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Mathematics: the greatest game changer in human history

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Does it blow anyone else mind just how incredibly recent in history that mathematics was discovered and invented? And how thanks to math the last 300 years seem more like they may as well have been 3000 years?
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But that's wrong, you fucking retard.

https://en.wikipedia.org/wiki/History_of_mathematics
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>>281589
No, the concept of industrialization changed the way the world works.
That and the invention of C.
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>>281589
If by recently you mean geologically, yes
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Does it blow anyone else mind just how incredibly recent in history that agriculture was discovered and invented? And how thanks to agriculture the last 300 years seem more like they may as well have been 3000 years?
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>>281708
That's hardly true. Numerous agricultural aspects have changed completely with time.
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>>281589
That's hardly true. Numerous mathematical aspects have changed completely with time.
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http://venturebeat.com/2015/11/20/nasa-and-google-invite-media-to-visit-quantum-computing-lab-on-december-8/

Hype?
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>>281667

How else do you think we have our modern technology and industry? Do you think a bunch of fedoras got into a room and chanted "there is no god" until we landed a man on the moon?
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>>281589
>mathematics was invented 300 years ago

back to the shame cube with you, OP
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>>282250
Comprehension: 0
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>>281598

Symbolic Algebra is a little over 400 years old
Calculus is a little over 300 years old
Probability and Statistics is a little over 200 years old
Analysis, Set theory, Riemann Geometry and Vector Calculus are a little over 100 years old
Linear Algebra, Abstract Algebra, Logic, Topology, Functional Analysis, Chaos Theory, ... are all children of the last century

Most of the math we know popped up within 200 years
>>
why are all those mathematicians so kawaii sugoi desu
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>>282282

Also this OP gets it, the history of math is pretty interesting. Math seems to rise up along with civilization and vice versa, although there are some exceptions. Mathematics at the moment seems to be more developed when 1. there is a need to predict the behavior of and and engineer the environment and 2. when there is enough free time and space to pursue the study of mathematics.

The math most people learn in the first 5 or so years of their school is a very simple concept that even primates and birds task, which is arithmetic. Counting among tribal societies is also not uncommon, as it's a very useful skill to have; depending on the lifestyles and needs of the community, though, determines how "fleshed out" or developed counting systems are.
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>>282362

cont.

From counting comes arithmetic, which is both the next step from counting mathematically speaking, historically speaking, psychologically speaking, in terms of the rise of society, etc etc

Arithmetic is important when you have lots of changes in the items you count, and the most prolific use of arithmetic is with economics and simple, fundamental market analysis. Adding how much crops you yield, how much you have traded, how much you might owe, the total amount of objects and goods that you have, and the four basic operations, addition, subtraction, multiplication, and division work nicely here. At this stage of mathematics, we see small bartering economies and villages.
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>>282373
>Mathematics as the primary driving force behind political economy
Hook line and sinker.
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>>282373
you state a tautology. arithmetic matters because arithmetic matters.

the question is not the one of the place of maths, but the one why we do economics, crops, trade in the first place.
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>>282373

cont.


Up to this point, most societies saw no need to develop further. This can be another subject of discussion, but it appears that humans just don't naturally derive mathematics much more advanced than arithmetic and simple geometry without a demand to engineer society in some way. This is where war, nation building, and large markets and government systems come into place. For with taxation of land and land surveying came the need of geometry and finding areas, and one of the most well known formulas of all math, the Pythagorean theorem. Here we have middle school geometry, and small pockets of people studied mathematics for specialized situations and soon enough for pleasure. For literally thousands of years, it was geometry and some use of primitive algebra to figure out the areas, volumes, and relationships of angles and lines for the use of architecture, land surveying, and economic purposes, and science was still not really a thing and was seen as "philosophy" for most societies. Mathematical progress was so slow, that most complex socities had the same amount of complexity around the world before global colonization made greater Europe the center for science and mathematics for centuries.
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>>281589
because the classical rationalist spouting memes like
>muh mathematics gives truth about reality
without any motivation for this.
whereas it is a personal choice to see mathematics as more than human conventions.

here, some whores working at the CERN
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>>282389

I meant political economy as being a powerful driving force for mathematics, I don't think that can be argued against much
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>>282399
>Adding how much crops you yield, how much you have traded, how much you might owe, the total amount of objects and goods that you have, and the four basic operations, addition, subtraction, multiplication, and division work nicely here. At this stage of mathematics, we see small bartering economies and villages.
Legit why bother
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>>281589


Linear algebra is one of the first "abstractions" that you encounter in mathematics that is not very well motivated by experience. (Well... there are numerals, which are a pretty tricky abstraction as well, but most of us don't recall learning those.)

It helps to have the backstory.

Mathematicians studied geometry and simple transformations of the plane like "rotation" and "translation" (moving everything to the right by 3 inches, or up by 7 inches, or northeast by 3.2 inches, etc.) as far back as Euclid, and at some point, they noticed that you could do things like "do one translation after another", and the result was the same as if you'd done some different translation. And even if you did the first two translations in a different order, the resulting translation was still the same. So pretty soon they said "Hey, these translations are behaving a little like numbers do when we add them together: the order we add them in doesn't matter, and there's even something that behaves the way zero does: the "don't move at all" transformation, when composed with any other translation, gives that other translation."

So you have two different sets of things: ordinary numbers, and "translations of the plane", and for both, there's a way of combining ("+" for numbers, "composition of transformations" for translations), and each of these combining rules has an identity element ("0" for addition, "don't move at all" for translation), and for both operations ("+" and "compose"), the order of operations doesn't matter, and you start to realize something: if I proved something about numbers using only the notion of addition, and the fact that there's an identity, and that addition is commutative, I could just replace a bunch of words and I'd have a proof about the set of all translations of the plane!
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>>282482

And the next thing you know, you're starting to realize that other things have these kinds of shared properties as well, so you say "I'm going to give a name to sets of things like that: I'll call them 'groups'." (Later, you realize that the commutativity of addition is kind of special, and you really want to talk about other operations as well, so you enlarge your notion of "group" and instead call these things "Abelian groups," after Abel, the guy who did a lot of the early work on them.)

The same thing happened with linear algebra. There are some sets of things that have certain properties, and someone noticed that they ALL had the same properties, and said "let's name that kind of collection". It wasn't a pretty development -- the early history of vectors was complicated by people wanting to have a way to multiply vectors in analogy with multiplying real numbers or complex numbers, and it took a long time for folks to realize that having a "multiplication" was nice, but not essential, and that even for collections that didn't have multiplication, there were still a ton of important results.

In a way, though, the most interesting thing was not the sets themselves -- the "vector spaces", but rather, the class of transformations that preserve the properties of a vector space. These are called "linear transformations", and they are a generalization of the transformations you learn about in Euclid.

Why are these so important? One reason for their historical importance is that for a function from n-space to k-space, the derivative, evaluated at some point of nn-space, is a linear transformation. In short: something we cared a lot about -- derivatives -- turns out to be very closely tied to linear transformations.

For a function f:R→R , the derivative f′(a) is usually regarded as "just a number". But consider for a moment

f(x)=√x
f(100)=10
f′(100)=1/20
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>>282483

Suppose you wanted to compute the square root of a number that's a little way from 100, say, 102. We could say "we moved 2 units in the domain; how far do we have to move away from 10 (i.e., in the codomain)?" The answer is that the square root of 102102 is (very close to) the square root of 100, displaced by 2⋅1/20 , i.e., to 10.1 . (In fact, 10.12=102.01 , which is pretty accurate!)

So we can regard "multiplication by 1/20" as the derivative of square-root at a=100 , and this gives a linear transformation from "displacements near 100, in the domain" to "displacements near 10, in the codomain."

The importance of derivatives made it really worthwhile to understand the properties of such transformations, and therefore to also understand their domains...and pretty soon, other situations that arose in other parts of math turned out to "look like those". For instance, the set of all polynomials of degree no more than nn turns out to be a vector space: you can add polynomials, you can multiply them by a constant, etc. And the space of all convergent sequences of real numbers turns out to be a vector space. And the set of all periodic functions of period 1 turns out to be a vector space. And pretty soon, so many things seemed to be sharing the same properties that someone gave those properties a name.

Nowadays, seeing each new thing that's introduced through the lens of linear algebra can be a great aid...so we introduce the general notion first, and many students are baffled. My own preference, in teaching linear algebra, is to look at 3 or four examples, like "period-1 periodic functions" and "convergent sequences" and "polynommials of degree no more than n", and have the students notice that there are some similarities, and only THEN define "vector space". But that's a matter of taste.
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why would that be surprising? mathematics is invented in the same way words are invented. we can invent new words very easily. they're just arbitrary meanings. math is a social construct with no basis in reality. it's entirely subjective. want 2 to equal 1? just define it that way. you are now a mathematician. numbers aren't literally real.
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>>282487

Sounds like a pretty good strategy, examples and letting the students catch on is always a fantastic way for engagement, taking into consideration how utterly boring it is to be taught every theorem after another. Wish I could be a student in your class, anon

Also, this is a history board, so I guess I should add commentary on how linear algebra and other abstract mathematics have really defined how crazy society was in the 20th century. But even then, some of the advances of mathematics at this level define a level of complexity that goes beyond the scope of this board, since most of the peoples and civilizations that are discussed on here never had the opportunities to pursue levels of this thought aside from open philosophy and discussion. The times have indeed changed.
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>>282506

yes, but they served a purpose in any society, and math still does.
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>>282516
pure mathematicians are as useful to society as philosophers and theologians. ie they're really fucking useless. people who think otherwise are popmath faggots who haven't look at the bullshit pure mathmos study.
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>>282528

People who think pure math is useless know nothing about math, science, or engineering.
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>>282528
woah there, take it easy now, you sound like one of those popmath folks right now. One of the purposes of pure math is based on the philosophy that all mathematics in one form or another is based off of physical reality. Cantor's mathematics, for example, is being used to model certain quantum field theories and as a possoble model for certain interactions of elementary particles.

In general, pure math finds many applications. Algebra used to be considered pure math ; pure math finds promising alternatives to better mathematical systems, applied math puts it to work. Everyone who knows math seriously should have figured this out by the very naming of the subjects
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>>282506
>mathematics is invented
>math is a social construct
>it's entirely subjective

FUCK NO. Take your postmodernism bs back to the women's studies department.
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>>282556

first /pol/ shitposters, now /sci/ shitposters.. you were good while you lasted, /his/
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>>281708
Fertilizer is as old as agriculture is. Terra Prata has most likely been rediscovered 10-20 times by different civilizations in the last 3 millenia.

I don't want to know how many times Crop Rotation was rediscovered. Since mono culture means death of crops in most cases, so its cyclic in rediscovery and implementation.

I also don't want to know how much has been lost to oral passing down of tradition.
Some countries lost 80% of their culture in fermentation and making of food when the freezer/fridge arrived. Most notably cheeses and milk products.
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>>281708
>No one gives the Haber process its rightful dues

;_;
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>>281589
>how incredibly recent in history that mathematics was discovered and invented
>the pyramids were built without math
Literally retarded.
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>>282681
>Haber process created the greatest pre Industrial industry
>We masturbate over the company instead of the process
Noice
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>>282691
>mathematics ends at arithmetic and synthetic geometry
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>tfw terrible at maths
It's the one subject I wish I was good at.
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>>282506
Did you try explaining that to your math teacher when he handed you a zero?
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I find alternative numeral systems fascinating:
https://en.wikipedia.org/wiki/Counting_rods
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>>282703
confirmed for never trying
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>>282702
>mathematics begins at calculus
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>>282785
I hate fake transparency
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>>282506
the actual word "bird" may be arbitrary, but the thing it refers to is very real.

>>282528
just because you don't understand math doesn't make it useless
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>>282808
More or less.
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>>281815
It's called rationality.
That is the game changer, maths has been around for thousands of years you bellend.

Go read some Descartes and more generally about the enlightenment.
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>>282945
>rationality
>enlightenment

Nice memes

>Go read some Descartes

How about you go read his "Geometry" and see the sad state of math at the time.
>>
this
>>281598

The Sumerians and Akkadians were working on Quadratic Equations and were on the cusp of Calculus.

Math began way over 5000 years ago.

Math is based upon fertility cults in Mesopotamia.

Math is entirely representative of human nature.
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>>282953
>nice meme

The enlightenment fundamentally changed the way we thought about the world and the sciences.
Darwin invented the modern scientific method by synthesizing the philosophical perspective of Descartes with Baconian empiricism.

The enlightenment is the result of the renaissance, and the reason the state of maths before the renaissance was so awful is because medieval scholars and universities worked on the basis that we could not contribute new knowledge, as the greeks and the bible had already figured it all out.

Then with Galileo disproving Greek astronomy and Columbus disproving Plato's estimation of the size o the world, people decided they could contribute new knowledge in the world.

Advancements in maths and science came from advancement in philosophy.
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>>282955
>were working on Quadratic Equations

Quadratic equations of the ancient world were like this:

>I have a square and extend a side by four units and get a rectangle of area twelve. To find the side of the square take half of four to get two, two squared is four, four added to twelve is sixteen, the side of sixteen is four, four minus two is two and you will find that this is the side of the square.
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>>282976
>Columbus disproving Plato's estimation of the size o the world

0/10. You got too greedy with your trolling.
>>
>thread about mathematics
>people fail to understand an exponential cumulative growth function

somewhat ironic desu
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>>281589
Stuff like 0 being invented or rediscovered relatively recently gets me.
Also interesting to me is the smattering of scientific terms that are derived from Latinised Arabic.
Not being a mathematician though it's only some of the recent fundamentals that surprise me.

I'm studying geology though, that something as fundamental as continental drift was highly controversial up to the mid 20th century is mind boggling.
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>>283017
>I'm studying geology though, that something as fundamental as continental drift was highly controversial up to the mid 20th century is mind boggling.
Because its bullshit.
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>>282976
>Then with Galileo disproving Greek astronomy and Columbus disproving Plato's estimation of the size o the world, people decided they could contribute new knowledge in the world.


typical rationalist

This is the indirect result of the detrimental divide between what is now philosophy and what is now physics [which splits into theoretical physics and experimental physics]
This is why the rationalism-realism is the default stance wherein the students leaving the university have faith. These students hardly question this faith until late in their careers, and, for the few who question their stances, generally, when they reconsider, it goes either into scepticism, or into pathetic chatting on fields such as philosophy and theology that they do not master at all, especially when they go in the entertainment industry in doing conferences, selling books and documentaries...
the same applies to biology thanks to the trendy mechanism [not theory] of the evolution. Many do not reflect on what they say and happily claim that, for instance, we are on earth to spread our genes.
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>>282506
>mathematics is invented in the same way words are invented. we can invent new words very easily. they're just arbitrary meanings. math is a social construct with no basis in reality. it's entirely subjective. want 2 to equal 1? just define it that way. you are now a mathematician. numbers aren't literally real.


this indeed

>1+1 = 2 is true.
but this is completely manufactured and you do not even know why you need truth in the first place. it is a choice to claim 1+1 = 2.
abstractions does not give you anything but nihilism and the fantasy of taking such analytical conventions as knowledge shows how lost the rationalist is.


all our logics that we today and the total lack of agreement [since agreement is what matters for the rationalist] shows how math are a matter of personal abstraction of our personal experience. logic.math is the continuation of the abstraction that we begin with our natural languages and remains a sterility. the sole advantage of formal language is the faith that the rationalist has in the communicability.
the fact that proofs by computers and long proofs are too tedious to read and need patches whereas their authors think that they are accurate shows how much math is fallible.

Also, Descartes supposed right form the bat that our senses deceive us and that logic is always right and then attempt to justify his claim [and fails miserably since whatever he does persuades only him]
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>>283017
Plate tectonics is a good one, since its one of those that isn't obvious.

Today, we lean on the fact Earthquakes work the way they work, where undersea volcano are, changes on height on mountains and undersea crags, satellite measurement of continent drift, and more.

When a Earthquake is just a Earthquake, a Volcano is just a Volcano, its really whatever.
Especially when "if you don't have proven evidence" sounds like something super harsh and critical.
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>>282556
>muh platonic math

And you're criticizing the pomos? You're on shaky speculative ground, mate.
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>>282282
No it didn't. Most of what we know were set up from thousands of years. Many were merely formally systematized as a group within the past couple of centuries. Newton didn't introduce 100% of whats considered Calculus, he probably did maybe a small percentage, the foundations for systematization were laid many hundred years before and got into the hands of great systematizers like Newton through the Arabic/Indian trade/communications.
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>>281589
(abcdef)=(ab)(ac)(ad)(ae)(af)

What objects are these?
Or is it just saying that a=1
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>>281589
No, that was fossil fuels.
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>>284067

permutations
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>>284067
You just triggered my math autism.
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>>283023
;^)
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>>283853
>Most of what we know were set up from thousands of years

No, there was nothing like vectors, quaternions, tensors, differential forms, functions, distributions, or topological spaces thousands of years ago.
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>>284067

One turn of the cycle:

a->b->c->d->e->f->a

equals

a->b->a
a->c->a
a->d->a
a->e->a
a->f->a

applied in succession
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>>282568
/his/ was always terrible if you're not a pure ideologue. /pol/ and /lit/ are possibly the worst combination in a board. Complete ideological opposites, but both are scholarly enough to not just immediately lose in the face of data, like in a theoretical /pol/ versus /co/ fight. Both boards have made most threads terrible because /pol/ can't not shitpost and /lit/ can't not be indignant little girls. To direct some of the blame towards a cunt like yourself, /lit/ has been the bigger problem. A thread can continue through shitposting, bitches like you can't tolerate anyone enjoying themselves as long as you're upset about something. You killed this board from day one because you had no intent on allowing free speech to happen. There are only a very specific amount of topics you can tolerate before you start menstruating on everyone. You are literally tumblr with a bigger library.
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>>286540
>being dismissive of something means you don't allow free speech
Not that guy but senpai, /pol/ is far effective for shouting people down than a few elitist and pretentious remarks
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>>286685
I disagree. /pol/'s objective is laughs and will generally let a left-wing conversation continue after letting you know they hate you. /lit/ actually thinks it's doing something meaningful and tries to derail the entire thread and being offensively un-masculine about it. /pol/ might be more initially aggressive, but /lit/ is far more mean-spirited and spiteful. I really can't stop making comparisons to women and femininity here, but I think my point is made with all of them.
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>>281708
You said it m8
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>>286764
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>>286706
I have been on both long to say this is completely untrue. /pol/ regularly sinks threads they don't approve of by posting roll pics(pic that people respond and their post number gets a result) while threads about Julius Evola still go uninterrupted in /lit/. I do envy your version of /pol/, getting labelled a commie when talking about policies people perceived as socialist can be exhausting.

Also with regards to /his/, there is chatter on /pol/ about taking over /his/, whereas in /lit/ the only mention of /his/ is that one faggot directly any threads he doesn't like to /his/. I don't find your comparison with /lit/ with feminity to be fair since the /lit/ just like /pol/ are just being contrarian in their own ways
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>>281589
no rationalist can disprove solipsism, because solipsism is a rationalist stance.
Thread posts: 74
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