I'm in a hipster cafe in hipster coffee shop central of the world - Melbourne. The coffee is delightful. The baristas are hungover. The sun is shining.

It's a good day.

Soon to be proceeded by scotch, music, beer, cheese and good company.

Is it a good day because of what's going to happen soon after? Or is it a good day because of what's happening now?

I cant tell and I dont care.

Right. i has magnitude 1 and is at a 90 degree angle to the positive real axis. So i*i has magnitude 1*1 and is at 180 degrees to the positive real axis. i.e. -1. This works for any (a+bi)*(c+di). The magnitudes are multiplied and the angles are added. It's called De Moivre's Theorem.

Fourier Series is awesome. It's like magic.


PairTheBoard

Everybody remembers the good old days right?
We didn't ask such questions did we?

I want to go to Aus more than anywhere in the world. I think it good cause Aussie Aussie Aussie OYE OYE OYE

So when we talk about numbers, we use distance as what we later call magnitude. Is it better, or a more pure way to think about numbers using revolutions and distance? I mean in the way that numbers are used these days, it is like every meaningful number has a set of parameters which all act like revolutions around different imaginary axis.

I don't know enough about how linear algebra applies to topology to really complete my thought here. I love low content threads, i dont even need to!

Wait a min you meant i^2=-1 because i^i is actually

due to e^(i*theta)=cos(theta)+i*sin(theta)

i^i=(e^(i*Pi/2))^i=e^(Pi/2*i*i)=e^(-Pi/2)~0.207879576...

Yes that is what is true.

I was just riffing and I what I should have said was "Would you be willing to pay $0.20 for an item that costs i^i?". Which was an old homework problem from when i was learning this. I have, of course, since forgot and started to blurt out nonsense. <3 thanks for saying so! <3

https://en.wikipedia.org/wiki/Fourier_series



There's a cool GIF in the Definition section of the link.



PairTheBoard

The magic happens with the Fourier Transform.

https://en.wikipedia.org/wiki/Fourier_transform
and


So it almost magically converts the solving of some differential equations into an algebraic solution in the Transform space. Then reverse Transform back to original space.

Somewhere along the line in Real Analysis you'll be introduced to the theory of Hilbert Spaces. These are basically Spaces with an inner product which provides the feature of orthogonality (perpendicular), like the Dot Product between vectors. Masque can tell you how important this is in physics. There's a beautiful application of Hilbert Space theory in the development of the Fourier Transform. It illuminates what's really going on.


PairTheBoard

At the liquor age-gate last night, a young-looking person tried to get in the door by pointing to their Maserati, stating it cost “100k” because of their family debt business. God must exist because it is a miracle all I said in response is “I still need to see your ID, thanks”.

Why is orthogonality important in physics?

https://en.wikipedia.org/wiki/Orthogonality

In retrospect, cutting my own hair while drunk was probably a poor decision.

I'm going to cut my hair today, still necessary even if nature has taken care of half of it.

How often do humans need haircuts to keep them current?

I have a minor in Physics. I have attempted to use FS many times, some even successfully! I decided to go into math since I was really interested in abstract use of Hilbert spaces. I really love the applied math classes but really struggle with the pure math stuff. Its cool to talk about and I can understand the content, but I can't really remember it all on test day.

Are there actual jobs solving Eigen-systems and stuff?

Keep it coming bro, thanks.

Back in my day it was a good day when some one didn’t have to use their AK. So I thinks it’s situational. Today it’s a good day anyway, whatever. Beats other options.

https://en.wikipedia.org/wiki/John_McCain

Country before party.

One day it may become clear that we can disagree because we care for each other more than our narrow self stupid interest and misread lower level insecure ego. It may then actually mean something important and respectful and uniting.

But it's only when you multiply with the complex conjugate that things start to get real.

I'll...I'll just see myself out.

why do we need doctors? surgeons, skills with medical equipment and technicians - yes! - but general practition seems like it could be done from home.

I can tele-doc on my smart phone as long meh insurance doesn’t “fly away”.

Saw someone do it and get a skin cream prescription in less than 20 minutes. 10 minutes at the pharmacy and that was that.

You mean web MD?

Just found out my state regulates thinking exercises. Yeah, some may say shoulda expected it, but I ain’t ever getting complacent expecting thought prohibition. What a time to live. Is it a philosophical duty to disrupt prohibition of thought exercises?
Drunk answers only. 🤣 just kidding.

Not if the prohibition pertains to thoughts on the treatment of animals.

Is your beer getting warm? Drink faster! Life is too short for warm beer.