Musicians practice; actors rehearse; athletes work out; and mathematicians play with numbers. Some of the games they play may seem as silly or pointless as musicians playing scales, but there is a point to it all. That old saying defining insanity as doing the same thing over and over and expecting different results was never really correct (or intended to be used as it often is).
An old joke is more on point: “How do you get to Carnegie Hall?” (Asked the first-time visitors to New York.) — “Practice, practice, practice!” (Replied the street musician they asked.) The point of mathematical play can be sheer exercise for the mind, sometimes can uncover unexpected insights, and once in a while can be sheer fun.
As when finally solving a 65-year-old puzzle involving the number 42!
I have always liked those comparisons that try to illustrate the very tiny by resizing it to more imaginable objects. For instance, one says: if an orange were as big as the Earth, then the atoms of that orange would be a big as grapes. Another says: if an atom were as big as the galaxy, then the Planck Length would be the size of a tree.
The question I have with these is: How accurate are these comparisons? Can I trust them to provide any real sense of the scale involved? If I imagine an Earth made of grapes am I also imagining a orange and its atoms?
So I did a little math.
In the last week or so I read an interesting pair of books: Through Two Doors at Once, by author and journalist Anil Ananthaswamy, and The Order of Time, by theoretical physicist Carlo Rovelli. While I did find them interesting, and I’m not sorry I bought them (as Apple ebooks), I can’t say they added anything to my knowledge or understanding.
I was already familiar with the material Ananthaswamy covers and knew of the experiments he discusses — I’ve been following the topic (the two-slit experiment) since at least the 1970s. It was nice seeing it all in one place. I enjoyed the read and recommend it to anyone with an interest.
I had a little trouble with the Rovelli book, perhaps in part because my intuitions of time are different than his, but also because I found it a bit poetic and hand-wavy.
Fourier Curve 1
Don’t let the title put you off — this is one of the coolest things I’ve seen in a while. It’s because of math, but there’s no need to get all mathy to enjoy this, you just need to think about clocks. Or even wheels that spin ’round and ’round.
The fun thing is what happens when we connect one wheel to another in a chain of wheels of different sizes and turn rates. If we use the last wheel to trace out a pattern, we get something that resembles the Spirograph toy of old (which worked on a similar principle of turning wheels).
And if we pick the wheel sizes and spin rates just right, we can draw just about any picture we want.
I’ve long been fascinated by stories about octopuses. I confess I’ve eaten a few, too, and it’s obviously a worse than eating dog, which I could never. (OTOH, properly done calamari is really yummy!)
It’s not just that octopuses (and it is octopuses, by the way; the root is Greek, not Latin) are jaw-dropping smart. It’s that their intelligence operates in a completely different brain than ours — an evolutionary branch that considerably predates the dinosaurs. It isn’t just the top brain and eight satellite brains; it’s that their entire body, in some sense, and especially their skin, is their brain.
Check out this 13-minute TED Talk by marine biologist Roger Hanlon:
Happy Tau Day! It’s funny. I feels like I’ve written a lot of posts about pi plus few about it’s bigger sibling, tau. Yet the reality is that I’ve only ever written one Tau Day post, and that was back in 2014. (As far as celebrating Pi Day, I’ve only written three posts in eight years: 2015, 2016, & 2019.)
What I’m probably remembering is mentioning pi a lot here (which is vaguely ironic in that I won’t eat pie — mostly I don’t like cooked fruit, but there’s always been something about pie that didn’t appeal — something about baking blackbirds in a crust or something).
It’s true that I am fascinated by the number.
I realized that, if I’m going to do the Mandelbrot in May, I’d better get a move on it. This ties to the main theme of Mind in May only in being about computation — but not about computationalism or consciousness. (Other than in the subjective appreciation of its sheer beauty.)
[click for big]
I’ve heard it called “the most complex” mathematical object, but that’s a hard title to earn, let alone hold. It’s complexity does have attractive and fascinating aspects, though. For most, its visceral visual beauty puts it miles ahead of the cool intellectual poetry of Euler’s Identity (both beauties live on the same block, though).
For me, the cool thing about the Mandelbrot is that it’s a computation that can never be fully computed.
Last Friday I ended the week with some ruminations about what (higher) consciousness looks like from the outside. I end this week — and this posting mini-marathon — with some rambling ruminations about how I think consciousness seems to work on the inside.
When I say “seems to work” I don’t have any functional explanation to offer. I mean that in a far more general sense (and, of course, it’s a complete wild-ass guess on my part). Mostly I want to expand on why a precise simulation of a physical system may not produce everything the physical system does.
For me, the obvious example is laser light.
I’ve been on a post-a-day marathon for two weeks now, and I’m seeing this as the penultimate post (for now). Over the course of these, I’ve written a lot about various low-level aspects of computing, truth tables and system state, for instance. And I’ve weighed in on what I think consciousness amounts to.
How we view, interpret, or define, consciousness aside, a major point of debate involves whether machines can have the same “consciousness” properties we do. In particular, what is the role of subjective experience when it comes to us and to machines?
For me it boils down to a couple of key points.
Philosophical Zombies (of several kinds) are a favorite of consciousness philosophers. (Because who doesn’t like zombies. (Well, I don’t, but that’s another story.)) The basic idea involves beings who, by definition, [A] have higher consciousness (whatever that is) and [B] have no subjective experience.
They lie squarely at the heart of the “acts like a duck, is a duck” question about conscious behavior. And zombies of various types also pose questions about the role subjective experience plays in consciousness and why it should exist at all (the infamous “hard problem”).
So the Zombie Issue does seem central to ideas about consciousness.