I
was recently re-reading Leonard Mlodinow’s book, The Drunkard’s Walk, and once again came upon an account of some
weather research done years ago that yielded unexpected results. I’d read about
Edward Lorenz’ computer simulations before, but the implications of his failed attempts
to build long-range weather prediction models hit me for the first time.
In
the 1960’s, Lorenz fed data about some hypothetical initial atmospheric conditions
into his early computer. He let the program run, watching how the computer’s
projected weather patterns would evolve based on this data input. After a
while, he recorded the results and shut down the program. A few days later, he
decided he wanted to see how weather patterns would have developed if he’d let
the program run longer. Rather than typing all that starting point data into
the computer again, he just used the printout information from his previous
session. He expected the projection to develop exactly the same way it had up
to the point he’d discontinued the experiment, and then to proceed into a more
distant future.
But
Lorenz got a shock. When the computer simulation reached the point where he’d previously
left off, it wasn’t reporting the same weather conditions at all. Its
predictions up to that point varied wildly from what the computer had
originally projected. How could this be? The computer had started with the same
data input each time.
But
wait a minute. Lorenz saw that the starting data fed into the computer hadn’t
been exactly the same in each of his
computer sessions. When he had fed in the data by hand for the first session,
he had carried out each data point to six decimal places. So for example, he
might have entered a number as 0.293416. But when he had just looped back the
computer’s print-out numbers, each data point had only been carried out to
three decimal places. The computer had abbreviated what Lorenz had entered when
it produced its final report. So Lorenz’ first number had been entered only as
0.293 for the second session. And that had made all the difference.
This
discovery played a big part in the development of chaos theory with its famous
“butterfly effect.” As everyone started to hear about chaos theory in the 60’s
and 70’s, we were learning that the tiniest alteration at the start can veer
the trajectory of events off into a different direction. A butterfly flapping
its wings in Brazil could create a breeze that would invalidate all
predictions, all projections that hadn’t taken that butterfly’s action into account.
After a relatively short period of time, such a small difference in “initial
conditions” could cause the trajectory of realty to diverge immensely from the
predicted trajectory.
Being
reminded of this statistical fact made me think again about current projections
of climate change. I certainly don’t mean to be a “denier.” However, the ideas
advanced by chaos theory, which had been such a popular subject of study some
decades ago, seem to be largely ignored now. Many individuals are speaking with
great certitude about how global warming will progress and accelerate in this
century. Well, we are certainly causing massive damage and depletions with our
run-away consumerism. However, we can’t be sure that the result will be global
warming for our generation and for the next few generations to come. The
climate is a complex system, subject to diverge from prediction with the
slightest change in initial conditions. It’s like two children of absolutely
equal weight poised level, motionless on a teeter-totter. Let one child put a
ribbon in her hair, and the balance will be tipped. She’ll go down. Or that
darned butterfly in Brazil might decide to flap its wings on a whim –
invalidating all our computer projections.
Seriously
though, there are potentially so many more substantial causes that could result
in unforeseen results when it comes to future weather conditions, or future
anything. Sticking with the example of weather prediction for the moment – we
might consider the effect of sunspots. These are flare-ups caused in part by
magnetic fluxing on the sun. The presence of a lot of sunspots seems to have a
small warming effect on the earth. We currently seem to be going into the
trough of a weak cycle of this activity. There’s disagreement about whether we can
expect a surge of sunspot activity in the coming decade, or if activity will
remain at unusually low levels. If the latter, earth might experience a slight
mitigation of any warming trend.
Then
there’s precession of the equinoxes. The earth can be pictured as a big
spinning top, with its spindle running from pole to pole through its center.
When a spinning top slows a bit, it’s easy to see the way the top wobbles. If
the tip of its spindle could be made to leave a trail of luminescence, a viewer
would see a glowing, irregular circle traced in the air. That’s the kind of
circle-path the earth’s axis is tracing in the universal skies. Depending on
how the tip of the axis wobbles, depending on how it’s oriented relative to the
sun - the earth (particularly its more northerly and southerly latitudes) could
experience periods of either sweltering heat or bone-chilling cold.
Many
scientists believe we are entering another ice age now, in large part because
of the orientation of the earth’s axis. They believe it’s only our burning of
fossil fuels that’s staving off the kind of mini-ice age that England
experienced in the early 1800’s when the Thames River froze over and when people
were literally skating on thin ice wherever they went. Despite all this burning
we’re doing, many still think an ice age is coming. Or not.
Then
there’s that question of pollution itself. The smog that’s being generated more
heavily now in developing countries could paradoxically prove to be a boon by
working to block the sun’s rays, resulting in a cooling effect. Some say we
didn’t do ourselves any favor in the long-run by reducing smog in Los Angeles,
in London, in other big cities in the West. This environmentally good deed has
let the sun beat down on us.
Our
pollution may have acted like a milder, more temperate form of the meteor that apparently
hit the Yucatan Peninsula sixty-five million years ago. The impact of that meteor
likely raised so much particulate matter into the air that the sun’s rays were
blocked, precipitating a deep ice age, killing the dinosaurs and 75 percent of
all other species.
The
eruption of volcanoes and the California wildfires could similarly act as a
sunscreen and lead to cooling. Whether or not there could be such a detectable
effect from these more limited catastrophes might actually turn on the color of
ash that they float into the air. Brown ash would intensify the greenhouse
effect and heat up the earth. But white ash would reflect the sun’s rays out
and away from the earth and lead to cooling. Or not.
Quite
a number of respected scientists in the 1950’s and 1960’s thought the pollution
we were generating might veer us toward a dangerous cooling. In fact, if any
kind of specter of disaster was being raised in those years, it was the specter
of an ice age resulting from industrial pollution and, more pointedly, from the
nuclear fallout that would result from failure of our Cold War negotiations. “Nuclear
winter” was the alarm of that period. However, the scientists were then
admittedly working with primitive computer simulations and they almost always
conceded that things could go either way. Or not.
Then
there’s the looming possibility of “geomagnetic reversal.” Every half-million
years or so, our earth flips polarities, with the North Pole becoming the South
Pole and vice versa. Or put another way, the positive end of our bar-magnet
earth would become negative, and the negative would become positive. Many
believe that the word “flip” carries a connotation of too much suddenness. The
earth’s entire iron magnetic core doesn’t flip all at once. In the course of
its molten fluxing, a section here will flip, then a section there, until
finally the balance shifts and the poles can be decisively said to have reversed.
There’s
a lot of evidence pointing to the fact that we might be near such a decisive reversal
right now. Instruments that detect the strength of magnetic fields have found
the earth’s field is clearly weakening, particularly in the Southern
Hemisphere. This is likely already the cause of the increasingly frequent
failure of satellite communications that has been noted especially in southern
latitudes. A weak magnetic field allows the sun’s ionizing elements to
penetrate our atmosphere and to wreak havoc. It’s not clear what effects
geomagnetic reversal might have on our climate overall. It could greatly
accelerate global warming. Or not.
There
are a thousand other factors that could play into invalidating any predictions
we might make about climate change. But the point of this essay is not to argue
either for or against the reality of global warming. I was only using our
climate as an example of how unpredictable any complex system of interacting
parts is.
The
larger point of this essay is first to issue a general reminder about the
lessons taught by chaos theory about attempts to project into a presumed
future. If we think we will ever be able to predict the weather, or political
outcomes, or social trends, or life, or the fate of the universe, for any
appreciable length of time – we should “fogedda aboud it,” to quote the
Sopranos. The lessons of chaos theory and of Edward Lorenz’ serendipitous
discovery should dissuade us from that kind of hubris. We have to remember the power
of that Brazilian butterfly to thwart even our best laid plans and to
contradict even our most careful predictions.
But
then I wanted to go on to make an even larger point about the nature of reality
that my re-reading of the account of Lorenz’ experiments suggested to me. This
time, I stopped to consider the results of further extensions of Lorenz’ simulations.
What if he had extended all his data points about humidity, barometric pressure,
cloud cover, etc., etc., out to one-hundred decimal points for an initial
computer run, and then increased the
accuracy of his measurements to a hundred-and-one decimal points for a second
run?
Chaos
theory and logic tell us that once again, the two predictions would eventually
diverge. Perhaps they would generally match for a longer time, although even
that isn’t certain. But they would eventually diverge. Well, then what if Lorenz
was able to achieve an accuracy in his measurements of a million and a million-and-one
decimal points respectively? But the result would be the same. Significant
divergence might be postponed for a longer period of time, but the two
projections would still be destined to diverge. It would be the same if Lorenz registered
his measurements to a trillion decimal points, a quadrillion, a quintillion… In
order to get absolutely congruent results between the two computer runs, Lorenz
would have had to carry out his measurements to an infinite number of decimal places.
But
then to extrapolate a little further, in order to get a prediction to be
congruent with what would really unfold in life farther ahead - a programmer
would similarly have to make an infinite number of measurements, carried out to
an infinite number of decimal places. The programmer would have to consider an
infinite number of variables because everything affects everything else. That
South American butterfly’s wing flapping, the leaking of your neighbor’s garden
hose, the degree of perturbation of an asteroid in our Solar System’s Asteroid
Belt (or any solar system’s asteroid belt), the splash created by a diving
puffin off the Hebridean Island of Stornaway, the barking of a dog in the
Melbourne suburb of Yarra, a supernova explosion
in the galaxy Messier 81 - and EVERYTHING – would all have to be quantified to
the nth degree and fed as input to the computer.
However,
the question of scale would have to be considered. All the above events come
about because of the actions of individual atoms. So the real operatives that
would have to be measured would be individual atoms and sub-atomic parts. The
actual barking dog wouldn’t count, only the minute particles of
chemical/electrical activity in its brain. You’d have to consider their
starting point and the starting points of all the universe’s minute particles.
What’s
more, this infinite number of measurements would all have to be made
simultaneously and fed into the computer at the same split second. If you
measured atomic events in the vicinity of the barking dog at 10:00 and then
waited until 10:01 to measure the atomic events impinging on the Earth from
Messier 81’s explosion – you would have already invalidated your results. That’s
because the conditions that resulted in the first reading could very well have
significantly affected the nature of that second thing you measured. Then while
you had dilly-dallied recording that second set of numbers, the first causative
agent would have changed, going on to radiate a completely different sort of
influence out into the universe.
You’d
be like the man with a clock in the bedroom and a clock in the kitchen, rushing
back and forth between the two trying to use the time showing on one to set the
time on the other. Let’s say the man heard a peal from the church tower and he
immediately set his bedroom clock accordingly. Then he’d remember that setting
and rush to the kitchen to set that clock to the same time. He’d calculate that
it took him thirty seconds to rush from one end of his house to the other, so
he’d allow for that when setting the kitchen clock. But when he got back into
the bedroom, he might find he had overestimated how long the journey took him.
He had set his kitchen clock to read 3:15:15, but the bedroom clock only reads
3:14:45. So if the man is a stickler for accuracy, he’ll feel bound to make
another mad dash between rooms, and then another, etc. He might eventually
enlist the aid of a friend. Standing in the bedroom, the man would yell out the
time he’s setting his bedroom clock to and expect his friend, standing ready on
the mark in the kitchen, to set the kitchen clock accordingly. But then they’d
have to take into account the fact that sound waves take time to travel.
Well,
you get the idea. There’s an old proverb that states “The man with one watch
knows what time it is. The man with two watches never knows the time.”
Going
deeper into the physics of the problem of taking a simultaneous measurement of
all elements – you’d run into other problems. Your hired phalanx of universal
measurers would immediately realize first-hand the truth of that part of
Einstein’s Theory of Relativity that found the concept of simultaneity to be
one of those relative things. Two events that look simultaneous to one man will
appear to be separated in time to another man. It all depends on where the men
are standing, and on how fast they are moving relative to each other.
But
then also Heisenberg’s famous Uncertainty Principle would have to be
considered. That principle says that you can never simultaneously know both the
position and speed of an object. Some popularizers of this concept have
explained it by saying the measurer himself will alter the position of an
object in the act of measuring its speed, and vice versa. So no one can
pinpoint both values simultaneously. The actual explanation of Heisenberg is a
little more technically mathematical and has to do with the dual nature of everything
as both particle and wave. However, it can be useful to think of the intrusive
measurer as a metaphor for the impossibility of simultaneously knowing both the
speed and the position of anything.
One
summary of all this physics and logic is that it’s truly impossible to measure
all relevant influences sufficiently to make detailed predictions very far into
the future. Scientists and philosophers have long debated the issue,
particularly from the Renaissance onward. Many were committed to the idea of a
“clockwork” universe, one in which all the gears that they saw as making up the
God-given universe would ratchet forward in predictable lockstep to a series of
inevitable positions in the future. If you knew the positions of all the gears
at the start, you could predict their positions at any given future time.
Most
of the philosophers taking this view acknowledged the practical impossibility
of knowing all the starting positions of the gears and calculating the
successive movements they’d make from there. However, they believed that such
knowledge of the universe was available in
theory. It was only the limited reach of the human mind that would forever
prevent us from such omniscience. But they believed the gears were grinding
away to a preordained terminus.
However,
I think the lesson of Lorenz and all the complications cited here lead to a
more radically disabling conclusion. I believe they demonstrate not only that
the future can’t be calculated – but that the future does NOT exist!
Despite
Einstein’s and Hawking’s extrapolations into how “the future” might conceivably
be reached by burrowing through wormholes and the like, there actually is no
“there.” Something that would require a simultaneous measurement to an infinite
number of decimal points of an infinite number of entities – is something that
goes beyond being practically impossible. It’s something that is also
theoretically impossible. The future is a fiction, a metaphor that derails
clear thought.
For
an episode of his “Genius” documentary series, Hawking divided his student
explorers into two teams. One team stayed with a clock close to the ground,
while the other team carried an initially synchronized clock up to the top of a
high mountain. There was an ecstatic exclamation of having ventured “into the
future” when it was found that, after a while, the ground team’s clock
registered a miniscule lag behind the mountain clock, due to gravity’s effects.
But calling that a glimpse into the future seems to be a misnomer. The somewhat
more obscure, but more valid term of “time dilation” fits better. However,
“time dilation” soon morphs in the public imagination into the possibility of
literal access to a future place, given the right technology. Given a souped up
DeLorean, the “future” becomes a definite, preexistent place you can visit.
It’s
a sliding of meaning that even scientists themselves fall prey to and promote.
Going in the other direction, it’s like saying that when you make your way down
into the Grand Canyon on the less high-tech conveyance of a mule, you are going
“into the past.” Well, yes, that’s true in a sort of metaphorical sense. You
are witnessing the successive effects of past geological events as you pass the
different layers of rock and sediment. But you are not literally going into a
place where your great grandparents might be seen, wafting through in their top
hats and crinoline skirts.
There’s
another aspect of Heisenberg’s Principle and of quantum physics in general that
might be considered to confirm this nihilistic view that there is no literal
future. Quantum physics teaches us that the future actions of individual
sub-atomic particles cannot be predicted. Like the manager of a lottery, a
quantum physicist can only inform you of the odds. She can tell you your
chances of winning, but she can’t tell if you or any other specific individual
will in fact win. Quantum physics is about statistics. It can tell you on
average how many atoms in a clump of Uranium-238 will emit an alpha particle,
causing those atoms to decay into Thorium-234 each year. But it can’t tell
which atoms will be responsible for that radioactivity.
Without
meaning to anthropomorphize the atoms, it could be said that even the atoms
themselves don’t seem to know the moment they’ll make the transition. There seems
to be no discernible precedent for any individual atom’s radioactive expulsion.
So it becomes evident that the non-existence of future states starts with the
lack of definite starting points at the lowest levels of matter and energy.
When
Lorenz’s repeat computer simulation showed that you’d simultaneously have to
make an infinite number of measurements to an infinite number of decimal points
– they not only showed the towering impossibility of making highly detailed,
long-range predictions, they also showed that there is no preexisting state
down the road that could be predicted. There is no room of the future lowering
ahead of us, no altered arrangement of the furniture of reality that we might
dimly glimpse through the haze of time. Just as some members of Columbus’ crew
feared a void in the space they were sailing into, so there is truly a void when
it comes to the future. There is no tangible certainty. There is only a
vanishing into what is an imminent (and immanent) nothingness. The concrete
reality of existence only comes into being each successive moment.
(In a future essay, I’ll examine the
impossibility of there being a preexistent future from another angle – from the
angle of the nature of time. Wait for it…)