Archive for April 2011
From Peter G. Casazza’s occasionally pessimistic A Mathematician’s Survival Guide (last emphasis mine):
Wonderful Advances. When I first joined the mathematics community I was excited to join a group dedicated to advancing mathematics. I had a rude awakening when it became clear that we were really working to advance ourselves. This is an unfortunate consequence of the reality around us. We must all compete for very scarce research grants, positions, promotion, tenure, awards, raises etc. But we need to be careful that this reality does not diminish our enjoyment of the subject.
One of the things I wish I had read a few years ago. Little niggles can also matter.
[I write this post with a certain degree of embarrassment, because in the end it turns out (1) to be more simple than I anticipated, and (2) already done before, as I could have found if I had internet access when I did this. :-)]
The so-called “Tupper’s self-referential formula” is the following, due to Jeff Tupper.
Graph the set of all points such that
in the region
where N is the following 544-digit integer:
The result is the following graph:
Whoa. How does this work?
At first sight this is rather too incredible for words.
But after a few moments we can begin to guess what is going on, and see that—while clever—this is perhaps not so extraordinary after all. So let us calmly try to reverse-engineer this feat.