Class: Informatics, Computing, and the Future
Instructor: Dan Berleant
Transcriber: Brooke Yu
Date: Tuesday, February 26, 2013
Professor: Okie doke. So did anyone make it to the research internship lunch thing this afternoon?
Male Student: I wanted to, but I couldn't make it.
Professor: Well, if you're interested in it still, just send the head of the program an email. Alright, and there's a homework due today. Any questions about it? More work on the term project- process some of the stuff we talked about with TRIZ, and the video we watched.
I notice a number of people are not quite up to date on their homeworks, so it's not too late to always catch up. Just because you didn't get to one doesn't mean you shouldn't go on to the next one. See me after class if you are concerned. The homeworks are not intended to be very difficult, so I strongly encourage you to do your best.
Any questions on the homework? Alright. So let's go back and continue talking about spoil sports of the prediction game. What I mean by a spoil sport is this- we'd like to be able to predict the future, but the problem is you can't, and it's intrinsic that you can't for several reasons, and those are what I call the spoil sports of the prediction game.
Do you remember what the observe effect is?
Male Student: If something is observed, then it changes the outcome of the event.
Professor: Exactly. Do know something about the world, you have to observe it, but by observing it you change it. So it's kind of a spoil sport of the prediction game.
But maybe if you observe it gently you don't have to change it much and you can predict to some degree, and that's very true, but you run into other spoil sports like the butterfly effect.
So let's talk about some of these.
Here's the observer effect [On board.]
This is the Heisenberg uncertainty principle named after Heisenberg, an early physicist. He was a famous physicist of modern times, but he's dead. Certainly the ancient Greeks had some philosophy on this, but modern physics didn't start until around the time of Newton.
He was way before Heisenberg, but he [Heisenberg] came up with the uncertainty principle. We'll look at a video soon. It says you can't know both the position and the velocity of a particle, so you might know how fast it's going, but you don't know where it is, or vice versa.
I read an example the other day- I don't know if I have the reference to this, but it's an interesting way to think about this principle.
Say you want to take a snapshot of a moving object- a ball flying through the air. If you take a picture of a moving object, you get a track, right? Do you know about that?
The shutter of the camera opens for a while, then closes. During that period of time, whatever you're taking a picture of may be moving and you'll get a streak on your picture.
That's why if you want to take a good picture, you tell the person not to move. Smile first, then hold it until the click is over.
If the object is moving and you take a picture of it, then you don't know what the location is at that point.
The length of the smudge tells you how fast it's going by doing some calculations.
So there's an example of how you can figure out how fast something was going, but where it was.
Say you get a high speed camera and you use bright light and make the shutter go really fast. So the shutter can open and close really fast and it doesn't matter if the object is moving- the image will still be pretty sharp. So you know where the object is, but you don't know how fast it's going.
So that's an example- an analogy of the Heisenberg uncertainty period- the better the know the position, the worse you know the velocity. You can't get both at the same time. It also works as a physical principle.
Let's look at a little video. It gives you the equation
It's pretty simple, considering the advanced physics.
It's the idea you can never know where the electron is.
The more you know about location, the less you know about momentum.
Here's the equation that relates this [On board.]
Alright, delta x is your position. How well do you know where the electron is? This is the mass of the object times speed. And it's greater than or equal to h, which is Plank's constant, over 4pi. If you do the math, you'll discover that the value for delta x is usually about a meter in in electron in an atom.
Now why is that a problem? A meter is like 3 feet, right? And 3 feet is much bigger than an atom. The ultimate answer is it feels like a joke. If you go to a hotel and it has a sign that says "George bush slept Here" well, they have "Heisenberg slept here" because you never know!
So that's probably as clear as mud, frankly. You can never know the exact position of an electron and if you did, it would have moved.
Professor: Okay, I just want to show you one thing about this before I go on to the next thing.
Okay, so I was saying, you now, position and velocity are the trade off. But they're talking about momentum which is mass times velocity.
In fact, it is momentum, but since the mass is usually not variable, if you pull this constant, then the uncertainty is in the velocity not the mass. Normally, you know what the mass is, so you could just think of it as uncertainty in velocity.
So that's the math of it.
And they talk about electrons, but it applies to all particles- protons, neutrons, orange folders. But the mass of the orange folder is much greater than that of an electron, so it makes the uncertainty less. When you're dealing with an object that's of normal size, these physics effects become very tiny. If it's an electron- really tiny and fast- the uncertainty is a meter. It's spinning around the atom, but you don't know where it is within a meter. It could spin a lot in that time.
Here's another video. This one talks about photons or light particles, okay? The interesting thing about photons or light particles is that they have a known speed.
So the Heisenberg uncertainty shows up in a slightly different way, as you'll see.
Heisenberg's principle is very strange. I call it bizarre.
Professor: Let's try this one. Ooh, now we're in trouble. We'll have to live with the flashing.
Frankly speaking, I call it bizarre. But you can see it at work. Suppose I have a laser beam for my light source. I make an opening- a vertical slit. And here goes the laser beam right through the slit. What do I see? You see exactly what you predict. Now I'll make the slit narrower and narrower.
You'll cut off the edges of the circle and the spot gets narrower. But now you come to the point that this narrow slit is only 1/100 of an inch wide. Now you know so precisely in the horizontal direction where it is, that as it emerges from the slit, the light is no longer determined. So now it will get wider. What am I doing? I'm making the slit narrower and narrower, and the beam becomes wider and wider and wider.
Now that is the way the world works.
I want to try to explain that little bit.
So it was kind of a cool experiment, but it's trick to understand. Does anyone remember what velocity is?
What is velocity?
Male Student: It's related to kinetic energy?
Professor: Anybody remember anything else?
Male Student: Speed and direction?
Professor: Right. Velocity is speed and direction.
So he didn't tell you that in the video, but what's going on with the light. It's really fast. It can go to the moon in less than a second. It takes 8 minutes for the sun's light to get to the earth.
So if we have uncertainty in the velocity. We know how fast it is, so the uncertainty is in the direction. When you send the light through the narrow slit, the slit is trying to make the direction.... it specifies the direction. So here's the slit, and as it gets narrow over here, it constrains where the photons move. The uncertainty shows up in the direction- the closer I try to specify the direction, the more the direction actually becomes spread out.
It goes from a spot to a bar and spreads out. They try to specify direction with the slit, and when they do that, the direction becomes less certain and the photons land across a range and you get a bar of light.
In the video, they showed a device that adjusts the slit, but you don't need that. You can do it with a piece of plastic. Let's take a look.
I want to turn off this thing temporarily.
So here's the plastic, and I'm going to shine the laser through it. Can you see the plastic has a V-shape cut in it? If I move the laser through this, it'll do what the video showed. When I move it closer, the dot will spread out. So be patient with me.
It will demonstrate principal using ordinary tools.
So I'll move the beam closer to the plastic. See that?
This is just getting close to where the v ends. You all saw that, right? It still works, but it's not as good up close.
So an ordinary laser pointer- it doesn't specify direction very well. Instead of getting an oblong dot, you'd get a pinpoint. If I only let a few through, it just spreads out.
Because you can't specify the exact direction.
Okay, turn this thing back on.
It applies to electrons. Photons are weird because they're particles of light but the particles of light are strange. There's some physics I don't understand there. I love physics even though I don't understand it.
So what did I do? I did what he did in the video but with a laser pointer and some plastic.
So anyway, the uncertainty principle says you can't, at the same time, know both position and momentum. By momentum, I mean mass times velocity. Mass is usually constat, so the velocity is what is unknown.
In fact, if you want to ask the ratio of uncertainty, they equal this number, which is a constant. [On board.]
This numbers says that the variation of uncertainty- the uncertainty in position times the momentum have to equal a positive number.
Planck is also a modern physicist.
Here it is. You know about delta, right? You know what that is in some of your classes? What does delta mean?
Male Student: Change.
Professor: Right. Here, it's uncertainty.
Male Student: Rate of change?
Professor: Well, they use the term rate in calculus. In this case, the delta means a change.
And when you divide a change by another change you get a rate.
The uncertainty of one in position times the uncertainty in momentum can't be 0. You'd like the uncertainty in both to be 0, but it's not, so we can't predict the future. That's why the Heisnberg effect is a spoil sport of the prediction game.
So there are some other things I wanted to say on that. Normally we focus on position and velocity than in momentum, because the mass is usually not in doubt. I mean, we know about electrons pretty well and we know what their mass is.
Okay, so you know, here's the theory. So what if we don't know the position and velocity. Would that even allow us to predict the future? Let's see. If you know the position and velocity of every pool or billiard balls- they're all the same size, they're very round. If you know the position and velocity of every ball on the table, you should be able to predict how it's going to pan out.
How many numbers are needed to describe the position of a single pool ball?
Here's a table. Here's a ball. How many numbers do you need to describe where it is on the table?
Male Student: x and y?
Professor: x and y. Alright, let's try it. It's 17 inches from the left hand edge, and 19 inches from the bottom edge.
And we can call this x and y. Let's say it's 17 inches from this side, and 19 from that side. Does that tell where it is?
Male Student: Unless you wanted to incorporate height.
Professor: Okay, that's the next dimension, but the pool table lets us just work in 2D. I'm reading a physics book right now and the author describes how different physicists think of the shape of the universe- he says they can't picture the 3D, so they picture it in 2D but they use equations and math to extend it to the third dimension
So now we know the position with 2 numbers. If it was in 3 dimensions, we could add height.
So two numbers tell where the thing. Exactly, and 3 dimensions 3 numbers. 4 dimensions, 4 numbers. 1 dimension, 1 number.
Okay, so how man numbers needed to describe position? It depends on the dimensions.
We can do that for all the balls. Okay?
In this case we'd need 8 numbers, but that doesn't tell us enough about the pool table to know what's going to happen. We have to know how fast they're going.
So how many numbers does it take to describe how fast one ball is going? Or the velocity- speed and direction together.
Well? How about another two? Because if it's rolling this way, okay, then it's going a certain speed in this direction and a certain speed in that direction. It's going 10 miles an hour in this direction, but that's the same as say it's go 5 in the other direction.
Because it turns out you could have a triangle and the numbers work out that way.
Does that make sense? If you want to say how fast it's going in this direction, you can describe how fast it's going both ways at once.
You can tell how fast and in what direction it's going with two numbers
The side to side motion and the up and down motion.
So in every ball, you can tell where it is and how fast it's going with four numbers in 2D.
In 2D, how many numbers for this? 3
How many for velocity. It has to be another three because if it's going this way- I can say how fast it's going this way at the same time I describe how fast it's going in other directions.
So this really says that on a billiard table you can describe everything about it in principle with 4 numbers per object. In the 6 dimensional world, you can use 6 numbers. If you have those 6 numbers for every particle, you can simulate how the atoms will bounce off each other, and if you do that you can figure out the future.
You can figure out where everything is going to be.
So here's another example of that in 2 dimensions.
So I'm going to use a marker on this a little bit.
This particle is 1, 2, 3.7 that way, and 3 that way.
So (3.7, 3). For velocity, I sort of graphically describe it using an arrow and I show the direction and put the speed which is 2 whatever's/second, say.
Say it's going in the upward direction, say 3 per second.
So we have a- the four numbers that describe this particle exactly are the two position numbers, which were 3.7 and 3, and the two velocity numbers which were 2 and 3, and that describes everything there is to know about this particular ball.
And in 3 dimensions I just use 6 numbers instead of 4.
So you need 6 numbers for every object. I didn't talk about mass, so you really need 7 to include mass. If you knew position, mass, and velocity of every object, you could predict the future.
But you can't get all of those numbers with full accuracy because of the uncertainty effect.
The better you know velocity, the worse you know position.
There's also the observer effect, where even if you measured the velocity, you would change it.
So that's two spoil sports so far.
Higher accuracy for one do those things means lower accuracy for the other.
[Teacher reading: [On board.]
What if you could control both? You can't. You can control them just enough to predict the future as well as you need to. You're a really good pool player. You know light shining on the billiard balls won't make much of an effect, and you're good at judging speeds and velocities, and the Heisenberg effect is pretty small on the pool table, so that means you could become a pretty good pool player.
But, just like a confident pool player, you can only go so far. No matter how much you look at the table, you're limited. You can only project the future up to a certain degree.
That's because there's several other wet blankets of the prediction game. One of those is quantum tunneling, which is weird.
This is spoil sport number 3. So what is quantum tunneling mean? Well, according to this advance physics theory, quantum physics, objects don't really have a specific location where we normally think of them.
They're actually smeared over a space, okay? And they exist- they don't own... they're not at a specific point. They're smeared over space and they only seem to be at a particular point when you observe them.
Remember someone said that if a tree falls in a forest is there a sound? Maybe not. If you don't observe an object, you can't know where it is. It's smeared over space. And if you do observe it, it'll appear in that space in which they exist with some probability
This leads to some really weird things. Here's an example. If an object is very near a barrier, okay, and the space over which it's smeared is large, it might be over the barrier.
If you observe it ,
[Teacher reading: [On board.]
It just existed with some probability in front of the barrier and some probability in front of the barrier.
It's weird, isn't it? And it applies to billiard balls too, but not in an observable way.
In that sense, quantum tunneling gives us this probability [On board.]
So if you observe it on the wrong side of the barrier, it's gone through without making a hole in it, and you have quantum tunneling.
Here's video about that.
Some of us were taught in high school that the electron rotates around the nucleus. There's an uncertainty to the very small. No one can tell exactly where something is. We can visualize this with a probability cloud.
Professor: Alright. Here's another example of quantum tunneling. This is not an example of something- not tunneling through a physical barrier.
You make the pencil tip really sharp and then you flatten it a tiny bit. We'll say the flat spot is only three atoms on that flat spot, but you're looking at the edge of the pencil and there are three atoms- if it's a flat triangle, it could balance on the point. So let's get a pencil and sharpen it like that on the point.
[Teacher reading: [On board.]
The pencil is actually smeared a little bit in space because no object has a specific location. If you smear the pencil a little bit, there's a probability that it won't be standing upright. It might be like this or like this.
If it is like one of these then it will fall.
And indeed, since the smearing is symmetric- if the pencil falls it could fall in any direction. So you think it's balanced, but after a while the smearing causes it to tip a little bit and it falls.
Well, it turns out that if we were to make a pencil with such a tiny flat spot, and you balanced it, it would be stable for a long time.
My recollection is one pencil would last a month before it fell over by itself. Oh, no. I think it was a lot of pencils. We'll see.
You could get a bunch of pencils. You make an array of 1000 pencils by 1000 pencils. This room would certainly hold those. They all have a tiny flat spot on the tip.
In about 1 month sitting here, if we waited a month, one of the pencils would still fall over because it's smeared.
Okay? Of course, once it falls it will hit neighboring pencils and they'll all fall.
They've actually done that calculation.
I don't remember what it was a caution for physics teachers, but they liked to talk about this pencil example.
So that's quantum tunneling, and they actually use quantum tunneling in modern electronics and so on. It also explains why the sun shines because I guess the hydrogen nuclei have to tunnel to turn into helium atoms.
Questions about quantum tunneling? Thoughts?
It is weird.
Okay, but maybe we can live with that. A month is a long time to store your pencil. So maybe we can control all of these effects enough so that we can predict, but unfortunately there are still troubles.
The next trouble is spoil sport number four, and that's called the butterfly effect.
The butterfly effect may be a little tiny bit more something that you might have thought about or noticed. I remember a couple people have seen the movie the butterly effect.
So what's the butterfly effect?
Male Student: It's been a while.
Professor: Well, it has to do with butterflies.
Male Student: Oh, the flap of the butterfly wings can affect hurricanes.
Professor: Right. The puffs of air from the butterfly wings eventually affect hurricane travel.
You can never predict which flap will make the hurricane go which way.
That's actually been proven in weather and meteorology that weather is highly, you know- small changes magnify over time. You can't predict how they will, but they do. The person who discovered the butterfly effect was a meteorologist.
Okay, so [On board.]
The effects tend to magnify over time, and at some time the paths of hurricanes will be changed by those flaps. In a couple of years, there will be a hurricane, so let's change where it goes. Don't blame me if it goes to the wrong place.
I mean, probably I really did change it. But someone just coughed, so that changes it back
Male Student: But it's contained in the building, isn't it?
Professor: Yeah, but there are drafts, so it might slip out.
Male Student: So we're probably all mass murderers in some ways.
Professor: Or maybe we've saved lives too. Here's a video showing the butterfly effect in action on a physical system that's not subatomic particles.
It's called the lorenz water wheel. He didn't discover the butterfly effect though. He designed a water wheel to demonstrate the concept though.
See, it's made from a bicycle wheel.
So let's talk about what's going on here. You have a bicycle wheel with little buckets attached to it. Each bucket has a drain pipe and then there's this water flow that drips water into the bucket. So you can see sort of what happens is that which side the wheel turns is adjusted by the water. Water is always flowing in and out of the buckets, but you can't predict which way it will turn.
The reason you can't predict which direction it's going to be turning is because a little tiny bit of water more in one bucket changes how much water drips into other buckets, and that expands over time, so a little change here and there makes the whole direction change later.
Of you wait several seconds, the amount of time it rotates changes drastically. It seem random, you know?
Because you can't predict
That is one of the spoil sports of the prediction game. Let's look at some different water wheels. They're all, in principle, similar, but there are different mechanisms.
Here's a double wheel. You can see the water is dripping in and you can see how the wheel is unpredictably spinning in different direction in different speeds. This one should reverse at some point.
I think this is made from a bicycle wheel too. Let's look at one more.
There it goes.
If you wanted to see some of these at home, just go to youtube and type in lorenz water wheel.
And there's zillions of them! Wheel, it's about 54 results. Some are better than others.
Some are made with bicycle wheels, some are not.
That may not be a lorenz wheel. I don't think it was. I think it was just an ordinary water wheel. But this is a chaotic pattern wheel. Let's take a look.
Here's one not made with a bicycle wheel.
So if you wanted to make one of these for your project for this course, that would be okay.
Okay, so let's see what Lorenz says about this.
Actually, this is what he wrote.
His name was Edward Lorenz. Read this [On board.]
Professor: Okay, so what he's really saying- right here- it can't be done
So, you know, how does that affect various things you might want to predict? We think about things like "when will flying cars be typcially Used?" If you mention it to someone, that person may tell someone else, and eventually the effect of you saying it could translate into having flying cars a few years sooner or later than it otherwise would have happened.
I'm trying to think of any other things like that. If you say something to someone, it might affect their mood, which might make them miss class and not turn in their homework, which affects their grade.
You know that fable about the nail in the shoe, which caused a problem in the horse, which caused a problem with the battle, and so the war was lost. Heard anything like that? I wish I knew the actual.
We have five minutes left and I don't want to start another one, so I want to see if I can find that. Here it is.
Male Student: So it's sort of like a chain reaction.
Professor: Yeah, and an expanding one.
Male Student: Because one thing causes something else to be in conflict.
Professor: Mmhm. Her's a thought. Suppose you've been falling behind in your homework in this class. If you spend five minutes getting started tonight, one thing will lead to another and you might end up on the dean's list.
Okay. Well, there's a few more spoil sports- 3 more. And we'll talk about those next time.