Self-study
P1
One of the foundations of scientific research is that an experimental result is credible only if it can be replicated—only if performing the experiment a second time leads to the same result. ███
Foundation of science ·
Experimental results are credible only if they are replicable
Replicable = doing experiment again leads to same result.
Problem ·
Somm. and Ott (S and O) came up with a new physical system
In this system, the tiniest change in starting conditions can change results radically. (What does this mean? Not sure.) This system can be represented by a computer model involving a particle's motion within a force field. (Not sure what this means either.)
P2
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Analogy ·
S and O's new system is similar to riddled basins of attraction
Definition of basin of attraction ·
Bodies of water have basins of attaction
The basin for a particular body of water = area of land where, whenever water is spilled on it, it goes toward that body of water.
P3
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Definition of riddled basins ·
Can't predict where water will flow for some points in between basins
The boundaries between these basins are riddled with physical irregulataries, which is why you can't tell where the water will flow. Need to spill the water at a point and observe. If you spill at any other point, even one right next to it, the water might flow toward a different body of water.
P4
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S and O's system ·
The riddled boundary expands to every single point
So, rather than just the boundary line between two bodies of water being riddled, every point in the whole system is riddled. You can't tell even the general destination of a particle from any starting point.
Distinction between S and O's system and chaos ·
In chaos, you can predict general destination, but not path or exact destination
In S and O's system, you can't predict any of the three things.
P5
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Implication of S and O's system ·
Other similar systems might exist, and if so, this would question the replication requirement
It's possible that some experiments can't be replicated because even the slightest, unnoticeable change in starting conditions leads to different results.
Passage Style
Problem-analysis
Single position
23.
The discussion of the chaos ██ ████████ ███████ ██ ████████ ██ ███████ █████ ███ ██ ███ █████████ █████████ ██ ███ ████████
a
emphasize the extraordinarily █████ ██████ ██ ████████ ██████████████ ██ █ ███████ █████ ██ ██████████
Sommerer’s and Ott’s system isn’t a riddled basin of attraction. The basin of attraction is a metaphor to help us understand the uncertainty that exists in their system. But their system is not itself a riddled basin of attraction. So when the author discusses the distinction between Sommerer’s and Ott’s system and chaos, we’ve moved past discussion of physical irregularities and riddled basins; the distinction has nothing to do with those things. The distinction has to do with the level of uncertainty in Sommerer’s and Ott’s system.
b
emphasize the unusual █████ ██ ████████ ██████████████ █████ ██ ████████ ███ █████ █████
Sommerer’s and Ott’s system isn’t a riddled basin of attraction. The basin of attraction is a metaphor to help us understand the uncertainty that exists in their system. But their system is not itself a riddled basin of attraction. So when the author discusses the distinction between Sommerer’s and Ott’s system and chaos, we’ve moved past discussion of physical irregularities. Sommerer’s and Ott’s system does have fractal properties, but it doesn’t necessarily have physical irregularities. Physical irregularities are things that do create fractal properties in a riddled basin of attraction, but as mentioned above, Sommerer’s and Ott’s model is not itself a riddled basin of attraction.
c
emphasize the large ██████████ ██ █ ███████ █████ ██ ██████████ ████ ████████ ████████████████
Sommerer’s and Ott’s system isn’t a riddled basin of attraction. The basin of attraction is a metaphor to help us understand the uncertainty that exists in their system. But their system is not itself a riddled basin of attraction. So when the author discusses the distinction between Sommerer’s and Ott’s system and chaos, we’ve moved past discussion of actual riddled basins of attraction; the distinction has nothing to do with actual riddled basins of attraction.
d
emphasize the degree ██ ████████████████ ██ ████████ ███ █████ █████
This best captures the purpose of mentioning chaos. She describes Sommerer’s and Ott’s model, in which it’s impossible to predict the general destination of the particle (along with the exact destination and the path the particle will take). This type of uncertainty is different from “chaos,” in which we can predict the general destination, even if we can’t predict the exact destination and path.
e
emphasize the number ██ ███████ ██████████ ██ █ ███████ █████ ██ ██████████
Sommerer’s and Ott’s system isn’t a riddled basin of attraction. The basin of attraction is a metaphor to help us understand the uncertainty that exists in their system. But their system is not itself a riddled basin of attraction. So when the author discusses the distinction between Sommerer’s and Ott’s system and chaos, we’ve moved past discussion of actual riddled basins, and the purpose of mentioning chaos wouldn’t be about actual riddled basins of attractions.