The very beginnings of science are taught on the same pernicious system. In most schools even arithmetic is taught in the abstract way, and mere rules are stuffed into the poor little heads. The idea of a unit, which is arbitrary and can be changed at will in our measurement (the match, the box of matches, the dozen of boxes, or the gross; the metre, the centimetre, the kilometre, and so on), is not impressed on the mind, and therefore when the children come to the decimal fractions they are at a loss to understand them. In this country, the United States and Russia, instead of accepting the decimal system, which is the system of our numeration, they still torture the children by making them learn a system of weights and measures which ought to have been abandoned long since. The pupils lose at that full two years, and when they come later on to problems in mechanics and physics, schoolboys and schoolgirls spend most of their time in endless calculations which only fatigue them and inspire in them a dislike of exact science. But even there, where the decimal measures have been introduced, much time is lost in school simply because the teachers are not accustomed to the idea that every measure is only approximate, and that it is absurd to calculate with the exactitude of one gramme, or of one metre, when the measuring itself does not give the elements of such an exactitude. Whereas in France, where the decimal system of measures and money is a matter of daily life, even those workers who have received the plainest elementary education are quite familiar with decimals. To represent twenty-five centimes, or twenty-five centimetres, they write “zero twenty-five,” while most of my readers surely remember how this same zero at the head of a row of figures puzzled them in their boyhood. We do all that is possible to render algebra unintelligible, and our children spend one year before they have learned what is not algebra at all, but a mere system of abbreviations, which can be learned by the way, if it is taught together with arithmetic.[190] The waste of time in physics is simply revolting. While young people very easily understand the principles of chemistry and its formulæ, as soon as they themselves make the first experiments with a few glasses and tubes, they mostly find the greatest difficulties in grasping the mechanical introduction into physics, partly because they do not know geometry, and especially because they are merely shown costly machines instead of being induced to make themselves plain apparatus for illustrating the phenomena they study.