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 Uncertainty Wednesday, we saw how diminishing marginal utility of wealth provides an explanation of risk aversion via Jensen’s inequality. Why would it be then that lots of people seem to like small gambles, like a game of poker among friends. One possible explanation is that the utility function is locally convex around your current endowment. So this would look something like the following:
In the immediate area around the endowment (marked with dotted lines for two different levels) the utility function is convex, but for larger movements it is concave.
In the convex area someone would be risk seeking. Why? Well because Jensen’s inequality now gives us
U[EV(w)] ≤ EV[U(w)]
Again, the left hand side is the utility of the expected value of the wealth, whereas the right hand side is the expected utility, meaning the expected value of the utility. Now the inequality says that someone would prefer an uncertain amount over a certain one. Here is a nice illustration from Wikipedia:
We see clearly that the Certainty Equivalent (CE) is now larger than the expected value of wealth, meaning the Risk Premium (RP) works the other way: in order to make a risk seeker as well off as accepting the bet, you have to pay them more than the expected value.
Next Uncertainty Wednesday we will look more at how incredibly powerful convexity is in the face of uncertainty.
Last Uncertainty Wednesday, we saw how diminishing marginal utility of wealth provides an explanation of risk aversion via Jensen’s inequality. Why would it be then that lots of people seem to like small gambles, like a game of poker among friends. One possible explanation is that the utility function is locally convex around your current endowment. So this would look something like the following:
In the immediate area around the endowment (marked with dotted lines for two different levels) the utility function is convex, but for larger movements it is concave.
In the convex area someone would be risk seeking. Why? Well because Jensen’s inequality now gives us
U[EV(w)] ≤ EV[U(w)]
Again, the left hand side is the utility of the expected value of the wealth, whereas the right hand side is the expected utility, meaning the expected value of the utility. Now the inequality says that someone would prefer an uncertain amount over a certain one. Here is a nice illustration from Wikipedia:
We see clearly that the Certainty Equivalent (CE) is now larger than the expected value of wealth, meaning the Risk Premium (RP) works the other way: in order to make a risk seeker as well off as accepting the bet, you have to pay them more than the expected value.
Next Uncertainty Wednesday we will look more at how incredibly powerful convexity is in the face of uncertainty.
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