Jay Lang

2² + 3² + 6² does equal 7² -- whoa!

Alright, time to generalize into a generic base.

b² + (b+1)² + (b² + b)² = (b² + b + 1)²

is an identity!

I wonder if there are any other identities like this. The reason this looks like it can be in binary is in how there are no coefficients anywhere. Hmm..

I was messing around, programming solutions to variations on the Pythagorean Theorem, and I found

10² + 11² + 110² = 111²

In fact, 100 + 121 + 12100 does equal 12321. Neato! But doesn't that also look like it's in binary? Hmmm...

OY VEY, it’s 5786 but I’m still writing 5785 on all my checks! :0(

“The last digit of pi in binary is 1, as trailing zeros are meaningless.” -Someone on Reddit.

Like, that’s not how math works. But also, I mean, there’s kiiiiiinda a bit of a draw to it, eh?

#mtbos #iteachmath #mathsky

My friend Chris is a mathematician, speaker, author, and former math classroom teacher. He is collecting data via a voluntary survey on a Google Form regarding one's thoughts on democracy in the USA. This dude is awesome, and produces awesome, and if this helps give him a signal boost, then great!

(2/2) I know that mental health has become main-stream for teens to hear and talk about: in music, in fashion, etc. I have seen this hoodie countless times. I wonder if teens will make it fashionable to wear self-harm bandages to take the stigma off of those who wear them out of necessity.

I have a student who has part of her upper arm wrapped in a kind of bandage. Maybe she just went to her dr and received a shot as part of a physical? Maybe something "else" happened? I don't know. It is immediately on my radar.

I also think about how teens make fashion out of everything. (1/2) >>>

Follow-up.

(Also, I love the "As predicted", as though it were the scientist equivalent of "as per my previous email".)

"Tides are one of the weirdest and most sci-fi elements of living on earth". A new thought I cannot unthink.

(From @xkcd.com)

"The President’s budget request for NASA in fiscal year 2026 totals $18.8B. This represents a significant shift from the $24.8B enacted in 2025..."

In 2024, NASA got 0.37%.
In 2025, NASA got 0.34%
In 2026, NASA is slated to be further reduced to 0.27%.

www.planetary.org/space-policy...

We don’t *spend* money on space exploration. We invest in it. Funding the nerds is a service that pays dividends-- often in unexpected ways.

The comment in this screenshot couldn’t align more closely with my views re: spending on “useless” experiments and studies. Yes, please! #Penny4NASA @esa.int

I like how each category notes approximately which "geomagnetic latitude" is likely to experience aurora overhead. This is different from "regular" latitude because the earth's rotational axis isn't aligned with the magnetic field's axis. Because magnet fields cause auroras, we use its lats instead!

At this link can be found a description of the categories in the space weather scales. It's the same idea as the category scale we have for hurricanes, or the EF scale for tornadoes, or the magnitude scale for earthquakes. I like the rightmost column the most. (www.spaceweather.gov/noaa-scales-...)

The chance for aurora is particularly strong at lower latitudes from Monday evening through Tuesday dawn. Yes, I mean your time zone.

We, the planet, are under a "Geomagnetic Storm Watch" for a category G2/G3 event. A neato chart is available below from the nerds at @noaa.gov about this scale!

I think this would go over their heads, and not just because it took place on a starship.

But for real: this is a moment in pop culture for adults to connect with teenagers about something cataclysmic happening in that space. Consider starting the year off with a bid for cross-cultural connection?

I love how little chill the wit on the internet has. I may just post this on the bulletin board in the corner of my classroom and see what happens. “Oh students, you know who Taylor Swift is, too?” #YouBelongWithMeme

..., then counted the third column as five again, and then subtracted one to correct for how the third column wasn't a full five.

I feel really, really gross at Brain right now.

I counted the leftmost column of five first upwards, then scanned the two downwards. Then the rightside almost looked like one block of 10. I scanned the rightmost column to verify that it had five in it (it felt more like, "I matched it to the length of the five that I had already measured"?)...

All to say: @acollierastro.bsky.social is one of my favourite YouTubers. She recently did a video on Vibe Physics which contained a chapter on vibe coding that left me considering what I've written in these posts. I don't know how I feel about it all yet. She influences me. It's fine. (9/9)

When calculators hit classrooms, did we not have the same argument about how they'll affect students' abilities to do arithmetic? It's mechanical advantage for human creativity. We can do more to get our creativity out, faster. Standards and use cases will develop. Best practices will exist. (8/n)

I think generative AI and LLMs are the next-gen high-level programming lang. "Prompt engineering" is a thing on which univ classes are focused. The syntax of the vibe code is in the structure of the English words chosen to trigger the generative AI to create the code-- GIGO is still a thing. (7/n)

Sure, the increased ubiquity of AI, LLM, and the democratisation of programming is going to have a hugely negative impact on the ability for programmers to be hire-able. But this is a flaw of capitalism that privatizes profit and socialises losses that is not being sufficiently addressed. (6/n)

"You're basically doing what anyone could do with an LLM, which seems bad for your career prospects. You are specifically and intentionally refusing to learn anything which seems problematic."

I see this as a democratisation of programming? As learning code in a high-level language? (5/n)

"An important component of vibe coding is that you don't know, nor wish to know, what the code does. It isn't "vibes" to go back through the code and read it line by line to try to understand the code." I cut my teeth on C, and I've no idea what the machine language is doing in the background. (4/n)

"Vibe coding [...] forgets the code even exists. You [vibe code] through English language text, not computer code. Then you just test it by running it to see if it does what you want. Then you iterate again through English discussion words and not code language." There's an XKCD for this. (3/n)

Of course, there is an abstraction penalty with each increment. Each level of coding still can be purposefully deployed. Lower-level coding can be more optimized (to make a task-specific machine for crunching math problems, say?) But have we become a bit too "Kids these days" these days? (2/n)

Devil's advocate: What if vibe coding is just... coding? What if it's just the next-gen of high-level coding? We went from machine code to assembly (which made machine human-readable). Then came autocodes which came with compilers and even more abstraction. Then C and Python and transpilers... (1/n)

What I was advocating for was presenting the idea to certain high school students. I’ve had some special cases last year that were just so happy doing mechanical computations that I showed them this neat thing they could do in their spare time. And they did. Nerds.

I took Diff Eq freshman year at 8AM and got a D… and then took it again at 8AM and got a B-… I mayyyyyy have missed that entire chunk of lessons.

I admit that I was not the best undergrad at studenting. 😬

But then I watched that Numberphile video and got to be one of that day’s “lucky 10000”!

But there are other numbers that you wouldn't use to "count". Numbers as a toolchest can do way more than count with what's inside. Pick the right numbers for the job.

So, if e^3 can be a thing, and e^(-2) can be a thing, and e^(pi) can be a thing... why not e^(M)? What step is stopping us?!