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Tag Archives: pi

*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.

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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.

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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).

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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?

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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.

4 gravitons

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**.

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138 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*!

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6 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.

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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

I misspent my younger days in the warm climes of Southern California. In particular, I went to high school and college there. I moved to the Midwest about seven years after college. For many, college was the end of anything resembling much in the way of time to call their own. I have many fond memories of idle times in perfect weather!

People who know me know I have a pretty intense work ethic. They also know I have a pretty intense *party* ethic. (Truth is: I’m just intense. Period. Work hard; play hard; relax hard.) This past week—my first week into retirement—I’ve been relaxing hard.

And the weather has been just glorious this week. So far, retirement is aces!

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Comments Off on Party Time! | tags: algebra, backgammon, humor, math humor, peach daiquiri, pi, retirement, weather | posted in From My Collection, Life, Math

You probably have some idea of what *infinity* means. Something that is infinite goes on forever. But it might surprise you to know that there are different kinds of infinity, and some are bigger than others!

As a simple example, a small circle is infinite in the sense that you can loop around and around the circle forever. At the same time, your entire path along the circle is *bounded* in the small area of the circle. Compare that to the straight line that extends to infinity. If you travel that line, you follow a path that goes forever in some direction.

What if we draw a larger circle outside the small circle. If there are an infinite number of points on the small circle and an infinite number of points on the large circle, does the larger circle have the same number of points as the small one? [The answer is *yes*.]

To understand all this, we have to first talk a bit about numbers.

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18 Comments | tags: countable, counting numbers, Georg Cantor, infinity, irrational numbers, natural numbers, pi, rational numbers, uncountable | posted in Math, Science