Explain this: take a three digit number, write it down twice. That six digit number oise always divisible by 13.

Not sure if this is the right thread (working my way through the code and techy threads too, stumbled onto posts by Lazy and quit for a bit)

I'm picking up maths again, mainly as I wanna learn to code (focusing on shaders and visual effects). I'm watching this series on linear algebra, and I feel like I understand what's going on, but every time I get stuck trying to write it down.

My main question is, I think, how do you go about that if you don't know where î and j^ will land? (sorry, can't find the correct j, ^needs to replace the dot.) I've made a polka dot pattern, but the dots are currently in straight lines next to, and on top of each other. What I've seen in examples is that I need to create a matrix, and rotate that by 45 degrees, so that they're organized better, like this
Ugh, img doesn't work, might give it another shot if I'm not on tablet and no one understands what I'm going for otherwise...

I don't know where my basis vectors will be exactly (he might point that out in a further video, but I feel like I need to write it down now). This confuses me, being able to do what he does seems to require a few known numbers already, am I right?
I don't think I'm ready yet to write it down in actual code (as that's even more complicated) but I wonder how the maths work if you only know your current point and rotation angle. He does 90 degrees in the video, but that seems easier as you land on the grid lines. I'm probably missing something

And another thing, I'm going through khan academy a bit, but the most annoying thing is he seems to learn how to solve things without a calculator. I'm not interested in solving square roots or powers (for example), but I am interested in when and how to use them. Anyone any tips for that? Or am I watching the wrong videos at Khan?

Vaped vs smoked/eaten i guess? Maybe i need to git gud at drugs.

Have we had this yet?

But then I'm a pure mathematician so I'm struggling to work out whether that's someone having an over-long laugh or actual physicists being nuts.

It may be a spoof

Well he's talking nonsense maths. Maybe there's some interesting related physics but he should talk about that instead. You can prove anything with divergent infinite series.

acemuzzy wrote:

Well he's talking nonsense maths. Maybe there's some interesting related physics but he should talk about that instead. You can prove anything with divergent infinite series.

You're just scared. Admittedly, saying it "sums to -1/12" might be pushing it, but it can certainly be "expressed" as -1/12. This is what happens if you have an infinite amount of dimensions in a (possibly) finite Universe.

That doesn't stop it being true!

I'm not a physicist either, if you don't know if an article has upspin or down spin do you assume it has no spin? Genuinely wondering because that is what he does to do those numbers

Vela wrote:

SpaceGazelle wrote:

That doesn't stop it being true!

That's the motto for string theory, isn't it?

It certainly could be. String theory, as I understand it which isn't that well, is all about the maths to an unusual degree. It's very wishy washy, but it's not the only branch of physics where that series is used. Physics had largely got away from using diverging infinite series, thank God, but they're not ruled out. You can use waves, like in Quantum Mechanics for example but there might be cases in the future that will need to use infinites.

Captain String would have something to say about all this nonsense.

Being falsifiable would help. It's allegedly very nice mathematics but terrible at making predictions and fitting with observations.

I'm a bit scared. Well maybe not scared but something. Personally I find it an exciting result and don't think it's totally bullshit. The fact you can substitute it for an infinite divergent series and get an accurate result is pretty mindblowing, however it turns out.

acemuzzy wrote:

How is "accurate" defined?

To about 10 decimal places apparently. One of my friends works at Stanford and I only see him over Christmas. It was he who mentioned this whole thing during a drinks the other day. I didn't know it was a thing but it's used in a few areas of Quantum Physics and apparently it works beautifully. It's clearly not the sum, but it's also clearly a good enough finite value to substitute for an accurate result. There's something in it, and that's mental.