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?

[Class
laughing]

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?

Any
ideas?

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.

That's
strange.

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.

Okay, so.

Let's
see.

If you look
at an exponential curve with a microscope, it'll look like a straight
line.

And....

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.

Okay?

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.

Professor: Okay

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.

Okay?

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?

Any
ideas?

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.

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