Sunday, 20 March 2016

significant digits or the life of pi

Sadly, we missed out on enshrining the day reserved on the calendar for the appreciation of Pi some how this year, but ought push out some belated returns, thanks to this investigation prompted by the never-forgetful Kottke.
While modern computing can deliver ฮ  calculated out to some thirteen trillion decimal places, in search of patterns in the chaos, space agencies only have needed to use a value of the ration calculated out to about fifteen—fewer than the numbers one can count on this pencil if you magnify the image, to send out all our emissaries over billions of kilometers. One might wonder if rocketeers loose fidelity with that level of precision, but it turns out that rounding the value to fifteen decimal places, but if the distance Voyager I is from Earth is the radius of a circle with a circumference of over a hundred billion kilometers, yields a circle that’s only off by a few centimeters difference. The Universe is unimaginably vast and exceedingly small, yet scientist pronounce that to describe a circle that would envelop it all, we would only need about twenty-five more additional decimal places to calculate out a circumference of billions of light-years where there would be less than one hydrogen atom’s breadth between that pi and the pi out to the nth decimal. That’s amazing and I wonder what it means that we can push so far out with numbers to the point where it seems meaning and relevance fall away.