The computational power of plants

Martin Howard and Alison Smith are research scientists at the John Innes Centre (JIC) in Norwich, England. JIC was founded as a horticultural institution by the philanthropist John Innes in 1910, and is today one of several independent institutes affiliated to the University of East Anglia. Howard and Smith are the senior scientists on a paper that claims to show that plants can perform arithmetic division. Their co-authors are Antonio Scialdone, Sam Mugford, Doreen Feike, Alastair Skeffington, Philippa Borrill, and Alexander Graf.

Today I thought we might look at their claim and see if theory can shed any light on it.

Their paper is titled “Arabidopsis plants perform arithmetic division to prevent starvation at night,” and appeared last June in the on-line journal eLife. It attracted quite a bit of general press coverage, and also created some not very nice comments by the paper’s readers. The claim is definitely a bit wild—many of us think of plants as, well, just plants. They have no neurons, so how could they do arithmetic operations? This was the cause of the negative comments, which I think are unfair.

Let’s take a high level look at the reason they believe that plants, in particular Arabidopsis plants, can divide. Note, I know nothing about plants, but apparently Arabidopsis is an important “model” plant that is often used in research.

From The Plant’s Point of View

A plant creates starch during daylight and then consumes it at night, when it is dark. Its survival is dependent on having enough starch to make it through the night. Otherwise, it will stop growing, and could even die. If the plant has ${S}$ units of starch and there are ${T}$ hours left till dawn, it wants to consume ${S/T}$ roughly units of starch. This is clearly optimal: a nice uniform rate of consumption of the available food.

Howard and Smith, with my apologizes to the rest of their team, varied the amount of light and found that the plants were very good at appearing to do the above calculation. The plants almost always consumed about ${95\%}$ of the total starch that was available at the start of the night. Thus, they seemed to be able to do the calculation and divide ${S}$ by ${T}$.

From the Scientists’ Point of View

One model that Howard and Smith propose is that the plants literally compute ${S/T}$ and use that to decide what amount of starch to consume. They are right that doing this at any time scale works from the mathematical point of view. That is, if every hour the plant consumes ${S/T}$ and updates ${S}$ and ${T}$ according to

$\displaystyle S' \longleftarrow S-S/T \text{ and } T' \longleftarrow T-1,$

then the right portion will be consumed. Note this is unit-invariant, in the sense that if we update every minute, the plant will still consume the same about per unit time. This is a very nice little fact. At first I thought this might have been an issue, but they are right that the plant needs a “clock” of some kind, but does not need to tell the exact time in hours and minutes till dawn.

The conclusion Howard and Smith make is:

The plants must have some biological mechanism that performs division.

This is the claim that I am not convinced follows.

They suggest a mechanism which at the high level is this—quoting them in the above-linked newspaper article:

We propose there is a molecule called S which tracks the amount of starch in the plant, and a molecule called T which tracks the time until dawn. The closer to dawn you get, the less of T and S you have. If the “S” molecule prompts the use of starch and the “T” molecule prevents it, then dividing the number of “S” molecules by “T” molecules would enable the plant to use up its reserves at a steady rate, [so that the reserves] expire at dawn.

This is correct, but must the plant do the arithmetic operation of division to create this effect? That is our question.

From a Theorist’s Point of View

Okay, let’s agree that there are quantities ${S}$ and ${T}$, and that we want the ${S}$ to be consumed at the rate of ${S/T}$ per unit time. One obvious way is to have the plant do a division. Is there some way to avoid doing a division? This is the question that I find interesting.

From a theory point of view, imagine that we have a black box ${\cal B}$ that inside has ${S}$ and ${T}$. Every unit time it “ouputs” ${S/T}$. Actually it only needs to output approximately ${S/T}$. My question is, can we simulate such a black box ${\cal B}$ by another box that avoids division and yet outputs about the same quantity per unit time as ${\cal B}$?

This seems to be a nice, basic, and interesting theory problem. Certainly not one that the biologists would perhaps consider. So can we simulate division without doing division?

I am not interested in hearing that we can do division by multiplication. Yes that is possible, but then we would still be left with “Plants can do arithmetic multiplication.” My conjecture is that there should be a random process that we can construct that would behave roughly the same as the black box ${\cal B}$, and yet does not do any division. It would seem to me that the assumption that the plants’ chemistry could be random is quite plausible, and would yield a much simpler and less strange conclusion.

Consider the following model:

There are ${X}$ bins and ${X}$ balls—we have rescaled things so that the denoted quantities of starch and time are the same. Suppose at each time interval we shake things up, and some ball lands in some bin. That causes the bin and ball to be consumed. We continue doing this. Then at roughly each step, one bin and one ball are taken out of play.

That is, we seem to divide, but just use a simple random action. This seems like a simpler model, and one that we might be able to make into a viable one that a plant could do. Note that division has been replaced by a simple random process.

Open Problems

Do plants do division, or can we show they achieve the same effect with a much simpler type of operations? Does the above random model make any sense? Can we create an even better one?

March 3, 2014 7:18 pm

Isn’t the most significant element here is the fact that they varied the light? If T is changing at some unknowable rate for the plant, then I find it hard to imagine how it could calculate S/T. Even if they did modify the light slowly over time, it seems so much more likely that the mechanics in the blackbox are some form of physical response (perhaps to yesterday’s T or the gradual change in T). If your model utilizes say an opening to allow the balls to fall into the bins, and that opening grows or shrinks with time, then I could see this working. Isn’t that just one of those old sand timers? You flip it each night and the sand slowly drains out, but in this case the remaining sand from yesterday influences the size of the gap between the the glass pockets…

Paul.

March 3, 2014 8:35 pm

Of course, if you see the grains of sand in an (egg) timer as the starch, then all you need is to open the diameter of its container to different sizes to make this work. You could even prime it over time by starting with a small opening and gradually increasing it each day until you hit the 5% mark. To match the seasons, sometimes you also need to decrease it…

2. March 3, 2014 8:09 pm

There is noise in the house 5 hours a day exactly but spread out unevenly. If a little toddler wants to sleep 18 hours a day and it decides to sleep only when there is no noise, does it mean it calculates 18 hours in the day?

March 4, 2014 2:38 am

Calculators don’t really perform arithmetic either. Their circuits are just manipulated with electrical impulses until their screens light up in appropriate ways.

Less flippantly — what I don’t get is the initial incredulity of some people that plants would be able to do division to support a biological process. This is neither particularly implausible, nor does it somehow make them math geniuses. Plants live very slowly compared to us, but they are very capable of two-way interaction with their environments, through a host of interesting mechanisms. Division isn’t that far out there.

Of course the question of the simplest possible mechanism that could support the behavior displayed is interesting — Occam’s Razor and all that — but if someone demonstrated that no, division is actually taking place (and not of the cellular kind), I wouldn’t be hugely skeptical just because “everyone knows” plants can’t think.

• March 4, 2014 8:05 am

@Jeroen but the logical intention of calculators is to simulate a calculation just as a lokgical interpretation of ring operations is to effect ring operations

March 4, 2014 3:18 pm

I don’t see how adding “intention” does anything but muddy the waters. Can I say evolution “logically intended” for plants to consume their food evenly? Presumably not. But I do not believe it is therefore valid to say plants don’t do division even if we should find out that, say, every plant happened to contain a molecular division circuit (which is not likely, I haste myself to say, but bear with me for the sake of argument).

Also, what does it mean to “simulate” a calculation? They’re abstract to begin with. I’d say you can perform a calculation or not, but 2 + 2 = 4 whether you’re pressing buttons on a calculator or putting two pairs of apples together and counting them. My point is exactly that claiming that calculators don’t “really” do arithmetic seems silly and arbitrary and sheds no light on what “really” doing arithmetic is supposed to be like — if indeed there’s any way of doing it at all.

However, we’re going quite a bit off topic; the original post probably wasn’t intended to kick off a philosophical discussion (mathematical or otherwise) and what I’m saying is not original, so I’ll leave it at this and clear the stage.

March 6, 2014 12:24 am

Can’t your argument also be used for humans? Does it make a difference if I divide numbers out of need or out of boredom?

As a complexity theorist, I would say no, there is no difference. As a scientist, I am merely interested if a system under certain constraints (arithmetic circuit , Turing machine , Arabidopsis , Homo Sapiens ) can execute an operation, in this case, arithmetic division.

March 4, 2014 3:21 pm

At written exams where calculators aren’t allowed, you might still bring your house plant…

• March 4, 2014 6:32 pm

@Serge that is a nice one!

5. March 4, 2014 5:09 pm

“If the plant has S units of starch and there are T hours left till dawn, it wants to consume roughly S/T units of starch. This is clearly optimal: a nice uniform rate of consumption of the available food.”

This is not at all clearly optimal. What *might* be optimal is to have a steady state of various metabolic quantities associated with the food consumption. In that event, having a sort of stochastic rate equation or something seems like a natural way to explain this without using ideas from computation.

March 4, 2014 5:45 pm

Plants do engage in some electrical signaling.

Meanwhile, here’s one elementary model for this phenomenon. A spike of a certain starch-metabolizing enzyme formation happens every dawn, enough for 24 hours. But this enzyme is not only inactive during the day, it is subject to light-induced decay, at a rate where one hour’s worth of enzyme is lost during one hour’s exposure to sunlight.

At first glance this seems ridiculously inefficient, and offers no advantages over a blunter overnight survival mechanism. But if you read “inactive” and “decay” above as with respect to starch-metabolism only, the enzyme can simply be something that also has a useful daytime function.

In other words, perhaps plants know how to subtract?

7. March 5, 2014 10:19 am

Let’s not forget that slime mold can compute shortest paths (this was discussed earlier in this blog).

March 5, 2014 7:19 pm

Similarly, there’s a programming technique known as “ant colony optimization”. (If there hasn’t been an article here on it, there should be!)

8. March 6, 2014 2:34 pm

Reblogged this on frugallivingingreece.