Category Archives: Mathematics

Taking On McGyver

Here’s a fun interview with the Mythbusters. I don’t get this, though:

My favorite episode, that I think the science is the most right, is ”Bullets Fired Up”: Will a bullet that you fire directly into the air kill you when it comes back down? We tried it in several different ways, and every single way we tried it — from a shop experiment, to a scaled outdoor experiment, to a full-size outdoor experiment where we fired a full clip of 9mm rounds into the air out in the desert — confirmed the same results. If it’s coming straight down, it won’t kill you. But if you fire it on an angle of even two degrees, it stays on a ballistic trajectory and it will kill you. So when you see someone in a movie fire their automatic rifle on kind of a spray up into the sky, probably all of those bullets are actually deadly. The amount of data we collected on it was more than anybody up to that point had ever achieved on firing bullets into the air.

I don’t get what they’re saying here. Why would it come down any harder if it’s at a slight angle? How did they determine whether or not “it would kill you”? If it’s in a vacuum, it should come down with exactly the same vertical velocity component it had when it left the gun (except reversed), but the atmosphere complicates things. It seems to me that any bullet fired in the air is going to be coming down at terminal velocity, unless the potential energy is so high that it doesn’t have time to get to terminal velocity before it hits the ground, but that’s pretty hard to believe. When it leaves the muzzle of the gun, it’s supersonic, but I would think that it won’t be able to be going that fast when it falls back down, because of air drag. This seems like something that should be simulatable with CFD (it might even be possible to do it analytically, if the bullet was round).

Tidal Asymmetry

This post set off a discussion in which I pointed out that tidal forces are asymmetric. Carl Pham expressed skepticism at this, asking if I was saying that the tide rose higher on the side of the earth closer to the moon. I hadn’t previously thought about this before, but since I do believe that tidal forces are asymmetric, this probably followed. Or at least it followed that they were different.

One attempt was made by Ilya to prove it, but I thought it flawed and oversimplified for reasons I pointed out in comments there, because one has to consider both centripetal effects and gravitational effects when analyzing tides.

Here’s my attempt. Caution, math to follow:

Continue reading Tidal Asymmetry

Go To: Heaven

John Backus, the inventor of FORTRAN, has written his last line of code.

FORTRAN wasn’t my first language. When I started engineering school in Ann Arbor, they told me I had to learn a programming language, but they didn’t say which one, so I took a CS course in which we were inducted into the programming world with ALGOL. I used it to write a simulation of heat transfer, with no problems, though the engineering professor didn’t know the language. But I had to take a graduate course in numeric analysis, in which one had to write in FORTRAN, to be able to interact with the instructor’s subroutines, so I went to a few free lectures on it that he held at night for the general student population (and in fact public). After learning how to program in a structured language, I was appalled at DO loops and gotos, and their potential for spaghetti. I’ve used it quite a bit since, but still try to use as much structure as whatever version allows. Still, as the article notes, it was a huge breakthrough in making computers practical.

And here, courtesy of wikipedia, are a few FORTRAN jokes:

* “GOD is REAL unless declared INTEGER.”

* Joke, circa 1980 (following the standardization of FORTRAN 77): “Q: What will the scientific programming language of the year 2000 look like? … A: Nobody knows, but its name will be FORTRAN.”

* A good FORTRAN programmer can write FORTRAN code in any language.

* Computer Science without FORTRAN and COBOL is like birthday cake without ketchup and mustard.

I Got Six Out Of Eight

I screwed up number two, because I didn’t read carefully, and thought it was asking about the minute hand (which was simple–a hundred twenty degrees). And I couldn’t manage number five in my head. I was trying to do the algebra, and couldn’t manage it. And a couple of them, as noted, are trick questions.

And I certainly wouldn’t have done that well at age eight.