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A network is classified as two or more connected devices that share information. In this world, the inhabitants use a system of trees that operate similarly to super-computers. These trees collect and share data about the world around them, and data can also be uploaded to them. They are connected all over the world through a series of underground roots that pass electric impulses to each other. In this way, they are like one super-organism, with each tree being one part of a bigger whole. Despite this, they function in the same way as trees do in our world, and have the same needs.

How can this be made possible?

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    $\begingroup$ trees already can conduct electricity, dry wood is an insulator not live wood. $\endgroup$ – John Nov 3 '18 at 12:58
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Conducting electricity is a matter simply of providing a medium through which electrons may pass and form a circuit. We use metal wires primarily because within a wire electrons flow so easily from one atom to another. Wires even have the wonderful property of conducting electric flow across the gap between two wires. This is handy, for example, when wiring up a new plug in the kitchen to run your new Whizzerizer 2000: so long as the two pieces of metal are sufficiently close, electrons can jump the gap and the juice will flow.

But other things than metal wires can conduct electricity. For example our bodies. Contrary to popular myth, our bodies are not made up "mostly of water". Closer to the truth, our bodies are made up of "mostly salt water". Water with stuff dissolved in it. The stuff dissolved in water creates an ionic solution -- positive & negative ions in free association within the watery medium -- and electricity can flow through that solution. This is why those "magic silver cleaning plates" you can buy on Amazon for only 19.99 work.

So it will be with your people's dendroupologiste. In this other world, trees live in a moist environment. Deep in the soil, their root tips stretch out into a medium of mineral matrix (soil) and water. Not so much free water as moisture bound up with the soil. What trees in this world also do, in addition to the usual chemo-fungal network communications trees ordinarily do, is have the added capacity to send electrical impulses via localised nodules of ionic solution. Basically, in the gap between two root tips, each tree exudes a tiny amount of salty water. This tiny droplet allows for electrical communication.

Those electrical impulses, generated deep within one tree's root body are carried through the fluid pathways down into the roots, leap the gap between root tips and travel up through the fluid pathways of another tree's roots and so on.

I leave for another question how your people can actually access this capacity of trees in order to use it as a functional computer!

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    $\begingroup$ You have made roots into nerves. $\endgroup$ – Willk Nov 3 '18 at 11:44
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    $\begingroup$ They kind of already are. The way trees communicate, that is. In my own world, trees form a collective consciousness. The Great Northern Forest being the oldest and most alert. And it's through the webwork of roots that the whole Forest maintains its awareness and consciousness; how individual trees communicate local conditions and needs throughout thousands of square miles of woodland. Also, when you look at a tree's root system, its branching rootlets and fine root hairs, and compare that with a nerve's dendrites (< Gk. δενδρίτης, pertaining to trees) the logical course presents itself! $\endgroup$ – elemtilas Nov 3 '18 at 12:38
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There are RL trees that have connected roots: https://en.wikipedia.org/wiki/Pando_(tree)

There are some chemical signals in plants: https://phys.org/news/2018-09-blazes-reveal-danger-distances.html

There is a mold that seems to solve complex problems: https://www.wired.com/2010/01/slime-mold-grows-network-just-like-tokyo-rail-system/ A mold could live in the interconnected tree roots, and actually benefit its host.

Now let's see how a tree system could evolve a nervous system. The point of nervous system is to respond to events. E.g. if you pinch a worm's tail, entire body will start to wiggle, trying to get out of your grip. Now let's see how the above Pando could respond to things:

  • If there is a mold attacking one tree, it would make sense to isolate it from the rest of the system, and maybe kill nearby trees to prevent spread. But that can be handled locally and chemically.

  • If some part of the system is hit by a drought, should the rest of the system send more water to try to save it? Or cut if off an save water? It is a all a single organism, and most organisms will sacrifice one body part to save the rest of the body.

    • If some part of the system finds more resources, should it share with the rest, or actually request more resources to grow more trees there?

    • If deer are eating one tree, perhaps the affected tree, and nearby trees can spray some repellent.

The above examples would be automatic instincts. Next step is to learn from experience, i.e. remember which events were good or bad, and which response worked.
But then you might end up with

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    $\begingroup$ Apparently the sentient trees got to @BaldBear before he could spill any more of their secrets $\endgroup$ – Dubukay Nov 4 '18 at 5:17

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