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.
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.
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).
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?
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.
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!
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.
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!
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.