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.
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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)
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”
—Blaise Pascal (1623–1662)