Byrne’s Euclid
December 16, 2018 4:02 PM   Subscribe

Nicholas Rougeux spent two months recreating the first six books of The Elements Of Euclid, Oliver Byrne's celebrated work from 1847 that illustrated the geometric principles established in Euclid’s original Elements from 300 BC. posted by urbanwhaleshark (46 comments total) 31 users marked this as a favorite
 
I had hoped for David Byrne. Much disappoint.
posted by hippybear at 4:25 PM on December 16, 2018 [1 favorite]


"You may ask yourself -- what is that parallel line?"
posted by escabeche at 4:40 PM on December 16, 2018 [22 favorites]


Neato as a weird passion project and quite attractive but any gains in accessibility from the interactive elements are as an ice cube in a volcano against the reproduction of the utterly pointless long S.
posted by rodlymight at 4:50 PM on December 16, 2018 [13 favorites]


I never ftudied Euclid, and, browfing through that, I am amazed at how non-rigourof many of the definitionf feem. But, I fuppofe this is where the rigor game began.
posted by thelonius at 5:02 PM on December 16, 2018 [13 favorites]


For the inevitable jokes, please use this Unicode long s: ſ. And don't end a word with it.

But I actually agree: the archaic typography spoils the work. Rougeux admits to the difficulty of the ſ (and the nonstandard greater-than sign), but thinks we'll get used to it. I wish he'd simply put up an alternative version with modern typography for those who want to use the book rather than just admire it.
posted by zompist at 5:17 PM on December 16, 2018 [8 favorites]


For the inevitable jokes, please use this Unicode long s: ſ. And don't end a word with it.

so the final ſ in "purſuit of happineſſ" is wrong?

P.S.: I love you all, that this is what I'm pondering this Sunday evening.
posted by mikelieman at 5:24 PM on December 16, 2018 [2 favorites]


Correct, it should be "happineſs."

Am I really the only person not bothered by the long s? I would think lots of Mefites waste their lives spend their free time reading texts from the 18th century. (You do get used to it.)
posted by ragtag at 5:34 PM on December 16, 2018 [13 favorites]


These are beautiful! Just horked all six books for the Darkstarchive!
posted by darkstar at 5:41 PM on December 16, 2018 [3 favorites]


You mean the Darkſtarchive?
posted by ragtag at 5:44 PM on December 16, 2018 [4 favorites]


Wikipedia, on the "long s":

It replaced a single s, or the first in a double s, at the beginning or in the middle of a word (e.g. "ſinfulneſs" for "sinfulness" and "ſucceſsful" for "successful")

Well done, Wikipedia, well done. My annual donation was not for naught.
posted by sjswitzer at 5:48 PM on December 16, 2018 [2 favorites]


For the inevitable jokes, please use this Unicode long s: ſ. And don't end a word with it.

You are not my real Dad.
posted by thelonius at 5:59 PM on December 16, 2018 [7 favorites]


1. build web service to de-ſ URLs.
2. ???
3. Profit!
posted by zengargoyle at 6:02 PM on December 16, 2018 [2 favorites]


build web service to de-ſ URLs.

Oh come on, someone build a browser plugin to re-ſ content!
posted by sjswitzer at 6:08 PM on December 16, 2018 [6 favorites]


Are all the mathematicians asleep or did we scare them off?
posted by Freelance Demiurge at 6:09 PM on December 16, 2018 [2 favorites]


All the mathematicians are busy deciding how much they can justify spending on size, paper-quality, and frame for the poster version (pro tip: it's heavily discounted until tomorrow).
posted by Alex404 at 6:14 PM on December 16, 2018 [5 favorites]


I would think lots of Mefites waste their lives spend their free time reading texts from the 18th century.

That’s actually my day job, so I’m not bothered by it, but what’s interesting to me about it is that the long s vanished from English printing pretty abruptly around 1800, so Byrne and Pickering were making a very specific choice to use an already long-outdated style. To me that argues for keeping it.
posted by Horace Rumpole at 6:18 PM on December 16, 2018 [8 favorites]


Are all the mathematicians asleep or did we scare them off?

what's escabeche, chopped liver?
posted by thelonius at 6:25 PM on December 16, 2018


what's escabeche, chopped liver?

Usually fish, actually. Sometimes chicken according to wikipedia.
posted by hippybear at 6:35 PM on December 16, 2018 [5 favorites]


OK, Euclid finished, now do Calculus please. I need it. Badly.
posted by rhizome at 7:03 PM on December 16, 2018


The exceſs of ſ's doeſn't distreact me as much as the st ligature. I can't stop staring.
posted by otherchaz at 7:05 PM on December 16, 2018 [3 favorites]


This is gorgeous and I was coming here to post it! The lines and colors on the diagrams are just so, so fuckin' good.
posted by cortex at 7:07 PM on December 16, 2018 [2 favorites]


Okay, okay, I made you all bookmarklets to convert to and from long s. 🎁🎄

[previously]
posted by ragtag at 7:11 PM on December 16, 2018 [9 favorites]


Long 's' you say?
posted by rhizome at 7:16 PM on December 16, 2018 [1 favorite]


mikelieman: "so the final ſ in "purſuit of happineſſ" is wrong?"

Yes, which ruined a joke on "Cheers" for me.
posted by Chrysostom at 7:39 PM on December 16, 2018


Well, I agree with him that I'd get used to it eventually (the 's' thing, that is).

This is a wonderful, beautiful project, and I appreciate him walking through the creation of it.

I am a tad frustrated that there is no mention of a license for the work. He doesn't have any copyright notice of any sort on the work itself. His website describing the project has a copyright notice on the bottom, but nothing at all in the work itself (that I could find).

He's free to copyright it any way he wants (not the words, but the layout and presentation), and I would respect that, but it's frustrating he doesn't have any copyright notice at all.

The font however (which is lovely) is a creative commons public domain license, so that's great.
posted by el io at 11:41 PM on December 16, 2018


I have the Taschen version and it's lovely.
posted by OHenryPacey at 11:50 PM on December 16, 2018


The Byrne work is on his website https://www.c82.net/ which has a copyright notice and terms of use (at the bottom of the main page).
posted by zompist at 12:36 AM on December 17, 2018


When I got into antiquated calligraphy (a byproduct of reading it all the time for school), I discovered that the long s is actually fun to write! I weirdly started to understand its utility once I got a feel for writing it. If you write it by hand it feels more like, well, an elongated s. It does somewhat resemble how an f is written (they’re both long characters with loops at both ends), so I imagine that’s why it resembles f in type as well.

Doing the Unicode long s on my phone is too much of a hassle, though.

I think this stuff is cool.
posted by shapes that haunt the dusk at 4:20 AM on December 17, 2018 [2 favorites]


I’ve seen one of the original volumes, thanks to Horace Rumpole, and it was astonishingly beautiful and almost modern in its aesthetic. I guess gorgeous timelessness is the best way to show off mathematics.
posted by GenjiandProust at 4:24 AM on December 17, 2018 [2 favorites]


so the final ſ in "purſuit of happineſſ" is wrong?
-a) Where did that quote come from? The image I have of the DoI from Wiki shows 'pursuit of Happineſs.'
-b) Why is it not 'purſuit' ?
-c) What's the Cheers joke?

I found the ſ to be distracting from the math, and I am generally comfortable with its use, especially in Fraktur.
posted by MtDewd at 5:50 AM on December 17, 2018 [1 favorite]


If I ever get a tattoo, it's going to be Byrne's diagram of the Pythagorean theorem.
posted by madcaptenor at 8:18 AM on December 17, 2018 [2 favorites]


In college we used to joke about how much of a pervert Lavoisier was: always "fucking the air" out of things.
posted by selfnoise at 8:44 AM on December 17, 2018 [4 favorites]


Well, this is in my wheelhouse! (Though I used Heath's.)

"In college we used to joke about how much of a pervert Lavoisier was: always "fucking the air" out of things."

You read the same Lavoisier translation I did.

It's sort of odd to me that the sigmas have never bothered me reading or writing Greek, but I've never managed to feel comfortable with the long s.

Anyway, this is lovely.

I absolutely loved studying Euclid. I have very strong geometrical intuition, but for most people I think that using color and animation and manipulable computerized figures is very helpful.
posted by Ivan Fyodorovich at 9:24 AM on December 17, 2018


This turned up on HN: GitHub - jemmybutton/byrne-euclid: MetaPost + ConTeXt rendition of Oliver Byrne's "The first six books of the Elements of Euclid". It's a TeX / Metafont version of certain parts of the book. Looks neat.
posted by zengargoyle at 9:48 AM on December 17, 2018 [1 favorite]


Somebody put up the Johnnie Signal. Having used this Euclid, it feels like cheating to have full color on a computer screen and not black and white on tissue thin pages that wouldn't stay open. I hope no one uses the easy availability of this beautiful thing as an excuse not to work out the propositions by hand. They are worth it.
posted by hydropsyche at 12:05 PM on December 17, 2018


I like the idea of transcribing old books for the web. One thing that is very powerful is the ability to crossreference, which this handles pretty well. The next step is to create interactive versions of these graphics which illustrate the construction process.

Each reference back to a proposition implies a subprocess of construction. People don't always do these constructions; perhaps because the relation between the state of the proof and the result of the operations is easier to think about than the myriad steps involved in applying the proof. Maybe putting all the shapes on a page would become unintelligibly cramped. In either case the expression of the mathematical concepts is dictated by the medium.

There are interesting properties hidden in the complexity of these proofs. One is the algorithmic complexity of the construction which can be studied separately from the specific problem of minds and pencils and paper. Another is the incidental relations between the artifacts of the proof construction. Insight might be lurking serendipitously in the trivial parts of the proof if only someone would look at it.
posted by ethansr at 12:12 PM on December 17, 2018 [1 favorite]


I would like to see Newton's Principia done this way. (Note: I have not actually read Newton. I have read Euclid.)
posted by madcaptenor at 12:41 PM on December 17, 2018 [1 favorite]


I fear I'm wedded to having the parallel postulate fifth rather than twelfth.

When I took geometry in 10th grade I hardly used pictures at all; it was just numbers and logic to me then. But now, pictures are virtually everything, with line-by-line proof as an afterthought at best.
posted by jamjam at 12:57 PM on December 17, 2018


Whatever this manuscript is, it's highly contagious.

Firefox on my debian-testing-based laptop has just started displaying fi as ß in the addressbar and search box, ffs.

e.g. "https://www.metaßlter.com/178260/Byrnes-Euclid#7589051" (copy-and-paste preserves the actual "fi", so I had to edit in the "ß" for illustrative purposes.
posted by sebastienbailard at 3:14 PM on December 17, 2018 [1 favorite]


"I hope no one uses the easy availability of this beautiful thing as an excuse not to work out the propositions by hand. They are worth it."

Well, also as a johnnie I do think that the ability to repeat the proof, as in a chalkboard demonstration as we do, is crucial. You can read through a proof, even painstakingly, and think you understand it, but to recreate it on demand requires deeper comprehension. Or rote memorization, but that will only get you so far. I think the goal is sufficient comprehension such that one is able to recreate it through intuitive understanding of the relationships and structure.

I'm blessed in that this comes relatively easily to me; I never attempted memorization but rather read and pondered until that moment when it all just clicked.

That's much more difficult for most people, I discovered, and developing that kind of comprehension is much of the reason for studying this work. This is a big part of why we do this at St. John's, it is (in theory) why schoolchildren are taught geometry. Understanding these relationships and developing the facility for this kind of reasoning, both at the proof level, and between and among proofs and the whole work is the goal.

That being the case, whatever is available to reach that goal should be utilized. I feel pretty strongly that the geometric intuition involved in this is greatly strengthened by various techniques that bring different relationships to the fore. I think that animated diagrams, color, hyperlinks to definitions and previous proofs, and an array of other approaches are extremely helpful.

I am emphatically not a traditionalist. I think much of what we do at SJC we do because it works, because (for certain self-selected students) deep learning and thinking are facilitated. I don't think that things should be done a certain way just for tradition's sake. Not that that sort of sentimentalism is invalid or worthless, but that the outcome of a strong education is more important. So in this and numerous other respects, I think a traditionalist resistance to innovation is a mistake.

In sophomore year, many of the students in my tutorial were having difficulty understanding Venus's retrograde motion in Ptolemy. So I wrote a program that graphically simulated Ptolemaic motions, with adjustable parameters in the user interface, and animated plots of motion that included color highlighting of the retrograde motion. We ran it in class and it helped most of the students who were having trouble.

I was attracted to SJC because I despise rote memorization and any sort of learning that's not relatively deep comprehension. I like to think, albeit of a traditionalist bent, that this spirit is the essence of the school.

That raises the question of why one would work from historical works and recapitulating the historical evolution of the topic -- in math and science, this is mostly very frowned upon.

But I very strongly disagree with these critics for both of the reasons they (such as Dewey) usually use to make this argument. The first and foremost is that much of this historical work is wrong. But my response to that is that this is very instructive in multiple, crucial respects. Not the least of which is that the process of being right involves being often wrong along the way. The second reason is that it's more efficient and elegant to start from the finished product and then create for pedagogical purposes a pristine progression from scratch, from foundation to completion. But, again, I strongly disagree because I think this, likewise, gives the student a deep misunderstanding of what it is to actually do this work and to understand it as a process. Both of my counter-arguments are easily refuted to the degree to which one sees an education in these subjects as a matter of purely working knowledge and technical competence. If to be a mathematician or a scientist is to be a technician, then my preferred approach is very inefficent. And in many or most contexts, that's what it is to be a working mathematician or scientist! So, that's okay. But, clearly, SJC isn't a vocational school.

During my time at SJC in the early 90s, I took a C++ course at the local community college. This was one of a number of CS courses I took over the years, before and after SJC, but this stands out because it was concurrent. And, wow, did I feel like programming could be very effectively taught the way we learn math at St. John's: read through an introduction to syntax and such, then read through an example algorithm. Then be able to recreate the code for that algorithm at the chalkboard. And so forth. Also, OOP, which was relatively new at the time, warranted a lot of class discussion at the outset.

I mention this just as an example of the premium I place on more substantial comprehension when deciding on pedagogy. I don't care about tradition or convention. Mostly, I want to burn rote memorization down to the ground. Studying Euclid is anachronistic in any case, thus implicitly you're privileging a certain kind of learning over others. That being the case, hobbling that kind of learning out of purely traditionist sentiment is folly.

I hope that wasn't too tendentious -- I completely agree with you if all you were saying is that recreating the proofs by hand is worth it. Indeed, I think it's crucial. But I support a variety of tools for the student to have available to make the proof apparent to their comprehension (as opposed to merely memorization).
posted by Ivan Fyodorovich at 5:06 PM on December 17, 2018 [3 favorites]


This document is notable for its use of colour and design instead of letters to make the topic more accessible.

It's infuriating that this person kept an inaccessible letter in the project. Utter betrayal of the very values the original strove for.
posted by rum-soaked space hobo at 1:16 AM on December 18, 2018 [1 favorite]


Ivan Fyodorovich I don't see where we were disagreeing but it's hardly worth belaboring.
posted by hydropsyche at 5:03 AM on December 18, 2018 [1 favorite]


This document is notable for its use of colour and design instead of letters to make the topic more accessible.

Although that might make it less accessible for the color-blind.
posted by Chrysostom at 9:21 AM on December 18, 2018 [3 favorites]


Well, also as a johnnie I do think that the ability to repeat the proof, as in a chalkboard demonstration as we do, is crucial.

St. Johns sounds cool, except for having to call yourself a "johnnie". Must everything in life be ruined with a cutesy diminutive name?My father attended, but dropped out because he didn't want to read St. Thomas Aquinas.
posted by thelonius at 2:52 AM on December 19, 2018


I pretty much zoned-out on Aquinas. It was interesting to see which students were heavily engaged, though. It's a personality type. (No judgement, just an observation.)
posted by Ivan Fyodorovich at 11:21 AM on December 19, 2018 [1 favorite]


No problem! Dad was really young too - he got accepted with some kind of deal where he finished high school early. This was about 1944 or so. He threw the hospital chaplain out of his deathbed room 30 years later; I guess he felt pretty strongly about his atheism.
posted by thelonius at 12:01 PM on December 19, 2018 [1 favorite]


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