Class: Informatics, Computing, and the Future
Instructor: Dan Berleant
Transcriber: Brooke Yu
Date: Tuesday, January 22, 2013
Professor: Hey folks, so I realize I don't make a detailed announcement about homework one last night, so I'm go to hand it out now. Some have already handed it in. I think some of you didn't realize that there was anything to turn in.
Professor: Did everyone get a copy? Did anyone not get a copy?
Professor: Raise your hand if you didn't get a copy yet.
Professor: Okay, so the reason I handed these out is to just give you a minute to look over them if you have any questions. You know, I like to do that when we start a new course. Homework is available online, and usually I won't hand out a hard copy. I just wanted to clarify today. So, any questions?
No? Everything's good? Some people already handed it in.
Okay, well, if there's no questions on that, then let's talk about some things about the future today.
So to get to today's lecture notes, I just clicked on the date in the syllabus and here we are.
Okay, so what I'd like to do is talk today about the speed of change. That's essentially what it is. To illustrate this, I'd like to start with an odd example- a colony on mars, then we'll see how that colony grows, and we'll take that specific example to a more general idea of accelerating curves.
They start out slowly then go faster and faster and faster
And we'll see later in the lecture that actually, as you might expect, things don't go on forever. They level off and then I'll claim that if you go far enough into the future they'll start to come down again.
Okay. Who just came in? Okay. Let me give you one of these.
So, to kind of start out our example, it might seem strange- a Martian colony, but some people are trying to make one. There's a group in the netherlands who want to have a Martian colony by the year 2023. This year they'll start to take applications for astronauts.
This year, you can start to apply. I'm probably too old. I'll show you where it is.
The organization is called Mars one, and here it is. This is is a set up of what their colony will look like.
It's like pods all put together. So it's a nonprofit organization that will go to Mars in 2023 to settle a permanent settlement.
If you do decide to go, ijk you should plan on not coming back because that's not in the plans. It's a one-way trip.
How many people would go? One way trip. Just a couple, huh?
Last year like half the class raised their hands.
Male Student: If I had the choice to come back if I didn't like it, I might try it out
Professor: The problem is that sending someone to mars is so hard that bringing someone back is really kind of unreasonably difficult.
I mean, I guess it's possible, but it's so much more difficult that it would take longer to develop that technology.
I'm just looking for where you can apply. I know only a couple of you want to.
Male Student: I just signed up for updates. Go to the FAQ and click that.
Professor: Yeah, did it say when?
Male Student: There's a thing about astronauts at the bottom.
Professor: There you go. And you can fill out a form.
Male Student: Can you apply somebody else?
Professor: It says they'll start the application process this year. They've already received more than 1000 emails, but they haven't started taking applications.
Okay, well, let's suppose they succeed in getting that colony on mars. What could happen after that?
I'm going to bring up a spreadsheet to analyze this. If you like, you can brine one up and follow along. It's totally up to you.
I just want to make the font really big so you can see it.
Okay, here. 2023 is the year, and I don't know how many astronauts are going to go. Let's say 20.
We're going to start with 20 colonists in 2023, and I'm going to chart down the population of this colony as the years go by.
The way to do that is... you know how to do that?
I can type equal A1 + 1, and it says 2024, right?
And I can copy this- I just dadda CTRL C for copy and I'll past it way down say 1000 years or so.
Paste it all in and if I scroll down the years just go on and on. Each one is the previous cell plus 1.
We're now in cell A85 which is A84 + 1 year.
Now things get more interesting when we talk about the population. We don't just add one each year, but we can hypothesize a rate of increase
We're going to have fractions of people here, but this is an approximation.
So the colony is healthy and it's working. What's the increase of population?
Male Student: Do you think they'd send people every year?
Professor: Well, they probably will want to do that, but we want to make a permanent self-sufficient colony that will grow naturally because there's an equal number of men and women there. So how many percent/year do you think it'll grow?
Male Student: 22%
Professor: 22% per year? No human society increases that fast. People have to have time to grow up.
Male Student: What about 5%?
Professor: That's actually quite high too, but at least it can happen. We'll say 5%, and I'm just going to fill in this cell with =B1 + 5% of B!
I did something wrong. I was in the wrong cell.
Alright. So =b1.... [On board.]
I know the problem I'm way off. I'm not at the beginning of the spreadsheet.
[Teacher reading: [On board.]
Okay, here we are. [Teacher reading: [On board.]
I'm going to do the same thing, but I'm just going to paste the same thing here. I'll do this for all the following cells.
I don't want you to see the answer. Close your eyes for a second. We'll look at it later just close your eyes for now.
Okay, you can open your eyes now.
You can see what's going on. In the first year, there's a 5% increase. Then it keeps increasing. The bigger the population, the more people are added every year.
One of the problems with 20% is that it's not just births, it's deaths.
You know, births minus deaths. So people get old.
So where are we going here?
Okay, so 20 people is a pretty reasonable start. How long do you think it will take before mars is overpopulated? The Martian surface has the same land surface as earth.
So how many people do you think would constitute overpopulation on mars? Just give me a number.
Male Student: 6 billion.
Professor: Okay. What year do you think we hit the 6 billion mark?
Mean, you can guess whatever you want. I can put this down as far as we need to go.
Male Student: 2970
Professor: Any other guesses.
Male Student: 3491.
Professor: Haha, alright.
Male Student: 3050
Male Student: 4023
Male Student: I think we have a good range there.
Professor: Anyone else? Okay. Let's see how long it takes.
Okay. 6 billion is 6 E + 9, I believe.
So here we are. It's 399 years, which isn't much. That's not much to go from 20 to 6 billion, but the's because even though in the first years it's increasing slowly, it gets faster and faster.
In fact the type of curve that does this is an exponential curve- it increases by the same percentage each unit of time.
If we're going to go up 5%... it'll go up slowly, then get faster until it looks like it's going vertically, though it never actually becomes vertical.
The interesting thing about exponential curves is if the rate of change is reasonable like 5%, things get there really fast- faster than you would have expected.
If we tried a different percent, 3 or 4%, it would still be faster than you might have expected.
Now you might have heard that there are things which are improving much faster than 5% a year. Can anybody think of anything?
Male Student: The rate of sales in companies?
Professor: Okay, so the overall economy. Well, the Chinese economy probably is increasing like that. A couple of decades ago china was an economic nothing. They didn't matter. Now it's like the second biggest economy in the world now.
So a few percent compounded over a couple of decades has propelled china from being a poor country to an economic power house. People there are still poor, but the country is more economically powerful than it used to be.
Okay. We could go back and talk more about exponential curves. Does anyone want to try a different numerical parameter?
Male Student: What's the rate of increase of the population on earth?
Professor: The rate is much greater now. It's taken many years to happen though. You might ask why though.
Male Student: Environment maybe?
Professor: Yeah, that's right. Someone else was saying something. Well, what about the environment that would cause use to take so many thousands of years to get to the population we have now?
Male Student: Mass disasters.
Professor: Like disease, pandemics, wars.... historically, pandemics have killed lots and lots of people. I mean, a hundred years ago they didn't have antibiotics and the average family would have to have quite a few kids to have some that would make it to adulthood
So yeah, the rate of increase would have to be really tiny for us to be where we are right now, and that's mostly because life was really hard.
Male Student: The peak was around 2.19%
Professor: For the earth. That makes sense. That was probably in the modern era after antibiotics and modern medicine. If the populations runs out of food, that takes an effect too as we'll see next. Here's the surface area of these places [On board.]
Okay, well, as we saw with the population of our mars colony, it went up by 1% every year in the first few years. For the first few years it'll look like a steady increase.
20, 21, 22, 23... it's changing a little bit, but especially if there's some noise in the reality of it, it'll just look like steady change.
And so that's true for almost any phenomenon. If you look at it over a short period of time, it looks like a steady increase. Let's look at this graph again
We'll go up after a few decades. What's going on here? That's about 39-79.9. Alright, to's a lot like 30. In here's another- we're up to 33 or so. So over the span of a few years, it'll be steady. Especially if there's noise involved where things jump around. So anywhere in this curve, if you pick a small piece of it, it'll look pretty straight.
If you look here, it looks straight.
Okay... but if you start looking at the longer terms, then you start to see that acceleration. In fact, just to make this curve, I sort of made it by hand. I used straight segments and linked them together to make an exponential looking curve.
So here's another example. A couple of years ago people just started to get fluorescent light bulbs in their house and they got a few more each year.
But things are picking up now and probably people are accelerating the number of bulbs they get because I think as of Januay 1st you can't get 100 watt traditional bulbs. How many people have these bulbs? What do they have in the dorms?
Male Student: Those.
Professor: Oh, these are regular fluorescent, not compact.
Well, your parents are probably getting more of these light blubs. They screw into regular light bulb sockets but they're spiraled.
It's kind of accelerating- the number of bulbs people are getting is starting pick up. It'll hit a maximum and then it'll level up.
Alright, so this gradual acceleration is called exponential, but it's a pretty simple concept- it's just adding a percentage every year
It goes up faster and faster and has a doubling time. If the 20 people double to 40 in 20 years, then the 40 will double to 80 in another 20 years. That doubling is constant.
Let's see what the doubling time is in this case. Let's see how many years it takes to get from 20 to 40.
2023- 2037. That's 24.5 years.
Alright, let's just say 24-25 years
Now let's go down where things are different. You're up to, you know... here's a round number. Here we go 240... that's not that round
Female Student: Up a few more there's 208.
Professor: Okay, so 208. If that happens in 2071. If we add 24-25 years to that, we should double that to 416.
So we have 2071 + 25 years we'll get 2095 or 2096.
That's my prediction. When we get to that year we'll have about 416 people. Let's see what we get.
Is that right?
What did I do?
Hmm, I made a mistake. Something's not right.
Oh, okay. I'm totally confused.
2071 was 208. And if we add 25 years....okay, so.... let's see how long it takes to get to 416. 2085 or 2086 which is only 15 years or so.
Okay, no. That works out. It was 25 or 26. It was 15 or 16 years. We made a mistake.
So it takes 15 years to double from 20 to 40 and for 208 to go to 416.
And you go to whatever it takes to get to 6 billion, 3 billion would have been 15 years before that.
Let's go see.
It hits 6 billion in 2422. Subtract 15 or 16 years from that and you get 2404, roughly.
Which is closing in on 3 billion, so it checks out.
By the way, this leads to some crazy things. If there was no check on the population, if you go to 2600 we're up to quadrillions of people, or whatever it is.
10 to the 14th. So billion, trillion- that's 400 trillion people. Of course, that can't happen, just like it can't happen on earth.
If you look at an exponential curve with a microscope, it'll look like a straight line.
As a doubling time, we looked at that. Here's something else. Here's another example of an exponential curve.
The number of transistors on a computer chip is doubling about every two years, not 20 years. So that means... that's why computers are getting so much more powerful more quickly. In 2 years your cell phone could be about twice as sophisticated as it is now.
And that's been going on for quite some time. Ten years ago computers were much weaker than they are now. Ten years ago they would have been 1/32 as powerful as they are now.
That's ten years ago.
Here's the equation for an exponential [On board.]
Does that look like something you've seen in any other class? Do you want to talk about it? Let's try it.
This represents the doubling time of three years
So this is the height of the curve f(t) is the curve.
This is equal to some initial value times this. Whatever t was, I add 3 to that. What happens in the parenthesized expression?
What's the value of this in the parentheses? It goes up by.... By how much?
I'm going to take some number t, add 3 to it, and this expression goes up by how much?
Male Student: One?
Professor: One! Let's take an example.
Let's take 9. Suppose t is 9.
Then this expression is 9/3 is 3. Now let's increase 3 by another 3 to get to 12. So now it's 12/3, so it change by 3 to 4. If you increase t by 3, it increases by another one.
So this is the exponent for 2- it keeps go up by one. Every time this goes up by one, what happens to the value of this expression?
Female Student: It doubles.
Professor: Alright, so we're talking about a doubling time of 3 years.
Every time you increase the number of years by 3, this goes up by one and this value doubles.
So for the 15 years or whatever, this would be 3/15, this goes up by one and population doubles every 15 years.
It's... the math here is very powerful but takes a little getting used to. It gets intuitive if you work these kinds of problems.
It's cool how this portrays the doubling every 3 years. If you want it to double every 4 years, make the number 4.
Or multiply it by 10. When I started teaching the department I was at had a new shipment of PC's for the lab. The hard drives had 20 mb. That was in 1991. In 2001, the new hard drive had 10 times that much. In ten years, the capacity of the hard drive had multiplied by 1000.
So here we have 10 years, so this is t divided by 10. And during that, there is a factor of increase of 1000.
This would be 1000^(t/10).
The hard drive capacity went up by factor of 1000 in ten years. Is that right? Or am I messing it up?
Yeah, that's right.
You want to restate it. You could say, well, a multiplication.... instead of 1000 but a 30 here so you can re-write it any way you want, but however you write it, it's still fast.
So by 2011, if the same trend continues, we'd be up to 20 terabytes. I'm guessing the reason things have slowed down is not because technology has slowed down, but because people don't need 20 terabytes on a typical PC anymore.
Anyway, that's a very fast rate of progress in technology.
And computers are like that, like some other technologies.
Anyone know of another technology that's increasing really fast?
Male Student: Medical
Professor: Yeah, medical, nanotechnology. That's increasing fast.
Alright. Here's some more interesting facts about exponential curves.
You can describe these curves as sort of shaped like hockey sticks. For along time they go up but you hardly notice it, then before you know it you really notice it
So they call these hockey stick curves sometimes.
And the thing about hockey sticks is they have an knee or an inflection point right around there.
That suggests that these curves have an inflection point.
Let's see if we can find some of those.
So the question is where is that knee or inflection point in the curves.
So I'm sorry the x-axis tick marks didn't all come out.
Anyway, what number do you think corresponds to the inflection? Pick an inflection point for this curve. What number does that correspond to?
Some people may have different opinions.
It's missing some of the tick marks, but this would be 16, 17, 18, 19....
This is 15, 14, 16 somebody give me a number for where they'd like to stick that point- the middle of the inflection point.
Male Student: 17
Male Student: 16
Male Student: 15
Professor: Okay, so you're saying 16, you said 17.
Now let's do the same thing for this curve. Find moire of the tick marks. Find the x-axis number that best describes the inflection point on this curve.
Male Student: 17.
Professor: Okay, 17. Let's get.... the two people who have picked one for this one, what do you think for this one?
Male Student: 17 again.
Male Student: Or 17.5
Professor: What about you?
Male Student: 17.
Professor: Okay, interesting. Let's look at this one.
So while the three of you are thinking of what number to pick, let me erase the board.
So what's your answer for this one?
Male Student: 18.
Male Student: 17
Male Student: 17-18.
Professor: Alright, well here's something interesting.
Let me get this centered just right.
These curves are absolutely identical. The only thing I did was stretch them.
Here, I stretched it using excel. Here, I actually probably did it in paint and just stretched the image.
And the inflection point seems to change a little bit.
So when people talk about the inflection point of an exponential curve, they're not speaking very precisely, because that inflection point varies depending on how you stretch the curve. It looks to me that the numbers are going up.
The more you stretch it, the more the inflection point goes up. As you stretch it, the slope decreases a little on the previous year.
So it's almost like the inflection point is an artifact of the picture- it has nothing to do with the mathematics of the equation.
So, what does that tell us? It tells us that exponential curves have no inflection point. They're always going up by the same percent.
It's just a percentage increase, And if it looks like it has an inflection point, it's just because of how the graph is drawn, okay?
Maybe you're not too impressed. Maybe the teacher just exaggerated. It's almost the same.
Well, let's take another look at this curve in a slightly different way.
Okay, first thing I want to show you is notice I haven't changed the vertical scale at all here. They all go up to 1.2 million.
They're all the same height. Let's change the height to see what happens.
What I've done here is I've changed the height and I've squeezed it way down. This is, you know, 10^17 is in the quadrillion range.
Oh, this is one quintillion. This is 800 quadrillion. Where do you think the inflection point is now? Any takers?
Pick a number I don't care as long as it makes some sense.
Male Student: 56.
Professor: Okay. 56. Before, the other graphs it was 17 or 18....
This is the same function- exactly the same function. All I did was squish it way down so that 1.2 million is next 0.
In this graph, it's still at 0. Before you can see anything happening, you have to get to 52 or so. By the way, this right here- if this is 200 quadrillion, each tick represents billions.
So, the inflection isn't noticeable until you get into the 50's, but it's the same equation.
Purely because of the graph, so clearly messing with the y-axis makes more of a difference than messing with the x- axis.
So a lesson- I may have said this a lot before- the knee on the hockey stick, if we're talking about an exponential curve, is not a mathematical property. It's just the way you drew the picture. It's kind of weird isn't it? Who would have thought?
So I graphed it with a bigger x and squished down the y-axis. I did that in excel, buy the way. The spreadsheet squished it when I calculated it to the 50's or 60's.
It does that for me to make it all cohesive.
If it didn't do that then the curve would have gone through the roof.
Okay one more example. This is the same kind of deal.
I did this in excel and I did this in paint. These are the same equations. You can see the so-called knee here, is the y-axis is in this range [On board.]
Here, I squished it by a factor of a million or something.
And here, you can see the same thing happen. When the first tick mark is at 200 trillion, then that's just right at 0.
Again, same equation, but just graphed differently. I left out the early part because it was boring.
And in fact, when I took these two pictures in paint and I superposed them to show the two curves, actually, graphically they're identical.
So all this is just these two superposed and cut off by a little bit.
So what's the lesson? The lesson is that the differing knees are a function of the graph and not the equation. Pretty cool, I think.
So this is just a description of what's going on here. So once again, the knees are an optical illusion and it's just based on the picture. It has nothing to do with the math.
Since the knee doesn't exist, what's really going on is that the curve accelerates smoothly at a constant rate forever and ever.
But when I say a constant rate, I mean at a constant percentage per year.
Okay, well nothing can go up forever, especially if it's going faster and faster.
You know, population on mars won't hit 100 trillion. It'll level off just like the population on earth.
Remember I said if you look at a little piece of this curve it'll look linear. If you look at even more of it then it starts to get S shaped.
It shows that for many kinds of natural phenomenon, they do show exponential increases at first, and then they level off. Why would that happen? Why would it level off?
Why would the human population level off on earth?
Male Student: No where to expand.
Professor: Okay, right. If the population never leveled off, this room would be cram packed. There wouldn't be enough space on earth for people. So things have to kind of hit a limit, and they do.
There are people who sort of see how computers are in this part of the exponential curve, and they think that in a few decades a single computer will be smarter than the entire human race. That's what the singularity theory says.
People who think that way don't think about the fact that everything has some sort of limit. Computer intelligence has been doubling ever few years, but something will limit computers eventually.
In my opinion, a single computer is not going to be smarter than the entire human race by 2045
Some other examples of this logistic curve- let's suppose you have a big room and you're raising mice in the room. Every day you go and take food in there and they gradually start to increase their population.
You can only afford a certain amount of food everyday.
Ultimately you can only bring in a ten pound bag of food everyday.
What happens is the mice increase exponentially, but soon a ten pound bag will only feed however many thousands of mice and they'll start to run out of food. When that happens, the population will level off.
Think about earth- the earth can produce a certain amount of food, and humans are going to hit that limit at some point, right? Maybe we're sort of getting there now. Agricultural technology is improving, but there have to be limits. Only a certain amount of sunlight falls on earth each day.
This sort of thing happens in the natural world when a new species is introduced. That's not quite natural. There can be a tremendous rate of growth, but then natural resources become a limiting factor and it levels off. This can be a difficult time.
Think of the mice- they're fighting for food. Things for them are much worse over here.
Here's another example- suppose you have an empty plot of land and you spray it with herbicides, then you plant a couple of weeds. You don't let any seeds get into the plot. Over a few years you'll have twice of many weeds. Soon, the number of weeds on this plot of land is growing exponentially. Soon, there's no room for more weeds and it levels off.
If you go to a wild area where the land is fertile, it'll have as many plants as it's capable of holding.
And you know, it's not that the plants are running out of food, they're running out of land.
Okay, what happens after this? I'm going to claim that in many cases, in reality, things level off after a while and they go down again.
I'm thinking about.... we can talk about mice and weeds, but let's think about the rate of pencil usage
One day long ago people developed the pencils and people liked them more than quills. How many of you have a pencil with you right now?
How many don't? It's about half and half. Interesting.
When I was your age, it would have been different. Most people would have had pencils. But I think the number of pencils is starting to decrease
Not just because people are using pens, but because people are using computers more. I think in 20 years people won't use pencils much anymore.
They don't even teach cursive writing in many elementary schools.
Male Student: We were told we could only use that for the rest of our lives.
Male Student: I mean, for my signature I use it.
Male Student: That was my hardest class.
Professor: So I think the number of pens and pencils is probably getting into this region here where there's a decrease and people use more hand held devices.
You know, a better one is typewriters. When I was your age I had a typewriter and I used it. Then when I graduated form college, the typewriter- I don't know what happen- it wouldn't work right and I paid a lot of money to fix it. They put it in a vat of water to clean out the gunk
I barely used it after that so it was a total waste of money. The ribbons dried up. The keys work great.
He cleaned off the gunk.
But you know, typewriters are another example of an amazing invention that took off then they leveled off and now we're down to about here. It's hard to find one anymore. I can't use it because I couldn't get a ribbon for it.
So so many things have a curve which needs up leveling off then decreasing.
You know, what about compact fluorescent light bulbs. It's probably increasing pretty quickly, but it's going to level off because people only need a certain amount of bulbs.
It'll start going like that soon because they'll come up with something new. Anyone know of a different kind of light bulb? LED bulbs. A lot of cars and vehicles have them now for brake lights and turn signals.
When the blinkers are on the light goes on and off instantaneously. An old fashioned bulb takes a little while to heat up and go down.
If you look at them, you can tell if it has an LED flash.
So yeah compact fluorescents are great, but soon we'll all have LED bulbs.
The problem with the LED bulbs is they're too expensive
This is what I call a plateau curve.
This is a graph of efficiency of light bulbs. This shows that LED bulbs are getting more efficient very quickly, and soon there won't be a reason to not get these instead.
I guess the theme of today was these trajectories. If you look at a small piece of this curve, it looks linear, then when you really look at the rest of it it has an exponential quality to it.
If you look at a bigger perspective you get the S curve. If you look at an even bigger perspective, it goes down again.
If you look at the number of mice in the room, if you wait long enough and you only feed ten pounds of food, after so long the number of mice will start decreasing.
I have a few more slides, but I think I'll dilute the effect. I just want to leave you with that concept that if you look at things over a short period of time they look linear.
Then it looks exponential, then you get the S shape, then if you look over a really long period of time, it'll plateau.
There are people who are, like the singularitarians- those people who think that way are looking at the exponential and their minds just don't consider that exponentials do level off after a while. The universe would be different if they went on forever, but they don't.
I'm not claiming there won't be a singularity, but I don't know.
Any comments or questions? Anyone not get a copy of the homework?
Are you all comfortable with getting this done by Thursday?
You have to start your blog and do a little writing. You all know what blogs are. Many of you may have not started one, but you know what they look like.
To start one, just go to blogger.com and click the button that says "start a Blog" or go to wordpress.com.
I'll show you what it looks like.
I have a bunch of blogs. If I wanted to start a new one, I'd just click the button. If you don't want your homework blog to have your name on it, just make a fake name under a new Google account and just send me the link
If you don't want to use Google, just use wordpress.com
If you want to create a new blog in wordpress, it's a little harder than blogger. You can start one there if you want.
Any questions about the blog?
I guess we're done.