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Updated: May 25, 2025
When, therefore, we attempt to extend the formulA| of differentiation to plant and animal life, we are confronted by a very formidable difficulty at the outset the impossibility of determining an invariable coA"fficient for any two variables.
This is wrong. Some people prefer leisure, or freedom, or predictability to expected money. In other words, people have many utility functions running simultaneously or, at best, one utility function with many variables and coefficients.
If the mathematical order were a positive thing, if there were, immanent in matter, laws comparable to those of our codes, the success of our science would have in it something of the miraculous. What chances should we have indeed of finding the standard of nature and of isolating exactly, in order to determine their reciprocal relations, the very variables which nature has chosen?
In most of these objects other vivid rays are associated with those due to hydrogen. A blaze of hydrogen, moreover, accompanies the recurring outbursts of about one hundred and fifty "long-period variables," giving banded spectra of the third type. Professor Pickering discovered the first example of this class, towards the close of 1886, in Mira Ceti; further detections were made visually by Mr.
The magnitudes are three and eight, distance 9", p. 9°. An interesting multiple is zeta, two of whose stars at least we can see. The magnitudes are three, nine, ten, and ten, distances 13", p. 207°, 90", and 112". The chief attraction in Perseus is the changeful and wonderful beta, or Algol, the great typical star among the short-period variables.
He can find no ground for abandoning his highest hopes and relaxing his conscious effort unless he chooses to regard the unknown as the unknowable, unless he elects to believe that what no one knows no one will know, and that what someone has not yet learned no one will ever be able to teach. This goes to show that there are many variables in each man's impressions of the invisible world.
We shall understand then why our science is contingent, relative to the variables it has chosen, relative to the order in which it has successively put the problems, and why nevertheless it succeeds. It might have been, as a whole, altogether different, and yet have succeeded.
It is as in some mathematical expression containing constants and variables; the actual result changes accordingly as we assign successively different values to the variables, yet in those different results, no matter how numerous they may be, the original formula always exists.
In any case, if it explains temporary fluctuations, it will not ascertain the point round which the fluctuations take place. But the two variables, wages and profit, are clearly connected, and if we can once assume that one of these variables is fixed by an independent law, we may explain in what way the other will be fixed.
Investigation shows that, in the function called truth, previous realities are not the only independent variables. To a certain extent our ideas, being realities, are also independent variables, and, just as they follow other reality and fit it, so, in a measure, does other reality follow and fit them.
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