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Why do we still teach people to calculate?

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Re: Why do we still teach people to calculate?

#81
post #3

It's interesting to discuss mathematical literacy with primary school teachers, mathematicians, statisticians, data scientists. I do periodically. Primary school teachers respect core fundamentals as kids acquire "mental muscle memory" and realize they have to both create some axiomatic knowledge (axiomatic in as much as you know 9x9 is 81 from rote recall, not because of a belief in inductive reasoning) as well as t…

> I also still don't entirely understand why school focussed on trig so much given that very few of us are navigating by sextant.

Trig is useful for practical problems involving angles, and ubiquitous in applications in engineering and statistics. One year in school we spent a long time on logarithms and trig. Approaching 20 years later I consider it time well spent, and my one regret is that I didn't strive to understand it more deeply at the time, and had to revisit some details later (mostly about logarithms, but same category IMO).

Re: Why do we still teach people to calculate?

#82
post #24

Earlier quoted context omitted.

> Dude was a math grad student. I narrowly restrained myself from saying ... Do not show restraint, and neither will I. For I am a mathematician, not a fucking calculator. But once, early in undergrad, I was capable of multiplying 4-digit numbers rather quickly. But tallying never seemed useful except while grading exams -- during which my brain populates a lookup table over the course of an hour, and then I can tall…

> Do not show restraint, and neither will I. For I am a mathematician, not a fucking calculator. I don't expect mathematicians to be lightning calculators, but expressing awe at grade-school arithmetic is a bit much.

It sounds like your rapidity was found remarkable. Not everybody has that. Not all mathematicians have that. Perhaps respect was due.

Re: Why do we still teach people to calculate?

#83
post #64

Earlier quoted context omitted.

I keep a fractional-inch tape measure in the toolbox in my work truck because that's what everyone else (in the US) has, and I need to be able to work with others. I also have to carry around two sets of wrenches, two sets of sockets, two sets of Allen keys, and it's all quite frankly absolute bullshit. But that's the world I get to participate in. At home in my own geeky little workshop, where I don't need to satisf…

> screws Torx?

For screws that go into wood (or thereabouts; sheet metal screws can count here too), Robertson is first on my list. The slightly tapered interface fits snugly and tends to hold screws onto a driver bit very well while providing good angular alignment, and it can do all of this without needing magnets. It can also allow for a bit of angular misalignment when necessary, and the chonky squared-off corners and flats resist cam-out/stripping rather well. I'm not even Canadian and I use Robertson wherever I get a chance.

Second general choice is hex-head screws. These snap into inexpensive shallow magnetic driver bits with a satisfying click. But they're ugly and kind of rough once installed, and they're not available in flat-head versions. (Hex-head shoulder screws are my only choice for drill-point screws: They maintain positive angular alignment by default and that's crucial for drilling holes in metal.)

Torx is fine too, I suppose. I don't have an anti-Torx rule in my workshop, but I try to avoid buying them. They don't tolerate angular misalignment as well as Robertson, and they don't maintain positive angular alignment like a hexagonal shoulder screw does, and they don't stay put with friction like Robertson or snap onto a magnetic driver bit like hex. There's lots of stuff Torx is not very good at doing.

Theoretically, I can probably put more torque into Torx than any of the other options listed here, but I don't find that to be a practical advantage in this kind of application: When I can already drive a Robertson screw through a chunk of old-growth wood, I don't need to improve that part.

---

For machine screws, I've standardized on stainless steel button-head socket cap screws as a first choice. I've got a deeper selection of them than a good hardware store does, and they're all sorted. (Why stainless instead of graded? Because I don't want them to rot, whether sitting in a bin for decades or used outdoors or whatever and I do not want to stock more than one kind. My fastener collection is crazy enough without also multiplying it by different grades.)

There's other stuff, though, too. For instance: Regular socket cap screws have their place -- it just isn't first place.

And at the scale of things I build, I mostly use M3, M4, and M5.

I buy regular-length Bondhus non-ball hex keys in simple bulk packaging to fit my standard M3, M4, and M5 machine screws. They're very high quality tools, and they're rather inexpensive in bulk. And thus, it is no big deal if I misplace one while I'm working -- I've got more on-hand, and I'm not afraid to get more coming if stock gets low.

Bondhus makes a decent-quality hexagonal screwdriver, too, and these are nice to keep around because the design is not like the gigantic T-handled abortions that so many other manufacturers sell: It's just screwdriver-shaped, and it works just like a familiar screwdriver does -- but for socket-cap screws! This was the discovery that allowed me to completely abolish Phillips screws forever from my workshop.

I've also got sets of hex keys -- of course I do. Long, ball-end, plain, whatever. I try to avoid cornering myself into a situations where these non-regular variations would ever begin to be useful to begin with, and the long versions are mostly only useful for disassembling stuff that someone else had overtorqued. (But overtorqued fasteners are different rant.)

Re: Why do we still teach people to calculate?

#84

Earlier quoted context omitted.

I got my degree in the mid 90's and let me tell you - high school guidance counsellors in the 1980's had no clue at all what computer science was. I arrived at university expecting to be writing a lot of programs and was soon struggling with a heavy load of mathematics and proofs. Our introduction to computer programming professor made it clear that that class was the only one where we would be taught to program. Com…

> high school guidance counsellors in the 1980's had no clue at all what computer science was. My problem was that the fucking college counselors didn't know either. When I signed up, I told the lady I wanted to be a computer programmer, and she said "You'll want computer science, then," and that wasn't true. The CS program was only interested in teaching me how to be a CS professor. A few years in I was scouring the…

> Just Telnet, vi, g++.

Those have absolutely stood the test of time than any specific IDE or debugger.

Re: Why do we still teach people to calculate?

#85
post #51

Earlier quoted context omitted.

At the end of the day, writing code is not difficult. Understanding what it's actually doing is the hard part. Moreover, understanding how to write code that reasons about code (and higher) is when you start to need computer science, or really just axiomatic systems (math).

> At the end of the day, writing code is not difficult. Understanding what it's actually doing is the hard part. That sounds nice in the abstract, but in practice it's slow going trying to do web dev when your experience is nothing but command line C++.

It's really not.

So you are typing Javascript into your browser's console to see what it does instead of a text editor and compiler. The iterative process is still very similar. Write code -> get the syntax correct -> see if output matches your mental model -> repeat.

You still want unit testing or some other system of reliably testing your code and detecting regressions. You need to use a distributed version control system to track your work over time and collaborate with others. You need to be able to figure out why your code is suddenly taking much longer to execute it than you thought it would. You need to figure out why the memory usage keeps going up and never comes down. You need to be able to gather requirements for the software you are writing.

All of those things are skills you need to learn regardless of the specific programming language.

Re: Why do we still teach people to calculate?

#86

Earlier quoted context omitted.

> At the end of the day, writing code is not difficult. Understanding what it's actually doing is the hard part. That sounds nice in the abstract, but in practice it's slow going trying to do web dev when your experience is nothing but command line C++.

It's really not. So you are typing Javascript into your browser's console to see what it does instead of a text editor and compiler. The iterative process is still very similar. Write code -> get the syntax correct -> see if output matches your mental model -> repeat. You still want unit testing or some other system of reliably testing your code and detecting regressions. You need to use a distributed version control…

> It's really not.

From personal experience, yes, it is. People spend years getting really good at Java, or Ruby, or SQL, or whatever. You'll get better quicker at all of those if you start with a solid grounding in basic coding principles, but basic principles alone are not enough.

Maybe you're one of those 10x programmers I keep hearing about who can master any subfield instantly. That's lovely for you. Most of us do better with a bit of specialization, especially at the beginning of our careers.

Re: Why do we still teach people to calculate?

#87

Earlier quoted context omitted.

> high school guidance counsellors in the 1980's had no clue at all what computer science was. My problem was that the fucking college counselors didn't know either. When I signed up, I told the lady I wanted to be a computer programmer, and she said "You'll want computer science, then," and that wasn't true. The CS program was only interested in teaching me how to be a CS professor. A few years in I was scouring the…

> Just Telnet, vi, g++. Those have absolutely stood the test of time than any specific IDE or debugger.

That doesn't necessarily make them a great choice for teaching.

A '57 Chevy has stood the test of time, but a modern car with an automatic transmission, power steering, power brakes, and air bags is probably a better choice for a driving school today.

Re: Why do we still teach people to calculate?

#88
post #14

Yes we should start my six year old with group theory. When we go to the farmer's market I can ask him under what transformations is an apple invariant, and then pay for it by having him solve a Rubiks cube.

A pile of apples (or a stack of one dollar bills) would make a pretty natural introduction to the Peano axioms, and from there the basic mathematical operations. - A pile without apples is a pile of apples. We call it the empty pile. - The successor function is to add an apple to the pile. Apply the successor function to the pile of apples and you still have a pile of apples. - A pile of apples is as large as itself…

Not sure if serious or you are the supreme master of deadpan humor. Or both.

Re: Why do we still teach people to calculate?

#89
post #83

Earlier quoted context omitted.

> screws Torx?

For screws that go into wood (or thereabouts; sheet metal screws can count here too), Robertson is first on my list. The slightly tapered interface fits snugly and tends to hold screws onto a driver bit very well while providing good angular alignment, and it can do all of this without needing magnets. It can also allow for a bit of angular misalignment when necessary, and the chonky squared-off corners and flats res…

I mostly use screws for metal and plastic, so I use metric hex as well. Therein lies one disadvantage of the metric system: M3 is often too large, M2 is too small, and M2.5 is not super common. I use 2.5, so it’s only a minor annoyance.
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