The h Bar

12:01 AM

Yep

Built a collaborative filtering algorithm the other day

I think what he means is

\begin{align}
L_{\mu}(\partial x, \partial^2 x) &= \dfrac{\partial}{\partial \tau} (\dfrac{\partial \mathcal{L}}{\partial \dot{x}^{\mu}}) + \dfrac{\partial}{\partial \sigma} (\dfrac{\partial \mathcal{L}}{\partial x'^{\mu}}) \\
0 &= L_{\mu}(\partial x, \partial^2 x) \dot{x}^{\mu} \\
&= [\dfrac{\partial}{\partial \tau} (\dfrac{\partial \mathcal{L}}{\partial \dot{x}^{\mu}}) + \dfrac{\partial}{\partial \sigma} (\dfrac{\partial \mathcal{L}}{\partial x'^{\mu}})]\dot{x}^{\mu} \\
&= [\dfrac{\partial}{\partial \tau} (\dfrac{\partial \mathcal{L}(\dot{x},x')}{\partial \dot{x}^{\mu}}) + \dfrac{\parti…

Which is a really weird, though apparently completely general, way of proving the Hessian is zero for two eigenvectors that completely avoids Qmech's proof

bolbteppa

12:53 AM

0

A: How to find the rank of the matrix $\frac{\partial ^2\mathcal{L}}{\partial \dot{X^\mu} \partial \dot{X^\nu} }$ for the Nambu-Goto string Lagrangian?

A general proof applying to reparametrization-invariant actions $$S = \int d^2 u \mathcal{L}(x^{\mu},x_{,i}^{\mu}), \ \ \ \ i = 0,1, \ \ \ \mu = 0,1,\dots, D- 1,$$ is to note that part of the derivation of Noether's theorem (the derivation where you assume the volume element varies also), schema...

Work of art

HsMjstyMstdn

2:20 AM

The absolute legend Jon Skeet hit 6 orders of magnitude of reputation on StackOverflow... When's our own Jon Skeet (John Rennie) going to do the same ??

Lol jk

Although I'm not a very active user, I just wanted to say thanks, @JohnRennie. Your questions, answers, comments, attitude and contributions in general have helped (and continue to help) me in my studies and in my life.

ooolb

2:33 AM

interesting choice of last name

0celo7

skrt

vzn

4:01 AM

@enumaris cool, would like to hear more & think others would too with speaker session in all your copious spare time :P ... ps would be interested to hear what you think of this (or other resident coders/ hackers/ intellectuals/ academics/ scientists etc)

in theory salon, Jan 5 at 2:45, by vzn

secret/ blueprint/ path to AGI: novelty detection/ seeking / Tmachine blog

Kane

4:26 AM

what happens if I take a measurement and get a 1% uncertainty i.e. the value is 500 Hz with uncertainty of 5 Hz. What happens to the uncertainty if I do this: y = 1 / 500 Hz. What is the uncertainty of y?

Secret

in Mathematics, 2 mins ago, by Secret

Therefore, one immediate consequence of being in a universe with a different value of $\pi$ is that you need to use more/less material to build some circle with a desired circumference

in Mathematics, 1 min ago, by Secret

and this can affect the length of rope you need to use for your pulley system, or the number of charges you can place in a storage ring as well meany other things...

Secret

4:50 AM

Last night dream, JohnRennie and I discussed about classical machines. A user then asked him certain questions, which he then posted a picture of some aircraftin a warehouse where its wings are attached with gears and mentioned how this is a counterexample because if the chain of gears are rotated clockwise, then the tri-ponged shaped gear become disengaged and thus not rotating. Only if the chain of gears are rotated clockwise will the full set of gears rotate.

He then mentioned that this is an example of a noncommutative gear system.

A bit earlier in the transcript, he posted a picture showing nonassociative gear systems, where the order of rotating the gears matter in that some gears will become disengaged when rotated in the wrong order

Finally, I asked him about whether there are other examples of simple (classical) machines that has this noncoummatative property as machines like levers, wheels don't have that. Johnrennie then mentioned that he only knew that the ancient civillisation had only ever made one such craft, implying that gears are unique in doing so.

enumaris

5:25 AM

hmm

Secret

The two pictures posted by Dream Johnrennie, reproduced as close as I can with my drawing ability (In the dream, they are actually photorealistic)

(NB Yes, I get the gear size wrong in the aircraft picture, there are actually 8-9 on each wing)

John Rennie

6:49 AM

@SirCumference It depends on the initial conditions. If you start with a Big Bang then only a universe with positive curvature can recollapse - NB recollapse.

If you start with a universe that started in the infinite past with a negative value of $\dot a$ then it will collapse.

Both of the above assume no matter with weird equations of state is present.

you might argue that a universe starting in the infinite past with a zero or negative value of $\dot a$ is a silly initial condition, and I'd probably agree with you. But then a universe starting at a finite time in the past with an infinite density isn't an especially sane initial condition either :-)

Secret

7:11 AM

It is still an open question whether bounded infinite sets and finite time blowups can exist physically in some form in reality

Rick

7:33 AM

How is $\overrightarrow{v} = \frac{\overrightarrow{p}c^2}{{E}_k}$?

My ${E}_k = \sqrt{(mc^2)^2 + (|\overrightarrow{p}|c)^2}$

John Rennie

@Rick It's $p^2c^2$ not $pc^2$

Rick

8:07 AM

yeah..I wrote it as $(pc)^2$

Physics Meta

1

Q: statistics on question types

I have been here long enough to recognize that most of the questions posted here fall into a short list of different classes. examples: obvious homework or exam questions, high-level mathematical physics enquiries, crank/goofball stuff, everyday physics, off-topic (engineering, electronics, etc.)...

discussion

John Rennie

@Rick not in your first equation you haven't ...

Presumably you meant $$ \overrightarrow{v} = \frac{\overrightarrow{p}c}{{E}_k} $$

Oh hang on ...

Transcript for