Plants are living beings, so it is normal to think that they can feel pain, but the answer to this concern is negative: plants do not feel pain, as they lack the nervous system and the brain to process stimuli in this way. Pruning a plant or biting a fruit is not painful for them, but this does not mean that plants are inert beings, quite the contrary. Their means of communication are very different, but they are present.
Why plants do not feel pain
Pain is an evolutionary mechanism that alerts us to something bad that is happening to us and forces us to flee or move away from that negative stimulus. For example, if you have brought your hand too close to the hot cooker, the pain of the burn alerts you to pull your hand away. Without pain, you wouldn't notice and you would end up with a burnt hand. So we should be thankful that we feel pain because it is our body's alarm.
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From this perspective, plants don't need that stimulus that we know as pain, because they have no way of fleeing or withdrawing from the situation that represents danger, so they have developed other mechanisms of communication.
How plants sense and communicate
One of many people's favourite smells is that of freshly cut grass. To us, this smell evokes summer and greenery, but the truth is that this scent is a chemical stress signal that alerts us to what is happening at the moment. Plants communicate, just in ways we can't so easily interpret.
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There are plants that use chemical alerts, which communicate to nearby plants that there are potential dangers. This allows them to attract certain insects to ward off other pests, as shown in this report. Other plants, for example, synthesise certain chemicals to enhance their pollination, such as some that produce caffeine to defend themselves, but the caffeine attracts bees that enhance the plant's fertilisation and ensure its survival.
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Several studies have shown that plants can communicate with each other using a complex network in the subsoil with the help of some fungi, which would communicate the roots of different specimens in a terrain almost like internet nodes. This would allow them to share nutrients and information about hazards and other events.
Plants are sentient. They can sense the sound of an insect chewing on their leaves, they employ photoreceptors that allow them to pick up the intensity of light, and carnivorous plants can sense when prey is approaching and close in to catch it. But don't confuse this with the ability to process these stimuli.
As mentioned at the beginning, there is no centre for consciousness and cognition, there is no brain; so all these forms of communication and response to stimuli are rather instinctive. Don't worry, you can prune and take cuttings from your plants with confidence that you are not harming it and it is not suffering but will benefit from the maintenance.