Information Tied to Chance: "Meaning was a hypothesis Shannon had no need of. Shannon's concept of information is instead tied to chance. This is not just because noise randomly scrambles messages. Information exists only when the sender is saying something that the recipient doesn't already know and can't predict. Because true information is unpredictable, it is essentially a series of random events like spins of a roulette wheel or rolls of dice."
The Incompressible Substance of Messages: "If meaning is excluded from Shannon's theory, what is the incompressible substance that exists in every message? Shannon concluded that this substance can be described in statistical terms. It has only to do with how unpredictable the stream of symbols composing the message is."
Humor Illustrating Information Theory
Phone Company Ads: "A while back, a phone company ran ads showing humorous misunderstandings resulting from mobile phone noise. A rancher calls to order 'two hundred oxen.' Because of the poor voice quality, he gets two hundred dachshunds—which are no good at pulling plows at all. A wife calls her husband at work and asks him to bring home shampoo. Instead he brings home Shamu, the killer whale."
Analysis of the Shamu Commercial: "The humor of these spots derived from a gut-level understanding of Shannon's ideas that we all share whether we know it or not. Try to analyze what happened in the Shamu commercial: (1) The wife said something like, 'Pick up shampoo!' (2) The husband heard 'Pick up Shamu!' (3) The husband wound up the conversation, said goodbye, and on the way home picked up the killer whale. It is only the third action that is ridiculous. It is ridiculous because 'Pick up Shamu' is an extremely low-probability message."
Communication and Information
Conversational Dynamics: "In real conversations, we are always trying to outguess each other. We have a continuously updated sense of where the conversation is going of what is likely to be said next, and what would be a complete non sequitur. The closer two people are (personally and culturally), the easier this game of anticipation is. A long-married couple can finish each other's sentences. Teen best friends can be in hysterics over a three character text message."
Improbability and Message Compressibility: "It would be unwise to rely on verbal shorthand when speaking to a complete stranger or someone who doesn't share your cultural reference points. Nor would the laconic approach work, even with a spouse, when communicating a message that can't be anticipated. Assuming you wanted your spouse to bring home Shamu, you wouldn't just say, 'Pick up Shamu!' You would need a good explanation. The more improbable the message, the less 'compressible' it is, and the more bandwidth it requires. This is Shannon's point: the essence of a message is its improbability."
Market Hypotheses and Financial Models
Efficient Market Hypothesis: "There is much truth in the efficient market hypothesis. The controversy has always been over just how far the claim can be pressed. Asking whether markets are efficient is like asking whether the world is round. The best way to answer depends on the expectations and sophistication of the questioner."
Markowitz's Portfolio Theory: "Markowitz created charts of mean vs. variance. Each stock or portfolio is represented by a dot on the chart. When you remove all the dots that are rejected by the above rule, the remaining portfolios form an arc of dots that Markowitz referred to as the 'efficient frontier.' This will range from more conservative portfolios with lower returns to riskier portfolios with higher returns. Financial advisers responded to Markowitz's model. They were growing aware of this new and threatening current in academic thought: the efficient market hypothesis. Markowitz demonstrated that all portfolios are not alike when you factor in risk. Therefore, even in an efficient market, there is reason for investors to pay handsomely for financial advice. Mean-variance analysis quickly swept through the financial profession and academia alike, establishing itself as orthodoxy."
Markowitz devoted a chapter of Portfolio Selection to the geometric mean criterion (possibly the most ignored chapter in the book) and cited Latane's work in the bibliography.
Markowitz was virtually the only big-name economist to see much merit in the geometric mean criterion. He recognized that mean-variance analysis is a static, single-period theory. In effect, it assumes that you plan to buy some stocks now and sell them at the end of a given time frame. Markowitz's theory tries to balance risk and return for that single period.
Most people do not invest this way. They buy stocks and bonds and hang on to them until they have a strong reason to sell. Market bets ride, by default. This makes a difference because there are gambles that look favorable as a one-shot, yet are ruinous when repeated over and over. Any type of extreme "overbetting" would fit that description.