Incorrect casual assumptions | Hacker News Reader

Incorrect casual assumptions

thonyc.wordpress.com

73 pointsdiodorus37 comments

I don’t know why the author wants to talk smack on Theon and Hypatia. Gatekeeping mathematics?

1. Theon added theorems to Euclid— by publishing mathematical novelties, he became more than just an editor. [1]

2. Theon’s version of Euclid has been considered the most important textbook ever published. [2]

3. Euclid himself created the elements by compiling theorems from prior mathematicians. So, was Euclid just a textbook editor? [2]

4. Who was a better mathematician in that century? Was Theon top 5? Isn’t that first rate or formidable?

Now, as for Hypatia, one of her biggest critics (Damascius) admitted that her “wisdom exceeding all bounds and especially in the things concerning astronomy,” but suggested that she was more of a mathematician than a true philosopher [3]. Her student Synesius wrote many letters to her, which survive [4]. Hypatia, on the other hand, was dragged to death by a Christian mob. SHWEP.net (my fave podcast) just did some episodes [5].

[1] https://mathshistory.st-andrews.ac.uk/Biographies/Theon/

[2] https://en.wikipedia.org/wiki/Euclid%27s_Elements

[3] https://en.wikipedia.org/wiki/Hypatia#Legacy

[4] https://www.livius.org/articles/person/synesius-of-cyrene/

[5] https://shwep.net/podcast/hypatia-of-alexandria-the-life-and...

There are great works of literature from those times that we only know about because someone else wrote about them and those accounts survived.

Copying is backups, on the scale of millennia.

As a math major, I would say that editing a textbook or even adding a few theorems or corrections would not make you a first-rate mathematician.

The ceiling in math is very very high. If we're calling Theon first-rate then what do we say about Gauss?

Gauss, you mean the guy who lived 1500 years later? Yeah, he definitely set a higher bar. But a “first-rate” restaurant does not mean “the best ever of all time.” Theon and Hypatia were probably some of the best mathematicians of their century. That is enough to be both “first rate” and “formidable” — and I’d be surprised if Gauss would talk smack about them.

You're talking about two people who don't seem to have contributed a single new theorem, proof, conjecture, or formula to mathematics. That bar is cleared by their contemporaries Pappus and Diophantus.

I don't think your idea that being "one of the best of the age" makes you "first-rate" holds any water. A reenactor at a local Renaissance Faire who has never worn a suit of plate armor or ridden a war horse is probably one of the best jousters of the current age, because it's not really pursued any more, but I would never call them a "first-rate, formidable jouster". The medieval scribes who wrote dry annals of what happened each year were among the best writers of their age, because writing was rare, but I wouldn't call them "first-rate, formidable writers". There is an objective component to this kind of language.

Is "first-rate" the top few mathematicians of all time or the top few mathematicians of their age? Or how many total "first-rate" mathematicians have their been? That ambiguity alone can explain this entire argument.

I found this site, which seems to collect usage examples (unfortunately no citations): https://sentence.yourdictionary.com/first-rate

Here are a few showing that, when speaking about history, it is normal to reserve terms like "first rate" for the truly exceptional:

"Jonathan Edwards, a very stern Calvinist, is one of the few first-rate geniuses America has to boast in theology."

"For excepting Philae, which belongs as much to Egypt as to Ethiopia, Abu Simbel is the only temple which can be ranked among first rate products of Egyptian genius."

"Pericles likewise is responsible for the epoch-making splendour of Attic art in his time, for had he not so fully appreciated and given such free scope to the genius of Pheidias, Athens would hardly have witnessed the raising of the Parthenon and other glorious structures, and Attic art could not have boasted a legion of first-rate sculptors of whom Alcamenes, Agoracritus and Paeonius are only the chief names."

Definition arguments are by their nature pointless, these concepts have no universally agreed meaning, but it's even more silly in this example where you changed the term used from "first rank" to "first rate."

Plus, all the actual definitions given there are vague enough to not actually solve the ambiguity.

the whole argument is about whether a sentence like "Hypatia was a first-rank mathematician" is accurate. Obviously that hinges on the definition of "first-rank" since no one is disputing her actual accomplishments or claiming that they really compare to all-time greats like Gauss or Archimedes.

It was the person I'm replying to who used "first-rate" actually. I don't think there's a big difference in meaning between the two.

Usage examples show nuance in the meaning of a word that are not captured in the definition.

My understanding is that they're synonyms, more or less:

“By the early years of King Charles I's reign, these four groups had been renamed to a numerical sequence. The royal ships were now graded as first rank, the great ships as second rank, the middling ships as third rank, and the small ships as fourth rank. Soon afterwards, the structure was again modified, with the term rank now being replaced by rate, and the former small ships now being sub-divided into fourth, fifth and sixth rates” --wikipedia

>Obviously that hinges on the definition of "first-rank"

When figuring out the definition for a term used, the best source is the context it is used. In this case, Hypatia is the benchmark given for what qualifies as "first rank."

You can then argue the author is misusing that term, but that's a different argument that the article doesn't make.

Nit: if it were top mathematicians of their age, then there wouldn’t be any ages without first-rate mathematicians, which is obviously wrong.

That said, the “of all time” version also doesn’t sound right.

"First rank" is the phrase from OP's link, not "first-rate", but in both cases it is not obvious to me that it is wrong for there to be mathematicians with that descriptor in every age. They sound like relative adjectives; "first rank" undoubtedly so, "first-rate" to a lesser extent.

"Who are the first-rate/first rank musicians of $YEAR" does not seem to me like it could be answered with "there were none in that year".

I don’t know about “first-rank”. To me it sounds like an RPG term (“first-rank mage”). But in the case of “first-rate” I see nothing weird about the answer “there were none this year”. When quality is lower, that’s what I’d expect, since I think about this term a bit like the A1, A2, B1, B2, C1, C2 etc language proficiency certificates. They’re not assigned based on quantiles in current population, but based on a set of requirements applied to skill in absolute terms, not relative to skills of other people.

I think you'll find that if you set an absolute bar on most skills you'll end up with zero people above the bar in the past and a growing percentage of people above it in the future. The first person to run a four-minute mile was Roger Bannister in 1954. Now, that achievement is basically table stakes for college-level competitors. Similar effects can be observed in chess, piano performance, and just about any other activity you can measure. Making "first-rate" an absolute bar results in all sorts of crazy answers to the questions "who is first-rate now" and "who was first-rate 70 years ago". If you set the bar such that only the top 10 players of this year cut it, neither Bobby Fischer nor Michael Jordan would be first-rate.

In maths though there was some fluctuation. Mathematics in Roman times saw a decline, and in medieval times a complete breakdown (at least in Europe). If we take Euclid to be the bar for a first-rate mathematician, then there were none in medieval times, but later there appeared Gauss, Newton, Leibniz, Euler, Galois etc. I’m also not sure if today anyone clears the bar for Hilbert-level genius. So I don’t think the bar for “top 10 today” keeps going up. From time to time it goes down.

I don't think the fact that our 90th percentile capabilities have been known to decrease at times in history refutes the idea that the broader trend is dramatically upward, in such a way that any absolute measure of skill is very likely to give you ridiculous results if you pick it based on the standards of year X and then try to use it in year X + 1000 or X - 1000. Was Pythagoras a first-rate mathematician? By what measure that wouldn't also capture millions of people--most of them not even self-described mathematicians--alive today?

I feel like I just took a peak into some debate that is happening somewhere else? Seems silly to worry about the exact abilities of people so many years ago. What is at stake here? And why do we have to take the position that teachers and editors are not, in general, considered a fine practitioner of what they are teaching/editing? Are they the pinnacle? Almost certainly not, but that will be true of most any particular example.

More I'd wager that the editor of the higher performers is better at whatever the topic is than a large enough portion of the rest of the crowd, that folks probably do hold them in some esteem at the topic?

https://en.wikipedia.org/wiki/Hypatia#Legacy

Yup, and that's why the bias of original sources matters too. Bias gets amplified over time. Or reversed at the same intensity, I suppose.

And then we end up with crazy, invisible to us bias in the modern sources. You get accustomed to the bias around the idea and you can't see it any more.

What biases am I supposed to be seeing here? Are folks upset that someone said a teacher was a good practitioner? Why should I assume otherwise?

Was replying to the link to Hypatia's legacy.

You have to look at the history of sources and their bias to understand the history of ideas. Historical sources don't necessarily contain facts; and they may also convey more than facts.

It's about getting to the spin behind the original sources, then you have a better idea of why the sources tell you what they're telling you. How you read them brings in your own bias (for someone else to examine and weigh up one day). It can be really powerful though, like in the example of Messalina.

I mean, sure? There seems an implication that these people were not good at their jobs, though? Why the odd vehemence here?

You are giving general advice that feels right. I'm asserting the stakes are basically nothing?

I also don't get the vehemence against Hypatia in the original link. It's tapping into something weird, for sure.

I think the stakes are really low too.

And I also think the original post is introducing modern values when it comes to people's work. I don't think in the ancient world that academic brilliance was thought of as a great thing in the same way or possibly to the same extent it is today.

And if that was true, it'd mean the sources wouldn't have thought it was worth remarking on, so we'd get silence. Even if that isn't true, the whole thing is still an argument from silence.

Like, let's bear in mind that most of the population couldn't read, even scribes couldn't read—they just copied. How few people could actually math?

This is sort of like crapping on a modern-day rocket engineer because Slate isn't writing about them. ¯\_(ツ)_/¯

tl;dr I think we agree :)

Yeah, reading back on my post, apologies if it sounded like I was upset. Kind of funny for me to gripe about what seems something overblown in that language. :D

I think what upset me is the downplaying of how good teachers and editors are. I will certainly make no claim that they are all amazing, but it is a worthwhile job and it doesn't help to dump on it. Punching down, as it were.

No worries! I didn't think you were griping or anything. And your comment prompted me to say, historical biases aside being ignored in the post, I thought you were right that it was weird to attack Hypatia and Theon. And when you look at the historical context, it seems even weirder to punch down at knowledgeable people and teachers.

You make a sensible point but scribes having been illiterate is surprising. Do you have a source about this where I could read more?

Honestly, I don't. This was just a given in literature I read and chats (about Greco-Roman antiquity, can't answer for other cultures). You may come across it in books about literacy in GR antiquity, but honestly that'd be a lot to read through to find a nugget or two.

Btw it's not that all scribes were illiterate, but definitely some were or perhaps they were just substantially less literate. For their job, copying out sheet after sheet of text, they just needed to know the alphabet. It'd be like learning to copy an alphabet you might not know, like Cyrillic or Arabic. And decent money too.

IIRC the argument for scribal illiteracy had to do with the kinds of scribal copying errors you would see.

There are some errors that suggest a person can read, like homoteleuton. That's when someone sees the phrase "I love you" in a love letter, copies it, and then starts copying from after a second "I love you" lower in the paragraph. "I love you. I'm a terrible person and I know I slashed your tires but... I love you, we should get married" —> "I love you, we should get married".

Other kinds of scribal copying errors betray a lack of reading ability. Like homearchy, where they skip a line because of similarities at the start of the line.

If you're reading along, it becomes obvious the sentence stopped making sense because you skipped a line. But if you're not reading along because you can't, you won't catch the change in meaning.

https://sites.ualberta.ca/~sreimer/ms-course/course/scbl-err...

I think it's pretty obvious that there has been a movement to dig up examples of superlative women in STEM, in both recent and ancient history. Unfortunately sometimes their rediscoverer's enthusiasm gets the better of them and they present these fine womens' accomplishments as being considerably greater than they truly were. Does that matter? Well I guess it depends. If you think an accurate historical record matters than sure it does. If you think history is pragmatically just a narrative invention and we should tell it however suits our present desires, like encouraging girls to go for a Fields medal, then one can argue for some inspirational embellishment shall we say.

Is this really folks getting upset that some women have been highlighted in history? I think that makes me more sad. We could use more heroes in life, no need to get upset that there are few comic book level heroes.

This is what I felt as well. If a time traveler were to tell me that people hundreds of generations in the future will be arguing that I was not good at higher math, I would be inconsolable (even if it's true).

I’d be happy if I was significant enough for future generations to conclude I was secretly (or not so) an idiot.

Sayre's law in action...

The one thing missing here imho is skepticism about the sources and their biases. They can be both factually wrong and also biased.

I could be wrong about this, but I think the Suda is somewhat questionable, isn't it?

Causual?

Casual.

Yeah, I first read it as "causal" also.

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