Paul Bourke

October 28, 2002 11:22 PM

Paul Bourke of Auckland has an excellent set of elegant and informative webpages for the kind of math you look at. Even if math perplexes you, his pages are still quite pretty and often make for interesting reading regardless. Every place I've worked between college and now, Paul has given me pages that nicely explained how to do somthing I needed to do and even personal help on occasion. Here's to you, Paul!
posted by tss (5 comments total)

Even if math perplexes you...

Ah, wild, perplexing infinity, sang Cantor as he diagonally slashed and burned: more reals than rationals, as it should be in life, love, and math.

And that same elegant argument can be used to show that no universal algorithm exists for deciding whether a Turing machine will halt, and lies at the heart of Godel's majestic, magic work.

Paul Bourke provides fun and exposition on his site. Nice post, tss. Thanks...
posted by fold_and_mutilate at 12:09 AM on October 29, 2002

I haven't read through the other links very carefully, but the page on "Wild Infinity" ("perplexes you") is both uninsightful and incorrect. I can't imagine that anyone unfamiliar with Cantor's diagonalization could gain anything but confusion from reading that page. Bourke summarizes his exposition with: "We have a table with all possible binary sequences and yet we can construct a sequence not in the table!" The statement is self-contradictory, and offers no insight into how the "contradiction" can be resolved. More informative but still cursory explanations may be found quite easily; here is one. The point, entirely ignored by Bourke, is that there are different "sizes" of infinity, and while some infinite sets can be "counted" or enumerated (listed one by one), some quite common ones cannot be.
posted by dilettanti at 6:57 AM on October 29, 2002

Although "nice thread" posts are generally frowned upon at MeFi, I'll offer one here.

I enjoyed the post, the links, and much of the math, though I have to agree with dilettanti that the link on infinity was a bit off.
posted by syzygy at 5:03 PM on October 29, 2002

Paul Bourke of Auckland

Are you sure?
posted by dg at 10:28 PM on October 29, 2002

The Mac came with a surface rendering piece of software....anyone know the name? I've forgotten.
posted by StoneRoseDesign at 4:24 PM on October 31, 2002