There are two different types of analysis and learning relating to our ability to see and recognize patterns and relationships. One method is extrapolative, which means finding the next item in a sequence of items. The second method is interpolative, which means finding the missing item somewhere in the middle of a sequence of items.
We are expressing ourselves interpolatively when we average items -- for example when you are told that an item will cost between $10.00 and $20.00, your mind averages the two together and you think of a "middle" or simple mean average price of $15.00. This is how most people think without realizing that they are doing it. In fact, if you were told that the price would be on the higher side, you would probably interpolate the anticipated price as $17.50 -- we do this by first finding the mean, and then by finding a second mean (or 'derivative mean') between the first mean and the maximum. Our mind dices and slices when we are asked to estimate "between" two things.
When we must find the last item in a sequence of items, we must recognize a pattern and then apply extrapolative thinking. An Example of each type follows, for a quick brain exercise:
1) We are on a 100 mile trip, and have gone three quarters of the way. How many miles do we have left? How many miles have we already traveled? In we are going to make a rest stop halfway between where we are and our final destination, how many more miles must we go before we can rest?
2) What is the next item in the series? ABD, BCE, CDF.... ___ .
Enjoy the TED Video (Goals Versus Behaviors) which follows!
Douglas E Castle for Braintenance
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