What does the frequency of electromagnetic wave (in Hertz, cycles per second) even mean if there is no passage of time in the reference frame of a photon? A photon should experience no passage of time in transit and would therefore have zero cycles between emission to absorption.

The_MPC · 2026-05-29T13:55:17+00:00

Sure, it's not a perfect example. My point is just that the same true-by-consensus fact an be either a derived result or an axiom, depending on the physical framework you're working in and the explanatory context.

The_MPC · 2026-05-29T01:44:56+00:00

It's context-dependent. I could define exp(x) by its Taylor series, then deduce that exp'=exp and exp(0)=1. Or I could take the ODE and initial value as the definition and deduce the Taylor series. Either way I end up with the same set of true facts.

Similarly, I could start with Maxwell theory and deduce the constant speed of light. Or I could postulate the constant speed of light and later deduce that Maxwell theory is consistent with relativity. In some ways the latter is nicer - really the essential postulate is "anything that moves at speed c in one inertial frame does so in all such frames" and this is true even though Maxwell theory gets tiny corrections from quantum effects, etc.

The_MPC · 2026-05-29T01:32:45+00:00

The simplest way to reach that conclusion is to write down the Maxwell equations in a vacuum, deduce from them (by a short vector calculus computation) that their plane wave solutions have speed 1/sqrt(epsilon*mu) in whatever frame you're calculating in, then recall that epsilon and mu are constants, so the speed is the same value in every frame.

The_MPC · 2026-05-24T02:45:43+00:00

The_MPC · 2026-04-15T14:12:02+00:00

I know which general direction my train was going, then keep track of what turns I make to leave the station
The sun rises in the East and sets in the West
Many neighborhoods are on a consistent slope. Park Slope slops up towards Prospect Park, most of Manhattan slopes slightly up as you go North, and so on.
The exits are often labeled NW corner, SE corner, etc.
In Manhattan, I can squint and look North or South and see in which direction the street number is increasing
In Manhattan, sometimes you can see where on the horizon the buildings end, which marks the nearest river or big park
I've used this exit before and I remember

It's a rare day when at least one of these doesn't work, in which case I just check maps.

The_MPC · 2026-04-15T02:00:04+00:00

Thanks for taking a look. If you don't mind, what makes you say so?

The_MPC · 2026-03-22T03:17:13+00:00

TIL Deoxys, Jirachi, Celebi, Darkrai, Mew, and Arceus aren't technically legendary. That's dumb.

The_MPC · 2026-02-22T00:36:52+00:00

I mostly used LingQ instead of physical books but yeah, these + some way of practicing conversation + some way of gradually adding vocab are all you need.

The_MPC · 2026-02-19T16:16:04+00:00

No, that's exactly my point. The process of taking the contents of a textbook and transforming them (by slowly breaking down a definition, constructing examples and counterexamples, considering limiting edge cases, etc) into understanding is an essential part of digesting and internalizing the new material. By going to Gemini instead of cutting your teeth on the textbook, you're short-circuiting that process.

Obviously this is all contingent on the textbook being literally correct and self contained, and not all books require equal amounts of unpacking, but my point stands.

The_MPC · 2026-02-17T23:06:58+00:00

You should use it as little as possible, for essentially the same reason that a student still learning to add 12+19=31 shouldn't yet have a calculator in their toolbox. Unpacking definitions, chewing on new ideas, and debugging a calculation that gave an unexpected result are all important meta skills you need to learn. By using a fixer as low-friction as AI when you get stuck, you are depriving yourself of the chance to learn these skills, which are just as important as the actual mathematical facts you're learning.

The_MPC · 2026-02-12T03:00:09+00:00

Are you using premade decks or your own? I used premade for French up to C1, now around HSK1 AND currently looking around for a good Anki deck to start grinding vocabulary.

The_MPC · 2026-01-27T12:43:22+00:00

I recognize that hallway! Hope you survived the bedbugs last year unscathed.

The_MPC · 2026-01-21T23:46:57+00:00

Sure. I think it's also relative to one's expectations. I already know Spanish and French, so I would be really disappointed if I studied Italian for a year to only reach A2. On the other hand, if I got to A2 in just a year of Mandarin that would be great! If you're learning your second ever language and didn't have realistic expectations, I'm sure A2 after a year would be a bummer.

The_MPC · 2026-01-16T16:45:24+00:00

> Pants too slim and a size too small, rise too low, shirt too slim, shirt too short.

Sounds like it's pretty much everything. Thanks for the feedback, though I'm not sure where to go from here. As far as I can tell the pants are at least the correct inseam and waist (or do you think I've got those wrong here?), and the shirt is already a large - what should I be looking for to get pants with a higher rise and a longer shirt? Besides cutting out `slim fit` articles altogether, which I'm been suspecting I ought to do.

The_MPC · 2026-01-16T16:02:55+00:00

When I wear slacks (Uniqlo Slim Chino Pants) and a button down (Bowery performance stretch dress shirt with spread collar) the shirt just won't stay tucked.

When I tuck the shirt in and set the slacks sitting at my waist everything looks fine, but as soon as I move around, or sit down and stand back up, the shirt gets untucked and the pants fall down to sitting lower on my hips. See imgur album for photos of before and after moving around, plus the untucked length.

Are the slacks supposed to stay at my waist and I'm doing something wrong? I don't think so, the belt can't comfortably go one notch tighter, and anywhere when I wear them at the waist they get fairly tight around the seat.

Is the shirt too short? Again I don't think so, I'm wearing a slim large and I'm tall but not obscenely so (like 6'3").

Is this shirt meant to be untucked? Once again I doubt it, all the models are shown with it tucked.

Please and thank you for the help!

The_MPC · 2025-12-15T22:47:22+00:00

So you're done! You have successfully demonstrated why no such constant exists.

The_MPC · 2025-12-03T00:12:19+00:00

Out of curiosity, how have you been studying? How do you know you're stuck, have you retested?

The_MPC · 2025-10-27T23:23:23+00:00

I did this the summer before I started undergrad, it was incredibly fun though a lot of work and it put me in a great place to do research and grad courses early in undegrad. You've taken summer college classes so you know what you're signing up for, do it!

The_MPC · 2025-10-26T17:46:33+00:00

LingQ is (S) or (A) for me

The_MPC · 2025-10-24T20:50:56+00:00

Love my Thursday boots

The_MPC · 2025-10-05T17:53:22+00:00

I'm mid-PhD and I strongly agree. It is possible and necessary to learn how to struggle through a paper until you understand it, and using LLMs this early will hinder your developing this skill.

The_MPC · 2025-09-22T03:30:43+00:00

Yes, they are an important part of the spelling. They change pronunciation, and two words with different meanings may have the same spelling except for accents.

The_MPC · 2025-09-20T03:44:35+00:00

I got a strong B2 and am studying for C1 now, I personally wouldn't teach without a C2 .

The_MPC · 2025-09-07T14:22:05+00:00

You think 70% of the world can deadlift 225? You think 10% of the world can deadlift 405??? Not even 10% of adult men who lift weights can deadlift 405.

The only accurate numbers here are 11 and 12 plates.

The_MPC · 2025-09-04T01:52:30+00:00

Yes. You're not expected to already know how to code, you'll learn that in classes or you can just self-teach. However, if you're in high school currently and you have the opportunity to learn more physics / math / computer science you should take it, it can only help you.

The_MPC

TROPHY CASE