Tag: algorithm

Bigger Numbers

The sequence of Busy Beaver numbers, BB(1), BB(2), and so on, grows faster than any computable sequence. Faster than exponentials, stacked exponentials, the Ackermann sequence, you name it. Because if a Turing machine could compute a sequence that grows faster than Busy Beaver, then it could use that sequence to obtain the D‘s—the beaver dams. And with those D’s, it could list the Busy Beaver numbers, which (sound familiar?) we already know is impossible. The Busy Beaver sequence is non-computable, solely because it grows stupendously fast—too fast for any computer to keep up with it, even in principle.

a fun mind expander with ackermann numbers and busy beaver functions

Seam Carving Demo

you can use your own images in this flash implementation of seam carving

Seam carving (or liquid rescaling) is an algorithm for content-aware image resizing. It functions by establishing a number of seams (paths of least importance) in an image and automatically removes seams to reduce image size or inserts seams to extend it. Seam carving also allows manually defining areas in which pixels may not be modified, and features the ability to remove whole objects from photographs.

The reinvention of air travel

It didn’t take very long to figure out that if you replace one $25M plane with 25 $1M planes, it fixes a lot of problems. And if you couple that with doing it by the seat instead of by the plane, that lets you interleave packets, or payloads, and increases the efficiency even more. So it became very clear that we needed to build a large, self-optimizing network that would take a lot of other factors into consideration, like the physics of the airplane, the temperature, the loads. The beauty of aviation is that it’s like physics meets business, right? How much you can carry depends on temperatures, altitudes, runway lengths — and safety is all expressed in terms of parameters that the optimizer has to take into account as it starts shuffling around customers. It’s not a straight optimization, it has to be done in real time, and it has an incredible number of constraints.

fighting the NP-complete fight to give passengers on-demand routing. no more sucky hubs, yay for small airports.

Nervous About Resizing

The idea is to not just squeeze or crop the image as it is resized to fit (say) a browser window, but to remove less informative parts so that important objects and people remain. the browser compresses the image and the designer has made Y a preferred seam. We will tend to see X and Z, and likely never think of Y. This is a form of manipulation more subtle than just removing Y, since the designer can now truthfully say that the photo is authentic