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Ole Peters
@ole_b_peters
, 3 tweets, 2 min read Read on Twitter
1/3 Yesterday @mjmauboussin sent me this page of Markowitz's Portfolio Selection, Chapter 6. An example computation of geometric and arithmetic means to illustrate that the geometric mean (important for compounding investments) is smaller.
2/3 One can take this observation as a starting point and discover that addition and multiplication can interact in rich ways, like in @Marc_Elsberg's Farmers Fable.
One can discover ergodicity economics.
Or not.
farmersfable.org
3/3 Over the millennia people have rediscovered this inequality many times and sometimes started to think about what it means for economics. Markowitz, Kelly, Whitworth (1870).

But the first to publish it was Euclid, in his Elements, Book V, Proposition 25. Here's how.
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Ole Peters
@ole_b_peters
1/5 An example of the kind of mathematics we find in economics. It's wrong: second underlined sentence contradicts the first.

It's psychologically hard: could this be just a cultural difference? Is there a way to make it true without abandoning the meaning of words and symbols?
2/5 To be clear, using what we learn in high school about probabilities, here's the natural immediate response to reading this passage.
@alex_adamou, @bermanjoe, and I had the same response independently.
3/5 In this case, as in many others, the difficulty goes back to the Original Sin of economics, which is to ignore time and work instead with expectation values - averages across the multiverse.

Read 5 tweets
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Ole Peters
@ole_b_peters
1/5 This deserves a thread, @hulme_oliver.

"Utility" can be a scientific concept, or it can be a just-so word.
2/5 Science operates as follows

a) propose a hypothesis, a mathematical theory (or model) of some physical process, e.g. of people making choices.

b) find a testable prediction.

c) check that prediction against observation.
3/5 Science can't operate without prediction. Prediction connects theory to data. Like the clutch in a car connects engine to wheels.

Utility theory makes the following kind of prediction.
1) Observe someone's behavior, and infer u(x).
2) use u(x) to predict future behavior.
Read 5 tweets
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Ole Peters
@ole_b_peters
1/7 Ok, here's another one. Say you want to decide how much to invest in a risky business. Do it with EE: first, consider time and write down a model for the wealth dynamic. Null model: noisy multiplicative growth.
2/7 Wealth is not ergodic in this model, so you know the expectation value doesn't tell you what happens over time.
3/7 Your task: find an ergodic observable whose expectation value does tell you what happens to wealth over time. Only one option: the ergodic growth rate. Write it down, optimize it, and you know how much to invest, given knowledge of the dynamic.
Read 7 tweets

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Dr. Gabriela Bailas
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Elijah J. Magnier
@ejmalrai
#Important:
Yesterday late afternoon #Russia/n forces took 3 positions in Qusseyr and Juseh and established checkpoints. #Hezbollah, not informed of the Russian presence, came close to these forces and asked their immediate pull out+
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hezbollah maantin and kept all positions. The #Russia/n move was not coordinated.+

#Hezbollah did not...I repeat, did not pull out one single element from the area.

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