English Language & Usage: Multi-Layered Discourse Room

tchrist

23:04

A velocity is something like 70 miles per hour east or 70 miles per hour west.

c ↄ

a vector

tchrist

It needs a direction.

c ↄ

or an (orthogonal) basis components

tchrist

Don’t even make me talk about 3-space vectors instead of nice 360-degree ones.

c ↄ

radial notation vs cartesian

tchrist

23:07

Ships says they are travelling at 20 knots north by northwest.

@cↄ You still need (x1,y1,z1) and (x2,y2,z2) in cartesian.

You can convert (x,y) to (rho,theta), yes, but you left out the 3rd dimension.

c ↄ

there's also (rho,theta, zheta) notation in 3D

e.g. Earth lat lon

tchrist

Imagine: A man owns a square plot of land that is one mile on each of its four corners. However, on this square is a mountain one mile high extending from each of the four sides. Question: if we assume it is all tillable, how much more land does he have to till than someone who lives in flatland?

RegDwigнt

0

Q: Does he like me and should I tell him I like him?

So there's this guy that I really like.... We are really good friends, like we are best friends! We hug, walk to lunch together and we are always partners. Does he like me? Should I tell him I like him or just wait? I'm really shy.

look-alikes

tchrist

Assume a perfect pyramidal mountain.

KitFox

None more.

It is the same amount of land. His is just stretched out is all.

@RegDwigнt Look alikes?

Cerberus

23:13

@RegDwigнt Pre-spam, perhaps?

c ↄ

no, there will be more surface

tchrist

@KitFox So you if you own an equilateral triangle’s bottom, the guy who owns the other two sides doesn’t own any more than you? I think otherwise.

In fact, I know otherwise and can trivially prove it.

KitFox

It doesn't work that way.

MετάEd

@tchrist Well in that situation you both own 0 acres.

tchrist

Sure it does.

Ask the oxen.

c ↄ

23:15

a flat surface is simply the minimal surface, so all other possibilities are bigger

tchrist

They know the truth of this.

MετάEd

@tchrist The oxen are dead after trying to drag the plow up the side of the mountain a bunch of times.

So don't ask the oxen.

c ↄ

like a sphere is the minimal volume for this surface, a cube would take more surface to contain the same volume

KitFox

You can't own the bottom of a piece of land and some others own the sides. It doesn't work that way.

tchrist

I am comparing a square mile in flatland with a square mile with a mile-high perfect four-sided pyramidal mountain on it.

MετάEd

23:16

@KitFox Sure you can. That's why they call it bottom land.

tchrist

Thus the triangle analogy is correct.

The answer is 2 square miles. Think about it.

Each of the four sides is one half square mile.

Because it is an equilateral triangle.

You need extra oxen.

KitFox

Yeah, OK, but land parcels don't work that way.

tchrist

Math works that way.

Oxens work that way.

The law, however, is an ass.

And burros grow tired quickly.

@KitFox You are correct that you would have bought 640 acres on paper, yet in doing so gotten yourself 1280 acres.

Neat trick if you can get away with it.

MετάEd

@tchrist You know the burro is tired when it's a little hoarse.

KitFox

No, I'm saying you wouldn't.

Cerberus

23:21

@tchrist Wait, why is it equilateral?

tchrist

@Cerberus Damn it.

MετάEd

@tchrist More likely it would be surveyed as surface area, not just surveyed at the boundary.

Cerberus

Shouldn't the eh long lines be the square root of 3/2?

What do you call those...the long sides of the triangles.

tchrist

You’re carving out a cube into a pyramid, and I am suddenly stricken with trigonometric panic.

Cerberus

The area of one of the triangles should be (5/4)^(1/2) * 1/2 * 1/2, I think?

Why a cube?

tchrist

23:25

Perhaps.

Because it’s easier to think of that way.

Cerberus

So the four triangles should have a total surface area of (5/4)^(1/2).

tchrist

The point of the mountain is in the center of the square.

Cerberus

You said the mountain was 1 mile high.

tchrist

Right.

I can’t justify equilateral triangles.

Cerberus

Because they are in a different land.

tchrist

23:27

I don’t think I like your solution. It isn’t a big enough number. Hm.

This is going to bug me.

Cerberus

Wait, it's actually 2.5.

I miscalced.

tchrist

Oh.

That’s better.

Cerberus

I always slip up when I don't write things down.

tchrist

I just went for the paper.

Cerberus

Too lazy.

It's 5/4 * 2.

tchrist

23:29

So 2.5 units not 2.

Because of the triangles being at a different angle.

Cerberus

It's 5/2 square miles.

tchrist

Right.

I kept thinking tetrahedra, but pyramids don’t work that way.

Cerberus

I just calculated the area of one triangle.

tchrist

Of course.

One triangle on the flat is 1/4 sq mile, but when you raise one of its points up a mile, it changes things.

With volume, it is enough to know that b=h at 1 mile each, and thus is simple, but with area you need to know s, which is not 1.

Cerberus

Arg, I miscalced again. It's (5/4)^(1/2) * 2.

So that's...the square root of 5, I think?

I know I shouldn't be so lazy.

But writing it down is so boring.

tchrist

23:37

s should be the square root of 5/4.

Cerberus

Uhuh.

Mitch

@Cerberus that's the belt of lower vaccinations, not religiosity. But does it correlate with religiosity? Is there a rural/urban difference? (I mean the whole country is urban separated by suburbs, the most uncivilized, distant countryside is at most 100 yards away from somebody's house.).

Cerberus

@Mitch Yes, it correlates very strongly with orthodox Protestantism.

tchrist

I'm up to 3.24 sq miles.

Cerberus

Which happens to be rare in urban areas, but also in many rural areas.

@tchrist I'm up to 2.24~ square miles.

I.e. the square root of 5.

Mitch

23:39

@Cerberus What about those big open places on the map (w > 90% vaccination)? why big areas like that as opposed to the linear conservative 'belt'?

Cerberus

@Mitch I'm actually not sure why the belt is where it is, or why it is a belt at all.

Mitch

I reread my first question to you. I thought it said 'the belt of lower expectations'.

Cerberus

Everything to the south of the belt is Catholic, so it can't be there.

tchrist

If s = (5/4)**(1/2), then it is ~1.118.

Mitch

I thought Netherlands was primarily Protestant.

Cerberus

23:41

@tchrist Times two.

Mitch

or is the population spread differntly

Cerberus

@Mitch Traditionally, 60 % Protestant.

tchrist

Than letting b=1, A = 2bs+1 is 3.23606797749979

Times two?

Cerberus

The south Catholic, the rest Protestant.

Mitch

oh. so up north are liberal vaccinating-loving protestants?

tchrist

23:42

Or A=2s+1.

Cerberus

@tchrist I think you're counting the underside of the pyramid, which is a tad hard to grow wheat on.

tchrist

Oh damn, you're right!

Well done!

Cerberus

@Mitch Umm...We have 1000 kinds of Protestants. The large majority were traditionally more liberal, a small minority orthodox. They populate the Bible Belt, for some reason.

Nearly all Catholics are a lot less orthodox than our orthodox Protestants.

They vaccinate all right.

@tchrist Semper!

tchrist

That’s not a very rational answer, you know.

Cerberus

But it is Latin.

tchrist

23:44

Insofar as the answer being outside J.

Cerberus

Who's J?

tchrist

The rational numbers.

Those numbers that can be formed by X/Y where X,Y are both integers.

Those are rational.

Fractions, if you would.

Mitch

J?

What does that stand for?

tchrist

No.

I meant ℚ. Sorry.

Cerberus

tchrist

23:46

J is usually integers.

Mitch

Maybe they're related?

Cerberus

The SGP is the most orthodox Protestant party.

Those are parliamentary elections.

tchrist

‭ ℂ  2102       DOUBLE-STRUCK CAPITAL C
        = the set of complex numbers
        # <font> 0043 latin capital letter c
‭ ℚ  211A       DOUBLE-STRUCK CAPITAL Q
        = the set of rational numbers
        # <font> 0051 latin capital letter q
‭ ℝ  211D       DOUBLE-STRUCK CAPITAL R
        = the set of real numbers
        # <font> 0052 latin capital letter r

Your answer is not in Q, but in R.

Cerberus

So even in the most orthodox district, they score only 30.4 % max.

tchrist

However, it is also an algebraic number not a transcendental one.

Mitch

23:47

@Cerberus That is just so weird. How do things like that form lines? Most information transfer is broadcast nowadays, so how could people maintain these old arbitrary divisions?

I will ask them.

tchrist

You have thumpers who don’t vaccinate? Perhaps Darwin still rules after all.

Cerberus

@Mitch Yes, I really wouldn't know!

Mitch

@Cerberus If they watched more TV it'd be more homogeneous.

tchrist

> Algebraic numbers are numbers that can be expressed as roots of polynomials with integer coefficients.

Mitch

More Gilligan's Island reruns. Takes the orthodox right out of you, makes a broth out of it, which you then add meat potatoes garlic tomato sauce, and you have nice tasting stew.

Cerberus

23:50

@Mitch Yay televangelists!

tchrist

Why are we talking about culinary doxology again?

Mitch

the nonorthodox...a little gamey.

tchrist

I thought your freaks all came to our country.

Cerberus

Red is Protestant, Green is Catholic.

tchrist

Shouldn’t that be Orange?

Cerberus

23:50

So you see how our orthodox Protestants kind of form a belt that protects us from the Catholics?

tchrist

That’s an interesting way of looking at it.

Cerberus

It is the only related factor I kan think of, why they are where they are.

The density of the population is by far the greatest in the area in the west that is shielded by the Bible Belt (but not part of it).

All the big cities are there.

tchrist

Pilgrims (Plymouth Colony)

Pilgrims (US), or Pilgrim Fathers (UK), is a name commonly applied to early settlers of the Plymouth Colony in present-day Plymouth, Massachusetts, United States. Their leadership came from the religious congregations of Brownist English Dissenters who had fled the volatile political environment in England for the relative calm and tolerance of 16th–17th century Holland in the Netherlands. Concerned with losing their cultural identity, the group later arranged with English investors to establish a new colony in North America. The colony, established in 1620, became the second successful ...

Cerberus

Yeah, also Puritans.

tchrist

I never figured out whether Puritans == Pilgrims.

c ↄ

23:54

imgur.com/gallery/zChSf scary

Cerberus

Puritans is broader.

tchrist

Don’t want scary.

Cerberus

Pilgrims is only a very specific group that emigrated at a specific time, right?

I would say Cromwell was a Puritan.

tchrist

But he never peregrinated, so could not have been a Pilgrim. Is that how that works?

Cerberus

@cↄ Book cases? That's scary?

c ↄ

23:55

what's behind

tchrist

Roundhead.

Cerberus

@tchrist No, I rather believe the Pilgrims is an even more restricted group.

tchrist

Hm.

Cerberus

As in a couple of ships full of migrants around 1620?

tchrist

The ones who went from Holland to England to Plymouth by way of P-Town?

Cerberus

23:56

Yes, those.

tchrist

And I mean the other Plymouth, of course.

Cerberus

Yes.

> Pilgrims (US), or Pilgrim Fathers (UK), is a name commonly applied to early settlers of the Plymouth Colony in present-day Plymouth, Massachusetts, United States.

This says it all: early settlers of a specific colony.

Not later settlers. Not people who settled in a different colony.

Like a specific, organised group.

I thought you learned these things in school?

tchrist

They signed the Mayflower Compact at Provincetown, MA.

Read the first landings bit. Horrible. 50% mortality rate that first winter.

Cerberus

Right.

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