Showing posts from 2017

New look!

A very short update to say that Blogger has launched a collection of new templates. They're a lot cleaner and more modern looking, plus have some nice customization options, so I decided to make the switch. The main difference is the layout is a lot wider, and the non-post stuff on the right has now moved into the left. Hopefully everything still works, but if anything's broken let me know.

Also, kudos to the Blogger team, the new ones look rather good! Plus threaded comments still work -(looks like the old code is still used for them, too :p) and the commenting experience seems a bit cleaner now.

Perceiving Frequencies

Fourier transforms are interesting things - a way of converting repetition to single values and back (roughly). Most commonly known in music (see my earlier post), it also shows up oddly as the relationship between position and momentum in quantum mechanics. While audio perception takes patterns over time and converts them to notes, our eyes do likewise, but taking patterns over space - called spatial frequencies. Just as with music, there's (bidirectional) ways to convert an image into its spatial frequency representation.
Part 1: Frequency swapped images
As an example, on the left is a (greyscale) photo of George Bush, and on the right is the frequency version. Note that frequencies are complex numbers: representing both how strong the frequency is (the power - top right greyscale image) as well as the phase - i.e. where in the cycle it starts. As this is cyclical, I'll represent it as colours, from red -> green -> blue -> back to red (bottom right). For colour pictu…

Project cutting floor

One class this semester is mostly aimed at coming up with ideas for what to study as a graduate student (not surprising, being a 4th year subject in a major that aims at getting people into grad school). I'm lucky enough to be in a position where I already have a project lined up for summer, but it was interesting instead using the time to come up with alternatives, and then try to convince myself they were worth discarding. Or at least...putting off until later. Hence this list, using a blog as my external memory of interesting things, so I can look back later and see if I was stupid or if any turn out to be interesting. Split roughly by subject, from the more abstract/philosophical to the concrete/engineering:
Philosophy:  1) For everything (possibly?) true, can it be thought? 2) For everything thought, can it be communicated? Consider this the philosophical version of the Incompleteness theorem (maths), or the Uncertainty principle (physics) or the Halting problem (comp sci). The…