Reasons: Sensing logarithms

The concept of human senses has been fascinating me lately. Most of our senses give us an entirely false sense of the world. Of course, this isn’t ‘new’ – we already know that even basic ideas like ‘colour’ aren’t entirely objective. People will disagree over what makes blue and what makes green. Over 5% of us have a form of colour blindness; the most common type is a mutation in the shape of the ‘green’ cone in the retina which shifts the sensitivity of the cone towards the red side.

photo of blue pink and green led light
Photo by Tabitha Mort on

Add to this that even with normal trichromatic vision, our sight (in particular – though most senses have some form of this) allows us to see the world in a very distorted way. Our perception of brightness is logarithmic. For example, for every ten-fold increase in brightness, we might only perceive a two-fold increase. This is a quite necessary adaptation to allow us to process the wide range in light level (from near-pitch black darkness to bright daylight). But it also means what we’re seeing isn’t accurate. Even stranger is that this effect is more pronounced at the extremes, making the real curve even more extreme – we are optimised to see small changes in the middle of our range.

This effect has been made into a law (the Weber-Fechner law). One of the fundamental concepts is that the difference between 10 and 15 is usually obvious, but 1,010 and 1,015 is not, even though the numerical difference is the same.

This idea carries on into just about everything, including things we don’t necessarily think of as ‘senses’. How do you feel about money? Would you spend more time debating over two items that cost you £10 and £20, or two items that cost £110 and £120? How about £1,010 and £1,020? Our ability to perceive the difference at those different points varies, even though the ‘savings’ are the same.

Weight is another good example. You’ll notice when you’re carrying 5kg or 6kg, but will you notice if you packhorse 25kg or 26?

Hair does the opposite – the daily (or hourly, in some people) changes in appearance of someone who has shaved their head are readily perceptible, but less so with each millimetre.

Taste is another one I am considering at the moment. The results of my first beer were very good, but I added a lot of hazelnut extract – too much, I feel – and I’m concerned about how much to reduce it by. If taste follows these rules, and we’re at “too much”, how do I get it to the subjective “a good hint”? Even if I quantify those subjective comments to “too much” being “10” and “a good hint” being a “3”, does that really mean 3 = 30% of 10? I doubt it.

Anyway, I’ll leave this here for now – interesting, isn’t it? Stay tuned folks, there’s science afoot! Maybe even science through beer!


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