Bus Stops and the Electron Charge
While I’m preparing the next part in our neural networks tutorial, let’s digress a bit and talk about something completely different.
You’re standing outside, waiting for the bus to arrive. Being a physicist, you busy yourself with building some model until it does. Assume the rate of bus arrivals is - for example, 5 buses […]
Neural Networks Tutorial, Part #1
This is the first part of a set of postings on neural networks (NNs). NN are constructs that attempt to mimic our brain’s activity to a degree. NNs have become so common that it’s useful to know what people are talking about, so I’ve decided to write a brief tutorial - in several parts - […]
The Ice, Water and Oil Riddle
Well, this is not really a riddle but more of a fun experiment.
We all know ice floats on water. We also know oil floats on water. Now the question is, if we take a glass and fill it with 50% water and 50% oil, and afterwards drop in an ice cube, where will […]
The Psychotic Train Riders Puzzle
Here is a somewhat cruel physics puzzle which illustrates the idea of momentum conservation.
Consider a train full of passengers moving along on a frictionless rail at a constant speed, v. In order to increase its speed, the passengers decide to throw themselves off the back end of the train, making use of the principle of […]
Getting Shot Isn’t So Bad For You
In this post we’ll be doing some simple, yet illuminating calculations.
A typical baseball weights about 150 grams and can reach velocities of up to 100 mph, or 40 m/sec, and so its kinetic energy is about and its momentum about . On the other hand, the bullets of a .38 special handgun - […]
Beating your Guitar into Tune
If you have any musical friends, this should get their attention (if it doesn’t, just spill petrol over their musical instruments and ignite. THAT will).
Basic trigonometry tells us that the rule for adding two sines is as follows:
It turns out that if our ear is exposed to two sounds which have similar frequencies, it only […]
Shearing your Data with a Fourier Transform
Here’s a neat little trick that has helped me out a few times.
It often happens, when acquiring 2D data, that the resulting data set seems slanted, or sheared in some way. This can be the result of hardware error or some other artifact in your system (it happens to me all the time when acquiring […]
An Energy Conservation Puzzle
Here’s a puzzle that makes lots of experienced physicists pause for a moment - or two!
Suppose you have a cart at the top of an inclined hill. Initially, the cart only has potential energy, equal to mgh. As it descends to the bottom of the mountain, its potential energy is converted into kinetic energy, […]
The Mathematics of Picture Taking
or: The Logic Behind Convolutions
When I was taught about convolutions in my undergraduate degree I found them somewhat puzzling. Somehow they always got tied up with the Fourier Transform and the convolution theorem. But any convolution really has nothing to do with Fourier Transforms. They actually have a lot to do with the science of […]
Incorporating MimeTeX into WordPress
I get asked all the time, “how did you manage to add mathematical equations to your blog?”
Well, maybe not all the time (actually, never, but lets pretend I do).
The mathematical equations in the blog are typed in a mathematical markup language known as LaTeX. LaTeX is widely used in prestigious scientific journals such as Physical […]