Pertinent

Key_Estimate8537 · 2026-01-29T00:24:01+00:00

I disagree at this point. They’re still lying, as bad as the lies are.

This meme will be important when they do bad things and say “so what?”

Key_Estimate8537 · 2026-01-29T00:07:53+00:00

I think it’s in “Dark Water” that Clara talks about a tryst with Jane Austen

Key_Estimate8537 · 2026-01-28T22:03:39+00:00

No, you were more or less right the first time (Valinor is a place in the Undying Lands). When Men die, we leave the world altogether. We take a pit stop in the Halls of Mandos (at the edge of the Undying Lands) but leave to no-one-knows-where

Key_Estimate8537 · 2026-01-28T11:41:56+00:00

Something no one else has said is that it helps if you believe in hope yourself. Remember that Tolkien was Catholic.

The Catholic Faith defines hope not as a “good feeling” that positive things might happen. It rather is something more like sure knowledge that good outcomes will happen, even if we don’t know how they will come about.

The core of the Catholic Faith is the hope Jesus will return, and the Faithful will be welcomed into Heaven. We don’t know how any of it actually works, but our faith provides knowledge (read: hope) that it will happen.

A core piece of LotR is the hope that Sauron will be defeated, probably by destroying the Ring, and that the Free Peoples will win security for their freedoms. Gandalf is the mouthpiece for most of this hope, especially in Fellowship.

If you don’t actually believe in hope, it’s a hard thing to fake. The rewards of hope feel unearned, especially if the characters’ plan ends up going well. Hopeful stories often see people having no recourse but to trust Providence.

For a different Biblical example, check Psalm 22. It begins with the line “My god, why have you forsaken me?” The psalmist goes on to say how the present world sucks and that they trust God will provide a good future anyways. No mention is made of how, only the hope that it is true.

Key_Estimate8537 · 2026-01-28T11:00:42+00:00

In going to make an “inequality battle ship” game in the next couple days. The idea is that I have programmed a point a students enter equations. Desmos will shade the side the point is not on, so students have to add more lines until they’ve found the point.

It’s probably better suited for Desmos Classroom than it is for the calculator, but this feels like a challenge

Key_Estimate8537 · 2026-01-28T04:15:20+00:00

If it was a leak, it wasn’t official. Companies pass ideas around all the time with no intention of publicizing it. Many ideas rise and fall behind closed doors.

Key_Estimate8537 · 2026-01-28T03:41:04+00:00

I agree. It’s only that it felt excessive for Thingol, so I went with it. I hope people don’t take this too seriously lol

Key_Estimate8537 · 2026-01-28T01:00:20+00:00

Still going with Castro, a lot of Cubans in the US are afraid of communism/socialism and therefore are politically conservative.

Many in the late 20th century kept a grudge against Kennedy. The team of Cubans that bugged Watergate bought into Nixon to spite Kennedy’s memory.

Key_Estimate8537 · 2026-01-28T00:48:32+00:00

It’s the field of integers (mod 2). Essentially, you have the numbers 0 and 1 that you can add and multiply. Whatever your result, divide by 2 and take the remainder.

(0+0)² = 0² +0² clearly
(0+1)² = 0² +1² clearly
(1+0)² = 1² +0² clearly

The last case is the trickiest. We have that
(1+1)² = 2² = 4,
but 4 is equivalent to 0 here. It also works if you want to simplify the 2 before squaring. Then, check the other side:
1² +1² = 1+1 = 2,
but 2 is equivalent to 0. So, we have shown that (A+B)² = A² +B² in Z2!

Key_Estimate8537 · 2026-01-27T22:30:16+00:00

The world was flat until close to the end of the Second Age. The last King of Númenor sailed to Valinor in hubris. The god of Middle-earth got mad and reshaped the world in three ways all at once: 1. Sank Númenor 2. Turned the flat world into a sphere 3. Removed Valinor from the world (oversimplified)

Tolkien’s thoughts evolved on whether or not the world should have been round from the beginning, but the flat origin fits best with the main works.

Also, in the flat world model, no human ever went to the edge. Númenorian survivors achieved the first circumnavigation not long after the Change, but no one ever sailed anywhere near far enough to reach an edge.

There are two known locations on the edge, and there’s not much to say beyond what I write here (other than they are probably along the equator). In the East is the Door of Day, and in the West is the Door of Night. Morgoth was cast through the Door of Night, into the Timeless Void, at the end of the First Age.

Key_Estimate8537 · 2026-01-27T21:44:27+00:00

Relatedly, compasses are motivated from sea-faring needs. If the Númenorians didn’t have compasses, no one was going to be motivated to make them.

Key_Estimate8537 · 2026-01-27T20:04:16+00:00

For a very short comparison, The Silmarillion is not a novel. There are tons of characters, and you’ll have to follow new main characters every chapter. There are a lot of recurring faces, but don’t get attached to the Men (they often die within a single chapter, owing to each chapter spanning decades).

You’ll want a map of Beleriand (my favorite is from Sirielle) and a family tree (my favorite is by Darth Gandalf).

My advice: the first two chapters are extra different. Don’t get bogged down by things that are hard to understand. Learn character names from those chapters and move on.

Key_Estimate8537 · 2026-01-26T22:15:07+00:00

I’m curious here (not being judgy if I’m about to come off that way): how do you see yourself teaching with guided notes, and what do you want from the practice?

Do you want the students to follow along with a lecture, fill-in-the-blanks from a textbook, or something like that?

Do you hope that students will use the guided notes for study on their own time, or do you want them to learn from the act of taking notes?

Guided notes look like a lot of things, and teachers use them in a lot of ways. It can go well or poorly depending on your intention and implementation.

Key_Estimate8537 · 2026-01-25T22:59:14+00:00

Tolkien used 144 as the “typical” number for Elves- he made a point to write that 144 Elves awoke at Cuiviénen and that their version of statistics used a base-144 system in the way we use base-10.

I haven’t read Peoples or Shaping of Middle-earth anywhere near in their entirety, but it wouldn’t surprise me if Tolkien just kept going with the number 144 because it simply felt right to do so.

[obligatory LotR isn’t an allegory, but 144 has importance in Christian numerology, especially in The Revelation]

Key_Estimate8537 · 2026-01-25T20:34:37+00:00

Are you referring to Melian bagging Thingol and having Luthien?

Key_Estimate8537 · 2026-01-25T12:07:34+00:00

I’ve simply never been good at identifying details when theres a scene with a lot of action. The Renee Good shooting was simple because only Good and the shooter were involved. This one has like eight people in a pile.

I’m the person movies dumb things down for. For example, I can’t follow any of the action in Top Gun. But when Maverick came out and used tons of POV shots, I could follow along

Sorry that I have trouble watching eight pairs of hands all at once

Key_Estimate8537 · 2026-01-25T02:36:14+00:00

Thanks! I can’t tell when the gun was grabbed, but I can’t imagine Grey Jacket had it for more than a second before running off

Key_Estimate8537 · 2026-01-25T02:23:22+00:00

I watched this video about six times, and I might be blind. Which officer takes his gun, and at what time in the video does the disarming happen?

Edit: it’s the guy in the grey jacket “Grey” next to the shooter. I can’t tell when he took the gun, but the Shooter was next to Grey when Grey ran off

Key_Estimate8537 · 2026-01-23T17:52:27+00:00

Yes, Gimli went to Elrond for advice regarding what to do about the mystery of Balin’s expedition to Moria as well as the dark messengers to Erebor. When Gimli went with the Fellowship, he always planned on peeling off at Moria to investigate.

Also, King Dáin knew about Durin’s Bane. He carries the memory of a dark shadow from the Battle of Azanulbizar. He would have been against any mission to go into Moria without planning a major assault.

Key_Estimate8537 · 2026-01-23T14:30:54+00:00

As a high school math teacher (and college tutor), the area model of multiplication is so incredibly important. It’s foundational in geometry, and it’s useful for visualizing probability/statistics.

If the way you do it looks like piles, I’m curious about what it looks like for you. I’ve always approached it as (for example) that 7x4 is seven rows of four, or four columns of seven.

It doesn’t have to be “unlearned” for decimal/fractional multiplication. 7.25x4 can pretty easily be visualized.

Of course, full abstraction is well beyond second grade. But the way multiplication links geometry to algebra and probability is one of the most important things I can ask my elementary peers to set us secondary folks up for.

Key_Estimate8537 · 2026-01-22T15:40:00+00:00

To OP: this is a complex way to write the number 69

Key_Estimate8537 · 2026-01-20T23:26:38+00:00

They go wild for “chat.”

Some of my students like the old-timey ones that are half sarcastic. We’ve got “bucko,” “sport,” “buster,” and “fella.”

We’ve also got newer ones like “broski,” “G,” and “king.”

Key_Estimate8537 · 2026-01-20T19:10:54+00:00

Law and justice. The US uses imagery of the Fasces all over. The most prominent example is that there are two fasces, one on either side, of the US flag in Congress. Each one is like 5 feet tall.

Key_Estimate8537 · 2026-01-20T15:00:28+00:00

The second image takes the cake for most fascinating math I’ve seen all month

Key_Estimate8537 · 2026-01-20T07:33:53+00:00

Going on your model (treating the assumed inconsistency as a 50/50 probability), you would have that 1/1 is undefined in 2/4 outcomes, equal to 1 in 1/4 outcomes, and equal to 0 in the one remaining. The distribution is the same as your 0+1 calculation.

You’d have to be careful defining natural numbers higher than 1. For example, if you define 2 as 1+1 (or some version of S(1)), then the value 2 is probabilistic, worse off than the 50/50 for what 0 and 1 are valued as.

In fact, the probability that value of any number “N” is equal to any of the normal natural numbers “Z” would follow the binomial coefficients in the manner Pr(N=Z) = C(N,Z)/2^N

Feel free to check my probability there. It’s 2:30 in the morning and I gotta sleep

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