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Isochronous Curves

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Re: Isochronous Curves

#41

Post by creato »

neverhigh wrote: post #26
tacon wrote: post #22

The same term has been adopted in transportation planning, for the curves of equal commute time to a job location, etc. Google has an incredible amount of data about this, but I don't know that it has been made available in any usable form.

Google offers it on a bilateral basis for cash. Resources of http://iso4app.net are great and prices are ok.

This comment is pretty interesting, it's almost indistinguishable from the "I work from home and make $10k a week!!" facebook posts plaguing comment sections... but it might make legitimate sense in context!

The only way to find out is to click the link.

edit: And it's legit!

Re: Isochronous Curves

#42

Post by enriquto »

ur-whale wrote: post #37
mlthoughts2018 wrote: post #34

Earlier quoted context omitted.

The variational representations used in image processing are much more complicated than you suggest. In many cases, they are developed with semantic models that inform grammars of what the image can be composed of, and directly model things like occlusion, cusps, edges, blur, etc., when postulating a joint functional space that can describe the “energy” of an image, which then minimizing gives not only pixel values b…

>The variational representations used in image processing are much more complicated than you suggest Fair enough, but my main point stands: has anyone tried to apply Euler-Lagrange and a PDE solver to the problem of training a deep net or is it obvious that backprop-based methods will work better?

not exactly the same thing, but here you have a "Deep Neural Networks motivated by Partial Differential Equations", that may pique your interest

https://arxiv.org/abs/1804.04272

Re: Isochronous Curves

#43

Post by ehsankia »

creato wrote: post #41
neverhigh wrote: post #26

Earlier quoted context omitted.

Google offers it on a bilateral basis for cash. Resources of http://iso4app.net are great and prices are ok.

This comment is pretty interesting, it's almost indistinguishable from the "I work from home and make $10k a week!!" facebook posts plaguing comment sections... but it might make legitimate sense in context! The only way to find out is to click the link. edit: And it's legit!

Aren't half the comments on HackerNews basically "I work on a similar project, check out my project"? Although extra suspicious when it's a green user.

Which to be fair, I'm entirely fine with as long as the projects are legitimate. In the world of programming, there are so many cool and useful libraries, services and tools out there that you have little hope to find out about them otherwise.

Re: Isochronous Curves

#44

Post by tobr »

quietbritishjim wrote: post #5
lifeisstillgood wrote: post #4

Is this off the back of a video of a 1970s Open University style presenter showing the properties of isochromus curves - i loved watching it and realised that these are national treasures of programs - and also was quite stunned by the assumption one would have a round empty tobacco tin lying around to do the experiment with - times do chnage :-)

I suspect it is... It turned up in my YouTube suggestions yesterday. Here's a link: https://youtu.be/eBc827pwKf0

Wow, I was recommended and watched this yesterday as well.

Re: Isochronous Curves

#45

Post by ur-whale »

montalbano wrote: post #39
ur-whale wrote: post #2

Variation calculus is a great lens through which to look at many physics and CS problems. It is IMO under-taught and under-utilized, especially in the machine learning discipline. The framework is basically minimization in functional space (as opposed to R^n or a subset thereof, the more common case). The (to me) surprising thing is that finding an extremum in functional space (i.e. infinite-dimensional space) can be…

Feynman on Calculus of variations: “When I was in high school, my physics teacher—whose name was Mr. Bader—called me down one day after physics class and said, ‘You look bored; I want to tell you something interesting.’ Then he told me something which I found absolutely fascinating, and have, since then, always found fascinating. Every time the subject comes up, I work on it. In fact, when I began to prepare this lec…

If physics is your thing, and it certainly was Feynman's, it'd be hard not to be fascinated by the calculus of variations, it shows up all over the place:

   - principle of least action (lagrangians)
   - adiabatic cycles in thermodynamics
   - quantum mechanics
   - etc..
and I'm probably missing another 100.

Looks like it's a fairly fundamental thing in the world.

Re: Isochronous Curves

#46

Post by SamReidHughes »

agumonkey wrote: post #8
davidmurdoch wrote: post #3

Adam Savage builds a brachistochrone curve, which is the same curve as an Isochronous, just with potentially different starting/ending points, with Vsauce's Michael Stevens. It's a pretty bizarre phenomenon: https://youtu.be/skvnj67YGmw

They should build tautochronous pendulums. Or just add a spring bouncer on the end of the tracks so to enjoy multiple simultaneous bounces of different heights.

The pendulums have been done. https://www.theatlantic.com/technology/archive/2016/01/pendu...

Re: Isochronous Curves

#47

Post by karussell »

tacon wrote: post #22

The same term has been adopted in transportation planning, for the curves of equal commute time to a job location, etc. Google has an incredible amount of data about this, but I don't know that it has been made available in any usable form.

Not really the same term as it is called isochrone map https://en.wikipedia.org/wiki/Isochrone_map and the curves are more popular under "brachistochrone"

( Shameless plug - an open source implementation of it: https://github.com/graphhopper/graphhopper#for-analysis )

Re: Isochronous Curves

#48

Post by tprice7 »

monochromatic wrote: post #12
agumonkey wrote: post #8

Earlier quoted context omitted.

They should build tautochronous pendulums. Or just add a spring bouncer on the end of the tracks so to enjoy multiple simultaneous bounces of different heights.

For small displacements, pendulums are already approximately isochronous.

Hence pendulum clocks.

Re: Isochronous Curves

#49

Post by saagarjha »

agumonkey wrote: post #9
ur-whale wrote: post #2

Variation calculus is a great lens through which to look at many physics and CS problems. It is IMO under-taught and under-utilized, especially in the machine learning discipline. The framework is basically minimization in functional space (as opposed to R^n or a subset thereof, the more common case). The (to me) surprising thing is that finding an extremum in functional space (i.e. infinite-dimensional space) can be…

I remember a physics problem where teacher explained that a ball on different paths, even if the height differences would sum to zero would arrive at different times. I often think about this when planning car drives because I believe you could make better use of gravity and use less fuel.

> I remember a physics problem where teacher explained that a ball on different paths, even if the height differences would sum to zero would arrive at different times.

A good way to think about problems such as these are to look at the extreme cases. In this case, consider a flat plane: the ball takes infinite time, since it never rolls at all. And the fastest path would be a valley (though, as far as being v-shaped as possible), with the ball accelerating part of the way and decelerating at the end, spending the majority of the time at a high speed.

Re: Isochronous Curves

#50

Post by hyyypr »

quietbritishjim wrote: post #5
lifeisstillgood wrote: post #4

Is this off the back of a video of a 1970s Open University style presenter showing the properties of isochromus curves - i loved watching it and realised that these are national treasures of programs - and also was quite stunned by the assumption one would have a round empty tobacco tin lying around to do the experiment with - times do chnage :-)

I suspect it is... It turned up in my YouTube suggestions yesterday. Here's a link: https://youtu.be/eBc827pwKf0

Me too, this morning.
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