What went wrong /his/?
>mindblowingly advanced maths (Archimedes almost invented Calculus)
>built machines and analog computers (Antikythera mechanism)
>most impressive realistic sculpting in history (pic related)
>society of many philosophical viewpoints
>sexual freedom, full tolerance of homosexuality
>refined naval and land warfare
>architecture, science, politics and so much more
And this is what happened to it:
>Invaded by innumerate Romans
>Converted by intolerant Christians
Not to mention, a full appreciation of the tragedy of life, and an amazing strength in the face of that tragedy.
Whereas faggots today can't even get out of the house, the Greeks basically knew life was death and still built cool shit.
>reading The Symposium, the greatest work by the greatest philosophical mind, Plato
>eager for a great discussion of epistemology or ethics
>instead read 50 pages discuss the nuances of fucking boys
Wasn't sexuality in ancient greece more concerned with who was topping and who was bottoming? Like, there wasn't "full" tolerance of homosexuality, because it was seen as unseemly to get fucked, but totally fine and manly to fuck someone of either gender.
On topic, though, I believe what happened to Greece was simply a matter of time. After enjoying hegemony over the region for hundreds of years, successfully beating back Persia, and allowing someone like Alexander to exist, Greece sank into political and cultural stagnation, while other powers carried on the torch. It's a huge testament to Greek culture that they managed to have the effect on their successors that they did.
The Seikilos epitaph, oldest known musical composition.
Euclids Elements, the most important maths book for 2000 years.
>Wasn't sexuality in ancient greece more concerned with who was topping and who was bottoming?
Yes and no. They usually had interfemoral sex in case of pederasty. However, when you spent so much time kissing men/boys, who says you wouldn't be willing to go the extra distance? Besides, they practiced heterosexual anal. And Lesbianism was also socially accepted.
The Elgin Marbles.
>And there was no concept of homosexuality anyway
Because they were progressive even beyond that. They did what was fun, without the need to justify it via a label. We 21st century western Europeans are even now barely emanicipated from the church's concept of marriage and monogamy. At the current rate, we will reach the level of consciousness in Ancient Greece maybe in 2050.
I just want to explain in case you people didn't get it:
The Ancient Greeks had already invented a way to compose music and write it down. It wasn't invented in the 17th century.
You fucking tard, they just didn't go around fucking each other, they mostly fucked young men/boys. It was not some sorta "Marriage" thing. The Greeks highly revered the institution of marriage, possibly more so then we do today (It was legal in athens to kill a man if you walked in on him fucking your wife), More over, prostitutes were looked down upon. Pericles wife was a prostitute, and non-citizen of Athens, and that tainted the man himself. Finally we have no fucking clue what the antikythera mechanism was even used for, and even if it was a computer as you say, the math did not exist to support the programming languages that would be needed to operate the more complex machines.
No opinion desu. I have only read the first part of the Peloponnesian war, I don't recall him being mentioned too much. Apparently he was for the Sicilian Expedition which was American-level retarded and ended in disaster.
kill yourself now.
> was even used for
You realize that this doesn't diminish the marvel of such a construction? If anything it enhances it.
I suggest you get some education before trying to "share your opinion" again. Thank you!
The Expedition would have worked but mainly got fucked over by Nicias' attempts to stop it.
In order to try and deter the Athenians, he made out they'd need a much larger force than they needed in order to succeed. They took him sincerely and made their fleet much larger than it should have been, and made a low risk expedition into a high risk one. He also forgot to bring cavalry, which messed up the Athenian's chances of destroying the Syracusan army (they defeated it in a Hoplite battle, but had no cavalry to succesfully pursue them).
Alcibiades was a cheeky lad, but he was a LAD.
>he made out they'd need a much larger force than they needed in order to succeed
That's always a double edged sword. Nobody wants to send a small expedition and then have them all die because they were too small. In truth, the Spartans, Syracusans and allies had a pretty sizable army. It was hostile land, and far away from Athens. The Athenians went because they believed "hurr durr we so strong" and got wrecked. Instead they should've stayed back and used their army in the Aegean theater. Nicias was right.
But if they sent an expedition that was small and it failed, it wouldn't be that damaging to Athens -- due to Nicias trying to stop it, they ended sending way to big a fleet, and losing.
Also, the Spartans weren't interested in attacking Athens that much at the time -- the first envoys the Syracusans sent to Sparta for military aid only got envoys giving motivation back.
And the Athenians mainly went out of fear of the Syracusans sending aid to the Peloponnesian once they'd taken Sicily.
Tbh they were many points in the war when things could have got sorted out, but both sides made fuck ups in some way.
>it wouldn't be that damaging to Athens
Well, the Athenians at that time were pretty conceited cunts, I don't think they expected to lose - ever. At least not against some superstitious Lacedaemonian blockheads who couldn't form a sentence.
The Spartans never could have attacked Athens. It was fortified and had a superior fleet.
>And the Athenians mainly went out of fear of the Syracusans sending aid to the Peloponnesian once they'd taken Sicily.
The Athenians were winning the war, no help from Sicily could've changed that. They should've just set back and tightened their grip, and soon they'd have the idle Spartans strangled.
The Athenians (and Alcibiades especially) were greedy. They wanted a quick victory, which is why the lost Mantinea. They had great advantages, a stronger fleet, money and smarts. But they couldn't force the issue, because the Spartans were just much better warriors.
Peace was impossible. All these city states were gunning for the top position.
It culminated with Alexander, but before him the Corinthians smashed the Spartans and were set up to conquer all that hellenic clay
Crazy /pol/(though I hate that place) tier speculation:
Maybe the ancient Greeks were just lucky that they had a founder population that was abnormally smart. Over time urbanization homogenized this unique population into a much more average people.
There is this strange sociological effect where "successful" populations in the intellectual and urban sense tend to have less children than poorer less elite populations around them. We see it today. The first world's native populations are pretty much all sub-replacement levels. While poor countries like Nigeria are exploding in population - in fact third world countries are the only reason the global population is growing at all. Within first world nations the most educated have the least children on average.
Though no one seems to know why this is and world leaders didn't seem to expect it or know how to counteract the effect there is reason to believe it might not be new. Augustus made laws for Roman women that encouraged them to have more than 3 children and criminalized not being married in an attempt to bolster the Roman aristocracy's population. The real end of Sparta was population decline in their true born citizens
>For Aristotle wrote in the Politics that under
one thousand Spartiates remained. This presumably describes the situation in the time
he was writing, the 330s or 320s.
>And in the year 244 the Spartiates numbered a maximum of 700 (Plut. Agis 5.6).
It's possible that a freak evolution accident created a population in the Aegean that had an abnormally high average IQ (or whatever). But after a period of success and expansion they fell into this demographic trap that others have fallen into as victims of their own success. Cities absorbed "barbarian" immigrants and promoted foreign slaves to keep economic numbers up until eventually the ancient Greeks had irrevocably changed like their own ship of Theseus.
Built on the backs of slaves. Also, they were bloodthirsty sellout retards with no loyalty to anyone.
Christianity was the best way. Marrying Plato to Semitic philosophy. Primitive Christians embraced communism, complex nuance, and learning. They lived for each other and were the best orators of the ancient world.
Then Paul ruined everything. Debased what should have been a sincere society.
Oh well, such is life.
>mindblowingly advanced maths
>throws people off boats for discovering irrationals
>implying concepts without formalization would have any use at all in mathematics
>implying Euclid's and Archemdedes' havewaving concept of limits is somehow on the same level as Newton and Leibniz's work
This is correct. The sex life of the ancients was ruled by many more taboos and rules than modern one, even pre-sexual revolution. "Homosexuality" certainly didn't exist, only homosexual relations did.
I wouldn't say there was stagnation just yet. Progress in mathematics and technology went on until later Roman times in the east half of the empire.
>Finally we have no fucking clue what the antikythera mechanism was even used for
I think the explanation that it was used for astrological and religious-calendrical purposes is pretty convincing.
>throws people off boats for discovering irrationals
That's a legendary story about a specific cult, the Pythagoreans. Ancient Greece was intellectually diverse.
>implying concepts without formalization would have any use at all in mathematics
If there's something the Greeks were better at than their contemporaries, it was that. That's basically the reason why Muslims ended up preferring Greek over Indian material.
One thing I'll agree with OP about is that the Romans were innumerate though. Latin writers didn't seem to even (want to) understand the Greek mathematical and astronomical material much of the time.
The early Christians were also very suspicious of their pagan heritage as opposed to later ones and that attitude continued to exist in Byzantium where continuity was greater as opposed to Western Europe which experienced a renaissance via the translation of Greco-Arabic material.
>If there's something the Greeks were better at than their contemporaries, it was that
The entirety of their knowledge was built upon discoveries of other cultures. The only impressive mathematics that came out of the Greeks was Euclid's complete formalization of geometry, which gave a way to clearly communicate mathematical ideas and which is instrumental in the development of mathematics as an abstract science.
>The entirety of their knowledge was built upon discoveries of other cultures
That's only accurate if you say the same about medieval Islam and early modern Europe, i.e. it's very misleading.
I'm glad you agree otherwise.
PS. Otto Neugebauer and Carl Boyer should be required reading
Women had little to no rights, not much different then Wahabist Saudis.
That is the elephant in the room, conservative folk knida sweep it under the rug. It's hard to admit shitskins in mesopotamia gave better rights to their woman than the european-white-rational greeks
The Greeks were racist as fuck and didn't tolerate gays, they just didn't consider it to be gay if you're a giver and not a taker.
Also what happened was Christianity, not because it's intolerant, but because it's slave morality.
The Greek states weren't united, different states gave women different rights. Interestingly enough, the areas we associate with 'high culture' like Athens and Alexandria were always more repressive than Sparta or the tribal states up north.
How was Sparta not repressive?
Sparta practiced strict eugenics, you'd be forced into the strict military from youth, you could only meet with your wife in secret, you had to eat the same coarse bread and muck everyday, if you were ever a chicken you'd be ostracised -- and don't even get me started on the Helots, they used to have a time of the year when it was legal to hunt them down and kill them.
The Greeks still discovered irrationals.
>comparing Euclid/Archimedes to Newton/Leibnitz
You do realize there is fucking more than 1850 years between them. 1850 FUCKING YEARS! 1850 fucking years of unsurpassed thought in mathematics! That is waaaay too fucking much, and expresses how much smarter the Greeks were to the Christians/Barbarians/Muslims/Idiots that came after them.
Daily reminder Greeks invented Fascism and Communism.
>The sex life of the ancients was ruled by many more taboos
The sex life of the ancients was ruled by much less taboos than the 20th century.
>comparing Euclid/Archimedes to Newton/Leibnitz
That's what the OP does you idiot. It's Newton's work that's known as "calculus".
>expresses how much smarter the Greeks were to the Christians/Barbarians/Muslims/Idiots that came after them.
They're all equally stupid you damn faggot, with the possible exception of Euclid.
The point I want to make is, whatever your occupation or your passion is today, you could have done it in Ancient Greece as well. That is a huge statement!
>Mathematician, engineer, scientist, you could've done that in Ancient Greece
>Professional athlete, soldier, sailor, all of that existed
>Composer, playwright, poet, historian
>Philosopher, priest, politician - absolutely
>Homosexual, heterosexual, lesbian, whatever floats your boat
And Ancient Greece was the only society in the last 3000 years that allowed the same (or similar) possibilites as the society of today - the 21st century. Do you even fucking realize how mindblowing this fact is? That's not even true for the 1950s!
>That's what the OP does you idiot. It's Newton's work that's known as "calculus".
I'm OP. I said "almost invented Calculus" not formalized. I'm a mathematician, I know what the difference is exactly.
>with the possible exception of Euclid
Whatever that is supposed to mean.
>Do you think Newton and Leibniz just had Calculus pop into their heads on day?
It actually builds on the Archimedean property. And yes, in the case of Newton it popped into his head one day. I'm unfamiliar with the history of Leibniz though.
>I'm a mathematician
Highly doubtful. What do you study?
>I know what the difference is exactly.
You don't. Calculus doen't become rigorous until Riemann and Cauchy. The concept of limits isn't the only thing Newton wrote about.
I'd like to add to this that the poison of Christianity was mostly the teleology within it, which was already supported by the Socratic idiots
The Greeks knew that life has no specific direction and essentially goes in every direction it wants to go, without any guidance whatsoever. It's no accident that in the Greek Epics, the gods constantly bicker and fight each other, as they should. Unfortunately, the combined forces of Jesus and Socrates convinced them that the world is moving in one fixed direction, which is complete nonsense
Let me just tell you OP, Greece was exactly tolerant of other cultures even inside of itself. With civil wars raging on every five minutes, like the Peloponnesian war, the war between Kerkira and Korinthos and a lot more. They called everyone was wasn't born in Greece a "barbarian", and considered them of no virtue. Of course with such diverse cultures residing in such a small space, it was almost an inevitability that wars would happen.
Also no mention of the fact that Herodotus, who basically wrote the first texts which can be considered historical, and Thucydides, who perfected the art of writing history?
>everything that follows from a certain object must be credited to whoever the concept is named after
Yeah, and I suppose you think Descartes nearly invented vector algebra right? And that Hilbert nearly invented functional anaylsis? Goddamn retard.
Do you think the average Greek could just become an Engineer or become a philosopher?
Most of the things you listed would only be available as careers to the tops of Greek society. Do you think an average farmer (which was the average citizen) could afford to learn mathematics?
Do you think a Spartan who was conscripted at birth had the opportunity to become a playwright?
Do you think a Helot could just move to Athens and pay a Sophist to teach him Philosophy?
And how were those things not available in the 50s? There were far more opportunities for the average guy to become a playwright back then due to education.
>What do you study?
>Calculus doen't become rigorous until Riemann and Cauchy.
Yes. Yet, the Calculus of infinitesimals was a formal system. Archimedes had ingenious ways of correctly calculating the volumes of geometrical objects - the same results that were "rigorously obtained" only with Weierstrass' Calculus. And Archimedes also had series.
I never said that.
I did not claim it was as accessible, it claimed it was possible. In the societies that were inbetween today and then, it was not possible. A qualitative difference, not a quantitative one.
Every Analysis textbook starts with Archimedes. Where are the "medieval scholars"? Nowhere, because Christianity was a fuck-up.
No, because Barbarians were a fuck-up
Just because they happened to be Christians, doesn't mean that it's Christianity's fault for that
In the Eastern Roman Empire, there was still Roman thought and Science, even thought they were die-hard Christians.
>Russell was a hack
No, he was a mathematician.
>Fuck off to Reddit
Never been there. But I'm sure you'll find a subforum for christians there too.
He really fucked up that party when he entered in Plato's symposium, it's like one of those board memes where a group of people are having an intelligent discussion but then someone jumps out of nowhere and everything goes down to shit
Epictetus was a slave who became a master philosopher.
It was possible just as it is possible today, most people just didnt/wont do it for the fear of losing a comfortable life, for the fear of hunger etc.
It's normal when you realize that Ancient Greece was stunning.
Pic related, they had already calculated the circumference of the earth.
Yeah what field of pure math, you autistic fuck?
>Calculus of infinitesimals was a formal system.
It isn't. It's a number system. Now I can safely assume that you have no idea what you're talking about since you can't even tell the difference.
>Archimedes had ingenious ways of correctly calculating the volumes of geometrical objects
Yeah the same concept that Euclid used to find the area of the circle. Literally nothing new.
>the same results that were "rigorously obtained" only with Weierstrass' Calculus.
Holy shit are you just randomly name dropping now? Weierstrass proved some important theorems in analysis (such as continuity of limits of functions and convergence of Tayloer expansion) but he's never made any version of calculus you goddamn idiot. Everything that involves adding things up to get integrals is formulated by Riemann and Lebesgue.
>I never said that.
You used the fact that sequential limits used the Archemedean property as support for your idiotic OP "Archimedes almost invented calculus".
Just fucking stop. You're embarrassing yourself.
Nothing of what I said is wrong. No field yet. I'm just in the third semester maths.
Everything that can produce proofs is a formal system AFAIK. Archimedes didn't use the same proof as Euclid:
Weierstrass is known as "the father of modern Analysis".
You seeem to be very angry for no reason. What field do you study and why are you so angry?
>still an undergrad
>calls himself a mathematician
>misunderstands basic concepts
>"hurr I'm not wrong because I say so"
>"father of modern analysis" somehow implies that he formalized integral calculus
>a GEB-tier understanding of formal systems
Embarrassing. I'm mad and mildly amused because in every intro course I teach, there's always someone like you who's proud of being partially knowledgeable.
I'm studying topological quantum field theories by the way, ask me anything.
Greece was not unified on morals, but there was no sexual freedom, unless you were a slave owner.
Here is how it worked:
- Free women had no sexual freedom.
- Men could have sex with their own wives, prostitutes (who they looked down upon) and their own slaves (having sex with someone else's slaves was not OK).
- Slaves didn't have much of a choice.
That's not much different from places with slavery in the 16th/17th century.
The only one that was a little different was Sparta. But there, women were baby factories. They didn't have sex for fun. They had sex so that they could have more kids. The closest to "sexual freedom" they had for women was in the case when the husband would get some strong soldier to impregnate his wife so that she would have a strong kid.
>string of nonsense
>"prove" an object
You really have no idea what you're talking about do you?
Cohomology groups are used to clarify forms on a manifold you idiot. If the symmetry group G of a Lagrangian had trivial second cohomology group then the the elements of its Lie algebra can be written as a G-invariant Lie bracket. This is what Yang-Mills theory studies.
Christian sexual morals are more advanced than that. They are very similar to late-Stoic sexual morals, but more forgiving.
One problem of yours is to think that more anarchic sexual morals are better. This is not the case.
I hate when people try to say the greeks thought the world was flat.
I bet even sea people knew that wasnt the case simply by watching ships "sink" into the horizon. Considering the greeks were excellent sailors, mathmaticians, and astronomers, they no doubt knew the world was round and probably assumed theyd hit the other end of mainland eurasia if they went west.
Not him but sometimes I present myself in arrogant ways on topics I know nothing about in order to bait strong oppositions that I then take pleasure in reading; no need to keep the ruse going.
Ancient greece was amazing.
Currently reading an osprey book about greek fortifications.
But im really not him and I really pretend to be a retard all the time. People are inclined to pull out the textbooks when they see an opportunity to sound smart and "win" an internet argument.
>implying people would need to pull out textbooks to dispute claims as stupid as his
>implying pulling out a textbook would somehow degrade the counterarguments
>implying you're not just pathetically samefagging
You're a damn idiot.
Rome was better at literally everything and you know it
You actually replied to 2 different people. I'm OP and I didn't ask you about "cohomology groups".
I don't see what you BTFO'd me about? You presented your opinion on Newton/Leibniz I presented mine. You think the Archimedes-Eudoxos idea of infinitesimals is wastly different from the Calculus of infinitesimals - okay, you are free to believe that. Then you went on to post your waifu and call me an idiot because Riemann defined integrals rigorously. I have no clue what the purpose of this statement was, but I guess whatever? Either way, obviously there wasn't anything to discuss in the first place, so why even reply? I think you want to argue for the sake for arguing. Being angry won't make you happy man.
>gets shown his beliefs are flawed and idiotic
>"hurr that's just, like, your opinion man"
Do you even understand what a fact is? You're basically wishing that this thread be an echo chamber for your stupid thinking.
Is there a reason why sometimes in Greek Art the people are naked and other times they're not?
Why don't you read the thread again? Or are you just selectively illiterate?
>Archemedes "nearly invented calculus" is idiotic
>"Weirestrass's calculus" isn't a thing
>formals systems aren't just something that can prove statements
>number systems that contain infinitesimals aren't part of standard analysis considered by Newton
>basically, you're just a fucking retard
Heracles fighting the sea-monster of Troy.
>And Ancient Greece was the only society in the last 3000 years that allowed the same (or similar) possibilites as the society of today - the 21st century.
As a thracian barbarian from up north, i feel that the achaeminid empire was better at social opportunities.
>The point I want to make is, whatever your occupation or your passion is today, you could have done it in Ancient Greece as well.
Half the things you do today are done in all societies.
Also, i'm a programmer.
Greeks used to just take off their clothes when they felt horny.
>doesn't matter if he said it or not, what matters is the content which i most surely agree with
Of course it matters where it comes from, you moron. Just like when people tie that idiotic "Live a good life" thing to Marcus Aurelius(which is doubly ironic, since such a quote fits more with his philosophical rivals, the epicureans). There are so many concepts in that quote that are dependent on the worlview of the speaker. What you are doing is just making a mess of philosophy and spreading disinfo.
A pic of the American ambassador to Greece.
You do know that this romantic vision of Ancient Greece is based on the fantasies of Europeans from the Renaissance to the Enlightenment, right?
In reality, they were superstitious hicks just like everyone else, but with a smart ruling class in Athens thanks to all commerce.
What, you're saying European Reneissance romanticed cultures and history? No way
Implying there is something wrong with that.
>Women played no part in Athenian high culture. They could not vote, attend the theatre, or walk in the stoa talking philosophy. But the male orientation of Greek culture was inseparable of its genius. Athens became great not despite but because of its misogyny.
Camille Paglia, Sexual Personae
Yes, but people still take it seriously and believe that Ancient Greeks were all rational ubermensch instead of people who sacrificed chicken like everyone else and offered libation to statues like everyone else.
They were in fact like everyone else at that time, just a 1000 times smarter.
These late Medieval scholars actually began the process of mathematization of physics that would culminate in the Scientific Revolution 300 years later (it could have happened sooner, if Renaissance scholars didn't went back to masturbate over Greek texts).
The reason they are "no-names" for you is because most intellectuals are communists who hate Christian Europe for being a decentralized society, so they slander it with lies and false propaganda to make the case that only absolute centralization of political power in the central government authority, as in Imperial Rome, can bring progress of prosperity.
Of course, that's false, since what made Rome (and even Ancient Greece) great was it's decentralization of power in cities and "collegia", but communists do not love history so much as they instrumentalize it for their own revolutionary purposes.
People write bullshit all the time. Are all Americans retarded because some retards in utah wrote the book of mormom? Will people think mormonism was a common belief system for the intellectual class when they find a book in a coffin or something?
Well should sexual freedom be concidered sexual abuse? When I use the term sexual freedom, I mean sexual acts between 2. consent adults, and I cant help but to sense you have a different meaning.
If you want to, you can put fowards what you feel sexual freedom means and stands for, and we can compare and analyze both of our answers.
>Well should sexual freedom be concidered sexual abuse? When I use the term sexual freedom, I mean sexual acts between 2. consent adults, and I cant help but to sense you have a different meaning.
Jacking off too much can result in a dopamine hang over. Not doing so is moderation.
Not being a slut is moderation.
sexualizing the underage subtly is not moderation.
So I think sex can go too far, and monogamy is better. "consenting adults" can make bad decisions that overall social shame can root out, so people don't waste their time.
also we don't need to be paying for people's mistakes if we are going to let them do whatever they want, like with those girls who get kids early and then can't work and no one wants to marry them because they got pregnant from a fucboy.
This is a very interesting view on the subject, thank you for sharing it.
Monogamy in humans is a rather interesting topic, since it appears in humans throught religious and social concepts and theres no arguing the moral beauty of it, but I don't think humans are strictly built for it. We can't change our nature, which is to breed alot and often, to spread our genes as much as possible. There are people who prefer monogamy but it's rather rare in people who havent been taught to be like that, is it not? We can learn to love other people even if our spouse passes away, for example.
Your point on the society paying for peoples mistakes (reckless sexual relationships and offspring that produces) is a fair one too. It is true this is a big resource taker and straight out can waste the life of clever, bright and potential young people.
But I have to ask you, is restricting peoples actions the right way to treat the problem? It will work on some people, but people will always be reckless and make mistakes.
I'd rather want to see more sexual education in schools for example, to teach young adults that their actions do indeed have real consequences and wild pleasure seeking can at worst destroy lifes.
Instead of trying to hide sex, it should be taught as a subject, on the morals of it and how to do it without messing up your life, since this is a possibility in our culture and society. You speak of moderation, so why not teach young adults to be moderate about it, rather than trying to cage their "wanderlust?"
I'm sorry for the long, unfocused reply, it's 3 am where I am and I'm not very studied on the subject.
>sexual freedom, full tolerance of homosexuality
More like, no sexual freedom and no tolerance of homosexuality.
To speak broadly of a people quite diverse in customs.. If you were a woman – no sexual freedom. If you were a common man (as in fact most Greeks were, 'Athenian'-style democracies were occasional, inconsistent and near meme-tier), you could either fuck your wife, or if you were lucky, fuck a slave.
Most all Hellene societies looked down, to speak gently, on actual homosexuality. Modern romantics have tried to present a different picture to suit their own sensibilities and fetishistic view of the Achaeans, but the fact remains that from a modern lens, the Greeks would have been seen as quite homophobic. What is presented to the modern audience as homosexuality was closer to paedophilia – or more specifically, ephebephilia. The targets of their affections were male, yes, but what made it socially acceptable (even then in only certain contexts) was that they were youths. To feel affection for a grown man, let alone to fuck him, was very much taboo and an affront to his masculinity.
This was hardly sexual freedom, though – there were specific customs governing which youths you could pursue, what you could do with them and when. Unless you were a slave, in which case you could simply be raped. Ah, freedom. Of course, the social politicking of established men often led to families essentially selling the 'affections' of their young lads to whichever old goat exerted sufficient pressure on them.. In theory, it was supposed to be a mentor/pupil relationship. In practice, they twisted it into institutionalized child abuse.
So please, can we stop with the Greek sexual enlightenment meme? They were socially repressed degenerates who locked their wives away and raped each others' sons. They were the classical version of an Islamic NAMBLA.
t. an actual faggot
>But I have to ask you, is restricting peoples actions the right way to treat the problem?
Not necesarily. Sometimes "shame" works well enough.
>I'd rather want to see more sexual education in schools for example, to teach young adults that their actions do indeed have real consequences and wild pleasure seeking can at worst destroy lifes.
>Instead of trying to hide sex, it should be taught as a subject, on the morals of it and how to do it without messing up your life, since this is a possibility in our culture and society. You speak of moderation, so why not teach young adults to be moderate about it, rather than trying to cage their "wanderlust?"
>I'm sorry for the long, unfocused reply, it's 3 am where I am and I'm not very studied on the subject.
In some US areas the kids are taught from a very young age, which seems to have the effect of encourage sexuality they should not even be experiencing. But yeah otherwise I agree with you.
>. There are people who prefer monogamy but it's rather rare in people who havent been taught to be like that, is it not? We can learn to love other people even if our spouse passes away, for example.
Not sure. I think women prefer monogamy, and since they're one half of the equation, this means most societies prefer monogamy. There is some cheating on the side, but this is not to my knowledge universal is "civilized" areas (China, etc). Like, if you look at lesbians, they're less polyamourous than male homosexuals.
First of all, "medieval scholars" invented jackshit.
Second, Christian Europe was almost exclusively super-centralized monarchies, as opposed to the Greek city states, so that's a retarded point too.
And clearly this thread is not about the Roman Empire.
"Sexual conservatives", dear ladies and gentlemen. Or in other words: Other people get laid and I don't, therefore I am angry.
Sexuals morals are shit, and everyone who contemplates sexual morals is intellectually inferior.
Do you really think Epictetus, Kant, Aristotles and pretty much every great Moral Philosopher that ever walked on Earth was intellectual inferior? That sluts and Charlie Sheen are the wise ones?
>>But I have to ask you, is restricting peoples actions the right way to treat the problem?
>Not necesarily. Sometimes "shame" works well enough.
This is the true face of "sexual moralists".
I most countries of the world, once you are 14 or 16, you can fuck whoever you want, when you want, how often you want. The very same rules apply to alcohol.
"Sexual morals" only exist in "Islamic Nations" and America (partially only, fortunately).
It is not because it is legal that it is right.
Drinking every day until you pass out is legal. Doesn't make it a good thing.
Sexual Morals also exist in other parts of the world. Actually, I don't think there is a place without some kind of sexual morals.
Were they intellectually inferior when they lived? Also, why would it be the case that "everyone who contemplates sexual morals is intellectually inferior"? Is being a sheep superior to being a man?
>It is not because it is legal that it is right.
That is exactly what legal means.
>Drinking every day until you pass out is legal. Doesn't make it a good thing.
You can do whatever you want with your own body. That is the only good thing.
>Sexual Morals also exist in other parts of the world.
No, people just rape each other, you know.
You so dumb. If you want to argue whether or not sexual freedom is a good thing, don't do it on /his/.
So get fucked >>>/pol/
>That is exactly what legal means.
No, it is not.
Legal means it is permitted by law. It doesn't mean it is right, but rather that the legislators decided that it should not be illegal.
>You can do whatever you want with your own body. That is the only good thing.
No, it is not the only good thing. Drinking every day until you pass out is not good.
>No, people just rape each other, you know.
This makes no sense.
>You so dumb. If you want to argue whether or not sexual freedom is a good thing, don't do it on /his/.
>So get fucked >>>/pol/
Are you aware that your are actually arguing "whether or not sexual freedom is a good thing"?
Part of the Parthenon Frieze.
Look, your opinions don't interest me. I know that's hard to understand for you, because you are dumb /pol/-trash, but that's just how it is.
Parthenon artistic reconstruction.
The Panathenaic procession.
Artistic reconstruction of Athens.
>Ancient Greek Warship 500–322 BC
That's the title of the Osprey book.
Battle of Syracuse during the Peloponnesian War.
> Camille Paglia
> quoting ever
She's the best articulated version of a terrible wrong way of thinking. Yes, Athens was wonderful... for the men. Those accomplishments wouldn't be so important if you were a woman or a slave. You may as well use the Koch brothers as an example of how America is a utopia.
>This is the true face of "sexual moralists".
Shame like "Murder is bad. You're bad for doing it." nothing wrong with this. Same goes with shame about "racism" (except I'm in favor of ethnocentrism).
>You may as well use the Koch brothers as an example of how America is a utopia.
You may not. The Koch brothers are 2 people out of 300million. If there were as many slaves as free people, then the male ("priviledged") population of Athens was still 25% of the population.
>Shame like "Murder is bad. You're bad for doing it.
But can and should the seeking of sexual pleasure be concidered morally wrong on the same level as murder? Don't you think that's a bit much?
>Shame like "Murder is bad. You're bad for doing it."
You are tripping all over yourself my fedora'd friend.
"Lesbian" originally meant a person from the island of Lesbos. Then a famous poet named Sappho was born there. She happened to be a female homosexual and wrote some love poems about women and girls. This led to the words "lesbian" and "sapphic" being associated with female homosexuality.
The claim that lesbianism was socially acceptable is debatable. It doesn't seem that Sappho was ever punished for her behavior, and she even managed to become famous for her writing. But ancient Greek references to lesbianism are pretty sparse and tend to be rather negative, giving the impression that it may have been frowned upon but not forbidden.
>some greeks run into two girls kissing and feeling each other up
>Promptly get boners
>"i guess...i guess this is ok"
And the rest is history. Lesbians have traditionally been more socially acceptable than gays because one reason and one reason only: girl on girl is damn sexy
>First of all, "medieval scholars" invented jackshit.
Just one example, and not even an specially relevant one.
The now published sources prove to us, beyond contention, that the main kinematical properties of uniformly accelerated motions, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college.... In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought.
>You will see, he said, in a moment what progress he has made and what he is like. He had scarcely said the word, when Charmides entered.
Now you know, my friend, that I cannot measure anything, and of the beautiful, I am simply such a measure as a white line is of chalk; for almost all young persons appear to be beautiful in my eyes. But at that moment, when I saw him coming in, I confess that I was quite astonished at his beauty and stature; all the world seemed to be enamoured of him; amazement and confusion reigned when he entered; and a troop of lovers followed him. That grown-up men like ourselves should have been affected in this way was not surprising, but I observed that there was the same feeling among the boys; all of them, down to the very least child, turned and looked at him, as if he had been a statue.
>He came as he was bidden, and sat down between Critias and me. Great amusement was occasioned by every one pushing with might and main at his neighbour in order to make a place for him next to themselves, until at the two ends of the row one had to get up and the other was rolled over sideways. Now my friend, was beginning to feel awkward; former bold belief in my powers of conversing with him had vanished. And when Critias told him that I was the person who had the cure, he looked at me in such an indescribable manner, and was just going to ask a question. And at that moment all the people in the palaestra crowded about us, and, O rare! I caught a sight of the inwards of his garment, and took the flame. Then I could no longer contain myself. I thought how well Cydias understood the nature of love, when, in speaking of a fair youth, he warns some one "not to bring the fawn in the sight of the lion to be devoured by him," for I felt that I had been overcome by a sort of wild-beast appetite. But I controlled myself, and when he asked me if I knew the cure of the headache, I answered, but with an effort, that I did know.
That doesn't seem to be true in ancient Greece though. Lesbianism is only rarely mentioned and seems to have been looked down upon to a degree. Male homosexuality is referenced far more often, and seems to have been more openly practiced and accepted.
>Because it makes you a slave to pleasure.
The same could be said of any motivating factor, you could be a "slave to _______" fill in the blank with any concept.
That's also not strictly a metric of inferiority.
I am terribly unsure Anon. Alexander made Greece strong, but someone the Romans still managed to roll over them, kingdom by kingdom.
The Diadochi left behind were each several times stronger than the Romans and anything could've happened.
Are you mentally retarded?
That was a guy with a huge sexual desire. The kind of person that I just called inferior.
Someone that wants to have sex with dozens of people but can't is as bad as a slut.
>In the societies that were inbetween today and then, it was not possible
Right, because we didn't have mathematicians, engineers, scientists, professional athletes, soldiers, sailors, composers, playwrights, poets, historians, philosophers, priests, or politicians between the fall of Greece and the 20th century.
>you'll never fuck up as hard as Nicias
He had so many opportunities to win the Sicilian Expedition, but his selfishness and lethargy essentially cost Athens the War. Like seriously Sparta sent 4 ships and he couldn't be bothered to intercept them till it was too late, he forgot to bring enough cavalry, he didn't finish the siege wall and made forts for himself instead, he missed many opportunities to attack Syracuse and inspire his men.
Ancient Greece blows me away. The rationality of their thinking combined with the aesthetics of their art and also of their environment.
>Imagine yourself sailing in a trireme along these shores, a midday sun shining incandescently, a glaring sea, a man in hoplite armor, with a long, curly, black beard stands at the bow, looking outward. Your turn your head and see the most beautiful young man, smiling, giggling, his full lips baring his lustrous white teeth. His eyes narrow when he smiles - how often were you lost in them? You were telling him something. There was this philosophical debate about the composition of the world. How would someone even find out the truth of these claims? A really surreal question. But there was a more immediate matter, a diplomatic mission, and you had to collect this statue. There could be a war if the deal works out. And you might die. But the warm sunshine on your skin wrests you from your thoughts. This moment is real, this much you know.
>formals systems aren't just something that can prove statements
>A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics.
>An uninterpreted symbolic system whose syntax is precisely defined, and on which a relation of deducibility is defined in purely syntactic terms; a logistic system
Too many proud subcultures and in-fighting.
Sparta fought Athens and won.
Macedonia steamrolled the country under Alexander+Dad, but there was almost constant insurrection under his rule.
Socrates was parodied in the theater and condemned for heresy. Plato was a Greek fascist who thought people were too dumb to govern themselves and Homer was a liar holding Greece back.
Ancient Greece had all kinds of internal tensions over its existence.
>literally showing the statement he replied to correct
>doesn't understand that the technical terms in the definition he's found has a precise mathematical meaning, and not just whatever he wants them to mean to support his stupid arguments
>what are well-formed sentences
>what is solvability
>what is completeness
>what is definability
>doesn't understand that just because Peano arithmetic is a formal system doesn't mean that any other number system is also one
>still being this braindead retarded
>what are well-formed sentences
>what is solvability
>what is completeness
>what is definability
yes and why are these things important again? o, so we can prove things.
Forests are made of trees you know
Except that you (or the OP's) conception of what "proof" is is different from that of mathematical logic.
>"hurr you just can't see the forest for the trees bro"
>tries to justify his shitty arguments without even understanding why we have the definitions
>What went wrong /his/?
>>mindblowingly advanced maths (Archimedes almost invented Calculus)
>>built machines and analog computers (Antikythera mechanism)
>>most impressive realistic sculpting in history (pic related)
>>society of many philosophical viewpoints
>>sexual freedom, full tolerance of homosexuality
>>refined naval and land warfare
>>architecture, science, politics and so much more
>And this is what happened to it:
>>Invaded by innumerate Romans
>>Converted by intolerant Christians
Good use of terms; obviously you have a rigorous logical mind.
We define concepts to show further things about them.
I also love how you get all butthurt with the other dude and have to cite your academic studies to show he's wrong because you literally cannot see the forest for the trees. Your inability to engage and disengage from these definitions is indicative of your complete lack of actual education and a reliance on memorization. You're so caught up in the idea of a deductive proof, being the only type of proof because your math teacher told you to learn it like that that you are completely inable to recognize that someone is saying that formal systems are for making logical arguments.
I'm not even the guy you were originally arguing with. You're just sperging out all over the place dude. It's embarassing.
Try to figure out what the person is saying before you weigh in on a discussion with the big boys
>doesn't understand what's being argued here
>still tries to butt in
>acts as if he knows anything about being mathematically literate
>using precise language is "not seeing the forest for the trees"
>living out the stereotype of an arts major
>You can call every single thread on /pol/ "a philosophical discussion".
No you can't. Nice false comparison, the thread evolved towards greek philosophy and then someone asked "Do you agree with the concept that this philosopher espouses?" At which point you went
>/pol/ wahh wahhh
>Says who? There is not an image on this board that can't be found on google. You are retarded bro.
Yeah, because once you post them, they go on Google. If you work in a museum or a college, and have some OC to post, by all means dump. But just dumping things you found on Google image search because "you knew what to look for" is just you pretending to contribute and artificially bumping a thread that has little interest.
>>hasn't read the thread
cute. I can do that too
>completely misunderstands the argument.
If you knew what a formal system was, rather than just having memorized the definition you'd understand his argument. You confuse "formal" with "formalizable" and many other basic concepts. Admittedly, he's the one starting the confusion.
But you are once again, trapped by your autism.
Here's an exercise for you. Try to make his argument for him.
If you can't understand what he's trying to say, or at least find an understanding that is internally consistent, you haven't actually responded to his arguments and simply reacted to stimulus you don't like. There's a great Descartes quote for this, since you're so good at Google, I'll let you find it.
Anyways, I'm going to bed.
Have fun intellectually masturbating.
>hurr watch me move goalposts
His argument literally doesn't rely on whether the hyperreals were formal systems, but this doesn't mean he wasn't talking out of his ass, which is the point, fucking retard.
His argument for how "Archemedes almost invented calculus", no matter how wrong it is, literally has nothing to do with your dumbass points.
Holy hell how hard do you have to grasp at straws to justify your mistakes? Just admit that you have no idea what was even going on and stop responding like a good child.
I haven't gone to sleep yet so you get one more, but it looks like the hive mind decided you're retarded.
> but this doesn't mean he wasn't talking out of his ass, which is the point, fucking retard.
Seems like you still haven't tried to understand his argument
>no matter how wrong it is, literally has nothing to do with your dumbass points.
once again fails to make an honest attempt to understand anon
>stop responding like a good child.
take your own advice. You're just sperging out on things you don't like.
...I'm the shitposting hive mind you so lovingly referred to, but nice try. If you like call the mods and check my IP or something faggot.
Archimedes clearly anticipated many of the developments that would lead to calculus. Considering that the majority of his work is lost to history. Him almost inventing calculus isn't beyond the imagination.
Maybe you're just a faggot and you're mad people disagree with you
I still disagree.
>Archimedes clearly anticipated many of the developments that would lead to calculus
What, the Archemedean property of N? Hopefully you know that this only applies to sequential limits, snd not the continuum limit that Newton was talking about when he defined the derivative, right? And the equivalence of continuity of a function and the convergence of the function of the sequences wasn't until much, much later.
>Considering that the majority of his work is lost to history. Him almost inventing calculus isn't beyond the imagination.
I'm not saying it is, I'm saying it's unlilkely. And definitively stating "Archemedes almost invented calculus" is obviously wrong.
Also me being a faggot has nothing to do with this you faggot.
This dude is lame, but totally correct.
If Archimedes was so close, then why did the four dozen or generations of mathematicians not bridge the supposedly tiny gap?
What Newton and Leibniz invented was revolutionary for a reason.
Also Newton's conception of limits and derivatives were intuitive but far from rigorous. His arguments were graphical, which required, you know, the cartesian plane a la Descartes in the 13th century.
You arrive at the continuum limit by collapsing the sequential limit on itself. Do you not into basic calculus? I'm done.
>yeah sure most of his works are missing but I can speak about what these books could have contained.
>has no idea what he's talking about
>"collapsing the sequential limit on itself."
>doesn't understand that convergence of limits on measure zero sets can be proved completely differently from that of those on contiuua
>implying the ancient Greeks had the concept of epsilon-delta proofs even though they don't even know what zero is
Now you've gone and destroyed your credibility. Good job, schmuck.
>Greeks didn't know what zero was but had a concept of numbers almost zero but distinguishable from it
>This thing can be proved a different way, therefore it can't be proved this way.
>Archimedes calculus would perfectly resemble our own
>This thing can be proved a different way, therefore it can't be proved this way.
I'm saying that things about calculus can't be proved with Archemede's concept of a limit, you dunce.
>actually saying "Archemedes' calculus" as if it's a thing
Please explain your understanding of his understanding, because you seem to be harboring the idea that Archimedes was uncomfortable with infinity like most other Greeks.
Have you read "the method"?
I don't think you have an understanding of how far ahead of his time he actually was.
Greeks being parochial city state and not unifying for greater good. This allowed Phillip and Alex to take them over. They never accept Macedonian hegemony and rebel a bunch. Then Alex's death and the Antigonid Macedonia rule takes which years later is weakened by Rome. Rome was basically just like Greece but eventually let other cities and Italian allies become part of them. So Greeks could have lasted longer with a modicum of unification like Rome.
Literally no one was talking about infinities here. And him being comfortable with it is would not imply that he "almost" invented calculus.
>I don't think you have an understanding of how far ahead of his time he actually was.
Did I say he wasn't? Galois was also ahead of his time, but literally no one would argue that he was even close to inventing algebraic number field theory.
Just to be clear, you were shifting goalposts all over the place and have no idea what a strawman is.
Please enlighten me on how Archemedes could've arrived at the calculus concept of limits and continuity in the sense of Newton.
You literally just said I claimed that him being comfortable with infinity implies he invented calculus. That's a strawman.
I've shifted no goal posts. You like to use that when you're losing an argument I've noticed.
The fact that you refuse to explain your beliefs and simply hand wave is quite telling.
Also the understanding of infinity is really important for limits, but you wouldn't know that, because you failed calculus. So people are in fact talking about infinity. Because limits and infinity go hand in hand you fucking plebian.
>in the sense of Newton
There you go again, you don't understand maths, you memorized them.
>You literally just said I claimed that him being comfortable with infinity implies he invented calculus
Then why would you bring it up in >>603053?
>I've shifted no goal posts. You like to use that when you're losing an argument I've noticed.
Bringing up infinities *is* shifting goalposts you goddamn idiot.
>The fact that you refuse to explain your beliefs and simply hand wave is quite telling.
I literally did; all over the thread. Here let me spell it out for you
1. Archemedes was not close to inventing calculus
2. See 1.
There. Got it?
>Also the understanding of infinity is really important for limits
Are you serious? Does epsilon-delta rely on infinities? Does the fact that n < n + 1 for every n rely on infinities? Does doing limits require knowledge of infinite ordinals?
Hint: it doesn't, you goddamn stupid idiot.
>hurr you memorize things
>even though he's been shown to be absolutely clueless multiple times
can we stop washing today and whatever ancient civilization togather to justify whatever policy?
ancient greeks also used slaves, spartans went on manhunts, the zillion ministates could not stop fighting eachother and by fighting i mean not serious enough to dominate the whole balkan peninsula as an outcome
you could expell someone from the city on popular votes and you can find alot more flaws
nothing went wrong, times change
>implies an infinite set
>hurr durr no infinity here
The limit of a function is defined with regards to infinity you dumb cunt. The first calculus proof you do is literally the exhaustion method ad infinitum.
You implied my argument was that because he was comfortable with infinity he invented calculus, when I said you seem to think he couldn't have Because he wasn't. Obviously you failed logic too.
>implies an infinite set
>hurr durr no infinity here
>dumbass actually thinks that the concept of a limit point needs infinities
>what is a topology
>what are neighborhoods
>what is the formal definition of a limit point
>The first calculus proof you do is literally the exhaustion method ad infinitum.
>actually implying element chasing has anything to do with infinities
>doesn't know what ad infinitum means
>You implied my argument was that because he was comfortable with infinity he invented calculus, when I said you seem to think he couldn't have
Why the fuck did you bring it up then you stupid autist? Was that just an irrelevant passing remark?
>Does epsilon-delta rely on infinities?
OP here. This is just getting stupid now. It does in fact rely on quantities getting infinitely small - or that they can get smaller infinitely many times if you so will. It does not rely on ordinals and cardinals, but that's a whole different use of infinity. I've seen some of the proofs of Newton and Leibniz, and they use infinitesimals in ways which are close to how Archimedes used them. I read neither the Principia or the Method, so I can't point you to how exactly they tie together, but I'm pretty fucking sure they do. Now, you can call me an idiot, an ignorant or whatever (have you read the two books?), and say "you won the argument" - I don't care. I don't have sufficient proof to "win the argument" myself, but that doesn't mean I agree with you.
Also, Weierstrass' calculus is a thing.
If it doesn't need infinities why'd you have to imply an infinite set to get it?
To say for all n, n < n + 1 implies there is an n+1 for every n.
>infinitely small and large are not related concepts
>why'd you bring it up?
I brought it up because I'm trying to figure out why you're so fucking dense. You refuse to explain your position other than just blankly stating it and hand waving.
You're just all over the place dude. As soon as I point out you used infinity in your post you jump ship to other concepts and act superior.
Dude you suck at communication
Look, saying a statement holds for all quantities larger than zero does not involve infinity unless you're an ultrafinitist, alright? Do you want to be classified as such? Be labelled the same as the living meme Wildberger?
You can believe whatever you want to believe, I'm just offering the viewpoint of someone with a mathematical background.
>If it doesn't need infinities why'd you have to imply an infinite set to get it?
You don't, idiot. You can put topologies on a finite set and have limit points in them, goddamn retard.
>he's an actual ultrafinitist
>one that's even more stupid than Wildberger
>admits to just drail discussion for the fuck of it
>still doesn't address how Archemedes was close to invent calculus
Also, I want to say I never had a rigorous proof that "Archimedes almost invented calculus" - I have to suspend judgement until I've read Method and Principia. I just said it because:
a) The Ancient Greeks were clearly past "algebra with rationals" - or what most people think, when they think ancient maths.
b) It sounds spectacular.
Now you are sperging out about details - I get it, and I do appreciate it, and I agree with you that Calculus wasn't rigorous until Riemann, Cauchy and finally Weierstrass. However, this does not invalidate Archimedes contribution to Calculus' thought. Besides, Real Analysis itself is pretty fucking intuitive and considered baby maths nowadays (or so I'm told). So why all the anger? I just don't get it.
>still hasn't moved the conversation forward by explaining his understanding of Archimedes' understanding of a limit, so we can get into some meat.
Ball has been in your court for quite some time now, you seem to be running out the clock.
Instead of explaining how the uses of infinitesimals were different you >>603171
Decided to meme and say if you disagree you're retarded.
But I'm derailing the thread when I asked you to explain your reasoning you memed out for 10 comments and then tried to shift burden of proof.
You're making the argument it's extremely unlikely, make the case.
I love how you decided I'm an ultrafinitist
Let x be 0 < x < y for all y in the ordered number field. And let me tell you x doesn't exist in R.
See how I didn't make any reference to infinities and how I didn't make Cantor spin in his grave? "For all" is not equivalent to "for infinitely many".
You can still define a procedure that get's it ever smaller. And at infinity it will be an infinitesimal, that's literally the meaning of the word - the "infinite-th" term. The epsilon-delta defintion is useless if you could only use it for random epsilons. Only when using it in conjunction will f.e. null-sequences can you actually prove stuff. Sure, there is no formal mention of infinity, but we are not formal robots. All the rigorously written theorems in the world are usless if we have no understanding - because then we are just as good as automated theorem prover.
The difference is, they may acted the same way with others, but: wrote it down, resulting to writing history, criticised/made fun of it, resulting to philosophy/drama/comedy, made theatrical plays, resulting to art. etc
Not him, but there is some evidence to support an übermensch hypothesis. That is if you associate hair color and eye color with a certain ethnic group. With ancients such as Alexander and Augustus being blonde (amongst many other patricians) included with those red haired numbered in the nobility, and then you get things like king tut having a R haplotype, it does make you wonder.
What? Dude there is no "infinite-th" term. All it says is that whatever epsilon you give me I can find a number between it and zero. That's why your start with "given epsilon > 0" for every proof regarding continuity in metric spaces.
Also any other way to understand infinity than Cantor's "formal infinity" (as you put it) is not rigorous.
Also also hopefully you (and anyone else) understand that doing limits on N is fundamentally different from doing limits on R, meaning that Archemedes wouldn't have come close to inventing the concept of continuity even if he did come close to developing srquentual limits.
Literally all irrelevant to the diacussion at hand here. I'm impressed at how you're able to miss the point and still act so self-unaware.
>maybe if I keep repeating to myself that he's wrong it'll become true
I'm going to start smugposting because you don't deserve more
>Archimedes never could have have invented calculus because he used N and limits on N are fundamentally different
>Actually Archimedes very well may have been using R.
Do you read yourself?
>noting some numbers have endless decimal expansions is doing limits on R
>implying completing the rationals is somehow equal to doing limits on R
>implying Archemedes knows what completion is
>still memeing about how discovering a tiny piece of information is equivalent to "almost" inventing it
Whatever helps your sleep at night, good goy.
>maths must be exactly the same
>can't even define a finite set properly.
>I don't know what systems are
>implying I implied that
>missing the point
I'm literally just replying so someone doesn't think you're right.
Read the method and come back to me. Or just shit post. I don't care.
>implying he didn't bring up pi to somehow show that Archemedes did limits on R even though the denseness of Q in R still relies on counatability of Q
>thinks doing limits in Q is equal to doing limits on R
>implying I was even trying to define finite sets
>still this delusional
I can do this all day, chimp.
It seems like I'm doing that because that's how math works. Thank Euclid.
>implying I implied that
How are you this fucking stupid?
Dude you defined an infinite set while attempting to define a finite one and got mad when I used induction to show you defined an infinite set you launched into this tyrade about how for all != infinite when no shit nigger.
If you did actual math, you'd know that's exactly how the majority of math works.
what's the highest level maths you've taken?
>interprets whatever he doesn't understand his own way
>doesn't even have the humility to use google
>"Dude you did this thing because I said so"
>still thinks he understands whatever the fuck he's arguing about
>doesn't address >>602995
>what's the highest level maths you've taken
Symplectic geometry and differential topology. Want me to prove a few things from there for you big boy? Kek.
>projecting this hard
It's in the thread.
Ok this all makes sense.
This exchange makes sense now. You have your head so far up pure maths' ass hole you've lost sight of what you're actually talking about. I could literally find a lost work of Archimedes wherein he takes a derivative and solve for the area under a curve and you would say it's not calculus because its not rigorously defined.
>I could literally find a lot work of Archemedes
>I could find a lost work
>find a lost work
Are you dreaming child? Kek.
Even if given Archemedes did do that to approximate areas, that's not calculus is it, big boy? He's still working with polygons and using methods of exhaustion, mate.
>bro he did something similar to Riemann summation without even proving convergence but he's totally close to inventing calculus
>implying the credit of inventing something should be given to someone who came up with the initial rough idea
Do you attribute big bang theory to Lemaitre as well? Kek