Was Saint Just really terrible at math?
After a while and some curiosity, I think it became a local joke about the supposed math deficiency Saint Just had (a joke that went far, it impresses me haha). I understand that all of this begins with the following question:
(Barère’s memoirs (1843 edition, p. 411-426).
One ration weighs 24 ounces in poids de marc.
«A two-portion loaf must weigh 3 pounds, for which 58 ounces of dough are added, because the loaf, after baking, shrinks by 4 ounces per portion. A 200-pound sack of flour gives 180 rations: thus 600 sacks will give 1,080,000 rations, which will suffice for the bread of 12,000 men at 90 rations each. If we add 2,000 sacks of flour, we will have 26,000 more rations for the officers, their servants and the hospitals.»
As we can see, there is an error in the calculation of the rations; in my opinion, this is undoubtedly a finger error, and I will explain it in this space with ✨arithmetic✨. (In addition to considering that we do not possess the original document, then, we do not know what the writing that Saint Just addressed in the calculation actually looks like, but we will make an inference based on this premise.
This error is actually a systematic error based on x10. Here is the explanation.
The text tells us the following:
Base data: 1 bag (200 lb ≈ 90.7 kg) or 180 servings.
Applying the rule of three: 600 bags would then be: 600(180) = 108,000. (Here is the error in determining 1,080,000).
However, the text indicates that:
600 bags will give 1,080,00 (multiplied by base 10) 12,000 soldiers at 90 rations each (12,000 x 90 = 1,080,000) (multiplied again by base 10)
"If we add 2,000 sacks, we will have 26,000 more portions (in reality, it would be 360,000)
The error itself is systematic, a slip of the finger when doing the calculations, since the zero error does not only appear in one account, but is hierarchically repeated in the account: An extra zero was added to 1,080,000. (x10) The same x10 appears when writing 90 rations per soldier (where it should be, 9: 12,000x9=108,000) In the last line, "26,000" is consistent with this systematic error.
Missing a 0 and a 3—>2 misread or miscopied.
Final fitting: Repeated pattern in calculations independent of the base x10. (Explaining two inconsistencies at the same time)
Arithmetic coherence: when correcting the base of x10, everything fits together correctly.
The last data point could also be a finger error. Without searching for approximations, 26,000 would be 360,000 more portions. We can see that if there is a double failure on the 0, there is also one similar here.
Now, because I'm a nerd and a stickler for rules, I'll make a heuristic table about probability.
Conclusion of the first stage:
Priors (before seeing the data): failures of "zero more/less" and 9-90 confusions are very common in writing → I assigned 0.7 to "finger error", 0.3 to the other.
Probabilities: Under finger error: it is plausible that a repeated x10 appears (1,080,000 and 90) and that "26,000" comes from 360,000 with two slips.
Now, while it can be shown that a finger error is likely, I still think it is very likely that either the editor of Barère's memoirs made the error (which is more feasible because we do not have the original source) or Saint Just did not review his calculations.
Still, it gives the correct weight of the number of bags (600 bags), which is what matters at the end of the day.
Well, now, clearing up the doubts about arithmetic, are mathematics reduced to that? No. Not really. The field of mathematics is extensive, and arithmetic calculations are just one of the thousand languages that mathematics addresses.
The reason I'm writing this post is to demonstrate that Saint Just had a rigorous mathematical mindset. In addition to having introductory books on physics-mathematics in his library, I decided to review the original edition (which I have available in my digital library):
Referred to as introductory or elementary books, they are often categorized by many as "simple" or for beginners. Ah, what a mistake it is to assign introductory or elementary books in that way. An introductory book tends to have a more advanced level of complexity, as it must not only be systematized in a simple way, but also address each topic without getting into cumbersome explanations a priori:
Prior to the introduction to any area of mathematics, prior knowledge is certainly necessary. Usually formal logic and set theories. Do we care about that? No, but it's a demonstration that Saint Just must have had a basic knowledge before reading the book.
As I previously stated in this individual essay I wrote, mathematics is not just about doing calculations, but about seeking to understand, abstract, and systematize the observable phenomena of the universe.
When I talk about the universe, it's not just the branches of the exact sciences, but everything that lies within it: including political science. There is an interesting article about the analysis of the logical propositions within Rousseau's social contract. These logical propositions are known as axioms, which are the initial paradigm that is considered valid, and the rest of the argumentation focuses on demonstrating the truth of these axioms. As we can see in the following image about Rousseau's social contract:
Well, something similar happens with Saint Just and his logical thread. Which appears to be a correct method to explain the dynamics of investment made in his essay on social law, and in his draft of institutions. Here are some excerpts from the work I have done to analyze it from a mathematical perspective (which exists internally in his theory, however, it is usually ignored because it is cryptic, something typical of mathematical essays):
This work is only a fragment of the immense amount of systematization that still needs to be discovered. It is only the determination and elimination of the legitimacy of the power of the social contract. The philosophy of institutions is much more complex than it appears, but that is a topic for another post.
Thank you for reading, I hope you enjoyed this little essay.
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