It’s been a few minutes since my last post. Lately, the effort of writing hasn’t seemed worth the almost non-existent return. I find I’ve lost faith in humanity, and the phrase that seems most resonant is: “Really, when you come right down to it, what’s the point of it all?” I think, at least in our case, the Fermi Paradox seems resolved.
Perhaps more crucially, this damned dark cloud over me seems all I can write about. Everything else seems ephemeral. If we can’t solve our most basic human problems (education, race, gender, poverty, pollution) then the rest of it really is fiddling while Rome burns.
It makes me angry. Humanity can do better than this. I think.
16 Comments | tags: maze generator, mazes, pi, rational numbers | posted in Friday Notes
I posted a while back about the wonders of Fourier Curves, and I’ve posted many times about Euler’s Formula and other graphical wonders of the complex plane. Recently, a Numberphile video introduced me to another graphical wonder: Euler Spirals. They’re one of those very simple ideas that results in almost infinite variety (because of chaos).
As it turned out, the video (videos, actually) led to a number of fun diversions that have kept me occupied recently. (Numberphile has inspired more than a few projects over the years. Cool ideas I just had to try for myself.)
This all has to do with virtual turtles.
8 Comments | tags: geometry, Leonhard Euler, Numberphile, pi | posted in Math, Wednesday Wow
Venus emerging from the sea.
I’ve been thinking about emergence. That things emerge seems clear, but a question involves the precise nature of exactly what emerges. The more I think about it, the more I think it may amount to word slicing. Things do emerge. Whether or not we call them truly “new” seems definitional.
There is a common distinction made between weak and strong emergence (alternately epistemological and ontological emergence, respectively). Some reject the distinction, and I find myself leaning that way. I think — at least under physicalism — there really is only weak (epistemological) emergence.
But I also think it amounts to strong (ontological) emergence.
106 Comments | tags: determinism, emergence, ontological anti-realism, ontology, pi, real numbers, reductionism | posted in Philosophy
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.
3 Comments | tags: Andrey Kolmogorov, Champernowne constant, Gregory Chaitin, Kolmogorov complexity, normal number, normal sequence, omega constant, pi, tau, tau day | posted in Math
Happy Pi Day! Order some pizza and use pi to make sure you get the most pie possible! I made a handy chart that may change how you order pizza.
Or not. It’s something I heard about early in the year that caused a minor tweet storm (I’m not on the Twitter, so never saw nothing, which I’m fine with). It centered around how it was often better to order two smaller pizzas than one large one (depending on pricing and assuming your goal is the most pizza possible per peso).
Since pi is involved in this pizza pie probe, I thought it would make a fun topic for Pi Day (not to mention March Mathness).
15 Comments | tags: normal number, normal sequence, pi, pi day, pizza | posted in Math
Well, it’s Pi Day once again (although this date becomes more and more inaccurate as the century proceeds). So, once again, I’ll opine that Tau Day is cooler. (see: Happy Tau Day!)
Last year, for extra-special Pi Day, I wrote a post that pretty much says all I have to say about Pi. (see: Here Today; Pi Tomorrow) That post was actually published the day before. I used the actual day to kick off last Spring’s series on Special Relativity.
So what remains to be said? Not much, really, but I’ve never let that stop me before, so why start now?
10 Comments | tags: irrational numbers, normal number, pi, pi day, tau, tau day, transcendental numbers | posted in Math
I seem to be doing a lot of reblogging lately (a lot for me, anyway). But I’m on kind of a math kick right now, and this ties in nicely with all that.
You’ve probably seen it somewhere on your facebook feed, likely shared by a particularly wide-eyed friend: pi found hidden in the hydrogen atom!
From the headlines, this sounds like some sort of kabbalistic nonsense, like finding the golden ratio in random pictures.
Read the actual articles, and the story is a bit more reasonable. The last two I linked above seem to be decent takes on it, they’re just saddled with ridiculous headlines. As usual, I blame the editors. This time, they’ve obscured an interesting point about the link between physics and mathematics.
So what does “pi found hidden in the hydrogen atom” actually mean?
It doesn’t mean that there’s some deep importance to the number pi in nature, beyond its relevance in mathematics in general. The reason that pi is showing up here isn’t especially deep.
It isn’t trivial either, though. I’ve seen a few people…
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2 Comments | tags: math theory, mathematics, pi, quantum physics | posted in Math
It’s pi day! Be irrational!
Earlier this week I mentioned that “this coming Saturday is a doubly special date (especially this year).” One of the things that makes it special is that it is pi day — 3/14 (at least for those who put the month before the day). What makes it extra-special this year is that it’s 3/14/15— a pi day that comes around only once per century. (Super-duper extra-special pi day, which happens only once in a given calendar, happened way back on 3/14/1529.)
I’ve written before about the magical pi, and I’m not going to get into it, as such, today. I’m more of a tau-ist, anyway; pi is only half as interesting. (Unfortunately, extra-special tau day isn’t until 6/28/31, and the super-duper extra-special day isn’t until 6/28/3185!)
What I do want to talk about is a fascinating property of pi.
139 Comments | tags: cake, Carl Sagan, Contact (book), Ellie Arroway, irrational numbers, Magnum Pi, normal sequence, numbers, pi, pi day, pie, real numbers, tau, tau day, transcendental numbers | posted in Math
This might seem like another math post… but it’s not! It’s a geometry post! And geometry is fun, beautiful and easy. After all, it’s just circles and lines and angles. Well, mostly. Like anything, if you really want to get into it, then things can get complex (math pun; sorry). But considering it was invented thousands of years ago, can it really be that much harder than, say, the latest smart phone?
Even the dreaded trigonometry is fairly simple once you grasp the basic idea that the angles of a triangle are directly related to the length of its sides. (Okay, admittedly, that’s a bit of a simplification. The (other two) angles of a right-angle triangle are directly related to the ratios of the length of its sides, but still.)
However, this isn’t about trig; this is about tau!
7 Comments | tags: circle, circumference, geometry, pi, pi day, pie, pizza, radius, tau, tau day, trigonometry | posted in Math
We’re still motoring through numeric waters, but hang in there; the shore is just ahead. This is the last math theory post… for now. I do have one more up my sleeve, but that one is more of an overly long (and very technical) comment in reply to a post I read years ago. If I do write that one, it’ll be mainly to record the effort of trying to figure out the right answer.
This post picks up where I left off last time and talks more about the difference between numeric values and how we represent those values. Some of the groundwork for this discussion I’ve already written about in the L26 post and its followup L27 Details post. I’ll skip fairly lightly over that ground here.
Essentially, this post is about how we “spell” numbers.
1 Comment | tags: base 10, base 2, base 8, Frederik Pohl, Heechee, irrational numbers, Leopold Kronecker, natural numbers, number bases, number names, numbers, pi, prime numbers, rational numbers | posted in Math, Sideband