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Updated: May 10, 2025
Indeed, one man not being another man, the first cannot, for example, have rigorously and mathematically the same notion of unity as the second; seeing that an identical effect cannot be the result of two different causes.
In a way, economics has an affinity with some private languages. It is a form of art and, as such, it is self-sufficient and self-contained. Thus, the standard theory of utility is considered valid in economics despite overwhelming empirical evidence to the contrary simply because it is aesthetic and mathematically convenient. So, what are economic "theories" good for?
As to the mark in the uterus, he gave his opinion that it might have arisen from other causes than the one alleged; two phenomena were absent, and upon this fact he asserted it to be physically impossible that there could have been a recent delivery; and, moreover, in his "Remarks," he proved mathematically that the mark was four times the size it ought to have been on that hypothesis.
Huber has sought to explain this mystery by suggesting that the pressure of the bees' hooks and teeth may possibly produce slight projections, at regular intervals, on the opposite side of the comb; or that they may be able to estimate the thickness of the block by the flexibility, elasticity, or some other physical quality of the wax; or again, that their antennae, which seem so well adapted for the questioning of the finer, less evident side of things, may serve as a compass in the invisible; or, lastly, that the position of every cell may derive mathematically from the arrangement and dimensions of the cells on the first row, and thus dispense with the need for further measurement.
In the spot where they encountered, no mortal could observe them. Three little hills stood near each other, and down in the midst of them sunk a hollow basin, almost mathematically circular, two or three hundred feet in breadth, and of such depth that a stately cedar might but just be visible above the sides.
But cases thoroughly recorded and mathematically analyzed would always be available for future use, and when accumulated in sufficient number would lead to results which would be trustworthy, and belong to science. You young men who are following the hospitals hardly know how much you are indebted to Louis. I say nothing of his Researches on Phthisis or his great work on Typhoid Fever.
Further experiments are to be made; meanwhile, the inventor says, 'that the weapon of the earliest inhabitants of Australia has now led to the determination mathematically of the true form by which alone, on the screw principle, high speed on water can be obtained. The Ericsson caloric ship is launched; but if a new projector is to be believed, the maker may save himself all further trouble, for Mr Burn proposes to build square ships, with the bottoms constructed as double inclined planes, which shall cross from England to America in forty-eight hours!
This cannot be a solar atmosphere, since it is mathematically certain, as Laplace has shown, that no envelope partaking of the sun's axial rotation can extend farther from his surface than nine-tenths of the mean distance of Mercury; while physical evidence assures us that the actual depth of the solar atmosphere bears a very minute proportion to the possible depth theoretically assigned to it.
No bricklayer builds a wall perfectly perpendicular, mathematically this is not possible; a certain degree of perpendicularity suffices him; and he, like a good bricklayer, who must have done with his job, leaves it so.
She was so dainty, so beautifully gowned and elaborately coiffured, that Romeo compared her with his sister greatly to the disadvantage of the latter. Juliet's hair was unruly and broke into curls all around her face; Isabel's was in perfect order, with every wave mathematically exact. Juliet's face was tanned and rosy; Isabel's pale and cool.
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