動画数：214件
- Intro
why does bro have the channel logo on his eye 💀
How do you manage to have that visual environment in parallel and interact with this same environment.
clear view of the iconic eye! I didn't know it was actually exactly as in the icon! I thought there was a 3:1 ratio between blue and brown, maybe randomly distributed as spots. But it is pretty much exactly as the icon!!
finally the 3blue1brown eyes
- Hello World
*Revelation *Behold, I stand at the door, and knock: if any man hear my voice, and open the door, I will come in to him, and will sup with him, and he with me.
Anyone knows how to set that up? Or is it even possible in the community version?
In you've mentioned that you like having this jupiter-esque feeling to the code, while it's still a single file
- Coding up a Lorenz attractor
love that "I guess one thing I should mention before we move on" is identical conversation and in explainer videos. I really thought it was narration over the video:)
classic programmer moment when presenting a project XD
Showing your past ChatGPT chats like that is brave
nice to see some of chat gpt history from grant
Revelation -14And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be.I am Alpha and Omega, the beginning and the end, the first and the last.Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
this is because you've upgraded to Python 3.12 which includes PEP 709 "comprehension inlining". Comprehensions are now running in the same scope
- Add some tracking points
for any C++ devs interested in the zip command, you might be interested to know a zip view was added to the ranges library in C++23
lmao someone in the background forgot to save and their PC crashed right?
- The globals().update(locals()) hack
In python there is a `nonlocal` and `global` keyword which helps python to look for the variable(s) that's after the keyword
At I think you could have written:print(f"{f(10)=}")
One of python’s core philosophies is “were all consenting adults” (really) - and this is a good example.The idea being to not artificially enforce access rules and leave it to the programmer (and convention) to decide. Hacks like this serve a valid purpose for the context!
"it's not as dangerous" goes on my list of famous last words
- absolute horror! The atrocity of the thing in front of me is incalculable! The rate of change in my brain's capacity to think has gone to infinity and the area has somehow become negative! :Shock: and :horror:
Regarding the list comprehension: from the REPL in the bottom right I see you're now on Python 3.12. One of the changes in 3.12 is PEP 709, making list comprehensions are fully inlined as a performance improvement. A side effect is that they have access to the same scope as they're placed in, while they used to effectively be a single-use function call to their own inner scope.
Regarding the Ipython scoping "bug", I have a strong suspicion it's because it works the same way the eval() builtin does.In python3, if you dynamically evaluate some code and specify anything inside of the locals=some_dict parameter of the eval function, you get this unusual behavior where sub-scopes don't seem to be able to access variables defined in the same scope as they are (it's particularly annoying with lambdas).Declaring the variable you use that's from outside the scope as global with the "global" keyword does also resolve the issue (because it's properly moved into the global scope, where it would have usually been), but it is nowhere near as convenient as the cursed globals().update trick
the reason why this "bug" has been "fixed" is due to a change in the Python bytecode on how list comprehensions work. Previously, they would be translated to some sort of fake function with its own scope, but in 3.12, it has been changed for performance reasons, hence the issue disappearing.
I love cursed lines, you can't stop doing them but never stop talking about them.
I think the reason the bug with the list constructors doesn't appear anymore ( ) is because they changed their inner workings in some of the newer python versions (I think 3.12).
why not define the variable as non local in the function definition?
- Final styling on the scene
OK WTF I did not realize he actually has a quarter brown in his right eye. That's INSANELY COOL 😭😭
How is your camera rotating if you no longer have .reorient in the play function?
In it looks like the tail is not starting from the dots, but lagging behind. Is this the expected behavior?
- Rending the scene
Why are the paths so much more jagged here when they were very smooth a moment ago?
- Adding equations
what is the R followed by triple quotes? Is that a python thing?
on Wikipedia and generally speaking on websites rendering tex in browser you can often just copy the alt text or right-click on the image to export the underlying tex, no fancy OCR needed :)
what snipping tool are you using? or what setting to get the full screen guidelines?are the keyboard shortcuts (checkpoint_paste, reorient) within sublime app or automator?thanks!
- Where to start
Spotted a typo in the captions at : "Manim" became "manum". (Also, thanks for including full captions, and not just letting YouTube guess what you're saying!)
- What is a Hologram?
Manim has gotten really advanced, this is so life-like!
The first person to watch television
this is how consciousness works. It’s just an illusion.
are those your arms at ? do you have a license for those?
*I was like WOUAAAH😱 for the 'seeing through microscope' one.*
Missed opportunity to have the same image there
is pur-fict
"I want you to take a moment to reflect"pun inteneded?
ok i need a moment before finishing this, the looking inside the microscope broke me a little bit, just a second, i'll brb to finish up.
Holograms (like this one) were very common at exhibits and science museums in the 1970s but have now vanished almost completely. Younger people have never seen one and assume "hologram" means those rainbow stickers on credit cards etc.
that’s at the Exploratorium and everyone always misses it! I’m always so fascinated by it
YOUR HOLOGRAM STUMBLED INTO MY APARTMENT 😭😭😭
Omg the Taylor Swift reference at ... "Your hologram stumbled into my apartment, hands in the hair of somebody in darkness named Chloe or Sam or Sophia or Marcus"
the Taylor Swift reference made me smile soo wideee
- The recording process
is a very important frame to view. LOOK AT THAT GRUMPY CAT 😾 🐈 😻 🐈⬛️ 🤣 ❤❤❤❤
The first cat is shown at
at
: I knew it! When I first learned about how cameras work, and that the tinyness of the hole is necessary to get things sharp and not overlap things, I thought how much information is lost by that. And it works out right: In all that overlapping light are encoded so many different perspectives, you just have to record and recreate it in the right way.
I’m gonna guess have two waves form a different distance of (coherent) equal phase to see if they constructively interfere or destructively interfere
I love that you have faith in me but brother I ain’t that smart.
yup you took the words right outta my mouth there.
it might not be clear for most people why recording the phase of the light wave is relevant to record a 3d image on a 2d plane, but, being a physicist I will give a shot before watching the rest of the video.A point in a 3d object reflects light in all directions, so the light from that single point will essentialy hit all points of the film, but the distance between that point and the ones in the film will be different, therefore the time they will be hit is different, therefore the phase of the light that will initially hit each place will also be different. If you can record said phase you will have a vague record of the distance between each point of the film and the target point. If this effect is applied to every point in the 3D object, the sum of all the information may indeed create the ilusion of looking through a window. This would honestly be best explained with an animation (if I am even correct). I hope this is what the video has in store!
Would a different path not change the phase of the laser due to the difference in travel time? Is this accounted for or is it negligible/irrelevant because we are working with light?
Why is the polarization change by the beam splitter relevant? I thought monochromatic light polarization can't be changed, how is the polarization of a monochromatic laser light affected?
what did u use to make animations in ?
The purpose of the meditation circle is to get all of the humans on a single frequency so the individual frequencies do not interfere with the laser frequencies.🤍🤍🫧
It is like pars files to recreate a file. If you have any 2 of the 3 pieces you can recreate it.
was when it clicked for me how this works, thanks for great visual explanation!
Oh!! You just did an XOR operation on light in 3D space through a plane. Cool.
Grant, I know you love a good "Aha!" moment. For me in this video, it was around the mark. Suddenly, the broad strokes of holograms suddenly made sense. Because of course! If you record the ways that two things interfere, and then send only one of those things through the interference, you're going to get the other! Excellent video, as always.
@ You can almost hear you staring to smile as you start talking about this point of the explanation 😊
reminds me of old documentary’s where you just need to imagine things… like here.. a 3d set, on a 2d film, looks 3d, recorded on a 2d camera for 2d viewing… looks just like a green version of normal filming. As if it were a set bathed in green. The imagination comes in, when one must interpret it as a hologram for the purpose of understanding how one is made. For eg, what you (3b1b) see while recording is not what we see here on the tube.
That segment starting around ... i admit i cried. with dread? joy? how strange to be anything at all
Imagine learning that when You are 7 in 1986!, "You want to tell me Dad, that if i brake this Hologram ill will have 2 WHOLE pictures !? HOW?" .... Yeah your life is not the same after that .Sadly we dont have magazines like that now days ... except of course 3blue1brown :) .
Everyone has said it already but I'll say it again. is magical.
). Imagine a snippet of a hologram-films, like at , and a computer reading the binary out of the hologram bit-by-bit thru that window.
Bro casually drops the most mind-boggling detail of this whole process and then never comes back to it. Cutting a small disc out of the main exposure still retains the entirety of the exposure how?!
This is like the type of stuff you would find in a fantasy story.A small piece of a window into a moment of a past,you can look at some of it, but if you want to solve the grand mysteryyou'll have to find more of the pieces and put them together.
Chat, the comments are not exaggerating. I literally put my hand over my mouth in astonishment at
Imagine finding a person sized version somewhere. You'd think it was a magical portal to some unknown world.
Okay, the bit at where a small section can be used like a window to the whole scene... I think it's the first time a youtube video has actually made my jaw literally drop
is just the demonstration of the end result, you don't see how the magic trick works yet.
is the bit that really feels like magic. that every little piece still encodes the whole image, just at a lower resolution, is still mindblowing to me
, my brain just exploded, wtf! damm that is insane, even if it is explained, just insane
mind blown to see hologram on a primitive glass slice
absolutely blew my mind. What kind of voodoo shit is this.
-- what's cool/interesting here is that you don't reduce the scene size at all -- you decrease the resolution at which you can view the scene!
is like a dimensional portal 😮 wow
This feels like it would make an incredible element in an escape room. Have a table set up, and to solve the puzzle you need to find these chips with different scenes recorded on them at the same table
At I genuinely was so surprised by what I was seeing. I had no idea this was even possible. It literally looks like you’re looking through a portal to another world. Light is so cool!
- The simplest hologram
At only I could already anticipate (in abstract form) the answer to that question: If (film pattern) = (object wave) + (reference wave), then by simple algebra (reconstructed object wave) = (film pattern) - (equivalent reference wave), and the latter reference wave being inverted (subtracted) doesn't really matter to how our eyes detect the amplitude of light.
When the "click bait" thumbnail is the exact expression I had!!!
is literally a jaw drop!
It makes sense, but I am still amazed by that fact. It is like you peak into another universe :)
In the video Grant describes his strategy: "Universal problem solving tip number one is to begin analyzing any hard problem by taking the simplest version of that problem." Grant finds the most simplified case that still features the phenomenon of interest, and from there he builds step by step.
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This is something I've always wanted to understand, and already at minutes in I have a much better understanding of this phenomenon than ever before. Also, Grant, your animations were already excellent like 5 years ago, but these are on an entirely new level. I'm so excited for the rest of this video!
is the moment I finally understood how it actually works. Real "holy shit" moment ! Thank you
and
the two distances shown in have to be destructive at each black point. this happens when D and the distance of that other line to its right. The way of finding these distances and angles between the two lines functions THE SAME WAY we did in the section “Diffraction gratings”, so we end up with the same formula. @3blue1brown
the two distances shown in have to be destructive at each black point. this happens when D and the distance of that other line to its right. The way of finding these distances and angles between the two lines functions THE SAME WAY we did in the section “Diffraction gratings”, so we end up with the same formula. @3blue1brown (I wrote it twice to get your attention.)
thank you for doing things like this.
Frenell? Like the lenses in old huge tvs that people recycled into solar burners?
This is what made it click for me. - 16.20
At exactly I said to myself "it's just a bunch of goddamn double-slits."
: "Let's take a side-step into a mini-lesson so I don't have to rob you of that joy."lol, I love it! Never change, Grant!
- Diffraction gratings
and the part most directly applyin to the 2 slits at:
I just gotta ask. Does no one else see the shape with this? There’s these spikes and two roughly parallel lines.
Oh that’s outer spikes. But it’s a 5 5 thing. If you count the inside spike.
This uses the simplest version of the phenomenon's mechanism. In the video it is called "the problem".That problem, in the video, uses a point or very small single object. From there it can be inferred how two lines or slits are used to produce a series of lines, as seen in the far field pattern that is produced from those two slits.The main difference between how this is explained in the video, is the use of waves in an electro-magnetic field that fills all space as the mechanism to model light which, is accepted under Standard Quantum Mechanics, while light is modeled as 2-Spheres of charge currents under GUT-CP.The 2 slit experiment can be best explained by using the holographic principle where, light modeled under GUT-CP, provides the simplest and most intuitive mechanism for explaining that experiment; and avoid having to multiply the reasons for how that works and thereby satisfy a tool of the scientific method known as Occam's Razor.The key to realizing this simpler model is that the sine shape in this simpler photon model is what a point on the 2D shell of light under GUT-CP,describes on its path through space but, not an intrinsic feature of light. Einstein was right again, light is not a wave but, corpuscular, and not anything to do with fields that would place a photon everywhere at one time, as depicted in the video. That last also violates Occam's Razor. Those several violations point to SQM being an inaccurate or incomplete theory. Therefore the Grand Unified Theory-Classical Physics is more accurate by at least a factor of 100 times and also totally intuitive
I'm only up to , so if you mentioned this in the video, I'm jumping ahead of the class again... if so, that's pretty cool that someone is doing this already
I may be incredibly stupid, but ... light , waves, experiments - its just a wave as long as its not measured, right? I refer to quantumphysics as they proofed that light is not ALWAYS a wave...
Great video so far I’m always puzzled by explanations of quantum mechanics but at least the wave phenomena of light is intuitive.
Not only did this new visualization actually finally made it click for me how and why the 2+ slit experiment works, but gave new insight that these diffractions are actually more nuanced and intricate than I originally imagined! Kudos!
i love you bruh, fantastic explanation
it looks like pattern emerge on a small scale too.
) in-color holograms possible? I have zero idea how that’d work but 🤔 (I haven’t finished watching the video btw)
Cool tattoos, just like the inscription on the Voyager satellite Golden records.
tat is such a cool tatoo I love it
Anyone know what the tattoo is at ?
that is such a good tattoo. the hydrogen graphic off of the voyager 1 golden record ❤
- Reconstructing the simplest hologram
Start at if you want more context.
if u were wondering x/L should be tanθ, u r right, but x/L is very small here (we equating it to wavelength, that small) almost tending to zero, and if tanθ tends to zero, it is equal to θ itself and luckily that is also true for sinθ....so that's why, sinθ.....
I loved this video - as always, the explanations were really clear and the video was made beautifully. I did have a question though: at , isn't x/L equal to tan(theta'), not sin(theta')?
A potentially more elegant way to reason through this is:
Holy sh1t that's cool!
The actual highlight is at btw. That's where the magic is explained.
like looking at an airplane’s shadow in the trees while flying. The viewing angle from the sun creates this same effect in the leaves of the trees.
Notably at light from the observation side would be concentrated into a single point. A type of magnification lens called a 'fresnel lens', they are easy to make out of plastic compared to normal glass magnifications lenses. Perfect for starting fires or burning ants.
- Conjugate image
Oooh strong exp(i ω t) + exp(−i ω t) vibes here: a real-valued signal consists of two mirrored copies of a complex-valued signal, and similar phenomena.
holy crap my brain just exploded. So the higher order beams are a similar concept to harmonics. A traditional diffraction grating is like a square wave, whose frequency space is a series of (theoretically infinite) harmonic spikes extending from the base frequency, while a perfect sine wave is just a single spike.To make the analogy better, you'd have to apply it to something like RF mixing. A mixer normally outputs energy concentrated in exactly 3 distinct frequencies, centered on the frequency of one of the inputs. Injecting a square wave into one would probably yield a bunch of harmonics much like the additional beams. Still weird though since frequency space and angle seem very fundamentally different, and my physics foundation isn't quite strong enough to know how much actual connection there is there.
My first thought was harmonics. Like a radio wave that is a sine does not create harmonics, but a square wave does.
~ It's like the beam's order being the resulting frequency bumps of a fourier transform. Sine-like gradient slits can produce only the 1st order (the 0th being always the equivalent of DC 0hz on fourier). Square-like slits produce more orders, as their shaping is composed by many "sine-like gradient slits stacked"
intuitively this seems completely reasonable without explanation as it looks akin to squarewaves vs sinewaves. Whereas, if you're an audio or electrical engineer or know about it, squarewaves are known to basically be the sum of an infinite amount of sine waves.
That’s neat! Fourier strikes again: sinc ⟷ square wave, delta ⟷ sine wave, but again with complications because of spacetime nature of this thing except of just working with images or temporal signals.
That looks a lot like a Fourier transform of square wave vs sine wave
- More complex scenes
The visualization you have makes it exquisitely intuitive!
Rojo: Ooh! ok, now I'm getting excited about the idea of a low-resolution hologram... I'm thinking it might end up distorting the image in really interesting ways, but even if it's just like looking at a 144p version of a 3D object in person, that would look so surreal and cool!
to
makes me envious to the point of anger. He captures a fundamental driving philosophy of mathematics and why I love the fundamental and abstract maths so much in a way I've not ever been able to describe. And he does it as an ASIDE, a lemma stepping stool with which to jump right back into his real lesson!
- The bigger picture of holography
"Luck favors a prepared mind" is magnitudes better than the usual "Fortune favors the bold" and I will henceforth insert this quote into as many discussions as possible.
, nearly got a heart attack thinking the video was over
- The formal explanation
That is the way it was explained to me in college, almost 40 years ago.Thanks to you I finally got it!!!
RRRRRORROROO