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I went to Dutch Game Day earlier this month to give a talk, and I'm happy to finally share it with you all!

It's about an obsessive attempt at multiplying vectors! Not those pesky dot or cross products, but proper, canonical multiplying, whatever that means, and whether that even makes sense. I hope you'll find the answer interesting c:

The state of freya's brain

As some of you might already know, I've been in a very rough spot since the spline video - I've been going to rehab for burnout, which has been a slow and difficult process, as well as a month of a strong depression. I mostly retreated from making videos to switch gears, trying to take a break, but, that usually just means going back to my comfort zone of coding projects on my own. I think I've realized I literally don't know what it means to relax. I've come to notice that I only feel "relaxed" when I'm productive, working on my projects, which, doesn't seem healthy, but I don't know of any alternatives.

I made some gains immediately by fixing my sleep, which had been horrible for months. I would lie in bed for hours not falling asleep, only to wake up early, again unable to fall back asleep. I did a lot of reading on sleep hygiene in general, and I've been taking melatonin, the combination of which, has actually helped a lot. I've also been trying to get back to exercising, and I've gone swimming a few times, hopefully I'll be able to keep that up! It's always wild to me how important physical health is to mental health.

But not everything has helped, of all the things we've talked about at rehab, of meditation, breathing exercises, metacognitive exercises - I noticed that I have a veritable storm in my head, in a way that didn't seem to be an issue whatsoever for the others at rehab. In talking to my psychologist, we've decided I should probably get screened for ADD, because there certainly are signs. I'm hoping that might help me find answers and ways to, well, at the very least prevent this from happening again.

Anyway, I've been making some progress in recovering, I'm really happy I managed to do this talk without getting too stressed out about it all <3

The state of social media

It seems like social media platforms like twitter, which used to be my primary one, are struggling. The prospect of losing all the following and all the math content I've posted over the last decade on there because elon musk decided to steer the titanic into a 6th iceberg, isn't very fun, and has me worried.

With that in mind, I've started a mailing list! Whatever happens to social media, or even substack itself, they can't take email away from us right?

I'll probably only use the mailing list for project announcements, like, when I release new videos, new blog posts, or if I ever get around to making merch

As for the rest of my social media links, you can find them at acegikmo.com

Finally, thanks a ton for all of your support throughout this whole thing. The fact that you're all still here even though I am godawful at Posting Content™ and Providing Value™ on here, especially of late, it means a lot that you are still supporting me ❤

// Freya

Files

Why can't you multiply vectors?

..or can you? A deceptively simple question with a complex answer – come join a mathematical journey into madness and wonder, in search of answers that might just give you a new perspective on the mathematical constructs we use in our games Recorded at Dutch Game Day 2023, October 4th Timestamps: 00:00 Intro 04:34 Talk Start 05:17 Anatomy of a Vector 06:09 Products 09:14 Numbers of different kinds 13:32 Complex Numbers 18:10 Code for complex numbers 19:10 Complex multiplication visualized 20:22 Multiplying Vectors (an attempt) 24:08 Frustration 24:36 A Leap of Faith 25:36 A divine axiomatic truth 26:40 Squaring Basis Vectors 27:46 The Diagonal of Bases 29:09 Vector multiplication unraveling 29:36 Dot/Cross Byproducts 30:32 Complex Byproduct 31:17 Quaternionic Byproduct 31:52 The Answer 32:52 Beyond the Algebra 33:29 Basis Bivectors 35:06 Conceptualizing Vectors & Bivectors 37:08 Wedge Product 38:46 Curvature Bivector 40:59 Mental Gymnastics 41:56 Geometric Algebra & Multivectors 43:19 What does the multiplication represent? 44:10 Outro 45:53 Q: When is this useful? 48:11 Q: Does your math lib support geometric algebra? 49:22 Q: Do you plan on making tools for other engines? 50:53 AV team kicking us out 💖 Patreon ❱ https://www.patreon.com/acegikmo 🐦 Twitter ❱ https://twitter.com/FreyaHolmer 📺 Twitch ❱ https://www.twitch.tv/acegikmo 💬 Discord ❱ https://discord.gg/v5VWuga 📧 Mailing list ❱ https://acegikmo.substack.com/ 🌸 Instagram ❱ https://instagram.com/freya_holmer

Comments

Jesse Thompson

Scratches is happiest kitteh https://media.discordapp.net/attachments/307057157281677313/1166308676034900069/20171111_134338.jpg

Daniel Shimmyo

This is my favorite talk of all time. My mind is blown! Thank you for helping us to understand and appreciate complex numbers and quaternions!

Leonardo Taglialegne

This was amazing! I had tried to understand bivector before but this was so clear, I now get them!

Merijn Vogel

Always nice to see that whenever mathematicians came up with extensions to number systems out of curiosity, very useful things get discovered. Quaternions still baffle me a bit, and I will appreciate them when having my next boss fight in a game 🤣

Matthew Leighton

This is such a clarifying set of connections. I appreciate your content so much. Thank you for sharing this. That said, I hope you find a sustainable path to burnout recovery.

Morias

Thank you Freya !

Malcolm Ryan

Thanks! You led me down a GA rabbit hole this week. This makes so much more sense than Quaternions.