About a year ago, I was working on a machine learning problem. I had a lot of training data I wanted to manually classify, so I put together a Mathematica interface for the data that would let me browse the training set and assign classifications from a USB gamepad. It was pretty straightforward... only took an hour or two to implement, and it sure beat classifying with mouse clicks!
You've got to get some statistical mechanics on this list. One would have a very difficult understanding quantum field theory without at least some experience considering phase transitions in more familiar settings.
I used to be an experimental particle physicist, so I've certainly got some bias here, but I really think learning particle physics and the Standard Model is worth while. Halzen and Martin is a VERY good textbook and an excellent preparation for studying quantum field theory.
Yes, it is expensive. But it is very well written and thorough.
Also, I think it's always important to mention in these conversations that most physicists don't take string theory seriously. From the outside, it looks like the exciting frontier of modern physics. But that's more about Brian Greene's skill in marketing himself than string theory's explanatory value.
That being said, the Fabric of the Cosmos is a good layman's survey of the modern physics landscape:
More work to configure, but also works on Linux. There's a wonderful ncurses interface called ncmpc as well. mpd + ncmpc has been my iTunes in a terminal window for years.
It was actually a few annoyances with MPD that led me to create Dhun. This was a while ago so things might a have changed. But my main grievances were:
* Installation on OS X wasnt very straightforward. I think the MacPorts version was broken and I had to do some stuff manually to get it to install
* Some of my ID3 tags and MP3 files were not recognised properly, even though they worked fine on iTunes.
Z bosons decay into a lepton (electron, muon, or tau particle) and its anti-particle. Those decay products pass through a magnetic field and eventually collide with a material that absorbs all of their energy. Measuring the path of the leptons (in particular, the deflection caused by the magnetic field) allows you to determine their momentum. The intensity of the collision with the stopping material is used to determine the energy.
Knowing the energy and momentum allows one to calculate the path. Gravitational forces are also acting on those particles, and any changes in their paths caused will change the final calculated mass.
"final calculated [weight]" may be a better way to word it to avoid any confusion with the actual mass of the particle, as opposed to the calculation of how gravity at a given moment effects it.
So it's just the gravitational forces acting on those Z bosons that affect the measurement of weight? If so, I'm just blown away. Physics never ceases to make my day better.
At least in my last physics class, weight was defined to be the gravitational force of the earth acting on an object. Perhaps you're blown away because you're equating weight and mass?
To be precise, weight is defined as the magnitude of the force one must apply to an object in a gravitational field in order to hold it at rest.
If you're on the moon, the gravitational force of the earth acting on an object is not what matters. It's the gravitational force of the moon that matters.
They're not measuring weight anyway -- they are measuring mass. Maybe I'll write up a blog post with a picture of how mass spectrometry works. It's a fairly common homework problem in intro EM courses anyway.
With known equations, then yes, dimensional analysis is essentially just a form of bookkeeping that helps you verify your math as you go.
But once you get into using quantum field theory to study new systems, the standard approach is to concoct a conservation of energy equation by summing terms, where each term is a combination of the system's variables with units of energy.
From there, you can discretize the coordinates and predict the existence of various particles (or pseudo-particles, depending on what kind of system you're describing) and their dynamics.
I couldn't agree more. Grant money is precious. Instead of spending three or four grad student salaries to pay a programmer a competitive wage, it makes more far more sense to fund three or four students on research assistantships where they have time to learn Perl.
http://daringfireball.net/linked/2011/09/30/the-talk-show-61