If you haven’t seen it I can recommend at least browsing through the preface and the introduction.

Did anyone else here read this book, comments on it?

Have you read David Graeber’s “Debt: The First 5000 Years”? He argues that the idea of debt precedes that of money.

http://www.harvard.com/book/9781612191294_debt_the_first_5000_years/

“Here anthropologist David Graeber presents a stunning reversal of conventional wisdom: he shows that before there was money, there was debt. For more than 5,000 years, since the beginnings of the first agrarian empires, humans have used elaborate credit systems to buy and sell goods—that is, long before the invention of coins or cash. It is in this era, Graeber argues, that we also first encounter a society divided into debtors and creditors.”

He also argues that debt forgiveness can be an important factor in fighting climate change, one of the other major topic of this blog. I thought you might enjoy this if you’ve not seen it already. Cheers.

]]>Although I will be reading Feynman’s paper now, what about the discussion of probabilities in the initial chapters of E.T. Jaynes’ book?

I think you’ll find Jaynes’ ideas are compatible with Feynman’s when they’re both interpreted wisely. It’s really crucial that Feynman says:

It is not my intention here to contend that the final probability of a verifiable physical event can be negative. On the other hand, conditional probabilities and probabilities of imagined intermediary states may be negative in a calculation of probabilities of physical events or states. If a physical theory for calculating probabilities yields a negative probability for a given situation under certain assumed conditions, we need not conclude the theory is incorrect. Two other possibilities of interpretation exist. One is that the conditions (for example, initial conditions) may not be capable of being realized in the physical world. The other possibility is that the situation for which the probability appears to be negative is not one that can be verified directly. A combination of these two, limitation of verifiability and freedom in initial conditions, may also be a solution to the apparent difficulty.

Arjun wrote:

Also, as -ve probabilities do appear in intermediate steps, should we also start thinking about probabilities greater than 1, as calculations can be rearranged to show whatever numbers we want?

Yes, if the probability of an event happening is < 0 the probability of it not happening is > 1, and Feynman considers probabilities greater than 1 in his article.

]]>I don’t have an answer to your question, but you may be interested in this paper

http://www.cs.washington.edu/research/jair/abstracts/halpern99a.html

and its follow-up

http://www.cs.washington.edu/research/jair/abstracts/halpern99b.html

which give a critical review of the assumptions (both explicit and implicit) in the proof of Cox’s theorem.

]]>He proves that probabilities could either be from 0 to 1 or from infinity to 1, and according to the desiderata he considers, these are the only choices.

Do you think that a change in the desiderata will let us have negative probabilities? In the banking case, we had to change our assumption that each person could only have positive money, to allow for situations where money was owed.

Also, as -ve probabilities do appear in intermediate steps, should we also start thinking about probabilities greater than 1, as calculations can be rearranged to show whatever numbers we want?

]]>The other thing maybe interesting could be the interpretation of negative probabilities in cases where one does multiply different probabilities for independent events. Then one instance of multiplication would turn the probability somehow “around” while a second negative probability would restore the physical plausible picture. Maybe, this means, that negative probabilities should only occur in pairs, to give meaningful results.

Only spontaneous thoughts, I have to admit, and maybe not very well founded at all…enjoy nevertheless…

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