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Limits of growth — Weber’s law and its implications


One of the exciting things about founding Project Rosie (projectrosie.ch) is that I am able to totally geek out on science stuff on a daily basis. Even though I turned entrepreneur about 4 years ago (by founding my startup) I am still a scientist at heart — I eat and breath science day in, day out. By that I mean, I look at the world with skepticism. Some say that I question everything — I can’t help it but to stay curious and question what I see and experience.

In this blog post (maybe even blog-series) I want to take you — the reader — on a small tour. I want to give you a brief insight into what questions I ask myself and how I try to answer them. The information provided will sometimes be of scientific nature, and sometimes it will consist of me rambling and not finding my desired conclusion.

For today’s topic, I want to take you through a series of questions that started early morning when I entered my bathroom.

I woke up — got to the bathroom and turned on the lights. Immediately my eyes squinted from the brightness of the light source. Wow, this is bright I thought… .. . It got me thinking. Would I perceive the same intensity of stimulus if I turn on 100 more of these light bulbs? The obvious answer is: No, I would not.

But why?

As I tried to understand the phenomena I recalled something I once heard during some evolutionary biology lecture at Uni. The Weber-Fechner law, named after the German naturalists Ernst Heinrich Weber and Gustave Theodor Gechner. This law states that the ability to perceive a stimulus as different from another requires a minimum difference in intensity that is proportional to the intensity of the initial stimulus. The proportional processing of the stimulus results from the perceived psychophysical value function, in which value progressively increases with stimulus magnitude, but with a decreasing slope. It forms concave-down value functions if you so will. Interesting, isn’t it? Now that I understood what happened, I looked for more examples.

After a short while I had too many examples to name them all, so I want to share with you a fascinating one I found regarding the coevolution of species.

Coevolution of pollinating bats and nectar-producing plants

I stumbled upon a paper from the Humboldt University in Berlin. It stated that

“Plants pollinated by hummingbirds or bats produce dilute nectars even though these animals prefer more concentrated sugar solutions.”

This seems rather odd — odd because it is not obeying evolutionary principles. If one is dependent on another species to transmit genes the general feeling is that selection will drive to the apex of the possible. It didn’t — let’s see why.

Nectar is a sugar-rich liquid produced by plants in glands called nectaries. It has a particular quality and quantity. In our case, quality can be defined as the amount of sugar. If defined in such a way quality is genetically encoded — it represents the amount of photosynthate (the amount of work/energy) channeld into the nectar. The quantity is the actual availability of nectar. Quantity is thus not intrinsically defined but gets controlled by consumer behavior. It is controlled by the pollinators, they act as an economic decision maker if you so will.

Bat looking for a sweet treat.

The bats thus behaved uncommonly in both dimensions (quality and quantity). It was observed that neither did the sweetest plants win the biggest stake of the future gene pool nor the ones providing the highest amount of nectar. Both facts seem unusual, since growing to the limits of the potential should yield the greatest success when it comes to gene proliferation.

The answer to this paradox can be found by applying Weber’s law. For the plant, there is simply no evolutionary advantage to produce more sugar beyond a medium limit, since the rise in sweetness or quantity will not be registered (appreciated) by the bat (economic decision maker) any longer. The difference in the perceived stimulus is not high enough.

Yes, the bat might occasionally pollinate flowers with higher concentrated nectar, but the sudden rush of sugar does not outweigh the costs of competition and stress when visiting high-concentration flowers. A funny analogy to startups — the cost of switching a new product should thus be tracked on at least 2-dimenions. The cost of time spent and the perceived value of the overall offering, not just of the product. How big is the perceived value of a 10x better messenger app…

For me, this concludes this little mental exercise. It certainly is an interesting and different why to think about natural selection and the proliferation of genes. It appears that some genes can sneak their way past the maximalism by being the best compromise.

If you now leave confused — welcome to my life. If you leave enlightened — this makes at least one of us. If you leave curious — I have achieved my goal. As a scientist and entrepreneur, I believe staying curious and hungry to understand and search for the unknown is humanities greatest gift!

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