2205: Types of Approximation
| Types of Approximation |
 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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Transcript
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- Cueball: We'll assume the curve of this rail is a circular arc with radius R.
- Megan: Let's assume this curve deviates from a circle by no more than 1 part in 1,000.
- 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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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)
