Jay Lang

Also, if you haven't heard about these other, tangentially-related, fun "base" extensions (beyond non-integer bases, etc), be sure to check out Gray Code and Hamming Codes.

This is all so neat!

en.wikipedia.org/wiki/Gray_code

en.wikipedia.org/wiki/Hamming...

Then I went further down the rabbit hole and found:

en.wikipedia.org/wiki/Non-sta...

Aaaaaaaaah, this was such a good present from my student!

I thought it was problematic that some numbers had more than one representation. For example, one-half can be written as either

0.1111111... or
1. -1 -1 -1 -1 -1 -1 ...

...but then I got over it, because even in our normal notation, one-half can also be written as

0.5000000... or
0.4999999...

A student just taught me about the existence of counting in base three-- but in the "balanced ternary" base. That is, instead of using the numerals {0,1,2} in standard positional notation, we can use the "digits" {-1,0,1} instead. All integers can be represented!

en.wikipedia.org/wiki/Balance...

"Yeah, I see lower-case i all the time in my class, too." -me, without saying anything else about my sections of advanced algebra.

[Five entire eternities later]

The Engineering teacher: "WAIT A SECOND. Were you being CHEEKY?!"

i was.

In my teachers lounge with an engineering teacher and some male English teachers. Engineering teacher said, "Do your students use a lower-case i in your classes as often as they do in my class? It sucks. Their reflections seem so informal!" The rest agreed and doggypiled onto the kvetchfest. >>>

A student asked me to explain how to calculate the min v required to go across a loop-de-loop. I drew a FBD, drew weight down, drew centripetal force out. Student: “But we were taught that centripetal force always points towards the center.” I didn’t want to handwave, but I… don’t know? Please help?

Normalize hanging flags out of your window that represent your immigrant heritage if for no other reason than to mess with teenagers who are trying to get better at Geoguessr.

Relatedly, my students this year are absolute, complete nerds.

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)