2205: Types of Approximation

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Revision as of 20:23, 20 September 2019 by 172.68.211.154 (talk) (Explanation: merge explanations)
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Types of Approximation
It's not my fault I haven't had a chance to measure the curvature of this particular universe.
Title text: It's not my fault I haven't had a chance to measure the curvature of this particular universe.

Explanation

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In physics and engineering, problem solving typically requires approximations, as physical properties of the universe can be difficult to model. For example, in introductory physics classes, theories are introduced in frictionless environments.

In the comic, Cueball, the physicist, generally dealing with straight math, is introducing a problem with the assumption that the particular curve is a (perfectly) circular arc with a radius represented by R. Megan, the engineer, also assumes that the curve is similar to a circle, with a deviation factor of 1/1000.


The joke arises when Ponytail, the cosmologist, uses the ridiculous approximation of pi equal to 1. In actuality, pi is an irrational number, usually truncated to 3.14. Choosing the value of pi as 1, or 10, as later suggested, completely defeats the purpose of pi for describing a circle.

However, cosmology is a science that deals with the origin and evolution of the universe, so perhaps Randall is saying that exact measurements are not important in this branch of science.

Transcript

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[There are three panels, each labeled on top]

[Physicist Approximations]

Cueball: We'll assume the curve of this rail is a circular arc with radius R.

[Engineer Approximations]

Megan: Let's assume this curve deviates from a circle by no more than 1 part in 1,000.

[Cosmologist Approximations]

Ponytail: Assume pi is one.
Off-panel voice: Pretty sure it's bigger than that.
Ponytail: OK, we can make it ten. Whatever.


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Discussion

The cosmologist is probably using Fermi's a la What-If 84: Paint the EarthOhFFS (talk) 20:34, 20 September 2019 (UTC)

In that What-If, the rounding formula for Fermi problem estimation is given as "Fermi(x) = round10(log10(x))". log10(pi) (Google search, shows calculator) is roughly .4971... so close enough that someone could do a "Fermi rounding" to either 1 or 10 and not really care one way or another. 162.158.142.118 21:19, 20 September 2019 (UTC)

As a physics Phd (though not working in astrophysics), approximating pi to 1 is not all that bad. Especially when the measurable quantities that go into the calculation usually have huge error bars.--172.68.59.120 21:03, 20 September 2019 (UTC)

Using natural units (setting c=hbar=1) is different from setting pi to 1. Using different units is always allowed and not an approximation. Setting pi to 1 on the other hand, is an approximation and is only justifiable if the other quantities in the calculation have huge uncertainty. --172.68.59.120 21:07, 20 September 2019 (UTC)