Yesterday while waiting for my wife at the doctor’s office, I managed to take a peek at an older issue of the American Scientist.Ã‚Â Ever since I graduated from Pace University with my BS in Biochemistry, I rarely read anything too scientific and tend to browse more computer related magazines.Ã‚Â Anyhow, the very first article, “Gauss’s Day of Reckoning" by Brian Hayes caught my attention:
In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher’s aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + … + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you “fold” the series of numbers in the middle and add them in pairsÃ¢â‚¬â€?1 + 100, 2 + 99, 3 + 98, and so onÃ¢â‚¬â€?all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50Ãƒâ€”101. The more general formula, for a list of consecutive numbers from 1 through n, is n(n + 1)/2.
Carl F. Glauss was only 7 years of age when the above event took place!Ã‚Â Now, I have met a handfull of “gifted” kids growing up in Brazil, some of them even able to mesmerize people with feats like the one described above.Ã‚Â But the article goes a bit further into his earlier life, when he supposedly corrected his dad’s mathematical equation at the tender age of three!!!Ã‚Â I couldn’t possibly imagine any 3-years-old kid that I’ve met/seen doing such a thing.Ã‚Â Throught history, I’ve heard of famous composers who could write an entire symphony by the age of four, or recite Homer by heart while dancing the macarena!Ã‚Â Well, maybe not the latter, but I think you’ve got the picture. :)
I remember being 5… and I think I can vaguely remember one or two events from the time I was 3… and let me tell you something, I don’t remember doing anything out of the ordinary than playing in the sand, running around with the other kids, and watching lots of cartoons.Ã‚Â There was also a lot of learning going on, but mostly it was one sided, where my parents taught me about the world around me, and I tried to absorb as much as my attention allowed me.Ã‚Â :)
I wonder if all the technological “progress” we’ve undergone since those long days have actually been beneficial at all.Ã‚Â In a society that pretty much “learns” and “socilaizes” via the internet, television, and eletronic gadgets, how can one really learn to discover the world without interference?