Tickles to Turion's mind

When I lost my wallet recently, I was surprised how the recovery processes for my various important documents works.

First, credit cards. It’s simple and easy to lock them. And it’s as simple to order a new one. One click on my bank’s website, done. Soon, access to my money returns. Money works. It wants to work.

Then, official documents like identity cards and driver’s licenses. It takes ages to get them. You need to apply for them, and you need to pay for them. How, if I just lost my wallet? So, access to money is a prerequisite to official recognition of my identity?

This makes me think. We are quite far on the road down to Libertarianism. Maybe in 100 years, when they ask you to identify yourself, maybe all they want to see of you is your credit card..?

I’m mainly coding Python these days, and I’m using the Geany editor with a few Plugins to code. Why? Mainly because Geany starts faster than any other editor I know in a Linux desktop environment. And it doesn’t (yet) lack anything I need for programming. Or is there more to it?

Maybe little editors have their advantages over an IDE. An IDE can help you to code so much that you do code with less discipline.

• Have a too intelligent code completion? Watch your method names growing and growing.
• Great refactorisation tool? And suddenly you start copying code all the time because it’s so easy to adapt it to new uses. Don’t repeat yourself, we all know that.
• Your IDE gives you a structured overview over your file? But how big is it? More than 10 kb? Certainly too large, even if you have the feeling that the IDE somehow manages the content for you.
• Your IDE magically cross-references tooltips between different files. Great, no need of remembering which class was defined where and where you put what documentation. But have you separated concerns well enough? Each file should use as few information from the other files as possible, that way you’ll find bugs much faster.
• Your IDE lets you place that button in the tiny, simple dialog window very fast. You call it rapid development. But how does the window behave when you scale it or use it on a mobile device? Maybe the default values for the button placement were quite good ones, but the IDE hardcodes the exact coordinates of where you put that button.

Not all of these comments apply to every IDE. And not all apply to every language and use case. I’m speaking of Python here, and there are awfully big, repetitious C files better left untouched as they are. I’m also not saying that the argument against big IDEs is won. I’m just highlighting some ways how the simplicity of editing tools forces us to write with more simplicity and clarity.

In february, I did an improvisation concert on the Steinway in the Old Combination Room of Trinity College, Cambridge. The recordings are available here.

All improvisations are completely free.

Today, we developed a very general notion of differentiability in one variable. It exists on any topological ring.

I was asking the question “What is so special about certain the reals, the complexes or the p-adic numbers that you can do differentiation on it?” The most general definition of differentiability we could find surprisingly only required some basic algebra and topology. More specifically, it is perfectly possible to have differentiation on objects that have nothing at all to do with the real numbers.

The intuition is the following: Differentiating is approximating linearly. If a function is differentiable, then it is affinely linear up to corrections that vanish quadratically.

So we need to make sense of “linear” and “quadratic”. Here enter rings, which allow for addition and multiplication.
We also need to make sense of “approximating” or “vanishing”. Enter topology.

The rigorous definition now is:
Let be a topological ring. (This means it is a ring, it is a topological space and addition and multiplication are continuous.)
A map is called differentiable at with derivative if and only if for every sequences that tends to zero, there exists another sequence tending to zero, , such that the following equation holds:

Details:

• The is the affinely linear bit, the is the “quadratic” term.
• In a topological space, a sequence is called “tending to zero” iff for any neighbourhood around zero, only finitely many points of the sequence are outside the neighbourhood.

Now my questions:
If we take the reals, the complexes or the p-adics with the standard topology, do we recover the standard notion of differentiability?
What other interesting topological rings are there that we can do analysis on?

The previous owner (turion) of this blog was so friendly to transfer it to me (yet another turion) in order to actually have some posting being done here. I will make the promise true.

His active blog can be found here. Amongst shorter posts, it contains a pointed and entertaining criticism on Lierre Keith’s book “The Vegetarian myth”. Me being a vegan-friendly vegetarian, I enjoyed having this one-sided (as far as I can tell from the first few pages) book being ripped into pieces, but still I don’t agree on several points. I won’t comment on that any further, the web is already full with discussions on the v-question.

His other blog is called Inner Game, and I don’t know exactly what it’s about, maybe something like the psychology of men picking up women. It’s entertaining, though.

I always found it strange that the name “Turion” has been used by other people before me. I once made it up the way it is just because I liked the sound of it. Later I had to find out that AMD is producing a processor called Turion (I didn’t sue them for copyright infringement, though) and that “turion” is a word in french. There even exists a mediocre Progressive Rock band called “The Last Turion”.

So thanks, Turion, for letting me manage the blog with this sought-after name! Happy blogging!