abstractions and pattern recognition, we can see ways in which the brain is like a computer. Because a computer is a common schema in our modern society, it gives people a very rudimentary understanding of the brain. Without it, we are facing an incredibly complicated system to analyze - something well beyond the ability of almost anyone. After all, we learn simplified models for atoms, the solar system, economics, and just about anything learned... why not the brain?

We, Borg (1)

gmuslera (3436) | more than 3 years ago | (#34290468)

In the I, Borg episode of Star Trek TNG, they went a step further in this idea trying to shut down the collective showing them an unsolvable geometric problem. And as with this kind of traffic jams, we can always refuse to go thru this road, or even exit it if took too much time.

how I did it (1)

jdogalt (961241) | more than 3 years ago | (#34290470)

For fun I'll record in the slashdb record how I surprised myself and managed to correctly multiply 357 by 289 in my head. I don't have a history of being able to do such things, and it did take me a couple minutes, but I was pretty surprised to see bc confirm my answer.

I went with the route of breaking it down to 357 * 300 - 11 * 357. 357 * 300 is 35700 * 3. Even that is pretty hard so I figured 35700 * 2 = 71400, then + 35700 . ... 57 + 14 is 71 thus 1071, then add those 2 0's back on to get 107100. Then throw that pesky round 100K off to the side to be remembered later, and we have 7100 - 11 * 357. Which is 7100 - (10 + 1) * 357, so 7100 - 3570. Since half of 7100 is clearly 3550, then 3530 is the partial. now 1 more 357 to subtract from that. I went with 3530 - 400 is 3130, but have to add back the 43 to get 3173. Now just add back that big ol round 100K and we have 103173.

See, no sweat :) Of course I expect other people may have more digit storage memory than I do, and thus can just do it the standard simple way...

Re:how I did it (0)

Anonymous Coward | more than 3 years ago | (#34290530)

I did it correctly only at second attempt and it took me a lot of whispering numbers so I could remember them and almost 5 mins. I have to admit- it's really bottlenck-ish :D!
It all boiled down to:
multiply 357 with 3
multiply with 10
subtract 357 from it
multiply with 10
subtract 357 from it

Looks pretty cool and more like a computer loop :D.

Re:how I did it (1)

atari2600 (545988) | more than 3 years ago | (#34290854)

Pretty close to what I did. ( (300*300 + 50*300 + 7*300) ) - ( (300*11) + (50*11) + (7*11) ) This was reduced to (300*3+50*3+7*3)*100 - (3927) It's not hard at all but I learned mathematics in India.

Welcome (1)

toxygen01 (901511) | more than 3 years ago | (#34290548)

have you heard of associative processing/memory? That's CS concept with PoC that we can construct machines like human brain, but again, they could analyze face in fraction of second, but multiplying is gonna take some time...

Correctness (1)

PhrostyMcByte (589271) | more than 3 years ago | (#34290562)

Our memory gets things wrong all the time. We can scan a crowd and associate a face with someone who looks similar. When we multiply a number in our head, we're trying very hard to get the exact, correct answer. Perhaps the brain is just a lot better at fuzzy problems than those demanding strict correctness.

It might also be an input problem. Our number system is a very effective way to communicate math, but it may be a very foreign and sub-optimal way for the brain to process math. Maybe we need a new way to represent things that provides a better balance.

Is that all surprising? (1)

houghi (78078) | more than 3 years ago | (#34290636)

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.

People are great at recognizing faces. Computers are great at computing.

Re:Is that all surprising? (1)

ctmurray (1475885) | more than 3 years ago | (#34290958)

And recognizing a familiar face in a crowd might be a good survival skill for a species so it knows when to flee. Where as the math calculations are rarely fatal so no driving force for the species to develop speed at this task. Now if everyone who was slow at the task were to be killed off, then those genetically able to do the math would be left over to pass on those genes.

Brains don't do percision (3, Interesting)

DarkOx (621550) | more than 3 years ago | (#34290680)

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.

Re:Brains don't do percision (0)

atari2600 (545988) | more than 3 years ago | (#34290864)

I believe the other reason is that manors are usually fortified and building walls / moats around how the brain works makes it harder to work.

Uh, no? (0)

Anonymous Coward | more than 3 years ago | (#34290688)

The very fact that we have powerful computers that still can't do things my cat can, suggests that brains DON'T do anything remotely resembling calculations.

I think this is a case of having a hammer and everything looking like a nail. Yes, we have computers. Yes, we have math. After decades, our best technology barely functions at the level of a small rodent.

Either life functions at several orders of magnitude higher levels of computation, or it's fundamentally different, more like a huge analog ball of yarn that furthermore encodes itself.

The Chinese (1, Offtopic)

asvravi (1236558) | more than 3 years ago | (#34290700)

The Chinese used "GPU"s instead of "CPU"s for their supercomputer record - and that is supposedly "unfair". How is it anywhere close to fair then comparing the diverse capabilities of a brain and a computer?

Math is easy (0)

Anonymous Coward | more than 3 years ago | (#34290732)

357 TIMES 289? That's easy. It's uh...uh.... hold on...
errr.........

BLUE SCREEN OF DEATH! *Beeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeep*

An analogy (5, Insightful)

goodmanj (234846) | more than 3 years ago | (#34290784)

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."

The Traffic Jam in My Brain (1)

RoverDaddy (869116) | more than 3 years ago | (#34290810)

Makes me wanna scream and shout.

Router? Time to upgrade (1)

gratuitous_arp (1650741) | more than 3 years ago | (#34290862)

Time for that 7600 series you've always wanted. That or go with a nice ISR. You'll get used to the Cisco stamp on your forehead. :-P

Knowing (4, Interesting)

Sanat (702) | more than 3 years ago | (#34290872)

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.

Evolution and Survival (0)

Anonymous Coward | more than 3 years ago | (#34290944)

Being able to recognize friend or foe would have had great survival value in human evolution, as would the ability to identify a prey animal in a dark forest. Being able to do arithmetic in an instant would not have the same value.

Isn't it how you define processing? (1)

devent (1627873) | more than 3 years ago | (#34291134)

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.

Isn't it how you define processing? For a computer it don't make any difference if you process 5*5 or 123565*435456, because the internal representation of the numbers and the hardware paths are basically the same for both tasks. But our brain is a highly specialized device, specialized on tasks that help us to survive in the good old jungle.

So the task to multiply 357 by 289 takes only for our computers a puny amount of processing, because our computers are specialized on this tasks, but for our brain in takes a high amount of processing, because it is specialized for different tasks.

There are for some reasons FPGAs [wikipedia.org] out there which will improve the speed for a specialized task by 10 or 100 times.

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