![]() Cows, debts, paintings, and property were now represented just by a price. By the time you reached this book, everything has been translated into notional cash value. In this case, you might credit 10 soldi to your current account and debit 10 soldi to your assets. On facing pages you would have a list of credit (Latin for “he trusts”) and debit (Latin for “he owes”), with every transaction appearing on both pages. Finally, the third book would be the account book. Maybe you would have a column for date (June 14th), type of transaction (bought cow), and price (10 soldi). In the second book, this was reduced to a list of transactions. You might write that “On June 14th at the main market square, I received a good cow Daisy from Giovani in exchange for ten soldi”. In the first book, you recorded everything exactly as it happened with as much detail as possible. ![]() The standard system of double-entry bookkeeping in the Renaissance consisted of three books that proceeded up levels of abstraction. This was the only comprehensive mathematics textbook at the time and became a standard reference text throughout the 16th century and beyond. By 1494, Luca Pacioli had summarized and codified these Northern Italian practices in a section of a chapter on business in his mathematics book Summa de arithmetica. We see the first extant records of Italian double-entry bookkeeping from around the late 12th and early 13th centuries, with Amatino Manucci’s 1299-1300 records for a Florentine merchant partnership based in Nimes and the 1340 Messari accounts for the Republic of Genoa. In this case, an idea central to commerce was absorbed by Genoa, Venice and Florence from the Jewish merchants in Old Cairo : double-entry bookkeeping. But they were still all cows.Īs most good ideas in Latin Europe, abstraction really took off after appropriating ideas from the Muslim world. The particular cows did not matter for the accuracy of the record and thus, the numeric record abstracted over the particular cows. Three cows could be Daisy, Clementine, and Spots or Old Reliable, Salty, and Beatrice. This representation required a certain amount of abstraction. And this seems to be conceptually independent of or prior to writing more generally, at least if we take the Inca as a guide. This required seeing certain symbols of record as representing physical objects. Recording the number of goats or cows or bags of grain. If we look at the earliest forms of language, they were used for record keeping. In the process, he introduced both good ideas and bad ones. And in expressing his view, he covered both abstraction and idealization. He expressed his views on (proto-)scientific abstraction by analogy to bookkeeping. Now, this might not seem relevant to science, but for Galileo it was relevant. ![]() I will focus on double-entry bookkeeping as a motivation. In this post, I want to provide a semi-historical discussion of the the difference between (comp sci) abstraction vs idealization. And this idealization view of abstraction has a long pedigree. It is about making an idealization meant to arrive at some essence of a (class of) object(s) or a process. Rather, it is ignoring ‘the right sort of’ detail in the ‘right sort of way’. It isn’t ignoring any detail that makes something colloquially abstract. ![]() In hindsight, I think this colloquial sense was a straw-man and doesn’t do justice to David’s view. I said this colloquial sense was just that an abstract model is ‘less detailed’. I contrasted this comp sci view with a colloquial sense that I attributed to David Basanta. The concrete objects that implement an abstraction might differ from each other in various - potentially drastic - ways but if the implementations are ‘correct’ then the ways in which they differ are irrelevant to the conclusions drawn from the abstraction. An abstract object can have many implementations. For me, abstraction is defined by multiple realizability. In that post, I distinguished between the colloquial meaning of abstract and the ‘true’ meaning used by computer scientists. Two weeks ago, I wrote a post on how abstract is not the opposite of empirical. ![]()
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