Statistics are fun: The five quarterbacks drafted at No. 22 have combined for 123 NFL starts with 127 touchdown passes, 141 interceptions and 25,140 career passing yards. [Steelers quarterback Ben] Roethlisberger has started 158 regular-season games with 251 touchdown passes, 131 interceptions and 39,057 passing yards.
@StanShunpike (1) played 25 games in 5 years, (2) played 46 games in 7 years, (3) played 28 games in 3 years, (4) played 5 games in 1 year, and (5) played 54 games in 11 years
@StanShunpike No, forms are antisymmetric - they are constructed as wedges of the basic $1$-forms/tensors $\mathrm{d}x$ (In degree 1, tensors and forms/exterior elements coincide)
This is really just an addendum to David's answer.
The motion of an airplane is dominated by it's interactions with the atmosphere, and any Coriolis force is utterly negligable compared to this. Even for an airplane like Concorde,
which could achieve comparable speeds to a bullet, you are never...
@ACuriousMind Exercise: "Determine the homology groups of a complex of two points." My solution: The 0-chain group $C_0(K)$ is just the linear combination of two 0-simplexes, and is thus isomorphic to two copies of the integers. The 0-cycle group is equal to the 0-chain group because all 0-simplexes are 0-cycles. The 0-boundary group is empty because points are not boundaries of any simplex in the complex. Thus $$H_0(K):=Z_0(K)/B_0(K)=(\oplus^2\mathbb{Z})/\emptyset=\oplus^2\mathbb{Z}$$
The others are trivially empty because $Z_n$ for $n>1$ is trivially empty.
@0celo7 If you think of cohomology as all coming from Stokes theorem, where the emphasis is on the differential forms you're integrating, then cohomology is just the same theory where the emphasis is on the domain of integration you integrate the form over, that's why all the chains and complexes are defined the way they are, it's all just Stokes theorem with fancy words but it lets you do cool things I think
I was trying to look up the rho symbol my book uses (turns out it was $\varrho$ or some font variant of that) and so I googled "curvy rho" without thinking and got a porn star...
@ACuriousMind I have have two solid rings stacked on top of each other, is the moment of inertia of the whole thing the sum of of the moments of the rings by themselves?
If you do the calculation for one ring, and then another (thicker) one that is like the two rings, I think you will find it is 2X the first (assuming the rings are the same size).
I do not understand a Wick rotation, it literally looks like magic, just setting $\tau = -it$, and okay I'm sure there's some topological reason why you can't do it sometimes, but it still looks like nothing more than that baby change of variables no?
I know 'analytic continuation' is the fancy way of saying it
@bolbteppa It is nothing more than a change of variables as long as the functions you have are uniquely defined as complex function by their values on the real (or imaginary) axis. It can hypothetically fail in cases where the functions cannot be continued to the
@bolbteppa Mh, it can happen that the analytic continuations exist, but are not really unique because defining stuff only on the axis does not force two continuations to be equal, since the axis is not open in the plane. If you can show that the function is uniquely extendable to an open subset of the plane, then all continuations will be unique
So, there are subtle issue, but mostly, you can indeed just replace $x$ by $z$
@bolbteppa If you liked this, you'll probably love complex analysis as a whole. All kinds of situations where "trivial" information turns out to give you everything
On a related note: Does anyone have a good recommendation where I should go to study complex analysis (book-wise)? I'm not too psyched to try "big Rudin"
@Danu thanks I know tons of complex, the two best books are Goursat & Needham, I just never seen this topological argument as explaining the issues in going from R to C
This is really just an addendum to David's answer.
The motion of an airplane is dominated by it's interactions with the atmosphere, and any Coriolis force is utterly negligable compared to this. Even for an airplane like Concorde,
which could achieve comparable speeds to a bullet, you are never...
