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Needs (2007) in the title.
TL;DR: Archimedes discovered many of the principles used in calculus today.
So what is the plausibility of Archimedes getting help from time travelers to reach heights, depths and breadths of thoughts seemingly mystical in comparison with nearly everything else?
I think it's condescending towards the antique people to claim that they couldn't have figured these things out themselves. People were in all ways as smart and capable as us, they just had lower technology level and different concepts. I'm sure there were some concepts lost to the ages that could be developed into amazing modern technology. It's just how invention works - many times a great invention is not recognized as valuable. Zero is classic case. It was invented independently in various times and areas and forgotten. Without zero you can't have a positional numeric system.
Occams Razor states you should first look towards more plausible explanations (aka the simplest, but no simpler)
Time traveling does not fit that description. Archimedes was part of a culture of learning, and he was a genius / master of his field.
Another thing we should also remember is that just because most of the earliest sources we have are greek means less that the ideas were necessarily novel to those sources than that we simply don't have any earlier record of the ideas.
Consider Thamus, as reported by Socrates, as written by Plato, arguing contra legibility, against preserving knowledge in writing.
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%... (infra)
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%... (supra)
Socrates: Ancient Literature Theorists believe the written word will be used for disinformation campaigns.
(voiceover) Theban: You offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with, since they are not wise, but only appear wise.
Socrates: What if it were true?
Phaedrus: Are you just making up fake news about Egypt?
Socrates: To you, perhaps an ad hominem against the source is apropos, for you do not evaluate solely the truth of claim.
Phaedrus: True, the purported argument of this alleged Theban is sound.
Demang im bera vide fit welte na ye finyish kom sif weltemang. (Those who only watch welding tutorials haven't yet become welders.)
I think there will come a time when we come back to it. Today we have computers and very fast lookup, but an encyclopaedia won't tell you what you don't know. If you're a specialist, you'll have a hard time to making a discovery in an unrelated field. But a polymath, a renaissance man, a Leonardo, a man of many talents might. There's probably a limit of how much we can discover with current model. Far future inventors will need to have wide internalized knowledge and skills. A computer is a tool. A much more mentally capable person would do more with it.
Apparently HN doesn't recognize a joke and sincere awe at the face of stellar achievements :( .
And some even don't believe in progress, arguing that people of old knew what we, people of relative new, know. Wow.
If Archimedes' final diagram was indeed of curved figures, TFA gives new context to:
https://en.wikipedia.org/wiki/Noli_turbare_circulos_meos!
====
Roman: Kay-ting name toe?
Archimedes: Na, fodagut, du sabaka da duting xiya!
Roman: Right, he's resisting arrest! (stabs Archimedes)
Archimedes: (Wilhelm scream)
Funnily I litery just finished reading The Archimedes Codex by Reviel Nets and William Noel this evening. I highly recommend it. Part detective story, part rediscovery. Very easy to read.
The article discusses the different types of infinity known to Aristotle: “An infinitely long line would be actually infinite, whereas a line that could always be extended would be potentially infinite. Aristotle argued that the actual infinite didn’t exist." the article shows that Archimedes dealt with both, mathematically. And both are accepted today in mathematics, although calculus deals with the potential infinite.
There is another type of infinity I'm looking to understand or find a mathematical name for. I recently read Spinoza's Ethica (Ethics demonstrated in the style of geometric proofs) where he uses infinity axiomatically to refer to what might be called "allness infinity". I don't know another mathematical name for the concept, even though it is quite intuitive.
And awkwardly, this is how Spinoza defines God:
"By God, I mean a being absolutely infinite—that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.
Explanation—I say absolutely infinite, not infinite after its kind : for, of a thing infinite only after its kind, infinite attributes may be denied ; but that which is absolutely infinite, contains in its essence whatever expresses reality, and involves no negation"
What's fascinating about this rhetorically is that it forces theists to accept a lesser entity as God or to deal with the ramifications of infinity (which leads to a view that looks a lot like atheism). Einstein famously said he believed in the God of Spinoza.
"I believe in Spinoza's god, who reveals Himself in the lawful harmony of the world, not in a god who concerns himself with the fate and the doings of mankind"
Also when a logic meets a philosopher https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_pro...
Mark Twain, on concern for the doings of mankind and on infinity: https://news.ycombinator.com/item?id=24321794
Or one takes the tack of Aquinas and say that God is not a [bB]eing but rather Being itself; see his work De ente et essentia (On Being an Essence). Paul Tillich is someone more modern who argues the same.
Bp. Roberts Barron gave a good talk "Aquinas and Why the New Atheists are Right":
* https://www.youtube.com/watch?v=-NMex7qk5GU&t=7m
"Disappeared" is a Newspeak euphemism for "was stolen"[0].
[0] https://en.wikipedia.org/wiki/Archimedes_Palimpsest#Modern