#bistromath

Here, look at this.

It's the sticker they gave me after taking in my car for an oil change. Notice how it says you can use that barcode to pay at any register. I decided to go shopping and scanned this at the self checkout to learn THIS DOESN'T MEAN ANY REGISTER YOU STUPID AUTISTIC. It means only the ones in auto.

Walmart is trying to beat Elon Musk to space, and I am here for it. I'd rather have Douglas Adams's series over Dune.

Formalizing antisymmetry

Now, that probably sounds more complicated than anything needs to be. Obviously, what the "wobbly table theorem" was really meant to be was an observation that, for any function $f : \sph^1 \to [0,1]$, the related function $D_\mathrm{Aff}(\theta) = f(\theta) - f(\theta + \pi/2) + f(\theta+\pi) - f(\theta-\pi/2)$ is antiperiodic with half-period $\pi/2$: $$ D_\mathrm{Aff} (\theta) = - D_\mathrm{Aff}(\theta + \pi/2) $$ and, if $f$ is continuous, so is $D_\mathrm{Aff}$; and if $D_\mathrm{Aff}$ is ever positive, then it is also negative; so continuity of $f$ implies vanishing — somewhere, of $D_\mathrm{Aff}$. Now $D_\mathrm{Aff}(\theta)=0$ exactly when $f(\theta) + f(\theta+\pi) = f(\theta-\pi/2) + f(\theta-\pi/2 + \pi)$ --- exactly when one diagonal mean and the perpendicular diagonal mean are equal, or refering to this picture:

You may have heard of a cute application of the Intermediate Value Theorem concluding that you can set a square table with all four feet on a good-enough™ function graph $S$, by turning the table through something less than a quarter turn; there's a description here of a partial proof, and the Real Difficulty is all hidden in the evocative first line,

Turn the table around a center in such a way that three legs A,B,C stay on the surface.

A year back, I attended my first WWDC. It was a fantastic experience and upon coming back, I set to create an iPhone app as a precursor to starting development on the Mac.

Now the inspiration simply came from splitting the bill with friends when we went out to eat. I set to create a replica of an actual check and gave an iPhone user the power to accurately get the amount payable per person based upon the numerous taxes and weird charges that local eateries have.

It was an exciting time, I came up with concept art, I coded, I designed. Then reality set in and school consumed me. I had interesting ideas about the input methods and various other functionalities.

I never really did get to it ever again despite getting numerous prompts from friends to continue. I knew it had potential.

So when I was working on Traversity, I told myself it'll be the next project once its done. Next because at that time and now, I know more than I used to, having pushed out a Mac app as well.

Then I found out about BistroMath.

The feeling was bittersweet. It was exactly the same idea, with a better UI. It was however something I am confident of coming up with if I had more time. I bought the app and spent some time playing around with it and was absolutely blown away by the whole thing.

It is simple, elegant and gets straight to the point. It was the whole thing I was writing about functional design. I loved the category selection. I loved the way you select and add other people to split the check with. It was genius. The intuitiveness of the whole process should not be underestimated as well. It is a fantastic product.

I'm happy that they didn't butcher the idea. And sad that it wasn't me that saw to its completion. So I'm dropping Go Dutch. Not really a point in duplicating features when they have such a sweet implementation.

I emailed the guys who worked on it with congratulations as well as a note to say that I've had something similar brewing in the works too. Daniel was nice enough to reply and I really hope to meet up with them come WWDC10.