Philosophy Mondays: Human-AI Collaboration
Today's Philosophy Monday is an important interlude. I want to reveal that I have not been writing the posts in this series entirely by myself. Instead I have been working with Claude, not just for the graphic illustrations, but also for the text. My method has been to write a rough draft and then ask Claude for improvement suggestions. I will expand this collaboration to other intelligences going forward, including open source models such as Llama and DeepSeek. I will also explore other moda...
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Web3/Crypto: Why Bother?
One thing that keeps surprising me is how quite a few people see absolutely nothing redeeming in web3 (née crypto). Maybe this is their genuine belief. Maybe it is a reaction to the extreme boosterism of some proponents who present web3 as bringing about a libertarian nirvana. From early on I have tried to provide a more rounded perspective, pointing to both the good and the bad that can come from it as in my talks at the Blockstack Summits. Today, however, I want to attempt to provide a coge...
Philosophy Mondays: Human-AI Collaboration
Today's Philosophy Monday is an important interlude. I want to reveal that I have not been writing the posts in this series entirely by myself. Instead I have been working with Claude, not just for the graphic illustrations, but also for the text. My method has been to write a rough draft and then ask Claude for improvement suggestions. I will expand this collaboration to other intelligences going forward, including open source models such as Llama and DeepSeek. I will also explore other moda...
Intent-based Collaboration Environments
AI Native IDEs for Code, Engineering, Science
Web3/Crypto: Why Bother?
One thing that keeps surprising me is how quite a few people see absolutely nothing redeeming in web3 (née crypto). Maybe this is their genuine belief. Maybe it is a reaction to the extreme boosterism of some proponents who present web3 as bringing about a libertarian nirvana. From early on I have tried to provide a more rounded perspective, pointing to both the good and the bad that can come from it as in my talks at the Blockstack Summits. Today, however, I want to attempt to provide a coge...
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Last week in Uncertainty Wednesday, I introduced functions of random variables as the third level in measuring uncertainty. Today I will introduce a beautiful result known as Jensen’s inequality. Let me start by stating the inequality:
f[EV(X)] ≤ EV[f(X)] where f is a convex function
In words, if we apply a convex function to the expected value of a random variable, then we get a lower value than if we take the expected value of the same function of the random variable. This turns out to be an extremely powerful result.
Jensen’s inequality explains, among other things, the existence of risk seeking and risk aversion (via the curvature of the utility function), why options have value and how we should structure (corporate) research. I will go into detail on these in future Uncertainty Wednesdays. Today, I want to show this wonderful picture from Wikipedia, which gives a visual intuition for the result:
And before we get into applications and implications of the inequality, I should mention for completeness that the inverse holds for concave functions, meaning
g[EV(X)] ≥ EV[g(X)] where g is a concave function
Next Wednesday we will look at utility functions and risk seeking / risk aversion as explained by these inequalities.
Last week in Uncertainty Wednesday, I introduced functions of random variables as the third level in measuring uncertainty. Today I will introduce a beautiful result known as Jensen’s inequality. Let me start by stating the inequality:
f[EV(X)] ≤ EV[f(X)] where f is a convex function
In words, if we apply a convex function to the expected value of a random variable, then we get a lower value than if we take the expected value of the same function of the random variable. This turns out to be an extremely powerful result.
Jensen’s inequality explains, among other things, the existence of risk seeking and risk aversion (via the curvature of the utility function), why options have value and how we should structure (corporate) research. I will go into detail on these in future Uncertainty Wednesdays. Today, I want to show this wonderful picture from Wikipedia, which gives a visual intuition for the result:
And before we get into applications and implications of the inequality, I should mention for completeness that the inverse holds for concave functions, meaning
g[EV(X)] ≥ EV[g(X)] where g is a concave function
Next Wednesday we will look at utility functions and risk seeking / risk aversion as explained by these inequalities.
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