Why did Bernoulli mention Plato’s Theory of Forms in Ars Conjectandi? What does this have to do with free will?
This video is a broad introduction to the Weak Law of Large Numbers, the Central Limit Theorem and how it all led to Markov Chains…
Next, play around with this interactive, graphical Markov simulator!
3 decades later, Claude Shannon famously applied this idea to generate “english looking” messages in his Mathematical Theory of Communication:
In order to understand the subtle conceptual shifts leading to the insights behind Information Theory, I felt a historical foundation was needed. First I decided to present the viewer with a practical problem which future mathematical concepts will be applied to. Ideally this will allow the viewer to independently develop key intuitions, and most importantly, begin asking the right kind of questions:
I noticed the viewer ideas for how to compress information (reduce plucks) fell into two general camps. The first are ways of using differentials in time to reduce the number of plucks. The second are ways of making different kind of plucks to increase the expressive capability of a single pluck. Also, hiding in the background is the problem of what to do about character spaces. Next I thought it would be beneficial to pause and follow a historical narrative (case study) exploring this problem. My goal here is two congratulate the viewer for independently realizing a previously ‘revolutionary’ idea, and at the same time, reinforcing some conceptual mechanics we will need later. It was also important to connect this video to previous lessons on the origins of our alphabet (a key technology in our story), providing a bridge from proto-aphabets we previously explored….
This is followed by a simulation which nails down the point that each state is really a decision path
I’ll never forget the first time I was introduced to Information Theory. My TA Mike Burrel began a lecture by writing a string of 0’s and 1’s on the board and asked us to think about what it meant. It was followed by a trance-like state of excitement…how did I not hear of this before? Three years later I’m thrilled to be launching an entire episode on the topic. It was a true joy to go back to square one and relearn the topic with a childlike curiosity…My goal is to create a Myst inspired adventure which includes various puzzles along the way.
Episode #2: The Language of Coins
How Efficient Is The Financial System?
Background
In 1948 Claude Shannon wrote a paper entitled ‘The Mathematical Theory of Communication,’ later expanding this into a book by the same name. Shannon’s work was the foundation to the stunning achievements of information theory. In many respects, Shannon’s work deserves recognition as the foundation of complexity theory as well. Continue reading
Brit Cruise 