How Marx used Hegelian Dialectics to do Calculus and develop Computational Mathematics

[Anonymous No.12464216]

According to the archives, this topic has been brought up and mentioned in threads a few times, but has never had its own thread.

Turns out Karl Marx made non-trivial contributions to mathematics.

>The Mathematical manuscripts of Karl Marx consist mostly of Karl Marx's attempts to understand the foundations of infinitesimal calculus, from around 1873–1883

>"Marx's operational definition of the differential anticipated 20th century developments in mathematics, and there is another aspect of the differential, that seems to have been seen by Marx, that has become a standard part of modern textbooks—the concept of the differential as the principal part of an increment."

https://en.wikipedia.org/wiki/Mathematical_manuscripts_of_Karl_Marx

[Anonymous No.12464219]

>>12464216
>Marx’s method is historical-genetic, identical to that used in his critique of Political Economy. His aim is to derive the derivative directly from the process of variation of the function, so that its algebraic, real origin is met. In previous methods, the differentials were individual entities with substantial content. In Marx, instead, they are inseparable as numerator and denominator in the differential ratio, which is a unitary operational symbol indicating an ordered set of logical operations. This notion is strikingly similar to the modern concept of algorithm, making Marx a precursor of the modern computational mathematics.

>Marx’s goal was to find a method to obtain the derivative of a function from the variation of the variable itself. To do this, he changed the starting point with respect to the previous methods: instead of the sum [math] x_1=x+\Delta x [/math] , he starts from the difference [math] x_1−x=/Delta x [/math] . In the first case, the increment is added to the original variable as a distinct and separate quantity, which exists independently of the process of variation and has the nature of a constant. In the second case, instead, the increase is an effect of the variation of the variable; it cannot be defined independently of it and actually represents a variable quantity. This different starting point brings with it two important consequences. From a technical point of view, an immediate application of the binomial theorem is no longer possible and this opens the way to a different differentiation procedure. From a methodological point of view, the definition of the increment in terms of negation of the original variable sets in motion a dialectical development that, through the subsequent negation of the negation, will lead to the final result.

[Anonymous No.12464222]

>>12464219

At the end of the procedure, Marx arrives at an equation in which the increments, in the form of the ratio [math] \frac{\Delta y}{\Delta x} [/math] , appear in the left-hand side of the equation, while the right-hand side only contains expressions in [math] x_1 [/math] and [math] x [/math]. This fact, Marx argues, is not accidental but expresses a qualitative difference between the two sides of the equation: the left-hand side has a symbolic nature, while the right-hand side has an algebraic nature. The first one represents the purely symbolic expression of the actual process of variation that takes place entirely in the right-hand algebraic side of the equation. The increments becoming zero, which in dialectical terms represents the negation of the negation, only takes effect on the left-hand side of the equation, which is reduced to the expression [math] \frac{0}{0} [/math], leaving the right-hand side unchanged. However, this time the ratio [math] \frac{0}{0} [/math] should no longer be dreadful because it does not denote an arithmetic operation, but is a purely symbolic operator, which as such can be replaced by the differential ratio [math] \frac{dy}{dx} [/math], without giving rise to any logical contradiction. Unlike the previous methods in which the differentials appeared as distinct entities having a substantial content, they are now inseparably connected as the numerator and the denominator in [math] \frac{dy}{dx} [/math], which only represents the symbolic form of a process through which the qualitative leap takes place from the algebra of the constant quantities to the differential calculus of the variable quantities. In other words, for Marx the ratio between the differentials is a mere operational symbol, which denote an ordered sequence of logical and algebraic operations necessary to compute the derivative of a function.

[Anonymous No.12464227]

>>12464222
>Here is, in a nutshell, Marx’s contribution to the theory of differential calculus... The definition of the differential as an operational symbol presents strong analogies with the modern concept of algorithm and this makes Marx a precursor of modern computational mathematics.

[Anonymous No.12464229]

>>12464227
Link to manuscripts:

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

[Anonymous No.12464230]

>>12464219
>>12464222
>>12464227

Source:
Ricci, A. The mathematics of Marx. Lett Mat Int 6, 221–225 (2018).

For some reason I can't link the doi

[Anonymous No.12464754]

What's with all th schizo posting today?

[Anonymous No.12465813]

>>12464216
>commie sociology majors think first week of high school calculus is hard
also no one cared about the tiny bit of trash that marx wrote about derivatives. it seems like its mostly just kant trying to rationalize it to himself. math was already way ahead of him.

[Anonymous No.12465946]

Oh My Fucking God. It has a wikipedia page???

No I will not donote $2.75. Fuck you wikipedia.

[Anonymous No.12466007]

1873–1883, so he would be 65 - 75 years old
Is this all his work on math?
To put it in perspective Abel was born 1802 and died 1829
fucking tarded commies

[Anonymous No.12466928]

this is just what leibniz did

[Anonymous No.12467423]

>>12466928
He discovered an alternative method to Leibniz's.
The first part of his work contains a review of 3 other methods used before him, one of which is Leibniz's.

>>12466007
Nobody's saying Marx was Ramanujan.

[Anonymous No.12467462]

>>12467423
The point was the level of calculus he wrote about was "settled" a long time any results he obtained that other did not were trivial, and he made 0 progress towards the foundational problems of calculus even though that was THE hot shit at the time. Riemann died 1866.

[Anonymous No.12467479]

>>12467462
It's not that he advanced calculus.
The point was that his independently developed approach towards calculus pre-empted certain modern concepts and techniques.

>>12465813
Nobody cared about the tiny bit of trash Archimedes wrote about integration either.

[Anonymous No.12467499]

>>12467479
>independently developed
no

[Anonymous No.12467523]

>>12464216
lmao. once again commies try to rewrite history.

[Anonymous No.12467534]

>>12464216
>marx invented calculus
>source: trust me bro t. commie
lmao. once again commies try to rewrite history. what's next? he invented the steam engine, radio, transistor, internet, wifi, etc? lmao, sure sure dear leader created everything. lmao.

[Anonymous No.12467543]

>>12467534
>lmao
>lmao lmao
seething much?

btw, did you know that more of pinochets victims were fascists than commies? of course you didn't

[Anonymous No.12467549]

>>12467543
>implying fascism isn't just socialism
lmao

[Anonymous No.12467552]

>>12467543
>implying fascism isn't just another word for socialism

[Anonymous No.12467555]

>>12467543
>>12467552
Ok, but none of this has to do with Marx's investigations in Calculus.
I think the point of the thread is just that Marx was good at math.
Not a math genius who secretly invented everything, but better than people give him credit for. I don't think there's any point in moving the goalposts and saying AKSHUALLY marx didn't invent wi-fi.

[Anonymous No.12467562]

>>12467555
according to:
>A Russian edition edited by Sofya Yanovskaya was eventually published in 1968, and an English translation was published in 1983 (Marx 1983).
sounds like ussr propaganda to me. where are the originals of his work?

[Anonymous No.12467567]

>>12464216
This isn't new information, Marxism is more than an ideology, its a science.

[Anonymous No.12467571]

>>12467567
the science of ending up with everyone equally in poverty.

[Anonymous No.12467572]

>>12467534
OP’s claim was that Marx made non-trivial mathematical discoveries. He never said they were amazing or newton tier. You’re straw manning hard to cope for something irl you should face head on instead of getting into hysterical internet turmoil.

[Anonymous No.12467578]

>>12467567
This.

[Anonymous No.12467580]

>>12467572
show me his actual work, it's all shit written from the ussr. that was the point i was making. marx is seen as a god figure to commie retards. it starts with he independently discovered x, and rolls down from there.

[Anonymous No.12467584]

>>12467567
>This isn't new information, Marxism is more than an ideology, its a science.

[Anonymous No.12467618]

>>12467562
> where are the originals of his work?
The International Institute of Social History in Amsterdam.
https://access.iisg.amsterdam/universalviewer/#?manifest=https://hdl.handle.net/10622/ARCH00860.A_104?locatt=view:manifest

[Anonymous No.12467620]

>>12467580
Just search all instances of "differentialrechnung" on this page.

https://search.iisg.amsterdam/Record/ARCH00860

[Anonymous No.12467629]

>>12467567
especially when pic related murdered all the scientists doing research on genes

[Anonymous No.12467640]

>>12467618
>>12467620
fair enough. he did write stuff down. the issue is ofc, we have to take engel's word that marx did this independently without looking at leibniz, cauchy, maclaurin, riemann, etc which is extremely doubtful. seems more probable, he found some book then tried to scribble shit to make sense of it.

[Anonymous No.12467658]

>>12467640
> we have to take engel's word that marx did this independently without looking at leibniz, cauchy, maclaurin, riemann, etc which is extremely doubtful

No, Marx did study Leibniz, Cauchy, MacLaurin (I don't know about Riemann though). He wrote a lot about Taylor and MacLaurin specifically. Actually the first part of his work regarding calculus is his review of 3 methods of derivation, one of which is Leibniz's.
He didn't "invent calculus" independently, he just developed one extra method, which happened to pre-empt certain mathematical techniques developed much later by the field at large (computation math, algorithms, etc)
I guess "independently discovered" was an inaccurate way to phrase it.

Here's what Marx says about Taylor and MacLaurin:
>"The real and therefore the simplest connections between the new and the old are always discovered as soon as the new takes on a rounded-out form, and one can say that differential calculus obtained this relation through the theorems of Taylor and MacLaurin. It thus fell to Lagrange to be the first to reduce differential calculus to a strictly algebraic basis."

[Anonymous No.12467664]

>>12467658
welp, respect to marx then. can't say anything positive about his contemporaries or ideology. but the man seems way better than his legacy.

[Anonymous No.12467668]

>>12467658
welp, respect to marx then. can't say anything positive about his fans or ideology. but the man seems way better than his legacy.

[Anonymous No.12467669]

>>12467543
He shoved rats into jewess commies vaginas.
Source: High ranking Chilean commie who was tipped off and left Chile 2 days before the coup

[Anonymous No.12467870]

Marx was a failure in life and his followers are all useless twats with inherited wealth. Fuck him.

[Anonymous No.12467871]

>>12467567
>In science, if your idea fails, try it again and again and again until it maybe works in future.

[Anonymous No.12468019]

>>12467871
but it worked? if it weren't for that bald faggot the Soviets would still exist

[Anonymous No.12468530]

>>12464216
I cant give Marx credit for managing to describe something that is common sense

[Anonymous No.12468547]

>>12464219
>In Marx, instead, they are inseparable as numerator and denominator in the differential ratio, which is a unitary operational symbol indicating an ordered set of logical operations. This notion is strikingly similar to the modern concept of algorithm, making Marx a precursor of the modern computational mathematics.

Talk about a stretch.

[Anonymous No.12468552]

>>12467572
>OP’s claim was that Marx made non-trivial mathematical discoveries.
>He never said they were amazing

Clear contradiction. Are you retarded? Do you think before writing?

[Anonymous No.12468557]

>>12467658
>computation math, algorithms, etc

Nah, you just don't know what those are.
t. CompSci

[Anonymous No.12468561]

>>12464216
Maybe he should have stuck to mathematics then, instead of creating a political ideology that led to the deaths of more than 100 million people and counting.

[Anonymous No.12468563]

>>12468552
Considering Marx was being compared to Niels Abel all of a sudden, I don't think it was.

[Anonymous No.12468570]

Marx's contribution to economics are well known.

He ironed out out the economic laws, for the theory of value. Declining rate of profit ect.

Only kveching neoclassicals who prefer feels>reals ignore them.

[Anonymous No.12468582]

So basically he contributed at the same level of the development of analysis where Tooker likes to jive in as well.

[Anonymous No.12468593]

>>12468561
If an idea leads to the deaths of 100 million people, the problem is not with the idea, but with the world in which it appears.
An idea merely makes a statement; it finds resonance only if that statement exposes the symptom underlying the contradictions within the system governing the world.

But of course the 100 million figure is completely ahistorical and has no relation to any of the demographic data.

[Anonymous No.12468628]

>>12468593
What is it that makes people want to defend communism? It SOUNDS so good that you ignore all the historical evidence of it being a failure?

https://en.wikipedia.org/wiki/Mass_killings_under_communist_regimes

https://www.wsj.com/articles/100-years-of-communismand-100-million-dead-1510011810

I suppose it is all "ahistorical" then?

[Anonymous No.12468637]

>>12468582
>>12468593

I assume the same person wrote these two posts. These were the most pretentious yet nonsensical sentences I have ever read.

[Anonymous No.12468666]

>>12468628
I accept that it was a failure. What I don't accept is lies about 100 million killed by communist regimes.
A wiki article with a "disputed neutrality" warning that cites the likes of Conquest and Volkogonov, and a wall street journal article written by an author with an anti-Soviet bias, are not examples of solid historical scholarship.
Next you're going to bring up Solzhenitsyn too.

I suggest starting with Grover Furr's debunkings of Kruschev, Kotkin, Conquest, Snyder, etc

[Anonymous No.12468686]

>>12468593
>If an idea leads to the deaths of 100 million people, the problem is not with the idea, but with the world in which it appears.
This is exactly what I have been telling people about National Socialism for years.

[Anonymous No.12468700]

>>12468686
And I would agree with you.
I think the mainstream accusations against Nazi Germany are just as unjustified as the accusations against the USSR

[Anonymous No.12469173]

>>12468686
>>12468700
you're both fucking psychotic

[Anonymous No.12469572]

>>12468570
>theory of value

his theory is the most retarded one a man can imagine.

he is popular because he's accessible to retards.

[Anonymous No.12469583]

>>12469572
I wouldn't exactly call das Kapital "accessible to retards", but ok.

[Anonymous No.12469605]

>>12466007
>>Is this all his work on math?
OP is conflating Marx's self-study on math with "work" on math. This was published by soviets well after his death as a curiosity.

[Anonymous No.12469613]

>>12468570
>Marx's contribution to economics are well known.

Karl Marx is the Samuel Birley Rowbotham of economics. His stupid cultists just make the world a worse place.

[Anonymous No.12469693]

>>12468570
>He ironed out out the economic laws, for the theory of value.
You know modern economics dismiss that as outdated and wrong right? Modern economics holds itself with marginalism, which is the opposite of the theory of value(LTV).

[Anonymous No.12469763]

>>12467479
>Nobody cared about the tiny bit of trash Archimedes wrote about integration either.
>no one cares about exhaustion
yeah, that must be why its wiki page is so much larger
https://en.wikipedia.org/wiki/Method_of_exhaustion

[Anonymous No.12469771]

>>12468593
>the problem is not *necessarily* with the idea
fixed

[Anonymous No.12469789]

>>12469763
Except the Method of Exhaustion was not originated by Archimedes, and the section on Archimedes is only a small part of that article.
Great comparison.

[Anonymous No.12469799]

all marx did was derive calculus 150 years after it was already derived, as an intellectual exercise
sure, that means he was good at math, but nowhere near the level of the experts of his day

[Anonymous No.12469815]

>>12469799
>sure, that means he was good at math, but nowhere near the level of the experts of his day

I'll take that

[Anonymous No.12469829]

>>12468666
Furr is not a historian. You can cite 1917bolshevik_liberal_destroyer.blogspot.com/debuking-liberal-lies-about-ussr just as well.

[Anonymous No.12469835]

>>12467658
I was expecting this to be another retarded shitpost thread but this is actually a good thread OP. I learned something new.

[Anonymous No.12469861]

>>12469789
>Great comparison.
the first 2/3rds of marx's article is filler, the only substantive part of it is
>Marx's operational definition of the differential anticipated 20th century developments in mathematics, and there is another aspect of the differential, that seems to have been seen by Marx, that has become a standard part of modern textbooks—the concept of the differential as the principal part of an increment.", implying that Marx's apprehension and interpretation of calculus was far from short-sighted.
which is just trying to give him credit for Taylor series, which was 160 years before marx

[Anonymous No.12469953]

>>12469829
>1917bolshevik_liberal_destroyer.blogspot.com/debuking-liberal-lies-about-ussr
sorry, your link is broken.

I don't care whether he's a "historian" or not. So far I haven't seen anyone challenge his arguments successfully.
Every criticism I see is ad-hominem after ad-hominem with no substance.

[Anonymous No.12469967]

>>12469835
I'm glad you liked it, anon.
If you're interested in more, I suggest looking up Hegel's writings on mathematics too.

[Anonymous No.12471576]

>>12468552
Is English not your first language or is the part of your brain that comprehends language disfigured? “Non-trivial” means “not trivial”, it does not mean substantial, it does not mean “amazing”, it means that it’s significant enough to not be waived off as useless. The OP only claimed Marx’s contributions were “non-trivial” whereas the anon i was replying to had responded with “Marx didn’t invent calculus!!!!” If you disagree with OP, it’s because you think Marx’s contributions WERE trivial and insignificant. It’s certainly true that Marx didn’t invent calculus, but to pretend that OP was claiming that or something similar is straw manning. Do you read chains of replies before attacking one comment at random by itself without context or are you just retarded?

[Anonymous No.12472973]

>>12467499
Explain