campaign 4 enjoyer

Moving roughly top to bottom and left to right:

This is basically nonsense. ma could be force, which could be F, but when you divide by the square route of x you'll have different units. All of these equations have different units. There are some pleasant looking trajectories though! Possibly particles traveling in a field, as prev suggests. I was hoping for a space-time diagram, but the only axis labeled here is 'y'.

No idea. You don't usually end up with a sine inside a cosine, but it's not unheard of. Essek erased his integrand but left the ghost of a calculation behind. I agree with prev that the diagram looks like a rotating object, and the trig functions could sort of fit with that.

Finally some good stuff! Still very difficult to parse. Prev is right that d pi is strange. I like the idea of the dynasty using different symbols but pi is universal, come on now. I think it makes more sense in context for it to be a dt, which matches the first part of the expression. It's very hard to identify the letters, and I did some wishful interpretation (for example, that 1/l looks a lot like 1/c, but it makes more sense for it to be a different variable). Are there two different Ps? Is there a rho? I don't know.

I don't see how Essek gets to line 2 here, he's skipping a lot of steps in those derivatives. But the second term must be close to 1 (perhaps rho is close to one, and P with mysterious subscript is close to P) so he approximates that term away and is left with 1/p squared! Physicists love to approximate.

Then line three he plugs in some nonsense and brings back the term he just approximated away. What? (I do think it's the same term, it's either a minus sign or a dot product in there and I can't tell which)

Anyway it doesn't matter because now he's arrived at an order of magnitude! It kind of looks like 10^-43 to me which would be... 24 orders of magnitude smaller than the most precise time measurement currently possible (10^-19) seconds. So maybe it's not that. One of the things you learn in physics school is "sanity checks" and if I ever got 10^-43 as the answer to pretty much anything I would assume I had made a mistake. You also learn to USE FUCKING UNITS!

But maybe he does this in the last line? Pr- (or maybe ~) 10^8 y. Could that be 100 million years? The length of time a soul could theoretically survive reincarnation in the absence of Typhros? Alas, we can only speculate.

Hard to tell what any of these symbols are honestly, but this looks like the beginning of a promising integral. Not related to the shaded in plot below it though, since it's integrating a single variable symmetrically across zero. I think the H might be a Hamiltonian, which I'll get to in a bit.

Shout out to the cool rotating circle drawing. Nice job, Essek.

TRIPOD!!!!!!!

Can we use this text as a cypher for the rest of the indecipherable text? No? Moving on.

I put a little note in here because I can sort of make sense of the algebra, if not the math itself. The delta (triangle symbol) is usually a spatial derivative, so it might be taking the derivative of p and M with respect to s, or to some other spatial variables Essek didn't bother to write. The operator that Essek pulled out on the right seems a bit more complicated than just the derivative wrt phi, but we're not seeing the whole expression on the left.

That fancy L may be wishful interpretation on my part, but it's for a reason: a fancy L usually denotes a Lagrangian. The Lagrangian and Hamiltonian are two different representations of the energy of a system. In classical mechanics, you can describe the behavior of variables in a system (like momentum, velocity, etc.) by manipulating its Lagrangian or Hamiltonian in various ways. Usually by taking a derivative!

This is as close we get to coherent physics, so it's kind of exciting. Maybe Essek has somehow figured out the equations of motion for a soul moving through the Beacon.

My overall impression of this is that it's basically nonsense (As are all science chalkboards on TV, yes?), but the symbols are being used correctly. Essek's handwriting is bad, but it's far from the worst I've seen in a physics class. And his diagrams are pretty beautiful, so I think we can assume he was just doing math in a frenzy. I'm sure it makes sense to him. The sins on display here - not writing units, units not matching, writing lines of math next to each other that aren't actually equivalent, writing Ps that look like ps that look like rhos - are all extremely true to life.

I hesitate to speculate at what the variables mean. There are very few letters that are reserved for a single concept in physics, you usually need some context. I love the idea that math is a universal language - Essek's writing is unintelligible and clearly not English, but he's using x and y, sin and cos, etc. But if he's making up variables on the fly as he works this out, who's to say what letters or symbols he would choose to represent those quantities.

This is probably a good time to mention that I probably know less physics now that I have at any point in the last 8 years or so. Getting a PhD will do that to you. I'd be very curious if anyone else can recognize an equation form that I didn't!