The Two Meanings of Probability, and False Retrospective Credit

“The impressive achievements of the Arabs suggest once again that an idea can go so far and still stop short of a logical conclusion.” This comes from Peter Bernstein’s Against the Gods. It’s an interesting title. Bernstein makes the distinction between two understandings of the word probability. The first refers to the question of if we should accept what we know, as in, he’s probably correct. The second refers to the frequency of past events, or the odds that something in the future will happen; it is grounded in mathematics.

The above quote refers to the observation that while the Greeks played with dice and gambled, they never explored probability or developed a theory of probability. That took several hundred years. The key people here are Leonardo Pisano/Fibonacci (1170-1250 – Liber Abaci, replaced Roman Numerals with Arabic-Hindu system, which included zero*) Girolamo Cardano (1500-1571 – Book on Games of Chance) Luca Paccioli (1445-1517 Summa de arithmetic, greometria et proportionalita) and a few more. Bernstein’s answer is that “the idea of risk management emerges only when people believe that they are to some degree free agents. Like the Greeks and Early Christians, the fatalistic Muslims were not yet ready to take the leap.”

(Here’s a thought experiment: if a religious fellow who believes that God predetermined his life wins big at the casino, he is simply “collecting his winnings?” Likewise, if an atheist also acquires a small fortune at the casino, is he simply “lucky?”)

If that’s my first takeaway, the second is that when we look back in history it’s often a mistake to credit individuals with creating an entire field. “Cardano’s Liber de Luda Aleae appears to have been the first serious effort to develop the statistical principles of probability. Yet the word itself does not appear in the book,” observes Bernstein. I’m reminded here of Smith’s The Wealth of Nations, the so-called bible of capitalism, even though the word appears in the text precisely zero times. Similar effects occurred for Darwin’s Origins (he never said “survival of the fittest”). I would never suggest that we ought to discredit these giants; simply, they had less foresight than we give them credit for.


* zero in arabic is cifr. In Russian it is tsifra, and in Bosnia it is cifra (digit, broj is number)

** another etymological note: ilis in Latin means able to be. Biti in Bosnian is the verb To Be. Wondering if there is a connection there.



1) NN Taleb book review on Amazon:

And most books such “Against the Gods” are not even wrong about the notion of probability: odds on coin flips are a mere footnote. If the ancients were not into computable probabilities, it was not because of theology, but because they were not into games. They dealt with complex decisions, not merely probability. And they were very sophisticated at it.”

2) NN Taleb on his Facebook page:

Friends, I need help finding a PDF of AlKindi’s treatise on decoding frequencies في فك رسائل التشفير (fi 3ilm rassa2l al tashfir; about probability theory), or I am ready to overpay for a hard copy of the Arabic text.
BACKGROUND: Every book written on the historyt of probability theory is bulls***ly based on some historian claiming that modern probability was “discovered” by Fermat, Pascal, etc., falling for the mential bias that the first account they could find in a language they could read is the first account that was made. And people cite each others and perpetuate the myth. For instance Bernstein’s against the Gods theorizes that Arabs figured out algebra but not probability. But in fact it is well known that in the Levant, (Omayad era) ~800 years before Fermat, there were mathematical methods to decrypt messages based on word frequencies. It turns out that Al Kindi in one of his treatises discusses “3lm al-Musadafat” , “the science of probability” and numerical theories of frequencies. The problem is that modern Arabic translates probability by “i7timaliyat” not “musadafat”, which prevented people from connecting.

So we need the book. I would love to translate the right segments of it. The original manuscript is in Istanbul which I assume should be digitalized.

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