Computer vs the brain
The methods are very simple and involve practice over a weekly (or monthly) period of time, with time varying depending on the last time you had any math courses.
If you have practiced these methods, you are witness of the proof of human innovation firsthand, yet technically speaking, your PC computes the results much faster, and most benchmarked speed differences are mostly relative to the speed that the computation is entered into the PC.
As the numbers get larger, your ability to pinpoint an exact value becomes increasingly difficult, similar to a PC. However, I have yet to see a PC compare to the estimating abilities of humans involving complex computations.
Enrico Fermi is a case in point. A physicist and mathematician, Fermi made and proposed solutions involving estimates that even today’s PCs would have trouble deliberating. One such example is the Fermi paradox; a mathematical counter-analysis made by Fermi in response to the Drake Equation – an estimate involving extraterrestrial life in our galaxy.
Can your computer estimate?
The drake equation is both mathematical and relatively computable (by machines with degrees of accuracy), as you can clearly see if you take a look at it.
There is a catch. Ultimately the results of the equation are of such a large scale, that the mathematical rules of indeterminate form apply, and while the computer is chugging along at finding an accurate result, you can come to the same approximate answer by simply saying the result is either “very big in the billions” or “0″.
While computers may be very good at getting exact results, likely faster than you can, a more interesting and probably also more applicable question is: can you computer determine the best degree of estimation?
The next time someone asks you who can compute faster – the brain or the PC (or Mac), you can safely quote me in response with something such as:
The PC is faster at many math problems, but when it comes to a fermi problem, the PC slows to a grinding halt.
After all, computers can currently only solve what we have designed them to. How could they possibly compute estimations at the same level as our brain if we do not understand the limitations of our own design?
Mentally Calculate… (ronniediaz), http://ronniediaz.com/2012/01/19/mentally-calculate-percentages-of-large-numbers-quickly-without-using-a-calculator/
Enrico Fermi (wiki), http://en.wikipedia.org/wiki/Enrico_Fermi
Fermi Problem (wiki), <a href="http://en.wikipedia.org/wiki/Fermi_problem
Fermi Paradox (wiki), http://en.wikipedia.org/wiki/Fermi_paradox
Drake Equation (wiki), http://en.wikipedia.org/wiki/Drake_equation
Indeterminate Form (wiki), http://en.wikipedia.org/wiki/Indeterminate_form
Computers vs. Humans (blog image), http://rksharma.wordpress.com/