Plant Intelligence
Plant's can certainty communicate with each other to some extent. But, different intelligences are good at different things. For example, slime molds outperforms humans at the traveling salesman problem, yet that doesn't mean that they are as good at understanding social queues as we are.
To figure out what an organism is good at there are two important things to consider:
1) What would be useful for it to be able to do from an evolutionary context.
2) What are the actually observations of its skills? Ideally in a reproducible confirmable way.
So, using these two ideas can we try to establish some idea of how good plants are at communication, and how they do it? Of course there is a great deal of uncertainty here, so I'll try to put and upper and lower bound with the reality hopefully lying somewhere in between.
The lower bound is simple. They are simple unthinking unfeeling mechanism of biology who release certain chemicals in response to certain stimuli. Here any apparent communication would simply be the byproduct of chemical algorithms encoded in the plants DNA.
In support of this idea is the simpleness of most plant reactions. Even more complex behaviors, like that of the Venus fly trap can still be tracked to pretty simple repeatable logic in the way that eating for other animals can not be.
The upper bound is more complicated, trees especially seem far more intelligent and complex than most people give them credit for. There definitely sold evidence for sensing and response to the environment, chemical communication between individuals, in group preference, and some degree of decisions making. There's limited but still evidence for memory and motivational trade off.
I think this points to the possibility of sentience in plants (ie: full emotions and a sense of self). In this upper bound case they would be able to recognize specific individuals, understand and respond to the affect of others, choose between different actions weight pros and cons, form relationships with each other, and perceive and understand their surroundings.
As for whether plants can understand and respond to human speech, there seems to me to be no good evidence for it. In addition evolutionarily hearing is not one of the primary skills of plants, nor is making sounds, so it seems unlikely that it would be very useful for them. Roots and chemicals have more evidence and I think make more sense for plants. To assume that they need to be able to understand and respond to our speech seems very anthropocentric to me (not to mention assuming they know you're language as opposed to another).
The best evidence for plants being able to understand people is the experiments about responding to complements vs abuse while growing. The evidence here points towards plants responding to affect, but the a study with a large sample size has never been done (that I could find). At most I think this indicated an ability to understand tone (something seen in many animals), and not an ability to understand speech.
One other thing to note is "plants", covers a huge range. It's like talking about the intelligence of all animals at once, that includes everything from humans, to bees, to clams and more. Plants certainty have a range of abilities. Large old living social plants like trees would probably have the most, and small, short lived, independent creates would be on the more limited end. (Sociability is often highly correlated with intelligence in animals)
Doing this research definitely upped my belief in possibility of sentience in plants quite a bit, but at most they seem around the intelligence of bees, and most likely much less.
NOTE: One thing that is missing here is just a bunch of examples. I know for me that's always really helpful. I don't have the time or motivation to do that right now, but maybe some other time or with some help.
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