Indy Telecom & Industrial Media

One of the things that I keep meaning to write about is Bathsheba Grossman’s amazing sculptures.

She creates some very interesting artwork and I have been a fan of her work for the longest time. For the most part, she creates sculptures that are inspired from math and science.

To that end, she has a math sculptures collection which features various “topologically-inspired” artwork. My personal favorite is the Soliton, which is simple, elegant and simply too beautiful to resist!

And there is also her math models collection, which, as the name suggests, has various math models. And since I do have a thing for minimal surfaces, I really like her Schwarz D Surface.

And as a (former, now dormant) graphics geek, I was also very impressed by her 120-Cell Sculpture. The only thing that could make that sculpture better is if one could play around and change the inner reference points for each inner layer.

Other than these, she also has an impressive collection of science and math inspired 3d models etched inside glass crystals. All the models are inspired from math or science and are just as fascinating.

Sadly, my favorite (the menger sponge, displayed above) is no longer available; however she has made available that and several other models as downloads.

I am rarely impressed by a lot of art-work trying to portray science, but Bathsheba’s work is truly awe-inspiring. Of course, that could be because she is someone who studied mathematics but became an artist.

So all you fine folks now know what to get me for Christmas!

Here is a 3d Julia fractal with a Mandelbrot pattern that I whipped up in POV Ray. I’ve done some 3d quaternions before, but I figured I’d try creating patterned ones and this is a starter piece.

And here is the starter piece on which I patterned this Mandelbrot from POV Ray’s documentation.

I do think that it needs a little smoothening and that there are some points that are disjoint from the central piece.

Recently, during a not particularly interesting meeting I began graphing. First, I’d draw a line between (0, 9) and (1, 0), then I’d draw a line between (0, 8 ) and (2, 0), then between (0, 7) and (0, 3)…and so on till I had drawn a line between (0, 1) and (9, 0), which resulted in an aesthetically pleasing curve.

Soon, I began to wonder if, instead of simply drawing the curve, I could express it mathematically. For example, a parabola can be seen as the set of points which are equidistant from a focus and a directrix. Was there some similar way to describe the curve I had been drawing? I decided that the first step should be to see if I could represent my curve as a function in the form of y = f(x). Unfortunately, taking that first step has proven to be more difficult than I originally expected. For example, I can express the slope of any of the lines as:

Slope = (n – MAX) / (n + 1)

and I can express the y intercept of any of the lines as

Y Intercept = MAX – n

With those two equations, I can find a general form of y_n = f(x) for any of the lines. Specifically,

y_n = x(n – MAX) / (n + 1) + MAX – n

Armed with that, I can find the point where line n crosses line n + 1, that is, the point where y_n(x) = y_n+1(x). Specifically, by using the formula for y_n above, I get:

x(n + 1 – MAX) / (n + 2) + MAX – (n + 1) = x(n – MAX) / (n + 1) + MAX – n

which, when I manipulate it as follows:

=> x(n + 1 – MAX) / (n + 2) – (n + 1) = x(n – MAX) / (n + 1) – n
=> x(n + 1 – MAX) / (n + 2) = x(n – MAX) / (n + 1) – n + (n + 1)
=> x(n + 1 – MAX) / (n + 2) = x(n – MAX) / (n + 1) + 1
=> x(n + 1 – MAX) = x(n – MAX)(n + 2) / (n + 1) + n + 2
=> x(n + 1 – MAX)(n + 1) = x(n – MAX)(n + 2) + (n + 1)(n + 2)
=> (xn + x – MAX(x))(n + 1)
=
(xn – MAX(x))(n + 2) + (n + 1)(n + 2)
=> xn² + xn – MAX(x)(n) + xn + x – MAX(x)
=
xn² - MAX(x)(n) + 2xn – 2MAX(x) + (n + 1)(n + 2)
=> xn – MAX(x)(n) + xn + x – MAX(x)
=
-MAX(x)(n) + 2xn – 2MAX(x) + (n + 1)(n + 2)
=> xn + xn + x - MAX(x) = 2xn – 2MAX(x) + (n + 1)(n + 2)
=> x – MAX(x) = - 2MAX(x) + (n + 1)(n + 2)
=> x + MAX(x) = (n + 1)(n + 2)
=> x(MAX + 1) = (n + 1)(n + 2)
=> x = (n + 1)(n + 2)/(MAX + 1)

Gives me the relatively simple statement that

y_n(x) = y_n+1(x) => x = (n + 1)(n + 2)/(MAX + 1).

Looking back at my notes (which were originally made on the back of an agenda and continued on a hotel notepad), it seems that I decided this would be a good time to go on a snipe hunt and find the distance for which any particular line was on the frontier of the curve. Using a bit more manipulation (which I may set forth in a future post), I found that, as MAX goes to infinity, the length of the longest line segment on the frontier approaches 2, while the length of the shortest line segment approaches 2^.5. This was actually something of a surprise, and it’s a result I’m glad I reached. However, it still didn’t answer how to express the curve in the form of y = f(x). My next thought for how to continue down that path is write an equation which will show which line segment I’m actually on at any point x. My guess is that it should be doable based on the formula for the crossing point of lines n and n+1 given above, though I haven’t actually done it yet. Am I right? Is it actually doable? Will it lead me to the desired y = f(x)? Only time will tell…

As a note, I normally blog about the law surrounding data privacy and information security here. Since I already have a blog devoted to those topics, my posts here will cover anything else that comes to mind.

Today, I was hanging out with some of Beck’s friends (who, ironically enough, are detectives at the Cincinnati PD) and I absent-mindedly forgot my copy of Fooled by Randomness at the local Starbucks.

I went looking for it and asked the people at Starbucks if they’d seen it around. Sean, the ever-insightful barista, returned the book with a quip –

“You’ve gotta watch out for that random chance when things go wrong, man.”

Indeed.

Is it me or does it seem like there is something to be said about Taleb’s rants against the traditional practices of Wall Street traders and progressive betting in Blackjack?

The fact that progressions cannot overcome expectation is also rather interesting, given the way some institutions work.

While normal distributions are nice and wonderful, they aren’t really feasible in the world of finance. This is because the market can be so volatile and fickle that variances become meaningless.

So, enter fat-tailed distributions. These are distributions where events deviate significantly from the mean in comparison to normal distributions. What this means in terms of the stock market is that assets and investments are prone to jumps (in either directions).

On this topic, Paul Kedrosky links to an interesting presentation on Fat Tailed distributions by Northfield, the guys that make analytical and investment software.

It’s quite interesting and talks about some work that’s being done in this area.

On a related note, another area of application for Fat tailed distributions is the CRM arena. Contact-centers and self-service applications (i.e. IVRs) receive millions of calls a day, and there is just as much variation in C-sats, agent performance, AHT and so on.

It would be interesting to apply some of these tools and techniques to call-center analytics and see how well those work.