discreteness

Lex Fridman has explored the concept of discreteness in various contexts on his podcast. Here are some key episodes where this topic is discussed:

1. With Joscha Bach:

   • They discuss the importance of the distinction between discrete and continuous in mathematics and physics. Infinity is challenging to express without contradictions. They also touch on the relevance of digital physics and theories of everything, like Stephen Wolfram's emphasis on discrete structures in his theories 1.

2. With Stephen Wolfram:

   • Wolfram believes the universe's fundamental fabric is made up of discrete points rather than continuous space. He explains that space can appear continuous at a large scale due to the connections between these discrete points, similar to pixels on a computer screen appearing as continuous images 2.
   • In another discussion, Wolfram compares the old caloric theory of heat, which saw heat as a fluid, to the current understanding of space. He proposes that dark matter might be a feature of discrete space rather than a collection of particles 3.
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       1

       Discrete vs. Continuous

       00:39:09
       
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       2

       Discrete Space

       01:19:29
       
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       3

       Discrete Reality Exploration

       03:46:39
       
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       4

       Exploration in AI

       00:25:01
       

3. With Oriol Vinyals:

   • Vinyals explains the significance of discretizing time in the context of training AI, like DeepMind's AlphaStar. In video games, although time appears continuous, it is typically broken down into discrete time steps (e.g., 22 ticks per second in StarCraft) for computational processes 4.

These conversations illustrate various perspectives on discreteness across different fields, from theoretical physics to artificial intelligence.