@Slereah My first modem was 300 baud. I could type faster than it could transmit without much trouble.
Before that my very first computing experience was on a teletype terminal my father brought home from work occasionally. It talked to the mainframe through an acoustic coupler at 150 baud.
In telecommunications, an acoustic coupler is an interface device for coupling electrical signals by acoustical means—usually into and out of a telephone.
The link is achieved through converting electric signals from the phone line to sound and reconvert sound to electric signals needed for the end terminal, such as a teletypewriter, and back, rather than through direct electrical connection.
== History and applications ==
Prior to its breakup in 1984, Bell System's legal monopoly over telephony in the United States allowed the company to impose strict rules on how consumers could access their...
talk about the influence a father can have on his son:
> I was going to engineering school but fell in love with physics. When I told my father I wanted to be a physicist, he said, "Hell, no, you ain't going to work in a drugstore." I said, No, not a pharmacist. I said, "Like Einstein." He poked me in the chest with a piece of plumbing pipe. "You ain't going to be no engineer," he said. "You're going to be Einstein."
Apparently you can rewrite the EH action via vielbein's as $S = \int d^D x \sqrt{-g} R = \int d^D x e R(e_{\mu} \, ^a, \omega_{\mu a} \, ^b (e)) = \int d^D x e (C_{ca,} \, ^a C^{cb,} \, _{b} - \frac{1}{2} C_{ab,c} C^{ac,b} - \frac{1}{4} C_{ab,c} C^{ab,c})$ with $C_{\mu \nu} \, ^a = \partial_{\mu} e_{\nu} \, ^a - \partial_{\nu} e_{\mu} \, ^b$, but what does $C_{ca,} \, ^a C^{cb,} \, _{b} $ mean, i.e. the , and '
Yeah but I don't see how that makes sense given the way $C$ is defined, if $C_{\mu \nu} \, ^a = \partial_{\mu} e_{\nu} \, ^a - \partial_{\nu} e_{\mu} \, ^b$, then $C_{\mu \nu,} \, ^a = \partial_a (\partial_{\mu} e_{\nu} \, ^a - \partial_{\nu} e_{\mu} \, ^a)$?
(The $b$ should be an $a$ in the $C_{\mu \nu} \, ^a = \partial_{\mu} e_{\nu} \, ^a - \partial_{\nu} e_{\mu} \, ^b$ above, i.e. it should be $C_{\mu \nu} \, ^a = \partial_{\mu} e_{\nu} \, ^a - \partial_{\nu} e_{\mu} \, ^a$)
You can get both calculus and manifolds to be part of commutative algebra springer.com/gp/book/9780387955438 and interpret this insanity in terms of "observables" and "measurements" so maybe that'a route to it
I was told that (Serge) Lang has never fallen in love with categories, to use a polite euphemism. Other people claim that, in some occasion, he has even declared his lack of interest in the subject in a somewhat harsh tone. However, I couldn't find anything (explicit) in his work in favor of thes...
In mathematics, the category of manifolds, often denoted Manp, is the category whose objects are manifolds of smoothness class Cp and whose morphisms are p-times continuously differentiable maps. This is a category because the composition of two Cp maps is again continuous and of class Cp.
One is often interested only in Cp-manifolds modelled on spaces in a fixed category A, and the category of such manifolds is denoted Manp(A). Similarly, the category of Cp-manifolds modelled on a fixed space E is denoted Manp(E).
One may also speak of the category of smooth manifolds, Man∞, or the category of...
So in ZFC a set is not actually a set, it's something restricted, so we can then define a class as another restriction on the idea of a set, because of a paradox, which is just pretending everything is fine it seems to me, idk
I'm happy to just call everything a set and not worry about the monsters of set theory
"The assumption that any property may be used to form a set, without restriction, leads to paradoxes. One common example is Russell's paradox: there is no set consisting of "all sets that do not contain themselves". Thus consistent systems of naïve set theory must include some limitations on the principles which can be used to form sets."
"ZF set theory does not formalize the notion of classes, so each formula with classes must be reduced syntactically to a formula without classes", maybe this is why I have no idea what a class is
"a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share", i.e. a set of sets that can be defined without monsters it seems like
Yeah, up until that axiom I think I got the sense you were defining things that would end up letting you do factorization and/or other basic NT stuff, I forget the details and thought it was half-crazy, will look into Peano arithmetic
There was a time I really needed to know those axioms cold and took it really seriously constructing $\mathbb{R}$ from ZFC as much as I could to get practice at abstraction but at the end of the day who cares once you have the jist, string theory is where the action is at (hmm)
$$0 \in \Bbb N$$ $$\forall x \in \Bbb N, x = x$$ $$\forall x, y \in \Bbb N, x = y \equiv y = x$$ $$\forall x, y, z \in \Bbb N, x = y \wedge y = z \equiv x = z$$ $$\forall a, b, b \in \Bbb N \wedge a = b \to a \in \Bbb N$$ $$\forall n \in \Bbb N, S(n) \in \Bbb N$$ $$\forall a, b \in \Bbb N, a = b \equiv S(a) = S(b)$$ $$\nexists n, S(n) = 0$$
@bolbteppa I always thought the fact that [X, Y] is a vector field is more intuitive when written in coordinates (the mixed partials cancel off, so you only remain with 1st order derivatives) than doing the derivations calculation
We are doing Lorentz-invariant Lagrangian field theory in Minkowski spacetime, and I'm now considering only the form of Noether's theorem where the fields are varied.
Assume that $\delta \phi$ is a symmetry of the Lagrangian. The variation is of the form $\phi_\epsilon(x)=\phi(x)+\epsilon a\delt...
Not really, my sense is that you're trying to set up concepts in a way that applies to multiple areas at once, e.g. group extensions applying to Lie algebras with modifications but the same idea 'really', or prove, say, 'Cayley's Theorem' from group theory in a way that applies to multiple structures at the same time, resulting in Yoneda's Lemma
Let $M, N$ manifolds without bundary and $f: M\to N$ and $g: M\to N$ embeddings. We say that a differentiable map $h: [0,1]\times M\to N$ is an isotopy between $f$ and $g$ if each of the maps $h_t:M\to N$ with $h_t(x) = h(t,x)$ is an embedding and $h_0=f, h_1=g$.
By a diffeotopy of a manifold...
"Finally we remark that it is sometimes desirable to glue together two parts of the boundary of the same manifold. If the parts are disjoint, ,we can use disjoint tubular nbds to effect this. "
This paper's pretty good
too bad it was written on toilet paper
So I'm pretty convinced that the cut and paste wormhole bullshit makes sense now
Though I don't know if the Israel junction thing does make sense
Also I need to check that the smooth structure is fine too because IIRC you have to smooth out the gluing