I don't get why mobile is taking over market space on the internet, it is such a horrible platfor, like a toy with no easy root access... I fear for the price of desktops in the future!
Yeah it's good to look where a bar is or what a menu says when travelling but bad for the FLOPS, memory, readability, writing real texts and your upper back!
To define geometric objects on a manifold, like tori, you can chop then up into simpler pieces, like chopping up the tori to a simpler square and identifying the endpoints, but these simpler pieces are linked to discontinuous groups, as with elliptic functions, but now we've linked groups to tori, so we're apparently one step away from the 'fundamental group'
@G.Bergeron "I don't get why the masses are not as nerdy as me, and I refuse to design for them" is a persistent problem, at all levels, in silicon valley.
yes, people want a device that works for them where and when they need it, not something with obscure features that will end up bricking their device because they're not steeped enough in the arcane knowledge needed to handle root competently
@bolbteppa I'll be specific; the part which I think sounds nonsensical to me is "but these simpler pieces are linked to discontinuous groups, as with elliptic functions, but now we've linked groups to tori, so we're apparently one step away from the 'fundamental group'". Can you point me out to where you got that from?
That link gives a summary of Poincare's book, skim pages 132-134, describing sections 10-12 of Poincare's book, one thing is section 12 of Poincare says, first sentence "We are led in this way to the notion of fundamental group of a manifold" which is not in this paper
and the intro to Poincare's book gives some more explanations, saying his perspective is a bit different but equivalent to the modern view, but more linked to discontinuous groups
@skullpatrol Perhaps more pointedly the only thing that the masses can do with root access is screw things up. Not having it protects them from themselves.
I have to root my phone because I'm out of space. Not because there isn't enough storage, but because ~25% of it is taken up by app I don't use but the manufacturer has left in the manifest.
Even though they have discontinued any support for the device.
@bolbteppa Mmm I see. Here's what my correction of your statement, which I have better perspective on now, would be: Any 3-manifold can be reconstructed from simpler pieces (you're right on this) modeled by quotients of the Euclidean space by a discrete group of actions (I see what you mean by discontinuous groups now). Also this is not quite how he recovers the fundamental group: section 12 actually describes it as a group whose elements are linear combination of loops on the manifold.
@G.Bergeron The only time I've even needed to really diddle a linux distro is when I wanted to use a minimalist window manager and raw X on a legacy machine and the distribution really, really wanted me to chose a fancy descktop environment that would have eaten all the ram on the machine.
@EmilioPisanty Never heard of it myself. The CC pages has always had the form where the hypenated group specifies the riders exactly.
@G.Bergeron Yep, stated in more concrete terms, it seems. It feels like he starts off with coordinate functions $f_1, \cdots, f_n$ on the manifold $M$ and considers the loops $\gamma$ which generate the fundamental group $\pi_1 M$ to be the ones such that $f_i$ has nontrivial holonomy along $\gamma$ (i.e., $\gamma$ lifts to a path with distinct endpoints in the universal cover).
@dmckee I don't think your question is a good way to demonstrate that coordinate speed has no absolute meaning. What I would do (and maybe will do) is start with the Schwarzschild metric then use a transformation to convert the metric to shell coordinates.
@BalarkaSen I think the natural link is, as the the intro written by Stillwell in Poincare's book says, the sides of say a square being identified - on a quotient surface (hence the link to discontinuous groups) the sides come together and form a closed curve, and this is how he thought of the fundamental group, and something to do with translations, it's a mess but he seen this as obvious apparently
@dmckee Then you can show that both the Schwarzschild and shell observers agree that the local speed of light is $c$ but disagree about the coordinate speed at all other locations.
@dmckee Since the transformation is purely algebra and involves no assumptions about the definitions of the meter and second this demonstrates that the coordinate speed has no absolute meaning.
@G.Bergeron It's more than that, actually, because he also talks about the transformation of local coordinates under holonomy about those nontrivial homotopy classes! So it seems he also found out the definition of fundamental group as deck transformation group of the universal cover $\widetilde{M} \to M$
My sense is rigor will let you start from the simple stuff and get to all this fuchsian stuff later, and that's cool, but these guys started from the fuchsian stuff and waved their hands and it all worked out
@dmckee Though it should be obvious to any but the completely brain dead that since coordinate speed is a 3-vector not a 4-vector it cannot possibly be a covariant quantity.
Hey @creativecommons, was there ever a time when the term "CC-Wiki" was an acceptable substitute for "CC BY-SA"? (& if so, until when?) I'm preparing a strongly-worded letter about infringement and I'd like to have that background solid.
@JohnRennie Such arguments are nice for people who have encompassed the mathematical structure of physics, but they come across as simple argument from authority for people whose exposure is purely poop-sci.
My guess is one is able to explain category theory in a way that taught you at least 6 subjects all at once and learn them simultaneously, it just needs to be written
@dmckee we get claims that confuse the coordinate speed of light with a covariant quantity from people who have ostensibly encompassed the mathematical structure of physics too
@JohnR And I am interested in having something to point to in the event that "relentlessly inaccurate" (to quote that authoritative figure D. Adams) information gets posted over and over again.
@G.Bergeron Oh ... I think that might be a archaic (or at least very rare usage). Something is "within ones compass" when you understand of grasp it, and following from that to encompass an idea is to learn it well or completely.
@dmckee Yeah I understood his sentence from context, but to me it meant something like ''above and around'' (figuratively speaking). But yeah, english is not my first language.
Within the context of isolated converters, the flyback topology is nice in its simplicity as can be the forward topology, in spite of needing a second primary reset winding. However, both make poor use of the transformer core in as much power is not continuously passed through the transformer. Wh...
Oh, well... I wanted to do that to show the mathematics in electronics for undergrads, but yeah I'm afraid my chaotic oscillator might just stop wanting to oscillate
Analog circuits always are a function of your temperament, the captain's age, and wether you had coffee this morning or not
