Today scientists are furiously examining this “elephant” with their senses or their senses augmented by special instruments, and are coming up with different ideas about what they find. Some are so busy cataloguing information about one end of the elephant that they cannot hear what their colleagues are saying at the other end. In the end we can only define what a perfectly straight line is mathematically, and this enables us to plot the line on a graph.
While still considering the nature of science, we digress for a moment to look at how science is communicated. The same applies to rectangles and other mathematical objects. Fortunately our measuring devices are accurate enough for us to be able to build things and use the abstract mathematical formulae as very good approximations to deal with real situations.
Furthermore, modern science has given us the laser that has the advantage that over short distances light travels in virtually a perfectly straight line so that we can use it for determining distances very accurately. Over very large distances, however, light can be substantially bent by gravity. We see then that mathematics can often be used to give us a very good approximation to reality that helps us when we carry out certain activities.
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