
Feynman's Lost Lecture (ft. 3Blue1Brown) [video] - espeed
https://www.youtube.com/watch?v=xdIjYBtnvZU
======
delecti
One of the most incredible feelings is when you make that new connection of
understanding on an idea. Sometimes it's when two things you knew get
connected in a way you didn't think existed, and sometimes it's when a
complicated idea all fits into place in your mind. It's probably the drug that
keeps people programming despite all the configuration hell we have to deal
with on any non-trivial project (and even most trivial ones).

Every single one of 3Blue1Brown's has given me a big hit of that new brain
connection drug. If you enjoy this video, I recommend checking out
3Blue1Brown's video "What does genius look like in math? Where does it come
from? (Dandelin spheres)", which deals with how and why ellipses and conic
sections are related.
[https://www.youtube.com/watch?v=pQa_tWZmlGs](https://www.youtube.com/watch?v=pQa_tWZmlGs)

~~~
knrz
I love the feeling you're describing! The understanding of an abstraction (or
in other words, a mental model) that links two parallel thought processes in
an unexpected, and fun way.

I like the term Kensho [0], thought you might too. Interested in thoughts from
other people as well.

[0]:
[https://www.lesswrong.com/posts/tMhEv28KJYWsu6Wdo/kensho](https://www.lesswrong.com/posts/tMhEv28KJYWsu6Wdo/kensho)

~~~
Jarwain
I like the concept of kensho. I find the idea that certain ideas can only be
accurately conveyed through experience to be interesting as well.

I'm working my way through a book called "The Book Of Secrets", which has 114
different meditative techniques for different kinds of minds. One of which, is
practically certain to work for any given individual.

------
stcredzero
3Blue1Brown is one of the best math educators on YouTube. As a matter of fact,
I would say he's the best I know of at the moment. I'm currently working my
way through his series on diff-eq.

~~~
seanc
I can certainly say that no one else has made me tear up.

~~~
adito
His later video where in the outro he mentions about going sponsor-free is the
one that made me tear up

[https://www.youtube.com/watch?v=rB83DpBJQsE&feature=youtu.be...](https://www.youtube.com/watch?v=rB83DpBJQsE&feature=youtu.be&t=1062)

Here's a little bit of quote from the video:

=====

So... typically this is the part where there might be some kind of sponsor
message. But one thing I want to do with the channel moving ahead is to stop
doing sponsored content, and instead make things just about the direct
relationship with the audience.

I mean that not only in the sense of the funding model, with direct support
through Patreon, but also in the sense that I think these videos can better
accomplish their goal if each one feels like it's just about you and me
sharing in a love of math, with no other motive, especially in the cases where
viewers are students.

=====

He's really a good person. I'm glad that now he is able to do this full-time
by just the support from his patreon.

~~~
MrQuincle
Yes, right then I finally thought I've to figure out this patreon thing. He
deserves it.

------
seanc
For those who want to support this work Grant has a patreon page:

[https://www.patreon.com/3blue1brown](https://www.patreon.com/3blue1brown)

~~~
tobmlt
Thanks for pointing that out. I'm a 1st time patreon thanks to you. This video
jiggled so many good mathy connections.

------
fapjacks
Grant (3Blue1Brown) sounds _exactly_ like a friend of mine named Brad. Just
absolutely uncannily sounds exactly like him, even in his intonations and
quirks. I've been watching his videos for over a year and using his epiphany-
driving videos as the triggers to dig into specific subtopics of math that I
used to hate (\ _cough\_ calc2\ _cough\_ ). Turns out _I love math_ and not
just discrete math!

Anyway, my funny story about my friend Brad. I have convinced our circle of
friends that Brad is actually the guy doing the 3Blue1Brown videos. He's
hilarious and just started playing along at dinner one night without even
knowing what I was talking about. So most of our friends now think Brad's got
a huge but secret Youtube channel where he teaches incredibly insightful math
perspectives.

~~~
dawidw
Maybe your friend Brad is 3Blue1Brown and uses alias Grant?

~~~
baodau
Now you want to beat him is his own game?

------
barcadad
There are times when I watch his videos that I wonder whether he could be an
alien from an advanced civilization sent here to help accelerate our
mathematical understanding and reach the singularity sooner. His explanations
are 5 standard deviations better than average.

------
espeed
A similar concept related to elliptical constants and proportional areas, is
the curve formed by the cycloid [1] of a circle, which is the curve formed by
tracing a point on the circumference of a circle as it rolls across a surface
from point A to point B.

For example, the fastest distance between two points is not a straight line,
it's the cycloid, specifically the Brachistochrone curve [2]. This is the path
light follows.

One common misconception of the cycloid is related to its arc-length. At first
glance many assume the arc-length of the cycloid is equal to circumference of
the circle, but this is not the case. The line-of-sight distance between the
cycloid starting point A and ending point B _is_ equal to 2πr, the
circumference of the circle -- however the arc-length of the cycloid curve is
8r, which is an integer value given an integer radius. The cycloid curve is
full of interesting properties, many yet to be discovered and all its
implications are not yet fully understood.

Another interesting aspect of the cycloid is not only is it the fastest path,
but no matter where two objects begin on the curve, they'll both traverse the
curve at maximal/optimal speed and both will arrive at the bottom of the curve
_at the same time_ , regardless of the delta between their starting positions.
This aspect of the cycloid is referred to as the Tautochrone curve [3].

So if you're looking for ways to distribute partitions or encode invariants in
your models, data or otherwise, the geometrical aspects of elliptical and
cycloidal curves are a good place to explore.

Grant did a 3Blue1Brown video with with Steven Strogatz on the Brachistochrone
a few years back:
[https://www.youtube.com/watch?v=Cld0p3a43fU](https://www.youtube.com/watch?v=Cld0p3a43fU)

And Vsauce did one with Adam Savage on the Brachistochrone where they build a
mechanical model of one that shows it's the fastest/optimal path among
different curves, and their experiment also shows the cycloid Tautochrone
invariant property where objects begin up the curve at different distances
apart and yet all arrive together simultaneously in constant time.
[https://www.youtube.com/watch?v=skvnj67YGmw](https://www.youtube.com/watch?v=skvnj67YGmw)

NB: Consider this, two seperate impulses of light beginning at different
distances away from the observer, both impulses of light traveling along the
optimal path at the optimal speed, and both arriving at the observer
simultaneously, without bending time. And as shown above, on a cycloidal
curve, this phenomenon is not unique to light.

[1]
[https://en.wikipedia.org/wiki/Cycloid](https://en.wikipedia.org/wiki/Cycloid)

[2]
[https://en.wikipedia.org/wiki/Brachistochrone_curve](https://en.wikipedia.org/wiki/Brachistochrone_curve)

[3]
[https://en.wikipedia.org/wiki/Tautochrone_curve](https://en.wikipedia.org/wiki/Tautochrone_curve)

~~~
speleo
>For example, the fastest distance between two points is not a straight line,
it's the cycloid, specifically the Brachistochrone curve [2]. This is the path
light follows.

You may be conflating [Bernoulli's solution to the Brachistochrone
curve]([http://www.math.rug.nl/~broer/pdf/ws-
ijbc.pdf](http://www.math.rug.nl/~broer/pdf/ws-ijbc.pdf)) with the optimal
path for light. [Fermat's
Principle]([https://en.wikipedia.org/wiki/Fermat%27s_principle](https://en.wikipedia.org/wiki/Fermat%27s_principle))
states that, when traveling between two points, light will always take the
path that minimizes the time taken from the first point to the last. In a
medium of constant refractive index (which includes free space), this results
in a line.

>So if you're looking for ways to distribute partitions or encode invariants
in your models, data or otherwise, the geometrical aspects of elliptical and
cycloidal curves are a good place to explore.

How do you mean? What sort of data can be encoded this way and how?

> NB: Consider this, two seperate impulses of light beginning at different
> distances away from the observer, both impulses of light traveling along the
> optimal path at the optimal speed, and both arriving at the observer
> simultaneously, without bending time. And as shown above, on a cycloidal
> curve, this phenomenon is not unique to light.

Two separate impulses of light beginning at different distances away from a
stationary observer will necessarily arrive at different times, otherwise you
violate the basis of special relativity: the speed of light is constant and
invariant of reference frame.

~~~
taejo
You can solve the brachistochrone problem using Fermat's principle, as shown
in the 3blue1brown video GP is referring to. Since you're looking for the
shortest time, if you can construct a lens where the speed of light is
proportional to the speed of the bead on a wire, then the shortest-time wire
is the path that light would take by Fermat's principle, and then you can use
(an infinitesimal version of) Snell's law to find the direction of the wire at
each height.

~~~
speleo
Yes, but they were saying:

>For example, the fastest distance between two points is not a straight line,
it's the cycloid, specifically the Brachistochrone curve [2]. This is the path
light follows.

Which is not true for free space, or any space with a constant index of
refraction.

~~~
taejo
Oh yes, they do seem to be confused! espeed, if you happen to read this, the
brachistochrone is the fastest path for something _accelerated by a constant
force_ (e.g. gravity near the surface of the earth).

------
shawn
If you haven't seen it yet, Feynman's podcast series _The Character of
Physical Law_ is quite wonderful:
[https://www.youtube.com/watch?v=j3mhkYbznBk](https://www.youtube.com/watch?v=j3mhkYbznBk)

~~~
stan_rogers
You mean the Messenger Lectures of 1964? I don't think they were originally a
podcast.

~~~
shawn
Podcasting was one of Feynman's lesser known discoveries. They would mail the
whole spool of film to your doorstep.

~~~
cema
That would be an invention.

~~~
quakeguy
It was Done Daily, the Services had extensive labs handling film.

------
korbonits
> One of the most incredible feelings is when you make that new connection of
> understanding on an idea

To paraphrase the ongoing meme on twitter, it's better than sex

~~~
jdironman
Or as Gov. Schwarzenegger once said in regards to how he felt when he worked
out, or went on stage.

~~~
tobmlt
I think I need to quote guy who inspired 3blue1brown's video now too: "Physics
is like sex: sure, it may give some practical results, but that's not why we
do it." R.P. Feynamn, you are missed.

