Second order polynomial growth for plants: data, model and explanation
Data for a lot of species (oil palm, soybean, sunflower, rice, sage) show plants not to grow exponentially but according a polynomial of the second order. The reasons this is not discovered earlier are:
- Not small enough time intervals of sampling
- No real distinction in the growth curve between development phases, e.g. germination, vegetative, generative.
- Not discovering the partition of the growth curve in number leaves (development units) and mean area per leaf (development unit). These two components showed linear relations with time within the phases.
A simple model, based on commonly accepted growth equations but adding an equation describing a balance between production capacity and competition (avoidance) ability, showed growth according a polynomial of the second order to be possible. Simulation of two-dimensional plants, growing according the model and competing with each other, as simple as possible, showed that second order polynomial plants can win from slower and faster growing plants, suggesting an evolutionary advantage.
Fundamental questions: a thought experiment
This logical reasoning with the Evolution Theory led to a thought experiment to give guidance in how fundamental this phenomenon is. It led to the provocative, but in the end at some point to answer question: how fundamental is evolution? Is it not only fundamental for life but also for the dead world? Notice, the not proven, implicit assumption of all the separate theorizing about the dead world versus about life is: There is no way to match them. The dead world is explained starting mostly with four (five?) fundamental forces and life mostly with the evolution forces. The thought experiment consisted of the following reasoning:
- Generalization everywhere anywhere is justified in natural sciences, when we try immediately find falsifications
- So, the generalization of the physical force gravity and the life force plant growth, just because of the observation that both show a polynomial of the second order in the direction of time, is an acceptable starting point.
- Seven falsifications did, as a big surprise for the author, not succeed until now:
- (1st ) The Correspondence Principle by reasoning that gravity can emerge by evolution: an energy attracting (intercepting) force, representing the “wish” to be, and a repelling force, representing the “wish” the other no to be in the same space. Only together they are fit enough to survive, and the fittest are those who show a second order polynomial in the direction of time.
- (2nd ) Schrödinger Wave Effect and Probability, because it can emerge as a winning feature in simulation of evolution experiments with 2-dimsensional plants, as simple as possible: Plants which concentrate their descendants around the mother plant and therefore causing a wave in subsequent generations, win from those who don’t.
- (3rd) Relativity, because an observed relativity phenomenon in biology by Kleiber. A species with a higher metabolic rate, i.e. energy consumption, tends to be bigger and live longer.
- (4th ) Quantum Theory, because the obvious observation, that a plant needs a minimum quantity of cells to start a life and the reasoning .
- (5th ) The theory assessing the bending of space by gravity did not succeed initially, because bended leaves did win of flat, horizontal leaves in in simulation of evolution experiments with 2-dimsensional plants, as simple as possible. It suggest bending of the energy intercepting space to be an evolutionary advantage in the biological plant world.
- (5th) On a second glance, the fifth did succeed, because second order polynomial growth disappeared for the 2-dimensional simulated plants, making the whole starting point of the thought experiment disputable.
- (5th and 6th ) The success of the fifth vanishes by a sixth falsification, the new insight that gravity is related to information. It did a contrary job. It did reappear second order polynomial growth by assuming that an increase in information is related to more differentiation in competitive ability. Not the competition by getting a greater height and overshadowing other plants is causing second order polynomial growth but the introduction of other factors at a certain speed.
- (7th ) Superposition and Entanglement, because it can emerge as a winning feature in simulation of evolution experiments with 2-dimsensional plants, as simple as possible. However, only when plants are growing faster than according a second order polynomial, i.e. when mutation is slowing down, see 6th.
Notice the bycatch: The simulations of growing, competing and reproducing 2-dimensional plants, as simple as possible, showed
- an optimal maximum age (death),
- The necessity of keeping a certain identity apart from a certain rate of new mutations (no chaotic mutations)
- The role of concentration which makes a lot of draws within individuals with almost the same genetic composition possible, while keeping others with a (more) different genetic composition out.
In the end he thought experiment helped by explaining more in detail why and how a system arrives at second order polynomial growth. In a simulation system of growing, reproducing and competing 2-dimensional plants the individuals grow according a second order polynomial when:
- they concentrate the offspring
- with bended leaves they
- introduce mutations to other factors at a certain speed
- keep the leaves symmetric (and therefore without entanglement)
If the mutation speed is too low they will grow faster and break symmetry, i.e. they let the leaves grow only on one side and they will produce entanglement in their descendants.