Gribbin, Wittgenstein, Amazon and the reasonable ineffectiveness of mathematics

The serendipity of modern life, abetted by the evolution of the podcast, the USB-equipped car stereo, and emergent algorithmic connections [1], has meant that I am simultaneously listening to a 2003 In Our Time podcast on Wittgenstein, reading a 1994 book by John Gribbin, and sluggishly pondering the limits to reason.

There's something in there I am not clever enough to tease apart, something about what mathematics can and cannot tell us about "the real" [2], and how our forms of expression (language, mathematics, visualization, etc) match up to the challenge of describing "the real".

The common thread, just on the tip of the cognitive tongue, feels like a extended debate about whether it is "true" (whatever that means) to say that mathematics is "unreasonably effective" at describing "the real", or whether a combination of metaphor, intuition and empirical intuition is a better guide.

If we go with the latter, then mathematics is "merely" a self-consistent (but limited and tricksy) toolkit with which an almost unlimited number of models of "the real" may be extended or manipulated. It is thus not "unreasonably effective" but rather "reasonably" (as in understandably) ineffective (and effective too).

Sigh. If I were to try to toss in 'Strange Loop' (Hoftstader) [3], Wolfram and (inevitably) Godel my head would probably explode, but if I had three times my currently declining intellect perhaps it would all make sense. Maybe if I keep rereading Gribbin (who is much underestimated I think) and replaying Wittgenstein I'll make a bit more progress. Or not.

Notes and asides

[1] Amazon, Google and Wikipedia all played their role in producing a never ending web of relationships. This blog, posting, in its own small way, will be one more bit of noise for our friendly reinforcing neural network. Of course we all know about Google and Wikipedia, but Amazon is continuing to add new layers of reinforcing connections between its artifacts, one of which led to this book: A World Without Time: The Forgotten Legacy of Godel And Einstein. Amazon's link to used books (how do they make money from that?) means I was able to pick it up for $5 impulse purchase. Hence Amazon gets in the post title.

[2] In parens since reality is starting to feel very different from our historical sense of it.

[3] Speaking of strange loops and the arrow of time, while writing this a funny stutter in the relationship between Blogger and my browser cache switched the post transiently back to an earlier version. Which did produce a weird sensation ...