RC - Around 1960, mathematicians Edward Lorenz

[ParthJ26]

Dear Instructors,

Hi.

RC guide, 6th Edition, Pg 124

Around 1960, mathematician Edward Lorenz found unexpected behavior in apparently
simple equations representing atmospheric air flows. Whenever he reran his model with the
same inputs, different outputs resulted—although the model lacked any random elements. Lorenz
realized that tiny rounding errors in his analog computer mushroomed over time, leading
to erratic results. His findings marked a seminal moment in the development of chaos theory,
which, despite its name, has little to do with randomness.
To understand how unpredictability can arise from deterministic equations, which do
not involve chance outcomes, consider the non-chaotic system of two poppy seeds placed in a
round bowl. As the seeds roll to the bowl's center, a position known as a point attractor, the distance
between the seeds shrinks. If, instead, the bowl is flipped over, two seeds placed on top
will roll away from each other. Such a system, while still not technically chaotic, enlarges initial
differences in position.
Chaotic systems, such as a machine mixing bread dough, are characterized by both attraction
and repulsion. As the dough is stretched, folded and pressed back together, any poppy
seeds sprinkled in are intermixed seemingly at random. But this randomness is illusory. In fact,
the poppy seeds are captured by "strange attractors," staggeringly complex pathways whose
tangles appear accidental but are in fact determined by the system's fundamental equations.
During the dough-kneading process, two poppy seeds positioned next to each other
eventually go their separate ways. Any early divergence or measurement error is repeatedly amplified
by the mixing until the position of any seed becomes effectively unpredictable. It is this
"sensitive dependence on initial conditions" and not true randomness that generates unpredictability
in chaotic systems, of which one example may be the Earth's weather. According to the
popular interpretation of the "Butterfly Effect," a butterfly flapping its wings causes hurricanes.
A better understanding is that the butterfly causes uncertainty about the precise state of the air.
This microscopic uncertainty grows until it encompasses even hurricanes. Few meteorologists
believe that we will ever be able to predict rain or shine for a particular day years in the future.


Q4. The passage mentions each of the following as an example or potential example of a chaotic
or non-chaotic system EXCEPT
(A) a dough-mixing machine
(B) atmospheric weather patterns
(C) poppy seeds placed on top of an upside-down bowl
(D) poppy seeds placed in a right-side-up bowl
(E) fluctuating butterfly flight patterns

My Question:

Is (D) not the correct answer because it is a "potential" example of a chaotic/non-chaotic system because the passage does mention poppy seeds placed in a round bowl, as well as bowl being flipped over, but it DOES NOT mention a right-side-up-bowl.

Please guide.

Thanks in advance.

Best,

Parth Jain

[Sage Pearce-Higgins]

The passage mentions a right-side-up bowl in the phrase 'consider the non-chaotic system of two poppy seeds placed in a
round bowl'. Clearly the bowl must be right-side-up if the poppy seeds can be placed in it.

RC questions will often expect you to make connections between two phrases that have the same meaning. They may not be phrased in exactly the same words.

[manojmeets]

Hi Sage,

I'm not sure I follow your explanation. The passage does state 'poppy seeds placed in a round bowl'. However, how do we make the connection to a 'right side up bowl'.

[Sage Pearce-Higgins]

The passage assumes that a 'right side up bowl' is one that is placed with the opening facing upwards, so that things can be placed in it, such as this one: http://www.ikea.com/gb/en/products/tableware/dinnerware/f%C3%A4rgrik-bowl-earthenware-light-green-art-20392002/