Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected. The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth." But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations—to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess. This imagining process is so difficult that there is a division of labour in physics: there are theoretical physicists who imagine, deduce, and guess at new laws, but do not experiment; and then there are experimental physicists who experiment, imagine, deduce, and guess. We said that the laws of nature are approximate: that we first find the "wrong" ones, and then we find the "right" ones. Now, how can an experiment be "wrong"? First, in a trivial way: the apparatus can be faulty and you did not notice. But these things are easily fixed and checked back and forth. So without snatching at such minor things, how can the results of an experiment be wrong? Only by being inaccurate. For example, the mass of an object never seems to change; a spinning top has the same weight as a still one. So a "law" was invented: mass is constant, independent of speed. That "law" is now found to be incorrect. Mass is found to increase with velocity, but appreciable increase requires velocities near that of light. A true law is: if an object moves with a speed of less than one hundred miles a second the mass is constant to within one part in a million. In some such approximate form this is a correct law. So in practice one might think that the new law makes no significant difference. Well, yes and no. For ordinary speeds we can certainly forget it and use the simple constant mass law as a good approximation. But for high speeds we are wrong, and the higher the speed, the more wrong we are. Finally, and most interesting, philosophically we are completely wrong with the approximate law. Our entire picture of the world has to be altered even though the mass changes only by a little bit. This is a very peculiar thing about the philosophy, or the ideas, behind the laws. Even a very small effect sometimes requires profound changes to our ideas. 24.
Which of the following options is DEFINITELY NOT an approximation to the complete truth?
A. I know that I know.
B. I know that I do not know.
C. I know what I know.
D. I know what I do not know.
E. I know that others do not know.
XAT SOLUTION: D A, B, C and E can be known with some errors. i.e., in each of the four options there is an approximation. In option D there is no way somebody can know what he/she doesn’t know. This is an impossible situation. Example: Somebody says “I do not know quantum mechanics.” But he/she cannot say what quantum mechanics is and what in quantum mechanics he/she does not know. Hence option D is the correct answer.
MY TAKE: But, option B should be the answer, as one definitely knows that he doesn’t know many things and even if he does, know it as approximation. Option D means I know which things I do not know, which is approximation as I cannot know all the things unknown to me. The above solution has construed this statement as a combo of 2 statements: ‘I know x’ and ‘I don’t know x’, which is obviously a contradiction. Kindly clarify. This is a xat 2016 question.