Archive for the ‘links’ Category

Do The Math

April 24, 2012

In a follow-up to yesterday’s post, I want to point out a blog by astrophysicist Tom Murphy at UC San Diego (I don’t know him).

Do the Math looks at back-of-the-envelope calculations related to energy, environmentalism, and related issues. Tom produces more high-quality material than I’ve been able to absorb, but what I’ve read has consistently been insightful and, thankfully, sane. Check out his post index for some food for thought.

Now I Know SCIENCE!

October 6, 2009

This is supposed to be a blog. It isn’t. It’s just the standard WordPress template with posts coming in irregular bursts.

Part of being a blog is that you’re supposed to be integrated into the blogosphere. This is because if you take a bunch of meaningless things and endlessly interconnect them, you get what’s known in science as an emergent phenomenon, in this case endless confusion. So I really ought to hook up to the blogosphere and get in on that.

On the other hand, it turns out there are these people who want blogs to be useful. So what they do is sift, organize, centralize, and bring similar bloggers together. GrrlScientist (real name, I think. You wouldn’t put a fake name in the internet, right?) is one such person. She (or he, I suppose) runs Scientia Pro Publica, a blog carnival whose goal it is to make science understandable to everyone by writing in Latin. She’s hosted the 13th edition of Scientia today on her blog, including about 20 essays in popular science. They’re heavy on the life sciences, discussing such topics as parasites that eat weaverfish tongues and why I still don’t understand evolution. (Seriously, I don’t.)

There’s some meta-discussion of science, a post about the suckiness of iPhone camera, and they graciously included my post about retroreflectors on the moon as the only physics/astronomy representative.

Random Spots on Earth

July 25, 2009

Don’t know where to take your next vacation?

Here’s some python code to generate a bunch of random locations on Earth. Copy and paste into python, run, then copy and paste a location into Wolfram Alpha or Google Maps. Google Maps has pictures, but is slower. Wolfram Alpha will tell you the country, and then you can click on a link to Google Maps (the link is just called “satellite image”) if it’s someplace interesting. Or, try guessing where the location is before you plug it in.

WordPress doesn’t allow javascript, so I can’t easily generate the locations for you or embed the Wolfram Alpha search bar. Too bad.

About generating random locations:
The longitude is easy, since you just pick a random number between -180 and 180 degrees.

Latitude is not so straightforward. If you draw a thin band (one mile wide, say) around the line of latitude at 60 degrees North, that band is only half as large as one around the equator, since it’s a shorter way around the globe up at 60 degrees. The size of the band at a certain latitude, relative to one at the equator, is the cosine of the latitude.

To get a random location on Earth (all locations being equally likely) we choose a random number from zero to one, and say that this is the percentage of land that lies south of our chosen location. The percentage of land south of a line of latitude \theta is
\frac{1}{2}\int_{-90}^\theta \cos\theta' d\theta' = \frac{1}{2} (1 + \sin\theta).

That’s equal to some random number r, so we need to solve for \theta.
\theta = \arcsin(2r-1).

The code accomplishes the same thing in a slightly more convoluted way, because I originally solved it thinking of the north pole as zero radians (as we do in math) rather than 90 degrees (as we do in geography). Okay, here’s the code


import random
import math

for i in range(1,100):
    
        long = random.random()*360 - 180
        lat = math.acos(1-2*random.random())*180/3.14159-90
    
    
        if(long>0):
            ew = "E"
        else:
            long = -long
            ew="W"
        if(lat>0):
            ns = "N"
        else:
            ns = "S"
            lat = -lat

        print "%.2f %s , %.2f %s" % (long,ew,lat,ns)

Rectangles Do Not Exist

May 25, 2009

While all the real physics students are doing fantastic undergraduate research, I spend my summers as a TA in the physics courses at EPGY. The relativity students cohabitate with the non-euclidean geometry students, and so last year I was privileged to receive a hospital-waiting-room lecture on the nonexistence of rectangles in hyperbolic geometry. (You always get to take at least one trip to the hospital at 2am when you’re a camp counselor. In the same waiting room, I met an old anthropologist who told me about his thesis work on Korean traditional witchcraft just after the war.) You can’t build a rectangle on the surface of a sphere, but you can build a plot with two North-South fences and two East-West fences (the N-S and E-W directions are only perpendicular at the equator).

This was the topic of Monday Math Madness #32 at blinkdagger, where you can see my solution to a question about the areas of such plots.

There’s also a puzzle 33 up on Wild About Math!

The Fastest Man Alive

February 17, 2009

At my friends’ group blog, I have a post about a paper analyzing Usain Bolt’s 100m world record.