
Cats and Butterflies: Two misunderstood analogies (2018) - bookofjoe
http://metaphorhacker.net/2018/11/cats-and-butterflies-2-misunderstood-analogies-in-scientistic-discourse/
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thaumasiotes
I've been deeply unimpressed by the "chaotic" behavior of Lorentz systems ever
since seeing a web page that showed an example (in only two dimensions), with
some discussion of what people meant by calling it "chaotic".

You could click anywhere in the plane to launch a particle. That particle then
moved in very regular figure 8s through the Cartesian plane. The idea of
calling the system chaotic is that, given the position of the particle at time
t_0, you can't answer the question "where will it be at time t_n?" in the form
of a coordinate pair. Two particles launched near-simultaneously from near-
identical locations may, at a particular future time, wind up in any two
arbitrary points in the orbit. So, "unpredictable behavior".

But it seems to me that you can make a lot of high-quality predictions about
the particle's position. You can say it's going to be in a small 8-shaped
region of space, which is pretty good when the universe is an infinite
Cartesian plane. If you know where it is right now, you can also say with
quite a bit of accuracy where it will be soon. But as your prediction gets
more remote in time, it will necessarily fuzz out spatially across the whole
8, as if the particle were an electron.

On the analogy to butterflies, this certainly can't justify claiming that a
butterfly can cause a hurricane somewhere by flapping its wings. The most you
can say is that the butterfly might move a hurricane that was going to happen
anyway from e.g. March to July. (Though even then, as this article notes, that
conclusion is only valid if the rest of the world is static; in reality, there
are millions of other butterflies.)

But though this article focuses more heavily on interference from many other
minor agents, what really bothered me about the popular concept of chaos
theory was the idea that a particle moving slowly in very predictable patterns
was a good example of "chaotic", "unpredictable" behavior.

~~~
simion314
Sorry if I misunderstand your point, but the point about chaotic systems are
AFAIK this:

1 there are always measurement errors(nothing is perfect)

2 a chaotic system is predictable but the problem is that is super sensitive
to the initial state so the error of the final state will be exponential
larger but probably not infinite.

~~~
thaumasiotes
It's only "super sensitive" to the initial state if you take a very narrow
view of what the possible states are. You can start at any point in an
infinite Cartesian space and, after enough time has passed for you to reach
the small orbital area, you'll stay there forever.

Viewed in those terms, not only can you make accurate predictions about the
future, but there are sharp bounds on the maximum error those predictions can
have.

Imagine rolling a bowling ball over an x,y plane with iron rods of positive
radius fixed at all the points with integer coordinates. The ball bounces off
rods as it hits them in much the same way a real bowling ball would if you
rolled it into a stop sign post.

Where's that ball going to end up after you roll it in a given direction?
Compared to that, a Lorentz system is a model of easy predictability. When you
want the particle, you know exactly where to look. The bowling ball could be
_anywhere_. The Lorentz particle is guaranteed to be in its orbital, because,
unlike the bowling ball system, the Lorentz system is extremely _insensitive_
to initial conditions -- if you view the problem that way.

~~~
simion314
I think you are missing teh point

1 Is all about errors in measurement

In the ball example, if it was in some chaotic system, a 1mm measuring error
could translate in 1km error for the final point, you could calculate that it
will not ever be larger then 1KM if error is under 1 mm but you will nevedr
land that ball on the exact spot because you always have errors in the real
world.

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stared
Quite ironically, it uses the phrase "And that is obviously nonsense." which
usually means that something contrasts our intuition, not that something is
not true!

Be aware of the word "obviously"! (And "obvious nonsense" is nonsense,
obviously!)

Vide:

\- [https://math.stackexchange.com/questions/151782/when-is-
some...](https://math.stackexchange.com/questions/151782/when-is-something-
obvious)

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rwmj
Do people regularly argue: _‘science tells us that there are machines that can
make cats alive and dead at the same time.’_ It's not an argument I've ever
heard.

~~~
Frenchgeek
Well, people do argue having a cold day means "gobal warming" isn't real... So
I wouldn't be surprised to find one person stuck so far up his own anti-
science bu..prejudice to do so. Especially on the Internet.

