Mathematical
A sanity test can refer to various orders of magnitude and other simple rule-of-thumb devices applied to cross-check mathematical calculations. For example:
- If one were to attempt to square 738 and calculated 53,874, a quick sanity check could show that this result cannot be true. Consider that 700 < 738, yet 700² = 7²×100² = 490000 > 53874. Since squaring positive numbers preserves their inequality, the result cannot be true, and so the calculated result is incorrect. The correct answer, 738² = 544,644, is more than 10 times higher than 53,874, and so the result had been off by an order of magnitude.
- In multiplication, 918 × 155 is not 142135 since 918 is divisible by three but 142135 is not (digits add up to 16, not a multiple of three). Also, the product must end in the same digit as the product of end-digits 8×5=40, but 142135 does not end in "0" like "40", while the correct answer does: 918×155=142290. An even quicker check is that the product of even and odd numbers is even, whereas 142135 is odd.
- When talking about quantities in physics, the power output of a car cannot be 700 kJ since that is a unit of energy, not power (energy per unit time). See dimensional analysis.
Read more about this topic: Sanity Testing
Famous quotes containing the word mathematical:
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)