Wednesday, February 22, 2012

Spoil Sports of the Prediction Game

"You can chase the future. But you'll never catch it."

Can one predict the
evolution of a system 
over time?

Weather,
pool (billiards),
family relationships,
Brownian motion,
technology about___,
etc., etc., etc....

Sometimes, everything goes wrong

   You predicted a normal college day

   Then your alarm clock didn't ring

   Running late, you couldn't find your backpack

      (or car keys, smartphone, etc.)

   You finally stagger out the door,

      but your car wouldn't start

   That's why you miss a surprise quiz

Basically, the future was unpredictable

   It's like that for the entire forecasting field...

   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.

   Problem:

      Observing changes what is observed

Example:

   You hit a billiard ball

   What happens next?

   What do you need to know to figure it out?












You need to know

    the current state of the pool table

    the speed and direction of the ball



Problem:

The observer effect

The principle 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-

        the observer effect
        is most noticeable for:
            very small things, or
           faint effects

        In principle,
        the observer effect
        applies to any scenario:

   Light pushes

         solar sails use that

         called radiation pressure

   Electrical measurements

      affect the electricity

         E.g. multimeters

   Asking someone
   about himself/herself
   changes the person

 "Measurement always changes the thing measured"
        Can you think of some examples?
        Counterexamples?
        What about BIG things?
        small things?

  Measurement thus can be inaccurate!

The observer effect on the web

Dr. Quantum (5:40)
     http://www.youtube.com/watch?v=fwXQjRBLwsQ

Feynman (56)
    https://www.youtube.com/watch?v=2mIk3wBJDgE is similar)

The observer effect is even popular in new age-y circles

    http://www.dailymotion.com/video/xewljq_the-observer-effect-an-historical-p_lifestyle

It is even a Star Trek episode:
    (30-sec. trailer) http://www.youtube.com/watch?v=9eqb9PDILMU


And not just physics...

    Social science also has an observer effect

    See first few seconds of:
    http://www.youtube.com/watch?v=1HhnUDqEfUo

    (1:02)
    https://www.youtube.com/watch?v=iIeRhPCYgIQ


So. . .
 . . . Can you think of
some example
of the observer effect?
  
     (You could write it down, or groups could jointly try to think of examples)
    











Does the observer effect
change futures
of things like

    prediction markets

    cars

    computers

    education

    the next presidential election

    children

    peers/older people

    yourself

    your project topics










Here are a few more

. . . if you are watching over kids, they act different

. . . What about adults?


. . . Ever try to look at
      the back of your head
      using two mirrors?

           It makes you move your head around

. . . What about fans watching a game?

. . . What about measuring the weather
      for weather forecasting?

. . . What about measures of
      the economy
      printed in news articles?



Suppose you could control the observer effect

     (Is this even possible?)


. . . now just figure out the 6-D position-&-velocity of every particle (etc.) in the universe

. . . . . . then crunch with a giant computer to tell the future! Right?

. . . Unfortunately, no.

. . . . . .This just brings us to:











2. Spoil Sport of Prediction #2: 
The Heisenberg Uncertainty Principle

https://www.youtube.com/watch?v=TQKELOE9eY4
("What is the Heisenberg Uncertainty Principle?"
4:43, 1,548,081 views)

Nota bene:
it applies to all particles
not just electrons

Here it is with
photons (light particles):

http://www.youtube.com/watch?v=KT7xJ0tjB4A&NR=1
(2:08)

. . . You could do it with
      a laser pointer and
      a piece of black plastic cut from a notebook cover!

The Uncertainty Principle:

It says you:

   cannot precisely know
   a particle's
   position and momentum
   at the same time

The best achievable

uncertainty in position,
delta x,

times uncertainty in momentum,
delta m,

= h/4*pi 

h is Planck's constant
So h/4*pi is a constant too

x*m=h/4π
 
What happens if we have
total accuracy for position, x
in other words, x=?

Since momentum m
=
velocity v times mass:

m=v*mass

so m=∆(v*mass)

with great uncertainty about momentum m
then or  mass has great uncertainty:

either
you don't know the velocity
or
you don't know the mass


What is momentum in everyday terms?

. . . Suppose you are on skates

. . . Something with momentum flies toward you

. . . You catch it

. . . The more momentum it had,
      the faster you slide backward

. . . . . . Don't like that it's not just you,
. . . . . . it's you and the object?
. . . . . . . . . then toss it back just enough so it has v=0

. . . It's momentum m transfers to you
. . . . . .the more momentum it had,
. . . . . .the more you have now
                  and
. . . . . .the faster you slide backward

. . . Momentum is different from kinetic energy

What is the
uncertainty about
momentum m,
that is, m,
if v=1mph 
and mass=5 lb.?
    (Recall   m=mass*v)

Typically we are
relatively sure about mass,
so m shows up as not ∆mass


So there is typically uncertainty about
position x, and velocity v
of any object

So let's focus on
position 
and
velocity v
 

Does the uncertainty principle apply to bowling balls? Asteroids?

Let's break m
(uncertainty about momentum)
into its components:

m=(mass*vel)
So x*m=h/4π
becomes x*(mass*v)=h/4π
Assume mass is known & constant (say 10 lb.)
Then x*(mass*v)=h/4π
becomes x*v=h/(4π*mass)
If  mass is high (bowling ball)
then
x*is: small or large?
...permitting and to be small

If  mass is small (subatomic particle)
then
x*v=h/(4π*mass)
is: small or large?
...permitting and/or to be much bigger


Some more details

To fully describe a system
     such as the universe
     or
     some small part of the universe
we need simply list
the position and velocity (and mass)
of every particle 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.

Plus the mass,
gives 7 numbers

This concept is
easiest to visualize in
a 2-D simplified example:


So we need
six numbers
for every object
to fully describe the system
(actually seven,
since each object has a mass as well).

Now for the bad news...
those 6 or 7 numbers are
in principle
impossible to get with full accuracy,
because
they include values for both
position and velocity (and mass, #7)

    The Uncertainty Principle tells us that
        higher accuracy
              for one results in
        lower accuracy
              for the other.

In short,
   if the Observer Effect
   doesn't stop
   our prediction ambitions,
   then
   the Uncertainty Principle will.

But what if we could control both?
Well we can't!

But just suppose we could
(maybe we could do it "enough")

Alas,
we're not out of the woods,
because of the
esoteric physics phenomenon called
"quantum tunneling."


3. Spoil Sport of Prediction #3: 
Quantum Tunneling

According to quantum theory:
    objects are not as
    localized in space
    as we intuitively think.

Instead, objects have
      wave-like characteristics
      and are actually
      "smeared" over a space
          within which they exist
          with some probability
          at each point
          in that space.

This leads to weirdnesses like:
    A tiny object
         such as a
         subatomic particle,
    if very near a thin barrier,
        has a certain probability
       of being on the other side!

    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
(4:12)

Quantum tunneling also applies to
the ability of objects to "tunnel"
through other kinds of barriers than solid ones.
For example, consider a notorious example:
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 should be possible
with sufficient care.

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,
http://iopscience.iop.org/article/10.1088/0143-0807/28/6/007/meta).

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
about a month.

What pencil will start the general crash
and in what direction the pencils fall is
impossible to predict.

Thus, quantum tunneling
prevents accurate prediction
and is a
spoil sport of prediction.

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!


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!

There is a movie The Butterfly Effect
Highly rated by viewers
Less so by professional critics


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://maxwell.ucsc.edu/~drip/talks/lorenz/media/wiel.MPG (download)
fire wheel: https://www.youtube.com/watch?v=MszbeTgpcDg
https://www.youtube.com/watch?v=7A_rl-DAmUE
https://www.youtube.com/watch?v=RG-MbYDjpGM
https://www.youtube.com/watch?v=r2A7Ii0ST5E
https://www.youtube.com/watch?v=Wv1KB1ohAlE
Why: https://www.youtube.com/watch?v=EF5Wvi_Iiy4

“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 term project topics!

         What about the observer effect,
         the Heisenberg uncertainty principle, and
         quantum tunneling?



So you think you've
controlled the Butterfly Effect
and all those others?
Then welcome to...










5. 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.

Consider pool again
    Say you know
        Every location of every ball
        The velocity of each
    A fast computer can
        Figure out what will happen
        Several seconds into the future
        Faster than it really happens!
            After that, various issues cause problems
                (Spoil sports 1-4)
            Suppose we tame them somehow (a big if)
            Our problems are not over:
    What if
         a draft hits the table?
         The table is very slightly tilted
         Someone bumps it?
         Etc.?

Those influences
can affect
the evolution of
the system
   that's why they're called
   "influences"

Another example
    A Lorenz water wheel,
    but it's raining
         Every raindrop is a butterfly flap
         ...whose tiny actions
         change the direction of the wheel
         at some future time.

More generally,
every
external nudge
to a system
is like a
butterfly wing flap








- how about the future of
       your car?
       you?
       a person's illness?
  How can we avoid
  total loss of control of
  society, systems, selves...?



Computer round-off error
      another source of perturbations
      from outside the system under study
      Example:
          Frictionless pool table simulation that repeats
          Weather simulation
                The butterfly effect was discovered as an effect of round-off error

Note the
"Lorenz attractor"
     (recall youtube simulations)





Let's identify some
      external influences
      likely to affect
      the future of
          some of your favorite topics
         (we could list them on the board)





6. Spoil Sport of Prediction #6: 
Existentialist Angst 
- Why Care 
(About the Future)?


Angst: 
a feeling of 
dread, anxiety or anguish 
about 
the "big questions" 
of the 
     world,  
    universe, 
    humankind, 
    etc.










Does the 
future matter?







Why?







Does 
the existence 
of humanity 
matter?







Why?














Does the kind of existence affect the answer?

. . . Difficult struggle for existence
vs.
. . . Prosperity





Maybe...
these questions
should not
be asked...

       "Eat dessert first" - Hitchhiker's Guide to the Galaxy

       "Eat,
        drink and
        be merry,
        for tomorrow
        we shall die"
            - Isaiah 22:13, etc.

       "Don't Worry, Be Happy"
         - Bobby McFerrin (after Meher Baba)



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?

. . . What about plants?

. . . 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?

What does short term focus say about existentialist angst?

What does long term focus say about it?


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?




Discussing the future of humanity is nice, 
but what about my (your) 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?

. . . Maybe 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



                         How about maximizing the integral
                         of positive feeling in the universe?



. . . . . . 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

                     Optimistic and pessimistic moods

                     Taken to extremes - bipolar illness

                     That's brain chemistry not choice

                           Yet... optimism can be taught & practiced


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

(Source: J. Diamond, Collapse: How Societies Choose to Fail or Succeed)

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 is happening
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"
           Try an images.google.com search on:
           average global temperature by year
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?

Trying but failing 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


So should societies think differently?




Why?






7. Spoil sport of prediction #7: The care horizon

Time value of money

How much is the future human race worth?

We'll increase it later, but...
    let's start with a 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

So: getting $100 one year from now is only worth having $98.04 now

      (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.

$100 is way too small!

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 within range.

Multiply that by the number of people in the world and you get a biggish number:

$100 quadrillion for the value of the human race (at most).


Is $100 quadrillion way too small?

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  $0.0000001.


It's STILL too small!

Wait - someone in the back has a question - yes? "But it's not just the value in year one 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 $0.0000001 even at a dollar an atom. The upshot of all this is that there is no good financial reason to care whether humanity exists in ten thousand or a million years - at least according to standard economics principles. Therefore there is no need to plan that far into the future, or go to trouble and expense to preserve the Earth indefinitely, or even to bother predicting that far ahead. 


The time value of money seems indeed 
to be a spoil sport of the prediction game.



Making it personal: It's not a money thing at all

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?


Maybe you and your great grandchildren will live long enough 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).

No comments:

Post a Comment