Mathematics is said to be a perfect science since there is no margin of error, unlike in history. To relate back to the question, when a mathematician says that he has explained something, he means that he has precisely proved a point based on the arrangement of elements and figures that can be reproduced over and over again.
Finally when a scientist explains something what does it mean? A scientist, will generally base his explanation on a theory backed up by a concrete experiment, in which he has actually participated.In the scientific world, if the finding is a considered an impressive break-through in its field, the same experiment will then be verified by many other scientists, trying making sure of the validity of the original experiment. The historian however bases his work on observation and deduction, no physical interaction is involved. When sodium is placed in water it spontaneously combusts, this is because it is part of the alkaline metals in group one of the periodic table.
That is an example a typical scientific explanation which is considered correct, since it has been tested over and over again. This suggests that many scientific problems are solved by allowing the applying the principle that, if an experiment works 100 times it’ll work 1000 more times. However this has often been a misleading idea, since in the biological sciences there are often many different variables that may affect scientific experiments, and misleading their explanation.For example the sodium mentioned earlier, it reacts not because it is in water but because of the temperature, it also combusts in air. Experiments therefore can become very complex and rely on the control of fine details. A convention then used, where the variables can not be controlled, is to do as many of the same experiment as possible, statistically calculating the possible margin of error ( another mathematical process), which if small enough, the results will be accepted as “true”.Therefore biological sciences differ in terms of the mathematical perfection.
Also unlike history, other human sciences are not affected by opinion, they work with universal elements. One could say that therefore there is only one unique possible explanation and that therefore when a scientist explains something he is either, right, or wrong. When a scientist explains something he refers to defined and ever existing elements that actively or passively interact with living organism.In contrast to this, a mathematician refers to conceptual, and man made elements.
So we don’t actually study or discover anything in maths, we apply maths to the physical world. Metaphorically speaking math is a jig-saw puzzle of which we have all the pieces, unlike in natural sciences where we are missing an unknown amount of pieces that are yet to be discovered.Biology as such is closely related to history, as it is strongly based on observation, such as through a microscope, animal behaviour in the field…
etc This comes under part of an experiment, if a scientist hasn’t witnessed what he is explaining, he has related the experiment of another, which may make it harder to believe him, without considering the eventual possibility that it could very well not be true.Therefore one could say that when a scientist says he has explained something he means he has put together a theory, backed up by his own previous knowledge, which he has used to set up experiments in which certain elements, through his own observation, seem to prove what he was setting out to prove in the first place.This kind of approach is very difficult to accept as a true explanation, as it’s a self fulfilling process. He has chosen the experiment that will support his theory. So as any good Theory of Knowledge question, opinion plays a large part in the different definitions of the word “explain”, depending on what you personally consider it implies, and what it relates to.
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