I continue to find interesting things in the area of astronomy, math, physics and more. Here are some of the best of them. I hope you like them! (Yes, there will be stoned earthworms, and something about Uranus. :))
Posted onDecember 10, 2022|Comments Off on Love and rockets (things I find interesting in math and science, Dec. 2022)
In the last few months my math and science reading has mostly been about space, with some smattering of other things. NASA in particular has been the focus. First up is a piece on the DART Mission which smashed into an asteroid and altered it’s path. No small feat, that. In other big feats, they are still in the planning stages of a a balloon mission to Venus . Given that landing on Venus results in a spacecraft being destroyed, a visit that stays in that planet’s atmosphere may be the only way for it to succeed.
One such mission that should definitely succeed is Artemis, NASA’s project to visit (revisit?) the moon, Here is the NYTimes on it. Relatedly, here’s the Atlantic with a piece on the the 50th anniversary of Apollo. We are clearly due for a return trip. I wonder if it will affect the new astronauts as much as it did William Shatner after his quick trip into space with Jeff Bezos? I suspect they will be more prepared than the TV astronaut was.
Finally, if you are interested in learning more about physics, I recommend you check out the web site DrPhysicsA. It’s good stuff. And you want to learn more about math, you can visit the blog of one of the best mathematicians in the world. Here is is writing on odds. Also good!
Comments Off on Love and rockets (things I find interesting in math and science, Dec. 2022)
Four mathematicians whose research covers areas like prime numbers and the packing of eight-dimensional spheres are the latest recipients of the Fields Medals, which are given out once every four years to some of the most accomplished mathematicians under the age of 40.
That piece in the Times goes in depth on each of the winners and is worthwhile.
Knowing when to quit is one of life’s great dilemmas, whether to persist in the face of diminishing rewards, or to quit now in the hope of finding richer rewards further afield. For every gold mine, eventually there comes a point when the amount of gold extracted can no longer justify the cost of keeping the mine open; once that point has been reached, it is time to quit, and start looking for a new mine.
Similarly, for a bird feeding on caterpillars in a bush, there comes a point when the calories gained can no longer justify the energy expended in searching for more caterpillars; once that point has been reached, it is time to quit, and move to another bush. And, for a honeybee, there comes a time when the weight of pollen collected can no longer justify the energy required to carry that pollen; at that point it is time to quit collecting, and fly back to the hive.
Fortunately, there is a mathematical recipe, embodied in the marginal value theorem (developed by the American ecologist Eric Charnov in 1976), which specifies when to quit in order to maximise rewards. More importantly, the marginal value theorem has an enormously wide range of applications, from its origins in optimal foraging theory to how brains process information. In essence, the marginal value theorem provides a general strategy for maximising the bang per buck, irrespective of the nature of the bang and the buck under consideration.
Wait you say: it’s Friday afternoon! You know when to quit (at least for this week). Ok, that works too. But if you need more general guidance, read the article.
Comments Off on Here’s how to know when to quit, using math.
Recently the Perimeter Institute held a contest called “Physics Frenzy – Battle of the Equations Championship”. I was sure James Maxwell and his equations were going to win. It turns out he lost (in the final, mind you) to Emmy Noether and her theorem!
Afterwards I wondered if people knew much about her. Besides being arguably the greatest woman mathematician, she was a significant contributor to math and physics in the 20th century. You can read a bio of her here.
Fun aside, the good people at the Perimeter Institute have a series of initiatives centered around Emmy Noether. They also have material where you could learn more about her. Read about them, here.
Of all the sciences, those having to do with space are the ones I enjoy reading about the most. I got interested in Lagrange points due to the James Webb Telescope. Here’s something on them: Lagrange points.
What has the columnist angry was the removal of several passages of progressive political text that went with the update to the recent changes of the math curriculum. I can see why that removal would anger some people with progressive political values.
I can also imagine how many conservatives would have been angry if there was text like this removed from a new curriculum: “recognize the ways in which mathematics can be used as a tool to uncover, explore, analyse, and promote actions to address greater productivity and growth within our economy and to lead Canada to a strong future of wealth and opportunity”, or if the government removed anything to do with teachers creating “pro-capitalist and pro-business teaching and learning opportunities.” Any group that tries to explicitly frame a curriculum and then have that framing removed will be upset.
Mathematics itself is not political, but it is always taught within a political and historical context. For example, I have math texts that make it seem that the only worthwhile math came from European men, while I have others that show mathematics has roots all over the world. I have math textbooks that mention 0 women, while other texts show the role women have played in mathematics and delve into why women had a hard time making more of a contribution.
Whatever context you want to frame a curriculum, I think that emphasizing politics and history with regards to teaching mathematics will not achieve some of the goals that progressive thinkers hope it will achieve. I think the new changes in the curriculum with regards to things such as streaming will help achieve those goals, as I wrote here.
Additionally, I think there are other things that can be done outside the curriculum that could help students that are disadvantaged when it comes to education in math. I am thinking of the work done by organizations like BlackGirlsCode. We could use more organizations like that who can provide specialized programs not just to help kids who are struggling with math, but to uplift kids that excel in math. Organizations that can support the next Maryam Mirzakhani, wherever she is. The kids who are struggling with math need more help than what the schools can provide: the same is true for kids that excel in math.
I like it for two reasons. One, it’s free. Two, it does not take itself seriously nor does it take calculus seriously. To see what I mean, here’s a clip from the beginning of the e-book:
Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult.
The fools who write the textbooks of advanced mathematics—and they are mostly clever fools—seldom take the trouble to show you how easy
the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.
So if you want to learn calculus but are struggling, give that book a look. Sure it’s an old book, but calculus is an old subject. It may suit you just fine.
Posted onAugust 23, 2020|Comments Off on Great insights on mathematics you should read about even if you don’t think you want to
I suspect many people will not want to read this article containing great insights on mathematics by Steve Strogatz. That’s a shame, because it is really approachable by anyone of any mathematical ability. It’s especially good for people with limited math skills, because he does a good job of showing the value and benefits to be gained from thinking mathematically. I highly recommend it if you read it.
For example, one thing I found fascinating is his discussion of the Prisoner’s Dilemma by comparing it to religion. You should read it, but in short, it’s been shown that one approach to succeeding in playing several rounds of the Prisoner’s Dilemma is to use a Tit-for-Tat strategy. This is highly effective and is similar to Old Testament Eye-for-an-Eye morality. However that can also go wrong on occasion, leading to long lasting feuds that never get resolved. Then he gets into a discussion of New Testament morality and how that can avoid some of the problems of Old Testament morality. It’s a great discussion, and one of the many great discussions in the article.
It’s hard to say why this interview with Strogatz is so good, other than to say he covers much ground on a variety of interesting topics and speaks lively on them. (Ok, I find game theory, “elegant” math, math education, etc, interesting, but you likely will too).
If you enjoyed this interview, he has a recent book out, “Joy of X: A Guided Tour of Math, from One to Infinity.” Worth a look.