In mathematics, the positive sentence is often used. I am thinking of positive three legs, or a positive angle in the XY plane. I assume that, for example, the 2nd is a ‘consequence’ of the positive orientation of the coordinate system, but where does it come from? Who ever introduced it and how is it defined? Because all in all it is strange that on an axis we are used to writing numbers in an ascending line from left to right (since we read and write from left to right), but still calibrate the y-axis from bottom to top (while you read my question nicely from top to bottom…).
Asker: Manuel, 19 years old
Answer
Manuel,
Nice question. Basically, we have two choices, one we happen to call “positive” and thus the other “negative” (one could also have chosen “red” and “blue”), but the choice for positive comes from the fact that we want to represent the real numbers by points on a line, and then it is obvious that the positive numbers are on the “positive axis” and the negative numbers are on the “negative axis” (however, there is no problem with to do it the other way around, but it can lead to a lot of confusion). For example, in the plane a rotation or rotation in the direction of the hands of a timepiece is defined as a “positive sense” and the rotation against the direction of the hands of a clockwork as a “negative sense”, this is a choice, and there there are a lot of people who do it the other way around. So it comes down to making the right agreements. When we think of graphing a function, it is “obvious” for mathematicians to draw the x-axis horizontally and the sentence from left to right, and the y-axis vertically with meaning from bottom to top. (some also take it for granted to draw these axes orthogonally, but why is this obvious?). In short, if there are reasons to do this differently, you can do so, but the question is whether this is necessary. Economists eg. sometimes the need to draw their x-axis vertically and their y-axis horizontally, why not …. a matter of agreement. So I don’t think there’s any deep philosophical thought behind this, it’s more about an agreement that instinctively counts as the most natural agreement.
Regards,
Frank De Clerck
Answered by
Prof. dr. Dr Frank De Clerck
Geometry and Agebra
university of Ghent
http://www.ugent.be
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