What is archetypal thinking?

The phrase is used a few thousand times on the internet (according to Google), and its use varies a bit. There are perhaps three common uses of the phrase.

a) Thinking that contains the actual content of popular archetypal stories (e.g. legends), including some hallucinations etc. In this case a person's thoughts are not so much "personal" and "local", but rather deal with universal themes.

b) Thinking in which Jungian archetypes clearly stand out. For example a person could be wrapped around Shadow elements, their thoughts revolving around powerful symbols relating to that archetype. The rare person who has an extensive understanding of archetypes can find these archetypal elements in anyone, but here we're refering to cases when it would be obvious to the casual observer. Very often people act with motives that seem mysterious until you realize their thinking is being guided by their need to integrate "something" they are lacking (i.e., an archetype, Shadow, Anima / Animus, etc).

c) Thinking that is at a very "pure" level, timeless, i.e., without the influence of short term motives.

This article will try to give a clear definition of the third ("c") category.

Mathematics is said to help thinking.

In some families, if a child says "Why do I have to study something useless, like math?". A parent may say "Math itself is irrelevant but it will help you think more clearly". The idea being that the math itself is not as important as the studying of math. Put another way, "When you understand something mathematical just once, for the rest of your life you will carry that "mathematical power", that "logical element" with you.

Understanding archetypes is like math in that way. It may have this or that small benefit (or it may not), but its real benefit is in improving the basic ability to think with a solid foundation. The reason being that the higher mind of a person (i.e., awareness)  actually "thinks" in archetypes.

We each live trapped in a small world.

We have certain fixed values in the mind that cannot be challenged. Imagine a person with an obsession or compulsion that controls their life. A girl who cannot eat enough food because she is convinced she will not survive properly if she is perceived as fat. A boy whose first goal in life is to grow up and be part of a modern bureaucracy, whether an army, a sports team or whatever.

Each of these people do not live in a "real" world. They live in a social construct. They are allowed to open their eyes only when they are being "proper" or "loyal". It is a reality that all social creatures live with to some extent.

But there is also a "real" world with realities that trump artificial social constructs. The raving lunatic who runs through the streets naked will probably slow down and unwrap a candy bar before eating it, or maneuver to avoid stepping on a cactus. That person is discarding some of the social nonsense but still is obliged to respect most of the rules that time has tested.

Are archetypes similar to words?

At the core of any being, including a human being, is just awareness.

Awareness by itself does not contain any information. It just "is". If you are alone and quiet somewhere and there is a noise you are aware of the noise. So some of your awareness has now gone from just "being aware" to "being aware of something".

If you are only aware of the noise then it ends there. But maybe you then think about the noise. You examine its qualities or compare it to something else. At this point if you want to communicate with another person about the noise you will use a social language of some kind. You have to use a language that was specifically developed over time for the purpose of sharing information deliberately with one or more others. Each word you use has a very clear historical trail, whether the trail is known or not.

Going back to the moment you heard the sound, people have been hearing sounds of all kinds for countless generations. For most of that time a specific sound had the same meaning it did 100 years earlier or 1,000 or however long. If you live near big trees then from time to time you may hear the sound of a very large tree cracking and falling naturally. It is a sound that has been similar throughout time.

So we described first words, which change dramatically over time. Then natural sounds, which also have meaning, but which do not change like words. Archetypes are sort of like a mixture of the two. An archetype is like a pre existing word built into each human mind, the same basic words (archetypes) are in everyone regardless where they live, what local language they speak, etc.