In a previous post on the missing faculties, I pointed out that the inductive faculty is the one that goes missing under the influence of drugs and dopamine self-addiction. The question is not ‘is there an inductive faculty?’ because those who have it, use it, and know that they use it – even if they don’t know what it is!
In the pic above, the youtube commenter promoting the use of Adderall XR asks:
“You know how [you] don’t think in words? Adderall makes you think in full sentences, with concepts depending on your mood. It calms you down more, so it’s A LOT easier to do things like this.”
There’s nothing inherently wrong with “thinking in words”, but if this is supposed to be a substitute for NOT thinking in words there IS a BIG problem.
Like dopamine self-addiction, the drugs work by turning off the portion of the mind that CAN think holistically, without words, leaving you with only the awareness that does the linear, deductive type stuff. But we need both. We need the inductive faculty to make sense of the layered patterns that fill the universe. It is essential if we are going to advance science, produce art, program computers or manage businesses. Original stuff always comes from inductive thinking. The work of the minority who actually do this is what provides the new stuff that everyone else works through with their strictly deductive kind of consciousness.
Even Gödel’s famous theorem proves that there are some truths that can be expressed deductively, but cannot be arrived at deductively – they’re arrived at with the inductive faculty – intuitively!
To demonstrate this missing kind of thinking, let’s use an example from Alan Carter’s Third Age of the World; where the kind of hidden rules that can’t be found by deductive reasoning can make all the difference. Imagine we have a city built on five islands connected by bridges like this:
The question is, can the people of the city take a stroll which crosses all the bridges (for maximum variety), but doesn’t cross any of them more than once (since that would be boring)?
One way to find out would be to use a pencil and several pieces of paper, and try lots of routes. After a while we’d probably come to the conclusion that it probably can’t be done, but we wouldn’t know for sure. We might make an exhaustive list of all possible walks, by starting on each island in turn and crossing each bridge in turn, then crossing each bridge we then have available in turn, and so on. By testing every possible route we could become more confident about our answer, but we still wouldn’t know for sure. What if we’d somehow missed a route, or made a mistake when checking one? What’s worse, if the city went and got itself another bridge, we’d have to go through the whole business all over again!
To get this puzzle under control, we need to step into the secret world of walks and bridges. 🙂 The key to it is the Zen like simplicity of the fact that every walk has a beginning and an end. Take another look at the map of the five islands. The island in the middle has four bridges connected to it. The walk could take the people over the middle island twice (which would account for two bridges both times), or over the middle island once (which would account for two bridges) so long as it also started on the middle island (which would account for one bridge) and ended on the middle island (which would also account for one bridge). It doesn’t matter which bridges are which, we just need to count bridges.
Now look at the other islands. They’ve all got three bridges connected to them. When we look at each island, we can account for two of the bridges by crossing over it, but the third bridge can only be accounted for by either starting or ending the walk on the island. If fact, because we can always account for an even number of bridges by crossing over the island, we can see that any island that has an odd number of bridges connected to it must be the start or the end of the walk. Since the walk can only have one start and one end, we can only do the walk if there are no more than two islands with an odd number of bridges connected to them. And the city has four islands with an odd number of bridges. That’s four ends, so it must take at least two walks. We can be absolutely certain that we can’t do the walk as the people want to do it! What’s more, a moment’s thought will tell us if the walk is possible when the city development program adds more bridges. Look at this proposal for a new bridge:
As soon as we look at this new plan, we can see that we have only two islands that have an odd number of bridges connected to them, so the morning walk is possible and what’s more we can see that it must start and end on the two islands shown at the bottom of the map. It’s ridiculously easy! Now look at this proposal:
Equally quickly we see that now there are four islands with an odd number of bridges connected to them, so the walk is not possible.
This little story is a true one. The city was Koenigsberg and the people of the Koenigsberg got so worked up about the puzzle of the walk that lots of them took to spending their Sundays walking round and round, trying to find the route that would let them cross all the bridges, once and only once. Eventually the problem was solved by Leonard Euler, one of the greatest mathematicians in history. The physical layout of Koenigsberg at the time looked like this:
All we need to do the apply Euler’s insight is to squeeze the two stretches of land at the top and bottom of the picture together, and draw the bridges as we’ve been drawing them up until now. How many islands are there with an odd number of bridges connected to them?
It’s the proceduralized kind of thinking – applying Euler’s insight – which our culture can cope with, and it’s the creative kind of thinking – which Euler did to solve the problem – which most cultures don’t recognize, understand or use.
Can this really be true? Can it really be that in most cultures, most people don’t use the most powerful part of their minds at all?
It seems like a bizarre idea, because we live in a culture which only acknowledges the part of consciousness that everyone uses. Because of this, there is very little in people’s day to day lives that points out to them that they are missing something.
Even so, once we have the idea that something odd is going on, it’s easy to find plenty of evidence that the whole culture really is oblivious to the most important stuff. We can only learn to see around the limited prejudices and assumptions that we have picked up from the culture around us since childhood if we understand the limitations.
Language offers a huge clue. Native American languages have evolved to enable their speakers to discuss the complex of relationships that are visible to inductive thinkers. The languages are process and action based and put their emphasis on verbs, while most languages have evolved for use by people who operate by sorting kickable objects into categories, are static and object based and put their emphasis on nouns.
Even within English, we find that mathematicians are aware of the two kinds of thinking, and use the words “deductive” and “inductive”. This awareness is in a rather specialized corner of the language though, and doesn’t usually penetrate to people’s day to day language. When mathematicians use the word “deductive”, they are usually talking about problems that computers can do really easily, of the kind:
A man goes to the shop with $10. He spends $7.50 on shopping, and puts $1.00 in a charity box. How much does he leave the shop with?
On the other hand, when they use the word “inductive”, they are talking about problems that computers can’t do easily, and can’t do with certainty at all, of the kind:
What is the missing number in this sequence?
2, 4, 6, ?, 10
The word “deductive” is not normally applied to people who work in call centers, having completely scripted conversations on the phone all day, but as they follow the little arrows on the scripts they are engaging in the kind of operation that a computer can do really easily. The word “inductive” is not normally applied to people who see that they can use modern computers and switchboards to sell motor insurance directly to the public, reducing costs to their customers and also make a profit, but as they do this kind of noticing they are doing something that a computer cannot do.
In their specialized field, mathematicians know that there are two distinct kinds of thinking, but this awareness is not common in society at large.
In most situations, deductive thinking is just called “thinking”, and inductive thinking is called “intuition” (when it is called anything at all). Intuition is supposed to be a vague thing, that many people don’t even believe exists at all, and certainly isn’t recognized as central to getting anything useful done at all.
In English, there isn’t any word for deliberately setting out to find an insight, even though no competent manager, poet or programmer can do their work without performing this crucial stage!
It’s because of this that many people think that mathematicians and scientists spend their lives grinding out deductive thinking, with lots of “therefores” in it, and live sterile and boring lives. At the same time, many people think that artists operate in a completely disorganized way, with no discipline or skill at all to what they do, and reject regimentation because they are “rebels”.
We often see value judgements that describe people who live in a robotic, reactive way, repeating the same behaviors over and over again as having “good” habits, while people who simply do not do this are “rebels” or “non-conformists”, irrespective of whatever it is they do in a non-robotic way.
It’s not what people actually do that makes them “good” or “rebels” in most cultures – it’s simply whether they do it in a robotic, deductively based kind of a way or not.