Can Plants Do Math?

How do some plants arrange their leaves in a whorl (e.g., see photo left) in order maximize sunlight exposure, and, thus, photosynthesis?

And how is it that plants consume stored energy in the form of starch at just the right rate so as to last them through the night?

To survive, plants must be able to adapt to changing environmental conditions, sometimes on a timescale of centuries. How do they do it?

Several recent reports have provided possible explanations for these questions.

The answer?


In Determining Pattern Formation

The arrangement of leaves on a plant is called phyllotaxis. Some plants arrange their leaves in a whorl, as shown in the picture above. Remarkably, the position of these whorled leaves on the stem can be often be predicted by a mathematical formula called the Fibonacci series. (The spiraling shapes in artichoke, cauliflower, and sunflower florets can also be described with Fibonacci numbers.)

As this phenomenon has been thoroughly described elsewhere (please see links below), I’ll not delve into it here.

I will, however, point you in the direction of a brief article entitled “Sunflowers Do the Math” that summarizes a new mathematical model showing how the distribution of the plant hormone auxin leads to this pattern formation in plants.

In Calculating Food “Burn Rates”

A recent article on the BBC website entitled “Plants “Do Maths” to Control Overnight Food Supplies” certainly caught my attention. The story was about scientists at the John Innes Centre in the UK who were studying how plants use their energy reserves at night.

Briefly, the results showed that “…plants perform accurate arithmetic division. The calculation allows them to use up their starch reserves at a constant rate so that they run out almost precisely at dawn.” (from: Plants do sums to get through the night.)

In Adapting To Change

Apparently, the scientists at the John Innes Centre have been real busy lately. Not only have they shown how plants can calculate how fast to use their food reserves, but also they are investigating how plant “intelligence” may be used to make better swarm robots.

Plants achieve exquisite organisation and spatially-controlled division of labour,” said Dr Veronica Grieneisen from the John Innes Centre. “They form complex patterns and deal with conflict or damage by acting locally but for the benefit of the whole.” (from: “Plant Intelligence for Better Swarm Robots“.)

Plants, like animals, use gene regulatory networks for control of their development and to respond to their environment. This is more analogous to computer algorithms than to simple arithmetic.

As I understand it, these scientists hope to apply these plant gene regulatory network algorithms to the computer programs controlling swarm robots.

Wow! To borrow a phrase from the 1960’s: “That’s really far out, man.

Bottom Line: Question: Can plants really do math? Answer: Well, no. (At least, not like people.)
But, because plants have complex biochemical and gene regulatory networks, with both positive and negative feedback mechanisms, the observed outputs from the workings of these networks can be mathematically described.

Online Resources for Phyllotaxis

1. Smith College has a great interactive website devoted to Mathematical Study of Plant Pattern Formation.

2. The Algorithmic Botany website at the University of Calgary offers a somewhat exhaustive discussion of the mathematics of phyllotaxis (PDF).

3. Yes, there are entire books on the subject of phyllotaxis. Here are two recent ones:
Phyllotaxis: A Systemic Study in Plant Morphogenesis

Solving the Riddle of Phyllotaxis: Why The Fibonacci Numbers And The Golden Ratio Occur On Plants

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