Can one predict the time evolution of a system?
(Weather, pool (billiards), family relationships, Brownian motion, the world's technology about___, etc., etc., etc....)
Ever have a day when everything went wrong? Say you predicted you would have a normal college day. But your alarm clock didn't ring. Already running late, you couldn't find your backpack (briefcase, USB drive, etc.). Finally you stagger out the door, but your car won't start. Later, you find out you missed a surprise quiz. It's a bit like that for the entire field of forecasting. Here's why.
1. Spoil Sport of Prediction #1: the Observer Effect
To figure out what happens next, you need to know where things are now. For example, if you hit a billiard ball, you can't predict what will happen next unless you know the current layout of the pool table. Unfortunately, as a matter of principle, the observer effect holds that the act of finding out "where things are now" (i.e. determining the current state of the system of interest) changes it to something else (i.e. perturbs the system). In physics this is most noticeable for very small things or faint effects. In principle though, it applies to any scenario.
Light pushes
Electrical measurements effect the electricity
Asking someone something about themself changes them
http://theobservereffect.com/ (This Kelly Neill apparently sings, but is not the same Kelly Neill who teaches voice at Harding U. in Searcy)
She also narrates http://www.youtube.com/watch?v=U3_FBisoKD8
("A conscious universe - the observer effect")
A little more detail... ("The observer effect - an historical perspective")
(2009) http://www.youtube.com/watch?v=OZj9Qps8H6M (removed - why?)
(2010) http://www.dailymotion.com/video/xewljq_the-observer-effect-an-historical-p_lifestyle
It is also a Star Trek episode: (30-sec. trailer) http://www.youtube.com/watch?v=uWujY5Hucf0
(11 minutes of the episode) http://www.youtube.com/watch?v=WU80TX4OOEw
2. So. . .
. . . Can you think of some examples of the observer effect?
Does the observer effect help understand
any of our topics of interest?
. . . Future of telepresence (P)
. . . "Unikey" (C)
. . . Template-based sentence analysis (C)
. . . Robotic surgery (O)
. . . Virtual education (M)
. . . How does our age affect how we think about the future (C)
. . . Future of government (M)
Here are a few more
. . . if you are watching over kids, they act different
. . . people in general
- remember we mentioned the
social competition theory of human brain genesis?
. . . Ever try to look at
the back of your head
using two mirrors?
It makes you move your head around!
. . . If you shine a light beam
through dusty air in a dark room,
the light will affect the dust a little bit.
Or dust in a sunbeam.
. . . What about watching a pool game?
. . . What about measuring the weather
for weather forecasting?
. . . What about measures of
the economy
printed in news articles?
3. So you've controlled the observer effect
. . . now just figure out the 6-D position-&-velocity of everything
. . . . . . and crunch with a computer to tell the future! Right?
. . . Unfortunately, no. This just brings us to:
4. Spoil Sport of Prediction #2:
The Heisenberg Uncertainty Principle
http://www.youtube.com/watch?v=iFwRAvpWDB8
(2:49) ("AP Chemistry: Heisenberg Uncertainty Principle")
Nota bene: it applies to all particles, not just electrons
Here it is with photons (light):
http://www.youtube.com/watch?v=KT7xJ0tjB4A&NR=1
(copy at http://www.youtube.com/watch?v=VH7z3TZFYWQ)
. . . And now, let's try it with
a laser pointer and
a piece of black plastic cut from a notebook cover!
(Since I demo'ed it last time,
let's pass it around
and you can try it yourselves)
The Uncertainty Principle says that
you cannot precisely know both
the position and momentum
of a particle.
The uncertainty in position,
delta x,
times the uncertainty in momentum,
delta m,
= h/4*pi
where h is Planck's constant.
∆x*∆m=h/4π
Since momentum is velocity times mass,
momentum=v*mass
we have uncertainty about velocity too (and mass too, for that matter). So there is uncertainty about position, velocity, and mass of any object. Let's focus on position and velocity, out of tradition.
5. More Details
To fully describe a system, such as the universe,
or some smaller part of the universe, we need simply
list the position and velocity (and mass) of everything in it.
How many numbers are needed to describe the position?
Three, a side-to-side location, a front-to-back location,
and a height (also known as x, y, and z coordinates).
How many numbers are needed to describe the velocity,
where velocity consists of a speed and a direction?
Three - a side-to-side speed, a forward backward speed,
and an up-down speed.
6. This concept is easiest to visualize in
a 2-D simplified example.
7. So we need six numbers for every object
to fully describe the system
(actually seven, since each object has a mass as well).
Unfortunately those six numbers are in principle
impossible to get with full accuracy,
because they include both velocity and position (and mass) values.
The Uncertainty Principle tells us that
higher accuracy for one results in
lower accuracy for the other.
8. In short, if the Observer Effect
doesn't stop our prediction ambitions,
the Uncertainty Principle will.
But what if we could control both?
Well we can't!
But suppose we could just enough
to predict futures with confidence.
Alas, we're not out of the woods,
because of the esoteric physics phenomenon called
"quantum tunneling."
9. Spoil Sport of Prediction #3: Quantum Tunneling
According to quantum theory,
objects are not as localized in space as we intuitively think.
Instead, they have wave-like characteristics and
are actually "smeared" over a space
within which they may be said to exist
with some probability at each point within that space.
A tiny object like a subatomic particle,
if near enough to a thin barrier,
thus has a certain probability
of being on the other side of the barrier.
It may be observed there, and if so,
it has thus "tunneled" through the barrier
without making a hole in it.
This is quantum tunneling.
http://www.youtube.com/watch?v=6LKjJT7gh9s&NR=1&feature=fvwp
10. Actually, the term quantum tunneling
is applied to the ability of objects to "tunnel"
through other kinds of barriers than a solid one.
For example, consider the somewhat notorious
example of an idealized pencil balanced on its tip.
Source: http://2.bp.blogspot.com/_cldxKGOzgeM/Sb-pzadDENI/AAAAAAAACFM/-u4n2s3-5q8/s400/A+pencil+on+it%27s+tip.JPG
If the tip is sharp, except for a tiny flat spot
(say, a couple of atom wide)
it might be difficult to balance,
but one might think that
with sufficient care it could be done.
Well not exactly.
Because the pencil is actually "smeared" a little bit,
it has a certain, rather small probability
of being tipped enough to lose balance and fall.
Since the smearing is symmetric,
it could in fact fall in any direction.
The probability of being tipped enough
to lose balance is small and a single such pencil
would be unlikely to fall for a long time
(Easton, 2007, p. 1103).
But get enough pencils together
and one will fall soon enough.
For example,
balance an array of 1000 x 1000 pencils
and one will fall,
knocking over other pencils
and leading to a general domino-like conflagration
with an average (but unpredictable) delay of around a month.
What pencil will start the general crash
and in what direction the pencils fall
is impossible to predict.
11. But maybe the system we're interested in
predicting the future of
is not so finely tuned.
Maybe we can handle the Observer Effect,
the Uncertainty Principle,
and quantum tunneling
adequately for our system.
Alas, our troubles are still not over!
12. Spoil Sport of Prediction #4: the Butterfly Effect
The idea:
a butterfly flapping its wings
will create a small atmospheric disturbance.
That disturbance will propagate unpredictably.
Some time later (how long?),
the paths of hurricanes will be determined by those tiny flaps!
One mathematical description
of atmospheric cycles
whose future behavior depends seemingly unpredictably
on small present events,
may be modeled by a special kind of water wheel.
http://www.youtube.com/watch?v=zhOBibeW5J0
http://www.youtube.com/watch?v=VumQmC2jJbU&NR=1
http://video.google.com/videoplay?docid=-355587954903008142
http://maxwell.ucsc.edu/~drip/talks/lorenz/media/wiel.MPG
“When our results concerning
the instability of nonperiodic flow
are applied to the atmosphere,
which is ostensibly nonperiodic,
they indicate that
prediction of the sufficiently distant future
is impossible by any method,
unless the present conditions are known exactly.
In view of the
inevitable inaccuracy and incompleteness
of weather observations,
precise very-long-range forecasting
would seem to be non-existent.” [emphasis added]
— Edward N. Lorenz
Let's discuss what butterflies might affect our topics of interest:
. . . Future of telepresence (P)
. . . "Unikey" (C)
. . . Template-based sentence analysis (C)
. . . Robotic surgery (O)
. . . Virtual education (M)
. . . How does our age affect how we think about the future (C)
. . . Future of government (M)
So you think you've
controlled the Butterfly Effect
and all those others?
Then welcome to...
13. Spoil Sport of Prediction #5: External perturbations
To figure out what happens next,
you need to know where things are now.
But you also need to know
what outside influences
will impinge on the system between "now" and "next,"
whenever "next" is.
Those influences
can affect the evolution of the system
- that's why they're called "influences."
Imagine, for example,
the Lorenz water wheel,
but while it's raining.
Every raindrop is another butterfly
whose tiny actions
change the direction of the wheel
at some future time.
More generally,
every external nudge to a system
is like that butterfly.
Let's identify some external influences
likely to affect
the future course
of some of our topics of interest:
. . . Future of telepresence (P)
. . . "Unikey" (C)
. . . Template-based sentence analysis (C)
. . . Robotic surgery (O)
. . . Virtual education (M)
. . . How does our age affect how we think about the future (C)
. . . Future of government (M)
Computer round-off error
is another source of perturbations
from outside the system under study.
14. Spoil Sport of Prediction #6: Existentialist Angst - Why Care (About the Future)?
Does the future matter?
Why?
Does the existence of humanity matter?
Why?
Does it matter what kind of existence?
. . . Difficult struggle for existence
. . . Prosperity
. . . Expansion beyond any set boundaries
. . . Regardless of what we should do, what do we actually do?
"Eat dessert first" - Hitchhiker's Guide to the Galaxy
"Eat, drink and be merry, for tomorrow we shall die" - Isaiah 22:13
"Don't Worry, Be Happy" - Bobby McFerrin
15. Decisions often focus on the short term
. . . Business decisions focus on short term
. . . Political decisions focus on short term
. . . Many people focus on the short term
. . . What about animals?
. . . Why is it good to focus on the short term?
. . . Why is it not good to focus on the short term?
. . . Why is it good to focus on the long term?
. . . Why is it not good to focus on the long term?
16. Existentialism
A school of philosophy
Søren Kierkegaard (1813-1855)
was a key figure in its development
. . . Danish philosopher and theologian
"...focused on subjective human experience
rather than the objective truths
of mathematics and science..."
"...interested in people's quiet struggle
with the apparent meaninglessness of life..."
- Wikipedia, http://en.wikipedia.org/wiki/Existentialism
What do you think of that?
17. Discussing the future of humanity is nice,
but what about my future??!
. . . If life is meaningless,
then does the future matter?
. . . Is life meaningless?
. . . Is the question meaningless?
. . . Is it important to give life meaning?
. . . What should one try to do with life?
. . . My conclusion:
reasoning from accepted first principles
does not resolve these
Therefore you can choose the answers you prefer!
(Or not choose, it's up to you)
Equivalently, you can choose
to add first principles
as needed to get the answers
. . . . . . You could pick pessimistic answers,
or
you could pick optimistic ones too
. . . . . . Pure logic won't say which is right
. . . . . . Better to pick the optimistic ones!
Because life's more fun that way
. . . That seems like common sense...
Yet it is not always a matter of conscious choice
"Breaking up is hard to do"
Optimistic and pessimistic moods
Taken to extremes - bipolar illness
That's brain chemistry not choice
Yet... optimism can be taught & practiced!
18. How societies "think" (actually, act) about the future
Source: J. Diamond,
Collapse: How Societies Choose to Fail or Succeed
Recall pre-"discovery" Easter Island and the canoes
A big palm tree was needed to build a good canoe
A good canoe was needed to get plentiful seafood
So why on earth did someone cut down the last palm tree?
(read aloud from p. 410?)
What do you think?
19. Why societies can collapse
(Another kind of existential problem)
You might think that societies would try to
anticipate and control existential risks
But sometimes they don't
What existential risks are possible for us?
Here is a taxonomy (from Diamond)
Failure to recognize a critical problem before it happens
Example: foxes and rabbits in Australia
Anasazi civilization (Arizona) did not anticipate local climate change (drought)
France built the Maginot line for defense, but lost WWII in mere weeks
Etc. (can you think of any)
Failure to recognize the problem when it happens
Examples: any slow-moving trend obscured by short-term effects
Note the noise-and-signal issue
(http://computinginformationandthefuture.blogspot.com/2009/10/trend-analysis.html)
Also called "creeping normalcy"
Let me read from Diamond (p. 426) more about the palm trees...
Etc. (Can you think of any examples?)
Failure to try to solve the problem after it is recognized
Why on Earth would anyone or any group do that??
Yet according to Diamond this "failure is the most frequent"!
. . . Failure may benefit influential special interests that therefore push it
. . . Greenland Norse leaders kept cows (unsuited to the cold)
. . . The few pike fishermen stocked pike in Montana waters,
destroying trout for the many more trout fishermen (p. 427)
. . . "Throughout recorded history,
actions or inactions by self-absorbed
kings, chiefs, and politicians
have been a regular cause of societal collapses" - p. 431
. . . Any examples closer to home of
benefiting a few at the expense of the rest?
. . . Is this rational behavior?
. . . Unregulated access to common resources
. . . . . . "If I don't take as much as I can, someone else will"
. . . . . . Pretty soon it's gone!
. . . . . . Any examples?
. . . . . . Is this rational behavior?
. . . . . . Solutions?
Irrational causes of societal collapse
. . . Beliefs that aren't right
. . . Taking a gamble and losing
. . . Etc. (any others you can think of?)
Try but fail to solve the problem
Greenland Norse colony: "The cruel reality is that...Greenland's cold climate and...limited...resources have posed an insuperably difficult challenge to...a long-lasting sustainable economy." - p. 436
20. Spoil sport of prediction #7: The care horizon
How much is the future of the human race worth? We'll increase it later, but let's start with an admittedly bargain basement $100. If you had $98.04 now, and put it in the bank at an interest rate of 2% per year, then in a year you'd have $100. That means getting $100 one year from now is only worth having $98.04 now, at least from a "Time Value of Money" perspective. Similarly, getting $100 in 2 years is only worth $96.12 now, because adding 2% to $96.12 gives $98.04 in one year, and compounding by adding another 2% gives $100 a year later. Extending this reasoning further, the human race in a modest 233 years would be worth just under a dollar now. In 466 years? Less than a penny.
It's fair to say that a hundred dollars is an underestimate for the value of the entire human race. So let's increase it to a fair (or at least fairer) price. We might multiply the number of people by the value of the life of each and every person on the planet. What is the value of a person's life? Economics (known as the dismal science, even to economists) tells us that the de facto value society places on a human life can actually be calculated, and courts of law in fact sometimes do such calculations. Answers vary, of course, but a few million dollars is often not that far off the mark. Multiply that by the number of people in the world and you get a biggish number, $100 quadrillion at the most for the value of the human race.
But wait - maybe you don't trust the financial and legal wizards with something so important. After all, we already trust them with some pretty important things, and they periodically betray that, seriously screwing things up. Maybe we should use a higher number, just to be more sure we aren't under-valuing ourselves.
How about a dollar for every single atom in the known universe? That's around $10^80 (1 followed by 80 zeroes dollars)? It is a lot of cash. Way (way way) more than the United States has ever printed. There are literally not enough atoms in the known universe to even print that much money. Yet, if that is the value of humanity's existence 9,070 years from now, the value at present would be...$100! A scant 466 years after that? Less than a penny. How about the present value of humanity existing in a million years? The answer is a fraction of a penny so tiny that popular spreadsheets, calculators and computer programming languages can't even state it. They typically just think it is 0, but if you must know, it's actually about $0.000
Wait - someone in the back has a question - yes? "But it's not just the value in year on million we're after. We also need to add in the value in year 1,000,001, year 1,000,002, etc., forever and ever. That's got to add up, eventually." Well, only a little, it turns out. The value now is "bigger," but still less than $0.000
21. Making it personal. Maybe you are still unconvinced.
Such sophistry fails to capture the real facts at a gut,
common sense level, you might say.
Then consider the following argument.
You care about yourself, so you don't want humanity to end while you are still alive (it might not be pleasant). You care about your children (or you will if you have any some day, or maybe you care about some or even all other children). So you don't want humanity to end during their lifetimes, even if you are already gone. You probably even care (or will care) about your grandchildren because you will hopefully get to know them personally. Furthermore, you care about their grandchildren (though probably less) simply because you care about your grandchildren, who care about theirs. But you have no gut level reason to care about the generations after that, because neither you, nor anyone you care about will ever know them. To put it another way, how much do you care about your grandparents' grandparents, and how much did they care about you? Still care in some more abstract, dispassionate sense? Then see the previous paragraph.
Maybe you are a fast enough breeder, and long enough liver, that you'll care about your great grandchildren and theirs, instead of just grandchildren. Yet that is still only 6 generations into the future, not even the biblical 7, a couple of centuries or so at the most. So relax, quit worrying, eat dessert first.... In particular, don't bother with predicting past the 2-century "care horizon," because there's little point to it. The 2-century care horizon is, thus, our last spoil sport of the prediction game.
References
D. Easton, The quantum mechanical tipping pencil - a caution for physics teachers, European Journal of Physics, vol. 28 (2007), pp. 1097-1104.
R. Posner, Catastrophe: Risk and Response, Oxford University Press, 2004
"Time Value of Money": TVM is standard terminology in the finance and accounting world.
"Well, only a little, it turns out." There is a formula for calculating the sum of a geometrically decreasing, infinite series. Look it up (or play with a spreadsheet instead).
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