Logistics : The first discussion will be held on Saturday 5/16/20 at 14:00 EST (19:00 UK or 11:00 PST). I will email you the zoom link. We will discuss this post
Keep notes/questions/ideas. See you there!

#### Wolfram is fascinated with cellular automata, which is simple recurrsive rules that can grow complex structures if run for long time. Wolfram likes to give interactive talks where he explores live random such structures and tries to understand their behavior. I saw one of his talks at the Museum of Math in New York recently. Normally speakers give the same talk twice for two different audience slots. But Wolfram gave two different talks because the experiments took different turns. It’s quite intersting, take a look (talk 1, talk2).

More recently, Wolfram published an article about his recent findings in automata. His new work shows how these structures can be more than just interestingly complex. They might be capable of explaining various aspects of modern physics. Here is some news stories about it (news1, news2)

Reading list

  • https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/

Debriefing

Wolfram’s new project is certainly interesting and intriguing, even if not materially different from his previous work “A New Kind of Science”. His work raised interesting questions. The main objection that we felt was left unanswered is how could one refuse this theory, given that it’s not possible to test experimentaly. This problem, someone said, is serious enough to lead us to question whether we can even characterize the work as a “theory”; suggesting that “framework” would be a fairer characterization. Nevertheless, the discussion that followed touched on a couple of different issues.

One thread developed around the scientific method. We seem to agree that there is a fundemental tradeoff in science between the complexity of the system and the amount of valid predictions one can derive from the system. In a sense scientific theories aim to “do more with less”.

Over time scientific theories succeed by striking at a novel improved tradeoff. The consensus seemed to be that it’s not enough to provide an alternative explanation for observed phenomena. The explanation needs to be either materially simpler than competitive thoeries, or be conisent with a wider number of observed phenomena. This is of course not rigorous, but there are plenty of good illustrative examples from the history of science to guide us. We discussed Newtonian mechanics and Einstein’s theory of relativity. This is an example of being correct with a lower accuracy. The rule of 80-20 was brought up, by which 20% of effort is needed to explain 80% of the observations, while the remaining 20% of the observations take 80% of the effort to be explained.

We also discussed the idea of alternative explanations. A good example is Ptolemy’s geocentric model which managed to have a great amount of accuracy in predicting planetary motions. This is an example of providing good predicitions but based on the wrong model. Ptolemy’s model turned out to be pretty complicated too, so that didn’t help.

We were not sure if Wolfram’s work falls into either category, with the general census being that it neither explains more nor offers a simpler explanation. Of course the description of a cellular automata is incredibly succint, but to truly use the theory one is left with finding the one configuration and initial value that agrees with our universe. Since searching the space of all possible configurations dominates the complexity of the theory, the theory does not seem to offer material advantages over competing established approaches on either side of the tradeoff.

Another thread developed around the idea of vacuum. It seemed that accepted physics has reached a level of understanding around the conditions that need to be satisfied in vacuum for our theories to be consistent. (This took a long time and went through interesting stages - a topic perhaps for a future meeting). We were not clear how Wolfram’s theory is consistent with these conditions, based on his explanation of discrete space and time.