Janet's Adventures Under Ground

Hi 🙂

There are tons of videos on the internet that teach you *things*. This is not one of those! What you’re getting is watching me learn, watching me follow my curiosity. Maybe it will remind you what learning and curiosity looks like (if you have forgotten). Maybe it will inspire you to follow yours.

It is SLOW. It’s about going on tangents, getting lost, and finding your way back. This is what learning looks like. This is not high dopamine content.

Grab a cup of tea, let this video be a bedtime story if you want. Let the video play in the background while you do work or study (if you’re one of those that likes someone talking about random things in the background. I like that sometimes.

Or, sure, listen to what I'm saying. I’m glad you’re along for the ride. What are you curious about learning? There are awesome people in the comments, I hope you connect with each other and I’ll drop in as well to respond to what I can, when I can.

Notes:

1. I did notice my microphone picked up some strange sounds because I clipped it to my sweater—lesson learned for next time!

2. My hair is messy, that's okay.

3. I accidentally stopped recording at one point, so the link to part 2 will be here once the video uploads:    • Math Rabbit Hole 2: The Number 9 :)  

4: The link to what inspired my exploration is here:    • Re-Learning Math with Scott Flansburg...   recommended to me by @VAVS100, thank you!

Topics addressed in this video: Symmetry, Numbers, Nine, Times Tables, Modular Arithmetic

_____________
Hi!
Thanks for watching :)
I'm Janet, the Architect of Ideas and aspiring Unofficial Professor of Patterns... creativity and curiosity drive my life.

I started trying to use MIT Scratch to do this, but it seems scratch doesn't do textual/numeric output so well, unless it's what the cat says, ... 

And anyway, my screen recorder drops so many frames you can't see what I'm actually doing!!

Part II:

My comment:

19:11 About logarithms, and looking for the other half of the argument, see this lecture given by Edsger W. Dijkstra at Newcastle-upon-Tyne sometime in 1992 https://youtu.be/4oir3ywNn_8?t=13m17s You can think of the base-2 logarithm of n as being roughly one less than the number of digits in the number n written in binary, similarly you can think of the base 10 logarithm of n as being roughly one less than the number of digits in the number n written in decimal. Then the question is what to do about the fractional part, because a number like 999 has as many digits as the number 100 but the base 10 logarithm of 999 is almost the same as the base 10 logarithm of 1000 which is 3, but the base 10 logarithm of 100 is 2. Another direction you can take your investigation is to look at operations like addition and multiplication when the operands are matrices rather than numbers. Then matrix multiplication can suddenly do things like rotate vectors, or scale them, and if the vectors are thought of as just column matrices then matrix multiplication gives you a way of combining operations on vectors. So you have groups of matrices which are much studied in physics.

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Yesterday I made a video before I saw Janet had also made one and uploaded it two hours before mine:


My video was this one, following on from last weekend (see Proof-Stories With Janet)


Then I went for a walk and made this one:

See Roger Penrose's talk at the Isaac Newton Institute a few weeks ago:


Then in the evening I made this one:


Then today I saw Janet's videos and made this one on my walk this evening:

See Steve Awodey - Intentionality, Invariance and Univalence.

Here's Johnny Ball on Russian and Egyptian Multiplication and the connection with binary numbers (Clock arithmetic modulo 2):


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