Scale of the small

What I want to do in this video is explore what happens when we get to really, really, really small scales. And before we even think about it, I want to familiarize ourselves with the units here. So, we're all familiar with what a meter looks like. The average adult male is a little under two meters. If you were to divide a meter into 1,000 units, you would get a millimeter. And I think we probably know what a millimeter is. If you've ever looked at a meter stick, it's the smallest measurement on that meter stick. So it's already pretty hard to look at. Now, if you were to divide each of those millimeters into 1,000 sections, you'd get a micrometer. Or another way to think about a micrometer is, it's one millionth of a meter. So this is kind of beyond what we're capable of really perceiving. If you were to take each of those micrometers and divide them into 1,000 sections, you would get a nanometer. So now we're at one billionth of a meter. You divide that by 1,000, you get a picometer. So a picometer is 1,000 billionth of a meter, or you could say a trillionth of a meter. You divide one of those by 1,000, and you would get a femtometer. So these are unimaginably small things. Now once you're familiar with the units, let's explore what types of things we can expect to find at these different scales. And I'll start over here. And I've written them on the left as well, but it's more compelling when you see the pictures. We'll start over here with the bee. And I've arbitrarily picked something of this scale. There's many, many, many, almost an infinite number of things I could have picked at this scale. But the average bee is about two centimeters long. This bee right over here. It's about, give or take, it's about one hundredth the length of the average adult human being. But once again, the honey bee not too exciting, although it is pretty exciting to see it zoomed in like this. But a honey bee is something that we can relate to. We've all seen honey bees. Now, what I want to do is zoom in, or look at something that's 50 times smaller than a honey bee. So something that if I were to show how big it is relative to this honey bee, it would look something like this. I'm doing it very rough. And that is a dust mite. And this right here, these are both pictures of dust mites. Now dust mites look like these strange and alien creatures, but what's amazing about them is that they are everywhere. They're all around us. You probably have many of them lying on your skin or wherever right now, which is kind of a creepy idea. But we're talking about scale here, and the average dust mite-- so we were talking about centimeters before, now we'll talk about millimeters-- the average dust mite is less than 1/2 of a millimeter. Or if you want to talk in micrometers, it's about 400 micrometers long. So this length right over here is about 400 micrometers, so about 1/50th the length-- remember, this huge thing that I'm showing right here, this is a honey bee. It's about 1/50th of the length of the honey bee. Or maybe to put it in other terms that you might be familiar with, this is a zoomed-in picture of human hair. And you might say, oh my god, this person has horrible hair, but no. If you looked at your own hair under an electron microscope, you'd be lucky if it looked this good. This person, actually I've seen pictures of more damaged hair than this. This is probably smooth and silky hair right here. But the diameter of human hair, and this is on average, it depends on whose hair you're talking about, the diameter of human hair is about 100-- you can't see it when I write in that color. It's about 100 micrometers thick. That's the diameter. So it's about a fourth the length of a dust mite. Or if I were to draw some human hair relative to this honey bee, it would look something like this. It would be about-- and I'm drawing the whole hair-- so its width would be the width of this thing that I just drew. Now remember, we're looking at a honey bee here. It looks like some type of giant, but it is a honeybee. Let's zoom in even more. So, we started with the honey bee. We zoomed in by 50 to get the dust mite. We zoomed in by another factor of 4 to get the width of human hair. If we zoom in, we're in the micrometer range now. If we zoom in by another, roughly, another factor of 10, we get to the scale of cells. And this right here is a red blood cell. I think this is a white blood cell right over here. About 6 to 8 micrometers. So once again, if I were to draw a cell relative to this human hair, it would probably look something like this. Something on a similar scale that we can still kind of relate to, is the width of spider silk. It's about 3 to 8 micrometers. So if I were to draw some spider silk on the same diagram, it would look something like this. This is an actual image of spider silk. So, once again, something that we can kind of perceive. You can bump into it, you can touch spider silk, you can see it if the sun is reflecting just right, or if it has a little bit of moisture on it. But it's about the thinnest thing that humans can perceive. And this is in the ones of micrometer range. At that same range, you start to have some of your larger bacteria. Bacteria can be anywhere from-- and I'm speaking very roughly-- 1 to 10 micrometers. So in general, they're smaller than cells. Most bacteria are smaller than most cells. And just to figure out where we sit on our scale, I have it over here. So we started off-- I want to keep reminding ourselves-- humans. You divide by 100, you get to the bee. So each of these slashes right here are dividing by 10. So this is divide by 10. Divide by 10 again, you're divided in size by 100. Divide by 10 again, you get to millimeter. You've divided by 1,000. Divide by 10 again, you are doing tenths of millimeters, which is about the size of the human hair. You divide again by 10, you're going to tens of micrometers. By 10 again, you get into the micrometer range. So now we're talking about human hair-- not human hair. Human hair we did up here. We're talking about cells. We're talking about bacteria. Now things are going to get really crazy. Now they're going to get really, really, really crazy. This was in the ones of micrometer range. Now we're going to start getting into the hundreds of nanometer range. And just to get a sense of things-- So remember, a nanometer is a thousandth of a micrometer, or 100 nanometers would be a tenth of a micrometer. And this picture right here, this big enormous planet or asteroid looking thing, this is a white blood cell. The enormous blue thing in this picture. And so if I were to zoom out, it would might look something like this right over here. But what's really fascinating about this picture for multiple reasons are these little green things that are emerging after essentially reproducing, emerging from the surface of this white blood cell. And these things right here, these are AIDS viruses. So now if we zoom in roughly another factor of, you know, about 100 to 1,000 from the size of a cell, you are now getting to the size of a virus. And all of the genetic material necessary to replicate that virus is right inside each of these little capsids. It's right inside each of these little green containers. So now, going back to our scale-- let me get my scale right over here-- we are down to the scale of a virus. So we're in the hundreds of nanometer range. If we divide by 10 and then divide by 10, you get to the nanometer range. And right in the ones of nanometer range, you get to the width of the double helix of a DNA molecule. So this right here is, if you were to zoom in, and this is an artist's depiction of it, obviously. Well, this is not a picture, so to speak, of a DNA molecule. But the width of this double helix is about 2 nanometers. Or another way to think about it, about 1/60th the diameter of one of these viral capsids. Which it would have to be, because it's going to have to get all wound up and fit into one of these viral capsids. And DNA, just to make it clear, this is just the width of DNA. It's much, much, much, much, much, much, much, much longer. And we can talk about that in future videos. So once again, we're at a very, very small scale. If you want to think of it in terms of meters, we're at two billionths of a meter. You could put 500 million of these side by side to get to a meter. Or you could even think of it this way, this is two millionths of a millimeter. So once again, super small. You could put these side by side, one DNA, and another DNA, and if you made them touch, you could put 500,000 next to each other in a millimeter. So this is unbelievably small amount of space. And now I'll introduce you to another unit that's not kind of in the conventional, you know, prefix followed by meters. And this is an angstrom. And 10 angstroms equal one nanometer. So the width of this DNA double helix, it would be two nanometers or 20 angstroms. Now, if we were to divide again by 10, you get to something that's 2 angstroms or 0.2 nanometers wide, and that is a water molecule. Maybe instead of using red, I should have used blue or something. But this right here is the oxygen, and it is bonded to the 2 hydrogens right over here. So we're getting, you know, this is beyond, frankly, human perception, I mean. Or even really, stuff that we can conceptualize. Not to even speak of perception, I have trouble imagining how small we're dealing with right over here. We're essentially dealing, remember, we're dealing with less, 1/5 of a billionth of a meter, or 1/5 of a millionth of a millimeter. Something that I really can't fathom. But we're going to get even smaller than that. If we were to zoom in on one of these hydrogen atoms-- and now things start to get kind of abstract, and we start dealing in the quantum realm. And it's hard to define where one thing ends and one thing begins. And what is real? And what is not real? And all of that silliness. But if we try our best to do it, if we were to zoom in and we sort of put some boundary on a hydrogen atom-- because electrons actually could jump around anywhere-- but if we set some boundary of where the electrons are most likely to be found, the diameter of a hydrogen atom is roughly 1 angstrom. Which makes sense from this diagram, too. It's about 1/2 of the diameter of this water molecule. What's extra crazy is one, this atom is super, super duper small. Something that we can't, you know, this is one ten billionth of a meter, or one ten millionth of a millimeter. So something we really, really can't fathom. But what's crazier than that, is that it's mostly free space. We've gotten this small, we're trying to get to these fundamental units, and this thing right here is mostly free space. And that's because if you look at an electron, and when we say radius here, it's really hard to define where it starts and ends. And you have to do some things related to the charge. And we're not even thinking about quantum effects and all of that. An electron has a radius of 3 times 10 to the negative 1/5 angstroms. And the nucleus of a hydrogen atom, which is really just a proton, has a radius a little bit-- and you don't even worry about this number right here. The general idea is, it's the same order of magnitude. It's about 1/10,000th of an angstrom. And just to give a sense of what it's like, if you have the entire, if you view the entire atomic radius to be about an angstrom, kind of, just have a conception for scale of the atom and how much free space there is in an atom, if we even want to think what is free space. Imagine a nucleus being maybe a marble at the center of a football stadium, of a domed football stadium. And imagine an electron being a honey bee just randomly jumping around random parts of that entire volume inside of that football stadium. And obviously, it's a quantum honey bee, so it can jump around from spot to spot, and it's not easy to predict where it's going to go next, and all of the rest. But that will give you a sense of the scale of the electron and the proton relative to the atom as a whole. But even more crazy, it gives you a sense for how empty atoms, and really all matter really is.