Hello,
I am not sure of the specific details that may (or may not) be required to ask this question meaningfully, and I apologise (though nobody is actually really offended) potentially for any lack of important details needed to answer the question meaningfully. But given my current circumstances (that I have limited access to the internet at the moment), I ask kindly that posters don't get me too bogged down on answering small details, and instead try and answer the question as meaningfully as possible given any possible limitations. Many times it may be preferable to pick apart the small details for accuracy and added meaning, but still there is always some intuition involved.
The question is about the number of equations in neuroscience research.
What I would like to know, is, as I put it, how many 'excess' equations would be involved in neuroscience research, when, combining potentially chips and computerised devices with the (biological) brain, and trying to extract a specific function from the brain which may be beyond or slightly beyond normal reach.
An example is: If researchers want certain objects to be invisible no matter what. Now, in this case, for this hypothetical example; an example chosen to illustrate that a specific function could be extracted, I am not talking about making something invisible according to the computer, or the chip, erasing the image from the environment and then transferring the changed image to the brain; I am talking about changing the actual mind's perception so that it cannot see the object, without a changed image being transferred (which would be easier). This satisfies a very specific example of manipulating the function of the mind/brain.
Now, I am aware that since there are, say, 86 billion neurons in the human brain, there must be at least millions upon millions of unknown variables for neuroscience in general. However, a large proportion of these unknown variables wouldn't become equations to be used in the calculation of this one specific function.
What I see, is that in neuroscience research, each function would require continual refinement of equations, or a series of equations that would be computed into the system. I wonder, and I ask, concerning the current state of our refined methods for neuroscience research, how many 'excess' equations would be involved, specifically as the calculations are refined and refined (further refined). By 'excess' equations, I mean that: say if you had 1000 ways of approaching the research to begin with, combining different potentials of the brain in different ways from known angles (known practical methods and equations), and then it is found that, say, many of these equations need refining further. Perhaps for each starting equation, you would then need to choose from different variables that may potentially work, so, although this may be grossly inaccurate, you have 1000, then 3 variables for each at step 1, then another 3, and another 3. You would have 1000 X 3 X 3 X 3 X 3 X 3 X 3 and so on. A bit like calculating the probabilities for unique arrangements in a deck of cards. I don't know how long it would go on for a specific function in neuroscience, but what I wonder is, how many 'excess' equations there would be. Because, 1 out of every 3 variables may be useful for the next independent equation, meaning that there would be 2 'excess' equations.
According to Khan academy website, and this is a topic about equations for 'circuits,' "As we learned when solving simultaneous equations in algebra, the number of independent equations you need to solve a system is equal to the number of unknown variables."
The next part of my question is: do you think each variable and equation would be tested extremely slowly, maybe with respect to chemical alterations to the brain and many kinks in the chips and computerised technology? I am aware that AI itself requires millions of equations for certain successful functions.
The last question is: If say, many teams of researchers found the solution to the hypothetical problem (of making an object invisible), how far may this reduce the number of 'excess' equations for another problem, such as, refining the next problem which would be, I don't know, maybe, placing your hand on different objects in the dark and your mind perceiving a hand print on certain objects, to the exact shape of your hand and the angle of the hand at the time?
I hope this is a well reasoned question, but I am aware that it may be highly inaccurate and potentially useless, because my background is not mathematics.
Thank you for your time.