Extreme Accuracy

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Accuracy is the degree of closeness of a measured (or set) value compared to its true value. It can be defined using the phrase, “one part in X”. For example, “one part in 1000” is equivalent .1% of accuracy. The required accuracy in setting many physical constants is extreme.

 

Describing big numbers is simplified using “scientific notation” (SN) for representation. For example, 2,500,000 is represented as 2.5e6 (or 2.5x10^6 or 2.5 x 10 to the power of 6) in scientific notation. Numbers can be extremely small too. Consider the mass of the electron; 9.10938e-31 kg. The Fine-Tuning Machine uses SN to represent large and small numbers.

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Some examples: if gravity was stronger by 1 part in 1e34, stars such as our sun would not exist nor would life as we know it (Carter). The Cosmological Constant (related to our  our universe continuously expanding) is on the order of 10e-122. This is unbelievably small, ~ zero. However, if it were much larger, the universe would expand too quickly for galaxies and stars to form; much smaller, and it would collapse back into a point.

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Hence, the need for accuracy when accounting for nature's constants. The diagram below gives examples of how many zeros it takes to define some enormous quantities using scientific notation. A similar diagram could be drawn for very small values. 

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Note: Related to the "grains of sand" in the figure, if only one grain of sand was red on all of earth’s beaches and you randomly picked the red grain, then your chance would be “one part in 1e19" for success. It is much much easier to win the full Powerball lottery twice in a row.