Editing 2205: Types of Approximation
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This comic is a parody of the tendency of {{w|cosmology}} to use much rougher approximations in their work that would horrify engineers, other physicists, mathematicians, etc. In general, cosmologists deal with distances, time spans, masses, etc. that are so vast, with such large estimated errors, that approximations that would be ridiculous elsewhere still yield useful answers in cosmology. When dealing with the large numbers in cosmology, small multiplicative factors like 3 vanish into the rounding error: there probably isn't a useful difference between 10<sup>100</sup> and 10<sup>100.497</sup>, even though these numbers differ by a factor very close to pi -- an error that would greatly disturb most physicists and engineers. | This comic is a parody of the tendency of {{w|cosmology}} to use much rougher approximations in their work that would horrify engineers, other physicists, mathematicians, etc. In general, cosmologists deal with distances, time spans, masses, etc. that are so vast, with such large estimated errors, that approximations that would be ridiculous elsewhere still yield useful answers in cosmology. When dealing with the large numbers in cosmology, small multiplicative factors like 3 vanish into the rounding error: there probably isn't a useful difference between 10<sup>100</sup> and 10<sup>100.497</sup>, even though these numbers differ by a factor very close to pi -- an error that would greatly disturb most physicists and engineers. | ||
β | Approximating pi as 1 may also refer to the habit astronomers have of changing the units of measure such that important constants of the universe (such as the speed of light or the gravitational constant) are equal to 1, which highly simplifies the formulas without compromising the math. The number | + | Approximating pi as 1 may also refer to the habit astronomers have of changing the units of measure such that important constants of the universe (such as the speed of light or the gravitational constant) are equal to 1, which highly simplifies the formulas without compromising the math. The number pi, however, is a dimensionless ratio, which doesn't depend on the unit of measure. |
==Transcript== | ==Transcript== |