But Scherzer's problem persisted. Spherical aberration set a hard limit on how small you could see. Even Crewe himself gave up on trying to get around it after over ten years of work.
So Euclidean space is a flat space. Spherical space-- think of just the surface of a sphere, like a beach ball-- is positive space. It's curved space that wraps around on itself.
In fact, it doesn't just affect magnetic lenses. Every spherical lens, from a camera to a telescope to a magnifying glass also suffers from it. But there is a surprisingly simple way to minimize spherical aberration. Just add a second lens, one that diverges light instead of converging it.
I feel like I'm in "The Graduate." It was plastic. The spherical attachment of the bell is just one component of ameliorating or masking the sound.
For example, rays that pass through the outer edges of most lenses focus light slightly different from those near the center. This is called spherical aberration. And normal cameras correct for this and other aberrations by using multiple lenses.
The blur starts out around the edges of the image, but it gets worse the higher the magnification. This is called spherical aberration, and it distorts every radially symmetric magnetic lens. In fact, it doesn't just affect magnetic lenses.
And this was, of course, a big roadblock for the development of electron microscopy, because people saw, okay, we can accelerate electrons as much as we want, the presence of spherical aberration will always be in the way. Because of this roadblock, advancements in the microscope's resolution slowed significantly.
In the middle, you see the bulge. This is a more spherical region of chaotic stellar motion. Outside of the disk, you see this big bubble that we call the Dark Matter Halo.
And then, I think Paul was like, I'm just going to see how far I can push this. It's not literally spherical.
What I want to focus on now is actually not the disk itself at all, but this outer region here that we call the halo, which is very thinly populated spherical envelope that kind of protects and swirls around the disk. And we have lots of things living in their, little old halo stars.
Do you know? Now, the bottom, you see it's not coming, the reflection, from our reflectors, diffusers. If bottle is like spherical, again, it's not going to work.
So there's a little timer which runs along the .. The nuclei have to be spherical and not linear.
Someone will call me up and they say, Jeremy, I went to that toilet paper aisle yesterday and I thought about you. where we would film in spherical video.
are going to end up in that one structure, the big central one. Notice that they're not spherical. They're elongated. The earlier they form and the more massive they are, the more elongated they are.
Every spherical lens, from a camera to a telescope to a magnifying glass also suffers from it. But there is a surprisingly simple way to minimize spherical aberration. Just add a second lens, one that diverges light instead of converging it. Now, a diverging lens also suffers from spherical aberration.
incredibly important he has an insociable curiosity about the world around him and he has the world's most powerful microscopes he makes them himself he grinds these impossibly perfect spherical lenses um and he sandwiches them between two brass plates to create this object that looks a little bit like a glorified door hinge
But perhaps most fascinating are these sort of birds here that look vaguely humanoid, and there's some sort of human bird mixing going on here. And this bird here seems to be doing something with a spherical object. Perhaps playing with a ball or something.
So our best picture of Galactic formation is that smaller protogalaxies were pulled together by mutual gravitation, produced the Milky Way, and the leftover is what is in a quasi-spherical shroud around our galaxy. And that's actually one of the more exciting areas of active research today.
So I thought I'd start off with analogy which is of course football. Whether or not you knew it I didn't know this until a few days ago. Football wasn't originally prolated. It was spherical and the game was invented effectively so college men could get out and practice sportsmanship, teambuilding. They could practice essentially military like activity without getting too badly hurt, without getting shot at. It turn out they
I will be developing a new search style called Spherical Search, which will be implementing soon.
But there is a surprisingly simple way to minimize spherical aberration. Just add a second lens, one that diverges light instead of converging it. Now, a diverging lens also suffers from spherical aberration. But if it has the same amount of aberration as your converging lens just in reverse, you can stack the two to essentially cancel out their effects.
Almost all modern lens systems in cameras and microscopes use some sort of correcting divergent lens. So you might imagine that the TEM simply needs its own version of a diverging spherical lens to magnify further. But with magnets, this is physically impossible.
I mean, in physics we joke about assuming spherical cows.
but lines diverging, or perfectly spherical.
Maybe it'll be r theta and phi if we were going to use spherical coordinates or some crazy coordinates in a weird kind of geometry.
The answer is, it looks like a spherical wave.
Yeah. But I'm not spherically symmetric.
it cause president, a few years later President Teddy Roosevelt to come out and say either change the game or stop playing it. And the point of saying that is sort of technilogical change from spherical ball to prolate ball which really did change the game. But also there was political intervention when you talk about energy you can't talk about one without the other. And you can ask me what's more important politics or let's call
the two within a thin, spherical shell with 8,000 miles in diameter -- the diameter of
But now they, calculated this new image might have the remnants of that tiny divergence still in its center, with spherical aberration pointing in the opposite way. So if they got their maths and engineering exactly right, they could feed an image with spherical aberration through these two lenses to almost completely counteract the effect. And I imagine a lot of people in the field thought it was a crazy idea when it was proposed, right?
It's the shape in the upper left here, spherically symmetric.
Someone will call me up and they say, Jeremy, I went to that toilet paper aisle yesterday and I thought about you. Back in 2013, it was really hard to do spherical video well.
As Alan Turing said, a horse is not a spherically symmetrical object.
So to quote him again, "why is a horse not a spherically symmetrical object?" There must be some variations in concentration of chemicals,
And then, there were these discoveries about you had to have spherical fuel tanks 'cause of some of the molecular structures and some of the compounds used in fuels, such as hydrogen,
also got brutalized a little bit. But there were real game changers and when I say game changer I don't mean winning a game like we see at Stanford University. I mean really changing the game. What changed the game in football was going from spherical to prolate. All of a sudden it we object from a game that was kind of slow maybe a little bit violent to one that was
If you choose that the fifth axiom doesn't hold, so there are no parallel lines, then you're playing in spherical geometry.
The stylus detects variations in quantum effects or nanoscale forces to then map the surface structure of the sample. These were easier to build, and because they didn't use any lenses, they weren't limited by spherical aberration. Their images were even 3D.
Their hope was that there would be a small part of this distorted image that would be slightly diverging. And maybe, just maybe, this small part could correct the spherical aberration of the original lens. So they got to work To distort the image, they used a massive nest of electromagnets with six, eight, or even ten separate coils and magnets with bumpy magnetic fields.
Then Rose, Haider, and Urban forced the beam through a second hexapole , one that worked the opposite way, so it would unbend the distorted image back into a circular shape. But now they, calculated this new image might have the remnants of that tiny divergence still in its center, with spherical aberration pointing in the opposite way. So if they got their maths and engineering exactly right, they could feed an image with spherical aberration through these two lenses to almost completely counteract the effect.
As they cross the event horizon, what I'm calling space, I'm looking on the outside at this spherical shadow of the black hole cast by maybe light around it,
Often what you're doing is you're doing, you know, sort of, you're assuming the planet is this sort of spherical ball, and then you're doing what, you know,
So that's the anatomy of the Milky Way. This project that I had a great time doing in grad school looked at the motion of stars in the bulge, so in that central spherical region. I simulated the orbits of millions of stars in this region of the galaxy to see how often they would come into close contact
And you'll see, in a minute, why we want it to be spherical, because it makes it easier to catch it on orbit.
I feel like I'm in "The Graduate." It was plastic. Yes? I'm curious on the Conn-o-Sax, is the timbral difference mainly from the spherical attachment on the bell, or are there other differences?
Recall earlier in the video, I showed you this round, mostly spherical object.
What is hyperbolic geometry or hyperbolic space? Well, it's an alternative to the two kinds of geometries you're already very familiar with-- Euclidean geometry or Euclidean space, and spherical space. Now, there are lots of ways of characterizing these spaces, but one way is to look at the curvature of them.
accept, we are still left with the fact that even the orbits of planets are not perfectly circular, obviously not perfectly spherical.
And the fun thing about writing Marooned in Realtime is, I have a small number of humans who essentially have using that spherical thing you see there.
lithium ion and all of the things you hear in the press about lithium ion. If we do great stuff and we are going to do great stuff we get a factor of two in energy density. The dot is actually spherical. And we're sort of at the bottom of that red oval. So we get a factor of two if we push really hard which means that the technology has to change. You can't use lithium ion