Moar Math!

But my brain is full!

You may have noticed that, in a number of recent posts, the topic has been math. The good-bad news is that there’s more to come (sorry, but I love this stuff).  The good-good news is that I’m done with math foundations. For now.

To wrap up the discussion of math’s universality and inevitability — and also of its fascination and beauty — today I just have some YouTube videos you can watch this Sunday afternoon. (Assuming you’re a geek like me.)

So get a coffee and get comfortable!

To start, here’s a pretty good TED talk that touches on many of the topics from the recent posts:

Here’s another from one of my favorite YouTube channels, Numberphile, that talks about three basic philosophical positions mathematicians take regarding the ontology of math: Platonism, Nominalism, and Fictionalism.

You might think of these, essentially, as: Believer, Agnostic, Atheist positions with regard to the reality of numbers. (Note that, other than Platonism, these are broad philosophical positions that extend beyond mathematics.)

There are, in fact, many specifically mathematical positions in the Philosophy of Mathematics: Constructionalism and Intuitionalism, for example.

This next video has a slightly poorer quality than the first two, but it’s worth watching if for no other reason than the speaker’s enthusiasm regarding math.

Much of the fascination and love of math is based on its surprising beauty and elegance. It is the purest of the sciences and has the strongest elements from a priori experience.

Here’s a video that explores the important difference between the transcendental numbers and all the rest that aren’t. Even irrational real numbers have an algebraic expression (√2, for example), but transcendental ones do not.

The video also touches briefly on Euler’s Formula.

The game of reducing an expression to zero is fascinating!

To wrap up, here’s video about math, sex, love, the human mind, and a bit more. It may also change your mind about what a mathematician looks like:

In the posts ahead, I’m going to explore the complexity of computers and the human brain. It’s all leading to a discussion about whether consciousness is likely to be algorithmic or not and what it might take to build an “artificial” mind. Along the way I’ll be referring back to some of this math foundation stuff.

Not that there might not be some diversions along the way. (Or do I mean divisions? After all that math, it’s hard to tell.)

Stay numerate my friends!