How can complex calculations be done in seconds solely using mental arithmetic?

[roger]

I once saw a programme not so long ago, showing a young man who was calculating something like 56^6 in a matter of seconds.
And also working out square roots of numbers in seconds all entirely in the head.

Could someone tell me how calculations like that can be performed so quickly ?

(I would have trouble doing square roots on paper let alone in the head

 

[Werg22]

I once saw a programme not so long ago, showing a young man who was calculating something like 56^6 in a matter of seconds.
And also working out square roots of numbers in seconds all entirely in the head.

Could someone tell me how calculations like that can be performed so quickly ?

(I would have trouble doing square roots on paper let alone in the head

Those people practice several hours a day and use their brain differently than we do in order to calculate. It's a matter of several years of practice.

 

[roger]

But how do these savants perform these calculations ?

Whats the method ?

 

[neurocomp2003]

certain tricks like
[(n+1)*10+5]*[n*10+5] has a nice trick though i can't remember.
but it may be memorization...or it may be factorization really quickly...ie 56->7*8.
and of course a lot of practice...its like watching someone work with a abacus except without the actual tool. Those people who work the abacus are amazing.

 

[nate808]

as was just stated, most of being able to do such large mental calculations is the ability to factor without hesitation. additionally, instead of visualizing the numbers that they are to deal with, it is easier to listen to the numbers. I;m not sure why, but i read that somewhere

 

[roger]

certain tricks like
[(n+1)*10+5]*[n*10+5] has a nice trick though i can't remember.
but it may be memorization...or it may be factorization really quickly...ie 56->7*8.
and of course a lot of practice...its like watching someone work with a abacus except without the actual tool. Those people who work the abacus are amazing.

I don't understand [(n+1)*10+5]*[n*10+5] ?

But this savant was apparently born with it, it wasn't supposed to be a trick.

So I don't really know whether or not it was a question of practice.

 

[neurocomp2003]

are you sure his parents weren't doing advance educational reading while he was in womb/birth.
multiplicatoin are not concatentated

35^2=((3*4)25) =1225 and in general n5^2=(n+1)*n25
35*45=((3*5)75) = 1575 and in general n5*(n+1)5=(n*(n+2))75

some types of tricks.

 

[amcavoy]

I read that human calculators use their long-term memory "actively." By that I mean that they use their long-term memory to remember steps, etc. instead of trying to do mental calculations like the rest of us, who sometimes forget steps mid-calculation. I know that some people with photographic memories can temporarily "shut down" areas of their brain in order to remember more efficiently. This probably has something to do with calculation too.

 

[quark]

I never did but you can practice them. Try your hands on Trachtenberg's Speed System of Calculations. You can also try Vedic Mathematics.