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Given that the different parts of our brain are constantly competing for brain real estate and learning requires brain real estate, is it the case that we can only master x amount of skills due to the limit of our brain size? If we train hard enough at something is it possible that that skill can remain with us forever? If so, how much training is required before a skill can become a permanent feature in our brain?

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Many skills complement each other. For example, the more languages you learn, the easier the next language becomes. Or, if you have great finger control and flexibility from playing the violin, learning guitar will be easier (and you already know lots about music, too!). So, basically, the more you can do, the more you can do. Simple. –  what Jun 21 at 13:05

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Given that the different parts of our brain are constantly competing for brain real estate and learning requires brain real estate

Nothing competes with nothing within our brain. In fact, it's a pretty harmonious machine. Literarily.

It is just a vast network of neurons where a lot of activity happens in parallel. Unfamiliar complex tasks pose greater load on the network (meaning they require activity to spread more and be sustained for longer), and such load may spread into areas that would have done other things otherwise.

is it the case that we can only master x amount of skills due to the limit of our brain size?

Mathematically speaking:

  • To learn an infinite number of skills we would need an infinitely neuron-dense brain and infinite time.
  • If each neuron in our brain would serve as a skill (obviously you need more than one neuron for a skill, but let's just say), we could have only acquired around hundred billion skills.

Then the brain size is a poor indicator to abilities. Elephants has a brain more than 3 times the size of ours, yet they exhibit a highly limited set of skills compared to humans. It's more about how much stuff there is there, and how is it 'wired'.

If we train hard enough at something is it possible that that skill can remain with us forever?

Even if you haven't or don't train at all some skills will remain with you forever (or in most people's case, until they die). Like your skill to speak.

But generally speaking, if something becomes a 'skill' it means that it is heavily integrated in our neural network in a way that makes interpretation and execution unconscious processes.

The brain has no native conscious mechanism to forget things (although in some cases and if you know how you can exercise a mild ability to forget).

If so, how much training is required before a skill can become a permanent feature in our brain?

How long is a piece of string? It depends of what you already capable of doing, how you train, how hard the skill you try to acquire is, etc.

But if I read between the words, then basically you can master any skill you wish, so long it is realistic and you spend the time practicing it. Some people who late in their life became blind later became proficient craftsman - the brain is a wonderful machine, just waiting for you to explore and utilise it.

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Forgive me, but don't people in isolation sometimes lose their ability to speak? –  blz Jun 19 at 23:08
    
I'm not sure I can link your comment to a particular part of the answer. –  Izhaki Jun 19 at 23:14
    
sorry! You said "Even if you haven't or don't train at all some skills will remain with you forever (or in most people's case, until they die). Like your skill to speak." I was under the distinct impression that this was catigorically false. –  blz Jun 19 at 23:15
    
I see. Good point. Obviously one can forget skills, like how to play the piano. The speaking skill was given as an example of a skill you acquire without an effort. But the 'some' serves as a guard there; obviously skills can 'diminish'. –  Izhaki Jun 19 at 23:30

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