So I found out about Marx’ mathematical manuscripts, so I say “Hey, I’ve been studying mathematics this year at university. I understand limits and derivatives, maybe I can understand something of that gibberish.” So I see the titles and the one called “On the Concept of the Derived Function”, I go there and I see some notation I don’t understand, he speaks about things I’m not clearly understanding, so maybe some of you could make it clear.

For example:

Why is this x sub 1 notation? Is this some other way to write derivatives? Because on the footnotes it says this:

  1. In order to avoid confusion with the designation of derivatives, Marx’s notation x´, y´, … for the new values of the variable has been replaced here and in all similar cases by x1, y1, …

Then I saw a talk about Marx’s mathematics and the infinitesimal and some of that stuff, but the one who was speaking didn’t went much into the mathematical part but was more like a history talk on how the Chinese were interested in the propositions of Marx because it liberated calculus from the idealist veil with which it was conceived by Leibniz and Newton, but the one who was talking mentioned Marx learning mathematics with whatever he had around and didn’t managed to read Cauchy so we was like “Yeah this is nice but it’s al shit now we have proved it fully works.” But well, he seems a bit biased, since he’s a Usonian, so maybe Marx’s writings are still relevant, I don’t even know who the fuck Cauchy is, so yeah, help.

Text: https://www.marxists.org/archive/marx/works/1881/mathematical-manuscripts/ch03.html

  • Soviet SnakeOPM
    2•1 year ago

    y = ax

    when x increases to x1,

    y1 = ax1

    First of all, where does he gets y = ax? Is this a linear equation f(x) = m⋅x-b with b expressed as 0 so he removes it or what? Then as I understand, increases x to x1, which in turns increases y to y1 since it is the dependent variable.

    and y1 - y = a(x1 - x)

    But then he makes appear these deltas which I don’t understand where do they come from.

    I could continue but I think that maybe if I can understand the beginning I could maybe figure out the rest.

    • loathesome dongeater
      4•1 year ago

      y=ax is part of the assumption. As you guessed, in this case the relationship between x and y is linear. If you read in the beginning, it says: let x be the independent variable and y be the dependent (on x) variable. Then it says that in case I), assume the “simplest possible case, where x appears only to the first power”. So y is proportional to x^1 rather than x^2 or x^3. It’s all assumed and then worked upon to come to new findings later on in the study (though I don’t know what they are but it looks like calculus).

      ∆ in mathematics is used to denote change. So ∆x is change in x. So ∆x is x1 - x. Same thing with y. They are equivalent.