wcarey

Euclid distinguishes the unit (VII, Def.1) and number -- a multitude composed of units -- (VII, Def.2). His definition of prime and composite numbers (VII, Def.11 and Def.13) clearly exclude one from the group of numbers, otherwise every number would be composite.

http://www.combinedfleet.com/economic.htm does a nice job of outlining how hilariously overmatched the IJN was in terms of naval production. In addition to that, the IJN didn't have an effective pilot training pipeline, so by mid war they were struggling to outfit their air groups for their carriers, and after the Battle of the Philippine Sea, their naval air arm was absolutely broken.

While that might (or might not) mitigate one perverse incentive, there are lots more. It's important for policy proposals to take unintended consequences into account. What others can you foresee and how would you mitigate them?

Have you thought out the perverse incentives your pay scheme would create?

A certificate authority (that only verifies surgeons' skills, and doesn't bundle the process with "learning").

It seems like you've just moved the cheating problem from one organization to a different organization? How would this new certificate authority measure learning better than universities are currently measuring learning? Are there examples of such certificate authorities existing now? Do they also have cheating problems?

Samuel Eliot Morison wrote a definitive history of the naval war in the Pacific, so your memory is good! Ian Toll's new series is shorter, but also top notch and benefits from more access to Japanese sources.

The fab I use has a minimum order size of 3. It's a bit more expensive, but double digit monies for three decently complex boards.

It's not exactly equivalent, but I think the TDRS provides communication between different objects in space.

Most households contain at least several poisons (and precursors to hazardous gasses as well) amongst their cleaning supplies.

Fair enough. I suppose what I'm asking is whether it's possible to purchase a more modern CPU independently of a SOC and design my own single board computer built around that. Can you buy a naked Cortex M0 in a PDIP package? Are there data sheets for it?

A search of the interned didn't turn up what I was looking for, but I'm very new at hardware work. Perhaps newer chips have such tight timing requirements that you can't work with them without using a SOC?

Are there any good sources of documentation for working with Arm chips? Like, a simple single board (or breadboard) computer?

I'd support this if app developers were also required to release their apps on all the available stores and obey the policies of a particular store for users who obtain the app through that store.

Check out the Apollo 10 mission; they in fact did that as a rehearsal for the landing.

Sure! It's good stuff.

#2 you could read, "[He] tells the sailor's story to the mistresses, because mistresses love stories", which does have a possessive genitive.

One way I've done that in the past is asking explicit questions about the syntax, like:

"If filiae is nominative, how would you translate the sentence?"

or

What cases could agricolae be here?

if you want to introduce the context sensitivity of the grammar.

That particular sentence is a really tough knot pedagogically too. As a teacher, you want a short simple sentence that includes a nominative, genitive, dative, accusative, and verb to habituate students to thinking about cases.

Unfortunately, in the first declension, the nominative plural, genitive singular, and and dative singular all look identical, hence the confusion here. Filiae and agricolae could be any of those three options, which means, as you rightly say, that we need context to render the sentence. That introduced students to another distinctive feature of Latin: like C++, Latin has a context sensitive grammar.

If you wanted to separate the introduction of the case system from the introduction of the context sensitivity of the grammar, you could do this sentence:

Filiabus aquam agricolae dant.

While that fixes most of the context sensitivity, it doesn't fix all of it, and introduces an irregular declension, also tough right out the gate.

Latin is a hard language to teach.

To be sure, the normative way of winning kleos was victory, to whit Marathon and Platea.

The Greeks also had very different rules awarding time for sea combat and land combat (rooted in Homer). In land combat, the model was Achilles, and stratagems and tricks detracted from the time of a victory, while in sea combat, the model was Odysseus, and metis ruled, so strategems and tricks were in bounds, hence the glory of Themistocles.

That presumes a modern strategic intent, though, which was often absent from ancient warfare. If the mission of the Spartans was to secure kleos -- the only immortality the the Greeks valued -- then they succeeded beyond their wildest imaginings. Almost 2500 years later we are still talking about them. J.E. Lendon presents a compelling argument that this was, in fact how ancient warriors thought in "Song of Wrath".

Right - that argument, I'm suggesting, is way beyond most fourth graders even in its modern algebraic form. It relies on lots of algebraic techniques that aren't generally taught until 7th or 8th grade.

It's not, like, rocket science, but it's not trivial either.

The author's take on V.18 is interesting. Clarke has the proposition here: https://mathcs.clarku.edu/~djoyce/java/elements/bookV/propV1...

It's not three pages long in Clarke (nor in Heath), and either way, the argument is only 10 statements long.

But the reader who takes the trouble to decode the proposition will see that it is trivial primary school arithmetic.

This is also not super obvious from Clarke or Heath. I'd love to know how the author would render this proposition trivial to a fourth grader.

To be sure, the mathematics of Euclid is a very foreign country from what's commonly taught in schools today. But Newton's thought is firmly rooted in that foreign country.

The approach you describe definitely does not work for all children. The vast majority (that I've taught) are better served by a scaffold of increasingly complex metaphors and definitions. The fact that the metaphor of repeated addition wears thin actually highlights the idea that different sets of mathematical objects have different operators for most students in a way that just telling them that ahead of time does not.

The changing of the rules is good preparation for scientific study where our understanding actually changes over time and we have to internalize new models regularly. I taught my chemistry students that quarks only combine in pairs or triplets, until one year Fermilab released evidence that quarks combine in quartets and quintets while I was teaching the unit. How could I avoid telling my students that what I'd taught them before was incorrect? Literally no one knew. So the practice of revising our ideas has utility.

Well, I'd be curious what your first ten sentences to a group of, say, 11th graders would be about Newtonian gravitation, and how those would compare to what you'd say about the same subject to 8th graders.

It seems elsewhere in the thread that you don't consider it lying if one gives a general disclaimer that models aren't perfect, but I wonder whether or not that general disclaimer wouldn't inoculate the idea that multiplication is repeated addition? It's an imperfect model that super useful for all the numbers available to students when they learn what multiplication is. And I wonder further whether there's not an implicit disclaimer that what you're learning isn't the final word inherent in the structure of the educational system?

How would you teach physics without lying to children?

Truth be told, I've never tried to use a gtk-based editor without a mouse. Which would you recommend? I'll try it out.

The need for precision is such a wonderful thing to teach young people. I start my class with the students typing in exemplar programs and discussing with each other how they think they work. It's amazing how many errors they make in that process; a good reminder of how imprecise we are by default and how unforgiving code is.

The biggest advantage of foregoing a GUI is that the experience of programming is totally modal: you're either in the shell, editing your program, or running your program. That allows students to focus on what they're doing without distraction.

A secondary advantage is that the tools are so wonderfully simple. On the first day we introduce ls, touch, nano, and cc. That's all you need to write your first program. The tool reference fits on one page. And that toolchain will do right by you for anything up to about a kiloline, and in an introductory course, that's about the biggest thing you'll write. So there's no more mussing with tooling. You can focus on algorithms and data structures.

A tertiary advantage is that it forces (and allows) the students to muck around with unix in a way that's oddly less threatening than a graphical user interface. Eventually they start rooting around in /etc and /var and /bin, and learn a whole lot about how computers are organized. So there's some serendipitous learning as well.

Our computers (intentionally) don't have mice.

A wonderful use case for nano is introducing students who have never used a command line before to unix. You can teach a classroom of students to edit files in nano productively in a single 45 minute class period, which means that an introduction to programming class can move very quickly into actual programming. If your goal is to have student produce a working program on day one of class, nano is a godsend.

By then end of a semester, the students will be running into the ceiling of nano as an editor and you can tell them about other more featureful editors.

In the high school computer programming class I teach we use headless Debian on a Raspberry Pi. The idea that you can rename files, move them, and organize them is mind blowing to about a third of the students. When I ask how they organize their school files, they either use Google Docs for everything (all in one folder) or, if they use Word, they have one folder with all their documents named, "New Document", "New Document (1)", "New Document (2)", &c. When I teach them Chemistry as juniors and insist that they use a spreadsheet (or general purpose programming language) for their complex problem sets, about 90% of them have never seen a spreadsheet before. We now have the "talk" with our juniors about backups, as more than one has lost their entire junior thesis because it was stored on their laptop and nowhere else.

It's frustrating that we spent decades developing fantastic tools to help ourselves with all sorts of intellectual work, and have more or less abandoned teaching people to use them well.

As the tower of abstraction has gotten taller, there's a temptation to teach near the shiny end; ML for high school! But that leaves students with huge gaps in their understanding of how things work under the hood, which impairs their ability to connect what they learn and build on it.