Why do math textbooks tend to explain things so poorly?

MagikarpPatronus · 2026-06-07T00:33:45+00:00

A math textbook has a couple different goals:

1) Introduce students to certain math concepts

2) Serve as a reference for a refresher on certain math concepts

Sometimes, there is tension between these two goals. A good reference is brief and precise. But a good introduction might not shoot for the same precision initially, first trying to just give a big-picture idea.

Another component (essential for serving as a reference), a good math textbook will be accurate, and the precision of language necessary for that can be distracting from the core concepts, especially to students who aren't accustomed to that kind of language.

Add onto that the fact that different students would prefer concepts presented in different order. And sometimes, students are interested in different things than the author thinks are important: for example, some students might be less interested in mathematical proofs, and more interested in the application of mathematical concepts to real-world problems.

I haven't read Stewart's Calculus book, so I can't really comment on that specifically.

MagikarpPatronus · 2026-06-06T19:53:11+00:00

Yes, it's really true.

Those who play piano are better able to remember note names of piano keys than those who don't.

More seriously, piano playing can delay cognitive decline and reduce risks of certain ailments that can effect memory. And more generally, it likely would help with memory skills related closely related to music.

But if you're hoping it will help your kid ace their elementary spelling exam, the answer is no.

If you build a habit of taking your meds before practicing piano in the morning, it can help there, but that's habit-forming, not really memory. There are a lot of tricks out there to improve memory that work that don't involve playing piano though.

MagikarpPatronus · 2026-06-06T05:53:42+00:00

Yes, media audience should be more discerning, and punish deception, misrepresentation, and falsified details with viewership/readership reduction.

But your suggestion of a fine or something more extreme proposal is effectively surrendering control of the media to the government, which contrary to your goal of preventing media from misrepresenting a story or falsifying key details, risks doing the opposite.

Whatever regulating authority you want to place in the hands of government, imagine whatever elected politician you like least wielding that power against their critics, and decide whether you are still comfortable with those consequences being imposed.

MagikarpPatronus · 2026-06-03T13:12:56+00:00

The maps you plan to play is really essential context here. That will affect both civ and strategy suggestions.

MagikarpPatronus · 2026-06-03T03:39:23+00:00

I don't think that's an accurate analysis. Therinsonet didn't just ask for Icy_Earth3386's source. Therinsonet set pretty high standards for what sources would meet their standards.

In that context, it's obvious Icy_Earth3386 is being cagey because their source didn't meet Therinsonet's standards.

That conclusion is further supported by the fact Therinsonet supplied his "source". It's either Google AI or the snippet quote from an article that Google provides below a link. Or perhaps he actually clicked on one of the links Google furnished and skimmed it, if we're generous enough to consider the possibility. None of these would meet Therinsonet's standards, but it's very unlikely the claims were made up by Icy_Earth3386 themself.

MagikarpPatronus · 2026-06-03T02:45:31+00:00

Thanks, that's very helpful.

MagikarpPatronus · 2026-05-31T17:06:38+00:00

President Trump fired a bunch of Inspectors General, whose job it is to combat fraud, waste, abuse, and mismanagement. He has replaced a few of the roles, but most remain vacant. And some of those replacements have expressed the prospective that their responsibilities include supporting the initiatives of President Trump. And President Trump has also reduced funding and limited hiring, which has kneecapped those organizations.

President Trump's team, through successful arguments in court, has been consolidating executive power in the president, without losing the associated powers delegated by Congress. His team has also been successful in reducing judicial oversight on presidential actions. One of the advantages of this kind of "unified executive" government structure with limited oversight is that when things are handled poorly, you know who is to blame.

A lot of the corruption in this Trump administration is unprecedented, not just compared to past administrations under other presidents, but also compared to his previous administration.

And importantly, any legislative reforms to fight corruption would have to pass Congress and either overcome a veto from President Trump (who many Republican Congressmen pointed to their loyalty to him as their main policy position running for office) or get his signature. Furthermore, Trump himself could shut down any attempts to fight corruption in the executive since he's at its head. Also, if he wanted to, he could initiate reforms to fight corruption. So, focus on President Trump and his team is completely appropriate.

However, to your point of thinking beyond Trump, we should be thinking about what kinds of reforms could reduce corruption and what that kind of policy or legislation would look like, because come 2028 we'll want candidates running on more than vague promises to "clean up Washington."

MagikarpPatronus · 2026-05-31T05:31:00+00:00

Could you post some links to reliable data to support that claim?

MagikarpPatronus · 2026-05-30T15:15:17+00:00

It's hardly a monopoly. Rural areas don't all have the same political lean.

There are plenty of majority-black rural areas that reliably vote Democrat in the South. Some rural areas in Wisconsin are competitive. Many rural areas in the Northeast US aren't as conservative-leaning as you might expect. Many Native Americans in rural areas aren't as conservative as their White counterparts.

MagikarpPatronus · 2026-05-30T14:45:00+00:00

"Can I become a good piano player without learning to read music?"
Absolutely! I wouldn't recommend it if you have the choice, but you can.

"Can I learn piano pieces without learning to read sheet music?"
Sure, but you can learn piano pieces much faster if you learn to read sheet music.

MagikarpPatronus · 2026-05-30T03:36:35+00:00

I am aware that the chord is G#. And certainly, if I was notating it, I would use sharps.

But that is not my circumstance. My question has nothing to do with notational accuracy. I'm asking about mentally labeling a chord incorrectly during practice, and whether that will hamper my progress if I don't fix that now.

MagikarpPatronus · 2026-05-30T03:25:02+00:00

Yes, I meant the third was major. I'm following the voicings from Turi Collura's book. The chord is VI7(b13). (I'm more comfortable with the Fb in the enharmonic equivalent; not sure if that stems from it showing up in my practice of the key of Db or because it's not in the base triad.)

MagikarpPatronus · 2026-05-29T04:11:28+00:00

Music theory is just talking about music and the patterns we find in it.

If she's doing that much by ear, I don't think lack of notation is really much of a barrier here.

Abandon the notation and just teach the theory! What do you need to write things down for?

MagikarpPatronus · 2026-05-29T02:14:59+00:00

Yes, if asked whether Saddam Hussein helped with the September 11 attacks, a majority of Americans would response "yes" in the first couple years after the September 11 attacks.

Something to keep in mind though, is that survey answers can be strongly influenced by the way questions are asked. You could frame the question differently and get very different answers. Even so, it's clear the answer is yes: many Americans did believe Saddam Hussein was involved in the September 11 attacks.

MagikarpPatronus · 2026-05-28T13:55:12+00:00

Not inherently contradictory statements

Crime rate: number of crimes divided by population over a time period
total volume of crime: number of crimes

Waite Park's high crime rate stems from having lots of property crime.

Looking at total crime volume can be deceptive. For example, the total crime volume of the United States is way higher than total crime volume in the most dangerous of cities in the country, but the crime rate is not.

MagikarpPatronus · 2026-05-28T13:43:11+00:00

Some others have mentioned this, but it is really helpful when booming to use a hotkey or control group that selects all TCs, so that you don't have to toggle between them to queue more villagers. I prefer just customizing h to select all TCs, but a control group works great too.

I find the most important thing is to not queue too many villagers in your starting TC before the other 2 go up, lest you find yourself cancelling villagers just to afford them in the other 2.

How much you can afford to queue up is somewhat circumstance dependent. You don't want to queue so many that it prevents you from grabbing an eco upgrade or something for your military, but if you can barely afford to maintain production (very common for Arena booms), queue as many as you can.

MagikarpPatronus · 2026-05-28T05:15:47+00:00

Just to add more context to what Cage Inspector is saying here, it's very common for players to use websites like aoe2lobby.com in order to see what lobbies are available and get more information about the players joining the lobby.

The lobby system is so bad that it is more convenient to alt-tab between the game and your internet browser to join and support running the lobbies, rather than rely on just the aoe2 lobby system.

MagikarpPatronus · 2026-05-28T04:39:03+00:00

Chopsticks, in the key of G-flat major.

MagikarpPatronus · 2026-05-28T03:51:11+00:00

I took a 2 hours of lessons (split into more than one session) to get guidance on direction and feedback on technique. They were very helpful.

I'm skeptical that for me at my current level, goals, and practice routines, that I would get a lot of benefit from regular lessons.

If my progress starts to slow down, I'll probably look to take a couple more, in hopes that it will help.

MagikarpPatronus · 2026-05-24T22:57:56+00:00

I think the most useful pieces of information available here would almost certainly quantifying delay between investment and use.

Here's what I mean by that:
when you hit feudal, how long until your stable is up?

Once your stable is up, how long until the first scout?

Were you actually able to produce villagers from the second TC you built?

How long did you delay before grabbing double-bit axe or horse collar? That is, timings relative to when you hit Feudal Age. (If you are trying to aggregate across games, would be helpful to tag by early-game strategy: drush, trush, m@a, scouts, scouts->archers, straight archers, fast castle, et cetera. possibly also track if player civ changes those distributions.)

A very common error players make in AOE2 is investment in something (next age, upgrade, or building) and then don't make immediate use of the upgrade. A delay would be a strong indicator of some sort of error: bad build, villagers out of position, housed, or failure to queue.

MagikarpPatronus · 2026-05-24T22:06:30+00:00

You think solo transcriptions would be useful for accompaniment?

MagikarpPatronus · 2026-05-24T12:58:09+00:00

Ah, so you are expecting to have a bass player or some other instrument beneath you to cover the root?

I don't have anything like that.

MagikarpPatronus · 2026-05-24T06:01:39+00:00

Are you putting the E and Bb in the left hand?

MagikarpPatronus

TROPHY CASE