
Laws or comets? - benbreen
https://aeon.co/essays/how-chance-and-probability-affect-the-path-of-big-history
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daveloyall
I understand that this article is mostly about history. I only read the part
that was about physics...

I think the author misunderstands chaotic systems. Despite the presence of the
phase 'deterministic chaos'...

Chaos, in math, is a technical term. It means, as the author said, that small
differences in the initial conditions result in major differences in the
outcome.

Imagine a small cannon situated in the end zone (or goal) on a football field.
You point the thing at a 10 degree angle (up from the ground), use half an
ounce of powder, and fire 100 cannon balls. Most of them land in around the
same spot, lets say the dead center of the field. It's a quality cannon and
there's no wind. You could plot the position of all 100 landing sites and
observe a sort of bell curve... The distribution of cannon balls on the field
has a point of highest density in the center.

Now let's focus on just that one most recent shot. Rewind time itself so that
every atom in the universe is back where it was, and take the shot again. If
cannon ball firing is truly deterministic, and even if it is chaotic, the
cannon ball will land in the EXACT same spot, roll in the same way, and come
to rest with the same side facing up.

Rewind time again. This time, change something... increase the angle to 20
degrees from the ground. The cannon ball will land farther from you than it
did before. Repeat, but with 30 degrees, and it will land farther still.

You can repeat this rewind/re-aim experiment many times and measure every
result and plot them and perform rudimentary number crunching and arrive at a
model of cannons, then you can use your model to PREDICT where the ball will
fall if you set the angle to 15.7 degrees... Cannon fire isn't particularly
chaotic.

Switch from the cannon to paper air planes. Throw an air plane, see where it
lands, rewind time itself, adjust the angle of your arm, throw again, and you
won't be particularly surprised to see that the relationship between arm-angle
and landing site is not as simple as the relationship between cannon angle and
landing site. The danged plane may well land behind you.

But let's explore that. If you don't change the angle at all, if you only
rewind time and throw again, and if paper airplane throwing is deterministic,
and even if it is chaotic, then the plane lands in the same spot it did the
first time, right? The exact same spot.

What happens if you only change the angle of the throw by 0.001 degrees?
1x10e-10 degrees? There is some change of angle that is small enough so that
the plane will still land near the original site.

For those small changes of angle, you might even be able to come up with a
model, and accurately predict where the plane will land.

Creating a model for larger changes of angle will be work intensive! If you
can rewind time, and if you're patient, it's merely labor. That is, assuming
that paper airplane throwing is deterministic and chaotic.

Of course, the model you come up with wouldn't be useful outside of that
moment. Stop rewinding time, and you'll have different initial conditions for
every throw. Air moves, grass grows, arms become fatigued, the sun moves, etc.

...In conclusion, if the universe is deterministic, then the only thing that
makes chaotic systems unpredictable is that we can't measure angles finely
enough--we can't measure anything finely enough.

Stephen Wolfram argues an additional point: that even with perfect
measurements, the maximum speed at which we could simulate truly complex
systems will always be slower than the natural execution of those systems (a
human, the weather, etc), so they are predictable in principle but
unpredictable in practice.

~~~
lamacase
Your explanation is wonderful, but I thought the article said pretty much the
same thing:

"So there is a subtle but important distinction reflected in the term
deterministic chaos – the motions of an orbiting body are fully determined by
the laws of physics, but they are unpredictable because we can never know the
starting conditions well enough."

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therealidiot
The content on this page draws off to the right of my screen, and I can't
scroll horizontally so it's unreadable...

This is on a fully maximised browser window at 1920x1080, normal zoom level.

How does this happen?

~~~
gjm11
Same for me in Firefox (on Windows 8.1); it seems to be at about 2010 pixels
that the text stops falling off the right-hand edge.

Works OK for me in both Chrome and IE. Also works OK for me in Firefox on
Android, at a couple of different widths.

