@Thomas, Interesting question.  About animals, of course they think.  "Linear and non-linear thinking", or thinking with gaps and jumps, is a very attractive way to visualize the environment. The last couple of years I worked on higher termites as a basis of host-cell interaction, bacteria & termites, termites & termites etc.

What is intriguing is their “thinking”.  In individual termites thinking gets a meaning when consider termites as a whole, we could in fact talk for a “group brain”. This “sum” creates a brain activity:  permit to the colony to create, defend, and evolve.  Cell fate: a huge queen carries identical eggs that differentiate upon an “environmental conditioning” to workers, soldiers with distinct morphological and functional properties and a “complementary brain”.   Identical eggs and distinct fates that orchestrate a group brain in harmony. 

Evolving form termites to humans, we could suggest that brain is built on two separate encoded systems the genome and what I call choros – chorobiology, which reflects the memorized space/environment.  Compare to termites, human has the capacity to incorporate this “group thinking” in one individual. “Non-linear thinking” should reflect the capabilities of human brain to visualize completely distinct phenomena (virtual or realistic) and to make assumptions and links.   Human has evolved.  In the much differentiated human societies, the environment delimits brain activities so, in that case human reflects more what you call a “linear thinking”. This is not as safe as you claim. To my opinion the “linear thinking” is dominated by the gut-brain axis and this controls emotional and logic.

In fact the real motion in all societies is the “linear thinking”, it provides to the individual safety and a real world.

See:

What is brain? Why we are forced to introduce a ‘higher dimensions’ analysis to describe brain? - ResearchGate. Available from: https://www.researchgate.net/post/What_is_brain_Why_we_are_forced_to_introduce_a_higher_dimensions_analysis_to_describe_brain [accessed Jan 22, 2017].

@Thomas, Interesting question.  About animals, of course they think.  "Linear and non-linear thinking", or thinking with gaps and jumps, is a very attractive way to visualize the environment. The last couple of years I worked on higher termites as a basis of host-cell interaction, bacteria & termites, termites & termites etc.

What is intriguing is their “thinking”.  In individual termites thinking gets a meaning when consider termites as a whole, we could in fact talk for a “group brain”. This “sum” creates a brain activity:  permit to the colony to create, defend, and evolve.  Cell fate: a huge queen carries identical eggs that differentiate upon an “environmental conditioning” to workers, soldiers with distinct morphological and functional properties and a “complementary brain”.   Identical eggs and distinct fates that orchestrate a group brain in harmony. 

Evolving form termites to humans, we could suggest that brain is built on two separate encoded systems the genome and what I call choros – chorobiology, which reflects the memorized space/environment.  Compare to termites, human has the capacity to incorporate this “group thinking” in one individual. “Non-linear thinking” should reflect the capabilities of human brain to visualize completely distinct phenomena (virtual or realistic) and to make assumptions and links.   Human has evolved.  In the much differentiated human societies, the environment delimits brain activities so, in that case human reflects more what you call a “linear thinking”. This is not as safe as you claim. To my opinion the “linear thinking” is dominated by the gut-brain axis and this controls emotional and logic.

In fact the real motion in all societies is the “linear thinking”, it provides to the individual safety and a real world.

See:

What is brain? Why we are forced to introduce a ‘higher dimensions’ analysis to describe brain? - ResearchGate. Available from: https://www.researchgate.net/post/What_is_brain_Why_we_are_forced_to_introduce_a_higher_dimensions_analysis_to_describe_brain [accessed Jan 22, 2017].

Thanks for inviting me to this question, Dear Thomas . It leads me to two levels of analysis.

In numerical methods, non-linear equations or complex differential equations without algebraic or formal solutions can be linearized and solved numerically with excellent approximation. Any curve can be plotted using very little linear segments whose distance depends on resolution intended. A simple binary code is capable of solving huge problems. Neuronal networks and many genetic algorithms, for example, work on this basis. If there are many complex problems with unknown solutions is probably just because we still hadn’t found the simplest solution for them.

Linear thinking versus non-linear thinking may be perhaps regarded in the context of this question as logical thinking, or formal intelligence, versus sensitive reasoning, or artistic intelligence. These two kinds of intelligence are equally important and can be developed. Remember for example the biblical expression in Mateus 4:4 “Nem só de pão viverá o homem”.

@Constantine Jeannocopoulis frequently brings up the idea of "reductionist" vs "holistic" thinking, and recently posited that this dichotomy in thinking is the same as "linear" vs "non-linear" thinking.  I think (no pun intended) that we all use both kinds of thinking although early education seems intended to stifle the latter.  "Keep to the subject.", "no day-dreaming", etc. are some of the things teachers try to instill in children (or used to).  It's almost like training a left-handed person to be a righty. 

The lucky child who manages to daydream her way through this kind of regimented control may be the one that ends up to be a more non-linear thinker.  Whatcha think?

The Uncanny Intuition of Deep Learning to Predict Human Behavior

"One of the most promising applications of Deep Learning (DL) is in its use to enhance interaction with computers. DL is particularly suited for this since it has an intuitive capability that is similar to biological brains. It is able to handle the inherent unpredictability and fuzziness of the natural world."

"This however does imply that improving AI to human interaction will require some level of capability of an AI to predict human behavior. This is a requisite capability and interesting enough there has been some recent research on this topic."

"The conventional behavioral model approach is to have social scientists build analytic models (statistical models in most cases) of human behavior and to employ a distribution fitting exercise to verify validity of the model. The DL approach however is different since a prior model is not required to begin with. Rather, the DL system learns to predict by observing the behavior of human participants. We can get a glimpse of this ground breaking technique by examining some recent research work that uses this approach."

"MIT trained a Predictive Vision system on YouTube videos from shows like “The Office” and “Desperate Housewives” to predict whether two persons will hug, kiss, shake hands or slap a five. The[y] trained the Deep Learning system on 600 hours of video. The system was able to predict an action 43 percent of the time. This compares to previous algorithms that could only predict 36 percent of the time ...[article continues ... with links to further research ... at link below]"

https://medium.com/intuitionmachine/deep-learning-to-predict-human-behavior-a2cd2ce14132#.spuc8ui63

Animals not only think, but many of them use "language" [including compositional syntax] to communicate "intelligently" with one another. For a better understanding of the evidence to support these assertions, I invite you to read the discussions on another question, here:

https://www.researchgate.net/post/Which_animals_are_most_likely_to_use_compositional_syntax_in_their_communications 

https://www.researchgate.net/post/Which_animals_are_most_likely_to_use_compositional_syntax_in_their_communications

If an animal is turning its head 360° to Watch its environment, how can the animal keep consciously thinking in a linear way in an environment that is not linear in structure, e.g. based on mosaic characteristics with unexpected features

Example

Patch A let me think about red and aspects associated with red, patch B let me think about green and aspects associated with green, etc...

Is there a logical connection between patch A and patch B that should provoke linear thinking?

Dear colleague

Non-linear thinking, a relatively new term, is vague enough (perhaps naturally so) that a simple google search will yield more beatings-around-the-bushes than formal definitions for the phrase. I think of it as follows:

Human thought characterized by expansion in multiple directions, rather than in one direction, and based on the concept that there are multiple starting points from which one can apply logic to a problem. Non-linear thinking is less constrictive – letting the creative side of you run rampant because of its inherent lack of structure. It’s kind of like letting a puppy run wild on a walk up a mountain – anything of interest will be thoroughly investigated (and perhaps peed on) before jumping to the next, possibly non-related subject! It’s very much like brainstorming – allowing thought to flow, unhindered, in attempts to arrive upon something special in the process. Non-linear thought increases possible outcomes by not being so certain about the starting point for any logic process. Non-linear thinkers tend to jump forward, and from side to side through the steps of a project, in an effort to see the big picture and tackle those areas where they have the most interest. Where non-linear thinking falters is in finally carrying out the required action, because as a thought process it often encourages a user to agonize incessantly over where to start (that agreed upon truth, from which logic can be applied and action can be taken). A new form of digital presentation created by the folks at Prezi.com is a great example of non-linear and linear thinking in action. Why? Because rather than a linear slide show, it’s ultimately a picture, into which you can zoom in and out, infinitely. It allows you to present a product, concept, or argument in a logically by moving from location to location what is essentially group of images, but at any point you can zoom out and suddenly.

Regards 

I think that the thinking is not geometric. A control to creative thinking is its logic, because illogic creation has not got reason of being.

Is creative art always logical in construction? Is intuition logical?

Dear Thomas:

Beyond the techniques that point to a more or less systematic use of non-linear thinking, my view is that we use this type of thought not oriented by rational operations more usually than we are aware. 

Many ideas come to mind without a conscious effort to produce them. Sometimes, in fact, ideas come to us while we sleep, when we are able to remember the dreams. 

In other words, the subconscious mind works all the time, it is highly productive and it does not necessarily follow logical paths.

@ Marcel asks "Is intuition logical?"

IMO  Yes, intuition CAN be considered a strictly logical process, but depends on the precise constraints of your definition of "logical." It may help to review what is meant between (believed about ?) being realistic, logical, rational and practical, using some "real" world examples?

"Basically, if you go by the definitions provided by Google, a realist would be person who carries an ideology most coherent with the "real" facts. Now, what is real and what is not can, itself, be a subject of heated debate. Some would say that in reality we are living, and breathing (100% biological) creatures, while some might argue that we are but comprised of information stuck in some sort of virtual reality, as portrayed in the Matrix movie series. Neither can be conclusively proved or disproved. Hence the need for the modifier ... "most coherent."

"A logician goes by some pre-established (stated or carefully defined) facts and figures (theorems) that he holds as undoubted universal truths. Facts which (he believes) cannot be disputed. Like, for example, the earth being round. Now, with his basic set of truths, he proceeds to twist-and-turn them, and come up with an inference regarding the situation at hand. So, for example, if a logician knows the earth to be round, he can infer that you won't fall off an edge.

"A rational person is kind of like a logician except that his set of beliefs may extend to a broader horizon than a logician. In other words he is a bit more flexible (accepting of unproved facts), and might be considered as a mix of "logical", and "realistic". A rational person, knows for a fact that the earth is round, logically infers that he won't fall off of it, but, would INTUITIVELY know better than to argue about it with a bunch of flat-earther fundamentalists wielding firearms.

"Now, enters the practical person. He knows that just knowing facts and figures (and how to logically manipulate them) won't get him much ahead in practical or "real" life. He cares more about what good things might befall him in the long run (and INTUITIVELY knows how to selfishly avoid all responsibility, pain, cost or loss to himself in acquiring them). He won't sit around arguing, trying to prove or disprove whether the earth is round or not, or wasting his time in trying to prove anything else. Not unless the proof concerns him in some practical (profitable or selfish) way. In a war between flat-earthers and round-earthers, he will try to sell weapons indiscriminately to either side (or ideally, to both), whichever way profits him most." [adapted from discussion at link below]

https://www.quora.com/What-is-the-difference-between-being-realistic-logical-rational-and-practical

Yourletter mentioned the word facts.  Since the inauguration, CNN has been talking about älternative facts. What in the world do you think that boils down to?

Alternative facts: The evergreen oak is gold coloured when the morning sun is touching its leaves?

https://www.youtube.com/watch?v=vq3RjZ2oZzM

Marcel, I'm not sure that is an alternative fact (the way it's used these days in politics it means a lie).  This seems to me to be a poetical expression showing that green is sometimes gold etc. due to the many ways we use the adjectives.  It's like my joke from some other thread long ago.  What's red, green and black at the same time?  Answer: A black raspberry.  It's called "black" - its name; But when it's unripe, that is, "green", (name of a state of ripeness or not), it is actually "red" {the color we see at that time).  I think there is a more cynical caste to the word "alternative fact".  Let's keep an eye on the times you (and I) hear something being called an AF and see what we are now doing to the English language. :-)