Wolfram Science

Slides for Matthew Szudzik's Presentation

Here are the slides from my presentation, "An elegant pairing function" (in Mathematica format).  Download ElegantPairing.nb

Generating Music with NKS: From Mathematica to a Live Performance by Katarina Milkovic, New England Conservatory of Music

Posted by Kathryn Cramer.

Katarina Milkovic showed a number of NKS patterns and described how she had transformed them into sound and played the sound compositions. She discussed the various things that were tried in 2004 when at NKS Summer School.

NKS Music - Katarina Miljkovic

• Rule 118
• Rule 30
• Rule 110
• Sound Synthesis Rule 30
• Sounds from NKS: Class 2
• Sounds from NKS: Class 2 - 3
• Sounds from NKS: Class 4
• Awakening, for Violin & Piano, Rule 30

 

In between the presentations there was an interesting discussion involving John Kiehl and others concerning the differences in the situation of Milkovic as a classically trained composer working towards NKS music as opposed to the situation of the people at Wolfram working from software towards NKS music.

Peter Overmann demonstrated the WolframTones site and showed us the various stages of developing WolframTones in Mathematica, showing how they built up to the system of WolframTones as it exists now.

Following the presentations, the question and answer session took the form of a group discussion of aesthetics.

(The blog post I showed involving the WolframTone my son created to go with a drawing he made is here: WolframTones: The Ziporps Gets a Soundtrack.)

Live Computer Experiment by Stephen Wolfram

Posted by Joe Bolte

After the Q&A, Stephen Wolfram performed a live computer experiment from scratch. He chose to search for complex behavior in a class of systems called step registers. Starting from a blank Mathematica notebook, Wolfram generated a ruleset and combed through it for examples of complex behavior, first using a two-neighbor rule and then a three-nighbor rule. You can see that in the two-neighbor case rules 6 and 9 yielded complex behavior and in the three-nieghbor case, rules 90 and 165 were the interesting results. Wolfram had an intuition that rules 90 displayed additive behavior, but he was not able to demonstrate anything before time ran out. Please take a look at the Mathematica notebook of the experiment.

Update: Christopher Haydock noted a problem with the notebook and submitted a corrected version, with the code extensively refactored to be clearer for those following along at home. Thanks Chris!

Exciting Announcements at the Keynote Address

Posted by Joe Bolte

After the day-long NKS mini-course, the 2006 NKS Conference kicked off this morning with an address by Stephen Wolfram. Since he was now addressing people who were already familiar with basic ideas of NKS, Wolfram covered the state of the art of our research, what new directions it was moving in, and what kinds of new tools we could expect from Wolfram Research.

He started by saying that although the activity in the NKS world might seem slow to people who were deeply involved in its development, it had only been four years since the public introduction of the NKS book, and the pace of adoption was consistent with, and even faster than other historical examples of major scientific revolutions. Every day, several papers are publsihed that involve methods he pioneered and the quality of this work has been increasing steadily. A few years ago, articles in Science and Nature had little to do with complex systems and simple programs, but now they are clearly moving in an NKS direction. In fact, many papers mention the kind of ideas he has been promoting for years, even though some authors seem unaware of the theoretical framework that he had already put in place.

The coverage of the relation of NKS to traditional scientific fields was complicated and fascinating, so I'll hold those out for separate posts and move on to two very exciting announcements that Wolfram mentioned close to the end of the talk. One is that he has moved from his "book-writing hermitage" and resumed a more active role in building research tools. It sounds like a major new version of Mathematica is on the way, which will be far ahead of the already unparalleled tools for studying simple programs in Mathematica 5.2 Hopefully as the conference progresses, we'll have more tidbits about the capabilities we can expect from Mathematica in the future.

The other announcement was that Dr. Wolfram is so keen on seeing practical applications of the theoretical ideas he and others are developing that Wolfram Research is interested in finding ways to support business models based around NKS. This could possibly come in the form of angel investment, NKS consulting services, or computer and legal infrastructure. The news that Wolfram Research will become even more actively involved in supporting other research efforts must be tremendously exciting to many people at the conference who are broadening and applying the foundation laid down by Wolfram's New Kind of Science over the past 25 years.

Stephen Wolfram's Keynote Address: "The core of NKS is exploring the computational universe."

Posted by Kathryn Cramer.

Stephen Wolfram gave a wide-ranging Keynote Address that touched on many (or perhaps even all) of the subjects of the papers to be presented at the conference.

The central organizing metaphor of the talk was the field of NKS as an exploration of the computational universe: The core of NKS is exploring the computational universe.

My favorite line from the talk, from the portion in which he discussed NKS and aesthetics is: We are seeing the beauty of nature but not just from our world, but from all possible worlds.

As I was listening to his talk I explored the relationship between the various items on the program today. Here is my first draft version of this. As I listen to the talks I will modify and improve upon this.

Larger versions of the graphic are available here: 1024 x 642 and 3869 x 2424.

The talk will be available later. We will post the URL when we have it.