Markov Chains: The link between Plato, Bernoulli, Markov & Claude Shannon

Posted in Research and Projects, Video / Theatre with tags , , , , , , , , on June 27, 2013 by Brit Cruise

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!

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3 decades later, Claude Shannon famously applied this idea to generate “english looking” messages in his Mathematical Theory of Communication:

Logarithmic Measure of Information (Entropy Primer)

Posted in Video / Theatre with tags , , , on June 1, 2013 by Brit Cruise

It wasn’t until 1920 that the question “how do we quantify information” was well articulated. This video introduces a key idea of Nyquist and Hartley, who laid the groundwork for Claude Shannon’s historic equation (Information Entropy) two decades later. In these early papers, the idea of using a logarithmic function appears, something which isn’t immediately obvious to most students fresh to this subject. If one ‘takes this for granted’ they will forever miss the deeper insights which come later. So, the goal of this video is to provide intuition behind why the logarithm was the ‘natural’ choice…

Link to Khan Academy lesson.

Symbols, Signals & Noise

Posted in Uncategorized with tags , , , , , , , , , , , on April 8, 2013 by Brit Cruise

The following video/simulation was an attempt to bridge the gap between information as what we mean to say vs. information as what we could say. I view this as an important stepping stone towards Hartly, Nyquist and Shannon – which I will deal with next. It covers symbols, symbol rate (baud) and message space as an introduction to channel capacity. Featuring the Baudot multiplex system and Thomas Edison’s quadruplex telegraph.

Play with simulations used in video on Khan Academy:

Symbol Rate

Symbol Rate

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Electricity, Magnetism, Morse & The Information Age.

Posted in Video / Theatre with tags , , , , , , , , , , , on March 2, 2013 by Brit Cruise

The follow three video mini-series is a bit of an Engineering detour in the story of information theory. In order to easily grasp the ideas of Hartley and Shannon, I felt it would be beneficial to lay some groundwork. It began with my own selfish interest in wanting to relive some famous experiments & technologies from the 19th Century. Specifically, why did the Information Age arise? When and how did electricity play a role in communication? Why was magnetism involved? Why did Morse code become so popular compared to the European designs? How was information understood before words (and concepts) such as “bit” existed? What’s the difference between static electricity and current?

All of these questions are answered as we slowly uncover a more modern approach to sending differences over a distance…

The History of Electricity

The Battery and Electromagnetism

Morse Code and the Information Age

Click below to practice Morse Code!

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Conditional Probability (Bayes Theorem) Visualized

Posted in Research and Projects, Video / Theatre with tags , , , on January 24, 2013 by Brit Cruise

It’s powerful to understand how conditional probability can be visualized using decision trees. I wanted to create an alternative to most explanations which often start with many abstractions. I was drawn to the idea of looking at the back pages of a choose-your-own-adventure book, and deciding how you could have arrived there. Here I present a visual method using a story involving coins… allowing you to decide how to formalize. Once we grow tired of growing trees, we may ask the key questions: how can we speed up this process?:

This is followed by a game I designed (built by Peter Collingridge) which introduces how branches can be weighted instead of counted.

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Thanks to Kalid Azad for reviewing this lesson.

Information Theory, a practical approach

Posted in Research and Projects, Video / Theatre with tags , , , , , on January 15, 2013 by Brit Cruise

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

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The History of the Alphabet

Posted in Video / Theatre with tags , , , , , , , on November 23, 2012 by Brit Cruise

Before jumping into Information Theory proper I decided to go back and explore the history of the Alphabet. This reminds us that communication, no matter how fluid it seems, is really just a series of selections. I’m using both Shannon and Harold Innis as inspiration for this series which is why I’m clarifying medium vs. message as well as information transmission over space vs. time – ideas which are popularized by Marshall McLuhan years later. By starting this way I’m able to carefully move away from the semantic issues of information and towards what Shannon called the “engineering problem”. This analogy will carry through the rest of the series so it’s important to lay the groundwork early on.

We are now ready for the problem…

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