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Wolfram Summer SchoolFounded in 2003

16th Annual Wolfram Summer School, held at Bentley University June 24–July 13, 2018


Horacio Hernan Moraldo

Class of 2008


Horacio Hernan Moraldo is a software developer from Buenos Aires, Argentina, and has been working with game development for many years from his own small studio. These days he teaches computer game development to undergraduate students at Universidad Maimonides and in an institute called Escuela Da Vinci, where he also advises the coordination department. In Maimonides he also teaches some basic material on complex and emergent behavior as seen in games and simulations.

These days he's working on the development of a massive video-streaming application, and on some basic research on computer vision interfaces on his own.

He's also starting a career in mathematics, as a student at Universidad de Buenos Aires, and has always studied subjects that are related to NKS; he's also very interested in foundational mathematics, so has read and studied the original papers on computability and limits of logic by Gödel, Turing, Chaitin, etc., as well as a lot of specific material from the Santa Fe Institute, and he has studyied much of Wolfram's work from before NKS's publication.

Project: The Impact of Lemma Application to Proof Length

In many cases, sets of proofs can be made shorter by the use of lemmas. The objective of this investigation is to find the limits of what can be done to decrease the length of proofs in this way. A mathematical demonstration of a first theoretical limit has already been completed for this project, and the next step is to find evidence that there are also more important practical limits to this task, by using the methods of research described in NKS.

In order to do this, an automatic theorem solver has been built in Mathematica. This has given an initial insight on this problem, with much work yet to do.

Favorite Radius 3/2 Rule

Rule 327339092129057936712242154502516840410851871501122748665036555382262271359779532 97000091948708935617298679098863211129678704870960091992194834755002434

If I have to be honest, my favorite rules are Conway's Game of Life and the elementary cellular automata. It's not that I don't like others more, but those have a huge nostalgic value for me: I programmed them in many languages, and I've been doing so since a child. I've also solved them with paper, and in many other ways. They made me very curious about this world of complexity, and they were my first introduction into this subjects.

Now, if I have to look for a different rule other than those, or if I have to look for different reasons, I'm probably going to be non-standard anyway. My favorite rule in this case is a very long rule, a 2-color, 8-neighbor (range 4) rule that goes by the following number:

327339092129057936712242154502516840410851871501122748665036555382262271359779532 97000091948708935617298679098863211129678704870960091992194834755002434

Of course I can't say it's a simple rule, but it has a few interesting properties. To start, if started from a single cell, it shows a delicate Sierpinski-like triangle.