I am going to teach you a shortcut in cognitive reasoning called Principle Problem Solving. Typically; if a person is trying to solve a problem they create a chain of reasoning. For example; if 8 + 8 is 16, and 7 is 1 less than 8; then 8 + 7 must = 16 minus 1. In this case the student is trying to figure out what 8 + 7 equals, and this is the chain of reasoning they used to figure the answer out. Now all cognitive reasoning relies on past observation. so, the student knew that 8 + 8 = 16. They knew this because at some point in their life they had done the cognitive work to figure that answer out. Now, in solving for this new problem they can use their past successes as a way of solving the problem faster. We all do this, but some do it more efficiently than others, and that is the difference I want to focus on in demonstrating genius level problem solving speed.
A genius in math is really just a person that took the time to learn the patterns needed to skip the logical processing steps that others would normally take. If u know the pattern you can jump to the answer faster and skip the logic. Most geniuses don’t just know one or two patterns, they are experts in the basic and advanced patterns of their fields which allow them to process information to solve problems not in steps (like the rest of us) but chunks. So if they are given a problem they look first for the cognitive jumps.
To illustrate this point lets pretend that a principle understanding or the knowing of a particular past observation is represented by 5 steps of cognitive reasoning to get to the answer. We will use the letter P to represent these already understood principles and the letter C to represent a single cognitive step in reasoning. X represents the unknown factor that we are solving for. Now lets plug this all in and look at what the difference between a genius’s thought process and our average Joe:
Genius → X = P + P + P + (C+C+C+C+C) + P
Ave. Joe → X = P + (C+C+C+C+C) + (C+C+C+C+C) + (C+C+C+C+C) + (C+C+C+C+C)
As we can see, the genius arrived at the answer in 9 moves (or cognitive processes) and the average Joe arrived at the answer in 21 moves. The Genius was only twice as fast because of the storehouse of ‘past solved for’ principles that they already had. Usually a genius’s genius only lies in a particular field or area of interest. You test them elsewhere and their cognitive processes will be slower. Though a true genius is someone who looks for these patterns in all areas, so they might start out slowly in a new field but they will adapt and learn very fast.
To apply Principle Problem Solving you must do two things:
1- Look for and learn the basic and advanced patterns/principles of whatever genre you are interested in.
2- Memorize them, and practice applying them as cognitive jumps in problem solving.
One last example to demonstrate what that looks like: Scott Flansberg is known as The human calculator and he can divide any # into another # and give you not only the whole # answer but also the decimals (the .263157 etc.) and he can do both with lightening fast speed and accuracy. Now hearing someone divide 19 into 765 is very impressive, just to hear them say 40. But to then have them rattle of the string of #’s after the decimal place, is mind blowing! “the answer is 40.263157” Wow!
But the truth is; every # has a set pattern of decimal repetitions. For example; 7 divided into 10 will always = a repeating cycle of .142857-142857-etc. So any number that 7 is divided into that ends with a 1 as a remainder (which will drop down to 10) will end in this decimal cycle. Such as 57, 78, 36, etc. So all you have to do is memorize these set patterns and when you get to the last remainder before the decimal, whatever that numbers relationship is to the number you are dividing with will trigger the already memorized set of patterns. All #’s have patterns like this and Scott pretty much knows them all, making him a calculating genius.
So there you have it: part of being a genius is just exploiting set patterns that most people are unfamiliar with. Just like how most of the secrets of a magicians set of tricks are not very amazing at all, they are simple, even a little silly sometimes, and they only create the illusions of magic because the audience is ignorant to the concept being used.