"Decisions went from being made for the benefit of users, to the benefit of Google, to the benefit of whoever was making the decision." This is definitely a small-to-large company pattern I've observed
My "stack" is just Apple Shortcuts making HTTP POST API calls to OpenAI, which does stuff in MacOS via BetterTouchTool. I trigger each by hotkey or typing a few letter into Spotlight (with Alfred). One transcribes and summarizes whatever youtube URL is highlighted. One does grammar and style correction of whatever is highlighted (and replaces it). One simply replaces the Dictate key with OpenAI Whisper but otherwise works exactly the same as voice typing. It's just way more accurate. One replaces the magnifying glass key to have a voice conversation with ChatGPT (using Microsoft voice synthesis). The built in prompt keeps it's answers short and conversational. It's like asking Siri something, but much better. One simply reduces the highlighted text by ~50% by rewriting it shorter, for when I have typed too much. One gives the key points of whatever article is in the foreground tab, so I know what I'm about to read. One outputs purely code, for example I use my voice to say "javascript alert saying blah" and alert("blah"); will appear at my cursor. Of course, it's usually more complex boilerplate stuff, but it helps speed up my coding. Every time I find myself using an LLM repeatedly for something, I make it into a little Apple Shortcut to streamline it into my workflow, as if it were a built in MacOS feature.
i am a former string theorist, pretty much turned and expanded Maxwell Einstein and Yang Mills in any possible ways, and those comments are garbage.
> original quaternion equations
quaternions are a 3/4d thing, you can write maxwell in any dimensions. sure you can rewrite some 3/4 d physics with quaternions but really no one does that for the last 30 years. we routinely use the group SU(2) or SO(3) but almost never it's quaternion representation. it's really not that practical.
> dumbed down vectors
i don't think it is the vectors that are dumb in this case...
btw it's not only a vector, it's a connection in a U(1) bundle over some spacetime manifold \cal{M}.
> Relativity doesn't play well with quantum mechanics
What in the f**** f**....
it works really well, we call that quantum field theory and it's the best theory ever found by mankind. it works so well CERN didn't found any deviation in 30 years or so.
> Maxwell's original equations are scalar in nature
Oh. My. God.
No. Any Maxwell or Yang Mills is a gauge theory with A_\mu the gauge potential which IS A SPACETIME VECTOR that takes value in some adjoint representation of some group. For Maxwell this group is U(1) so the gauge field aka photons is a real valued vector.
> removed the scalar (time) component entirely
a vector is a vector. a scalar is scalar.
a vector transforms with rotations a scalar does not..
> Can anybody here explain why this is so important
it is not important. it is the dumbest things i heard in a long time.
Silvanus P Thompson | Calculus Made Easy (html book) - https://calculusmadeeasy.org/ (This shouldn't be your only exposure to Calculus. It is more for building intuition.)
The Discrete Mathematics course above is probably the most important for your work. In fact I would look for more Discrete Mathematics courses if I were you as it is far more important than anything else here.
Marco Taboga | Probability and Statistics & Matrix Algebra (html book, need calculus) - https://www.statlect.com/
On YouTube you can literally watch a good lecture course for just about any typical undergraduate course. You just need to know where to look. Also there are even some really good master's degree courses out there.
Of course the only way to really learn the mathematics deeply is to "learn by doing", aka problems and proofs.
There are a ton of channels starting to pop up like Grant's 3B1B (I find like a new one every week). He had a contest recently so maybe look at some of the winners.
Lastly this is pretty useful if you get into higher mathematics:
Today, Twitter is a planetary-scale hate machine. By which I don't mean "people post hateful things on Twitter." I mean literally generates hate, as in, put a bunch of people with diverse perspectives on Twitter and by the end of the day they hate each other more than when they started. Common ground might have existed, but they won't find it, because Twitter, like any arms dealer, works better when they fight. It even benefits from collateral damage, when they hurt people they didn't specifically intend to hurt.
Through its core design—short messages, retweets, engagement metrics—Twitter incapacitates the safeguards necessary for civil discussion. It eliminates context, encourages us to present each other out of context, prevents us from explaining ourselves, rewards the most incendiary messages and most impulsive reactions, drives us to take sides and build walls.
If Twitter is going to foster healthy conversation, it will have to change fundamentally. It won't be a matter of tuning some filters and tweaking some ranking algorithms. A big part of it will involve making us the customer,
not the product (Zeynep Tufekci: https://twitter.com/zeynep/status/965937392942305280).
