Ratio
By Andrew Stewart-Brown
A ratio is a relation between two numbers. It is not a physical object but an abstract one.
Our senses of hearing and sight are able to apprehend the ratio between two sense impressions. When we hear an octave sung or sounded, we experience a distinct pleasure. Our ears are a measuring instrument but do not flash numbers on a screen for us. Instruments which do so, tell us that in an octave the number of vibrations per second of the lower sound is half that of the higher. A simple ratio of vibrations such as 1:2 is pleasant to the ear whereas complicated ratios sound discordant. To a certain level of accuracy, the eye is also able to detect ratios and see that that one length is, say, twice the length of another.
Our other senses can tell us of ‘more or less’ of the qualities they detect. For instance, chilis can be graded according to their heat, and a consensus may agree that one is twice as hot as another.
The word ‘reason’ is derived through French from the Latin word ‘ratio’. Reasoning will often be found to entail comparisons which might either be numerical or more informal. A reasonable man is expected to have a sense of proportion, a sense of how the whole of life fits together and to know how to treat their other people fairly.
The word ratio is often paired with proportion which means an equality of ratios That is, a ratio of 2:3 is the same as a ratio of; 4:6.; In the abbreviated notation of mathematics; 2:3::4:6. In words, we say two to three is as four to six. The simplest of all ratios is 1:1. Quite evidently 7:7 is in proportion to it. We might notice that two lengths, quantities or weights are the same. If a pair of scales balance, the ratio between the weights on its pans is 1:1.
Another well-known ratio is the ‘golden ratio’, also known as the ‘divine proportion’ or the ‘mean and extreme’ ratio. As in many subjects which have been studied for centuries, there are several names for the same thing.
The simplest ratio and the golden ratio may be illustrated by the geometry of our very human form. When we stretch our arms as wide as possible and measure the distance from finger-tip to finger-tip we find that the distance is the same as our height, measuring roughly to the nearest inch. The ratio is 1:1. When we take many measurements of the heights and full arm widths of different people and find their averages, the ratio of the averages will be closer to 1:1.
Somehow, as the human body grows, it ‘knows’ to stop the growth of the arms and the height when that height and the arm width are the same.
The golden ratio can also be well illustrated from our human form. Read on here