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Archimedes saw something interesting while taking a bath.

Heuristic Ways

It is said that the mathematician Archimedes jumped out of his bath tub one day and ran naked into the streets of Syracusee one day, joyfully shouting "Eureka!" It means "I've found (it) out!" He had solved a problem.
As he had watched water slosh out of the tub, he had suddenly realized that something that weighed the same as his body but was more dense would make less water slosh out of the tub. (Abbott 2004, 80)

There is a way to become better at finding out things than guessing and acting at random. It is called heuristics. Professor Andrew Abbott at the University of Chicago has written a good book about heuristics used in sociology. In short, Abbott provided ideas for coming up with ideas.

Heuristics . . . are general methods for solving problems that employ principles (rules of thumb) that usually lead to a solution (Schunk 2012, 302)

Heuristics is good in one of the phases in basic research, as shown on another page [Master's Thesis Steps]. Scientific inquiry starts with getting ideas. Some people get them from others, other people hatch them (bring out ideas) themselves, and in many cases we manage to import, borrow and hatch. Regardless of their source, ideas mark where scientific inquiry starts, and scientific inquiry is a procedure.

Learning to find out things on one's own may be helped somewhat. One way is becoming good at observing first-hand. It can be trained, and ideas may rise on top of observations.

Ideas then need to be sifted and arranged. Hermeneutics is for such work. But this page is devoted to heuristics, which could be called the art of finding out first-hand. This "finding-art" can be trained through steps, measurements, and routines. The acronyms IDEAL PUPILS (to be explained further down) sum up cores of the processes.

Working Against Heuristics: Much Fear

Fear can make conform in unfulfilling, unrewarding ways; fear may not help you to progress in life, even though there are sane sides to fear, such as proper precautions. But fears may block insights, maybe insights that could help you on and up. In order to ease the way for such insights, relaxation is advocated. Probably Rogerian councelling helps too.

In psychoanalysis the client is to lie down and relax in order to find out things. Relaxing is good for coping and seeing. Sigmund Freund found out parts of that. In Zen training relaxing is an integral part of the training itself - not getting tense and upset is vital for practical benefit.

High-strung persons who have a hard time relaxing, may find that their coping efforts breed stress, and stress can breed neuroses and physical illness. In fact, it is widespread [Link].

It helps to go against stress. And to think well, it may help too, just as suggested above.

"It is a humbug"

ANECDOTE Charles Darwin was once approached by two small boys of the family, whose guest he was. They had caught a butterfly, a centipede, a beetle, and a grasshopper. Taking the centipede's body, the butterfly's wings, the beetle's head and the grasshopper's legs, they had glued them together to make an original insect.

"We caught this bug in the field," they said innocently. "What kind of a bug is it, Mr. Darwin?"

Darwin examined it with great care.

"Did it hum when you caught it, boys?" he gravely asked.

"Yes, sir," they answered, while trying to hide their mirth.

"Just as I thought," said Darwin. "It is a humbug." (Fuller 1990, No. 1121)

Four Pigs in a Pigsty

It is the heuristic aspect of science that distinguishes it in good part from engineering and technology. On the basis of a heuristic hunch, the scientist takes a risky leap. . . . Heuristic may also be called problem-solving, but the emphasis is on imaginative and not routine problem-solving. . . . Alleged established facts and bodies of information are important to the heuristic scientist because they help lead to further theory, further discovery, and further investigation. (Kerlinger and Lee 2000, 9)

Jerome Bruner:

Intuitive thinking, the training of hunches, is a much-neglected and essential feature of productive thinking not only in formal academic disciplines but also in everyday life. The shrewd guess, the fertile hypothesis, the courageous leap to a tentative conclusion - these are the most valuable coin of the thinker at work, whatever his line of work. Can school children be led to master this gift? (Bruner 1966, 13-14)

It is rarely an easy path to tread:

Scientists may experience obstacles to understanding, a vague unrest about observed and unobserved phenomena, a curiosity as to why something is as it is. The first and most important step is to get the idea out in the open, to express the problem in some reasonably manageable form. . . . Without some sort of statement of the problem, the scientist can rarely go further and expect the work to be fruitful. (Kerlinger and Lee 2000, 15)

The steps further involve forming a hypothesis. "A hypothesis is a conjectural statement, a tentative proposition about the relation between two or more phenomena or variables (ibid.)" Many persons think they know when they believe they know. There is a problem there. Frederick N. Kerlinger suggests that man employs four methods of "knowing" (Kerlinger and Lee, 2000, 6-8). However, what Kerlinger calls "methods" intertwine and cannot be separated from one another full well, so let us just call them strands of a rope. Or compare them to four pigs in a pigsty, four pigs that mingle there, grunting at times, squealing at other times. They do not exclude one another mutually, nor are they independent of each other. It is often possible to know which pig grunts, but wehen they squeal together and move about, it may be hard. All the same it is possible to hold three grunting little pigs in one's arm without being overawed: Religious beliefs which are tenacious (wilful), authoritative (having respect) and reasonable (due to id associations, in part) may be held.

  1. STICKING TO SOME TRADITION: The first pig to catch hold of, hold up and inspect, is Obstinate Tenacity. Some persons think, "The truth is true, and because it is true it is true, and will ever remain true." Some persons will stick and cling to such a pig (belief) even in the face of convincing evidence contrary to their cherished ideas. In fact, Werner Heisenberg found that tenet tenacity (obstinacy) was in full play in learned people too, and among scientists (cf. Zukav 1979, 210-23)

  2. AUTHORITIES: Some think what is held to be true is true because someone who is thought to know that insists - also on record, as in a book. Authoritative Source is the name of that "pig". Kerlinger holds or hopes that adjusting to authorities can be better than adjusting to tradition (strand 1), because some progress can be made. Present authorities might change their minds; and some new authorities can emerge. Progress may be slow, but possible. The same goes for many opposites of progress. Which will it be?

  3. HAVING SOME HUNCH OR BETTER: Kerlinger calls the third pig intuition. Hunchy Intuition may be just as good. What is referred to is an a priori method, and a way of knowing. Jerome Bruner has shown that many scientists and mathematicians use hunches in their work: "Get ideas first, verify them next," is part of the sound allround program. (Bruner, The Process of Education, 1966)

    Many persons think that some insights are true because they seem to be - maybe they seem evident, even self-evident. Or perhaps certain ideas stand to reason, look plausible and reasonable. "We hold these truths to be self-evident . . ." is a famours phrase about equality of men.

    However, Kerlinger worries that two good men, both employing valid reasoning, might arrive at different conclusions, and that very often happens in philosophy. So mind to question: "To whom are these ideas self-evident? On what grounds? In what times?" Questioning reasonably well in such veins might help too.

  4. SCIENTIFIC INQUIRY: Test Ideas is the fourth pig in the sty. Kerlinger finds that science is where ideas (tentative knowledge) are tested against the real world (data), to either validate or falsify (invalidate, debunk) the ideas, and this is done in public, to enhance objectivity. Contrast the idealized openness of science with the closedness (firmness?) of tenacity and authority.

    Some go through the scientific processes more rigorously and formally than others, but there is space enough in the world to question, wonder, observe, and synthesise information if we please. We can adapt our behavior as a result of this natural incremental (gains-yielding) process: Then we learn.

    Kerlinger thinks that scientific inquiry leads to more "dependable" knowledge, because the method appears to be self-correcting. Well it seems to be so, up to a point.

Now let us bring the pigs together in their sty again, for they feel better than way: Having a hunch or better (third scenario above) marks the beginning of scientific investigations. A heureka squeal from Hunchy Intuition may be more or less completed by grunts of Test Ideas. If squeals or grunts by Obstinate Tenacity (to a harmonious Tradition) and those of Authoritatove Source fill in with their grunts and squeals, all the four pigs in the sty may squeal a medley more or less impressively. [Compare]

Much depends on the ideas you come up with, or import and borrow from others for special reasons. In practice, scientists make use of pigs as shown. Much may unite in a larger scheme or piece of work: [Compare]

He [Albert Einstein] often told me that one of the most important things in his life was music. Whenever he felt he had come to the end of the road or into a difficult situation in his work, he would take refuge in music and that would usually resolve all his difficulties. - Hans Albert Einstein, son of Albert, quoted in Calaprice 2011, 502.

Look to the best, not to the bulk. (Norwegian proverb)

In heuristics, some findings are helped by music, the Einsteins say above. Other things depend on sleep (Maisel 2006). Critical thinking helps us sort out fallacies at least (Shermer 2013) Relaxing deeply is another obvious means of seeing things, including finding out of things. It is used in psychoanalysis. Transcendental Meditation helps against stress and fears. [◦David Lynch Foundation: Research on TM]

Then there is the question of automatic writing and much more aboute em>guessing too. It is not only having hunches; there might be a touch of paranormal activity in it too, or more than a touch. Besides, prognostics may be termed refined guessing, if it is aided by statistics about trends, for example.

At any rate, when an idea dawns on you, the hard work is to verify it, if that can be. Or implement it for the good of wise persons. There are still many more sides to issues involved, as a little cavalcade of quotations below is meant to suggest.

Kerlinger thought of four "methods", but his thinking undermines the ideas of very separate (or mutually exclusive) ways or methods of gaining knowledge. Indeed, what is at work often looks like like a number of pigs in a sty or - different strands of a rope - the aspects of a process are working synergetically.

Another way of putting it: Various sides to what is called knowing may blend. And to many, to know is to believe one knows. There is a problem there.

Further, a researcher may shift back and forth between some of all the eared pigs in the sty or all of them as is convenient, if it is at all. It is much a question of where the focuses are, how open any involved persons feel they can afford to be, etc.

Naturally, it is as should be. And learning from great men is a boon - it is fit also.

Stuck With Infirm Teachings Or Better

If you are stuck with teachings that you and others are afraid to study in depth and understand, heuristics may not help very much at first, for example due to the dependency and blocking fears that could be involved. You could benefit from being somewhat penetrating too. Detectives should, at least, for there is much shamming in the human world, that is, much feigning, faking, pretence, similation, counterfeit and affected. Detectives may have a hard time finding out first-hand. One is to take that into account too. By penetrating the faking of others, you could - ideally - get a far better footing yourself.

However, your first need could be to reduce and hopefully overcome fear and anxiety and the like - not ignoring their causes. If you have done that, you may get skilled at finding out things, that is, in heuristics. It is much used in scientific study. What is more, it can help some to get a better life by living up to its stepwise methods, if the outer conditions are not all too bad. Much depends on them.


Let us say you want to get to grips with a few tenets that are help up by some authority figure. First, gauge your circumstances and try to assess how far the authority figure is presented as mighty, or revered in your circles, how far he or she is supposed be revered as an authority by "good (obedient) guys". They are the outwardly devoted, loyal members of a "clan" or "club", even sect.

In line with that you may realise that what you have to face, is not just a problem of assessing the validity of tenets by some folks. An even better problem could be that of coping with a somewhat totem-like figure status in the "clan", so to speak, and how it may be linked to your sense of belonging, your sense of security in a setting, and further. Ramifications could be many.

Let us say you have looked into the basic tenets of a big authority. Some evidently "buy" (accept) his tenets wholesale without inspecting anything, perhaps without understanding all he is into and seems to cover either. That could be quite a problem for common lay members of the community if the revered teachings work harm, for example because they are not fit, not really true or apt.

Your Tenet Investigations

Einstein Few people are capable of expressing with equanimity opinions which differ from the prejudices of their social environment. - Albert Einstein, in Calaprice 2011, 189.

To arrive at different conclusions than the authority figure, you have to estimate yourself: One of the things you have to do is to judge (evaluate) the essence of his tenets one by one and come up with some pertinent and as unbiased conclusions as you can make. These findings need to be well-founded under the circumstances - for in heuristic work there are dangers of not understanding full well, of going amiss, and much else. One has to take such things into account, and these matters can be helped by being careful. Further, authoritative tenets and given norms or values can be (1) normative or regulative on the one hand, and (2) assessing on the other hand. They may all sway or influence conduct.

Pepping up a message by popularisation brings nothing to the validity of a given tenet.

The logic of a tenet requires skills to find out of. There are more than a hundred possible logical fallacies to look up, for example. (Bennett xxx). It could work well to find some balance between the interests of those involved.

You have to ask: Is a tenet true (too?). How to make sure before you believe it and thereby do without believing it? That is the question. Wide-ranging statistics or inquiries may offer much help in that general "roads" get etched out, even charted.

Making statements explicit (and nuanced enough) can help investigation. That is one of the main principles used in academic writing.

We could learn to inspect methodically. There are levels of proficiency involved. Then it may be time the art and craft of considering and deep pondering. [Cf. Aronson et al, 2016].

Hypotheses (and propositions can claims) may or may not be confirmed by other well-educated ones. In some cases the thinking of TWO authorities may be set up against one another. That is a much resorted-to method in discussing teachings. In such a case it might be good to keep one's eyes open to such as consistency, that is, internally non-contradictive delivery, and study facts before "buying" (believing).


Many basic scientific ways of thinking and concomitant methods can assist coping in general.

If you now want to learn basic steps of investigation, two ways are shown in the following. First you have an IDEAL, and next you have the PUPIL(S) to serve you. Combine both acronyms to get IDEAL PUPILS, and try to learn what the letters serve as memory pegs for. Acronyms can make the steps much easier to learn and remember.


Bransford and Stein formulated a heuristic know as IDEAL:

I - Identify the problem.
D - Define and represent the problem.
E - Explore possible strategies.
A - Act on the strategies [when you are up to it, when conditions follow suit, etc.]
L - Look back and evaluate the effects of those activities. (see Schunk 1996, 240.)


George Pólya's list of mental operations involved in problem solving is included below as "upil" only. Two more mementos are added; they are 'P' and 'S':

P - Peruse well. (i.e. Polya's list of operations in problem solving is applied:
U - 1. Understand the problem: What is the unknown? What are the data? What are the "conditions"? Draw a figure. Introduce suitable notation. Separate the parts of the conditions." Something like Tony Buzan's mind mapping seems fit for this stage.
P - 2. Come up with (devise) a Plan: "Have you seen this problem before or something like it? Do you know another problem with the same unknown? If you have a related problem and its solution, how can you use that here? Can you restate the problem? Solve a part of it? Solve an analogous problem? Solve a bigger problem of which it is a part?"
I - 3. Implement the plan, i.e., carry it out: "Check each step. Are they really correct? Can you prove it?"
L - 4. Look back: "Can you check the result? Can you derive the result differently? Can you use the result to solve another problem?"
(S) - Solve things markedly better after listening and getting feedback [This item is added by me, and it is in line with general study and solution procedures, where you adjust or improve outputs on top of feedback etc.]. [Abbott 2004:82; cf. Schunk 2012:302-03; 1996, 240 (where Pólya's PUPIL is.]

Systematic Pursuits

Heuristic . . . gives you tools to question what has been said, transforming it into new ideas and new views. On the other hand, steady practice of heuristic will teach you rules for separating good things that could be said from bad ones. (Abbott 2004:85)

On the one hand complete freedom can be very good help for discovering things first-hand. Some progress may be made below that level (of freedom), though. Here comes:

If others have done similar things to what you need to do, and in fields that have transfer-value to yours, study their works and learn from them, for conducting research can be very time and energy consuming, and unless you're paid it may be much costy too. So it is wise to learn to learn from others, including interesting mistakes of others.

"The central heuristic rule of normal science – science within paradigms – is simple addition." - "There are several versions of this more-of-the-same heuristic. The simplest is more data: we take the same ideas to a new place. " And, "Addition sometimes takes the form of adding a new model or methodological wrinkle or theoretical twist." (Abbott 2004:89, 90, 91)

"Heuristic is useful to all of us, each at our own levels in the social sciences . . . the basic repertoire of heuristics can be deployed in a number of ways and at a number of levels." (Abbott 2004:88)

Have "practical" aims too. (Schunk 2012:302-11; 1996, 240.)

The instructional advantage of heuristics lies in helping students become systematic problem solvers. (Schunk 2012:302-11; 1996, 240.)

A heuristic may be more systematic than our present problem-solving approaches, and can lead to better solutions. "The ultimate aim of heuristic is to improve on . . . normal science. Remember Polya's definition: 'The aim of heuristics is to study the methods and rules of discovery and invention.' Invention is what we seek [at best], not just addition. How exactly does one go about creating rules for invention? (Abbott 2004:92 cited; Schunk 2012:302-11; 1996, 240.)

Heuristics should help somewhat when facing unfamiliar content, but heuristics is in part built on getting experience in watching other people solving problems as well. And there is flexibility in how steps are carried out. Allow for both search heuristics and argument heuristics, as you find it fit (cf. Schunk 1996, 240; Abbott 2004:.]

Heuristics has been shown to help if you aim at general features in your study, too. (see Schunk 1996, 240.)  1.1.

Every argument, every generalization, every background assumption that you run into, should be scanned with this simple check: Is that really true? Could I get somewhere by regarding this as a problem rather than as something taken for granted? (Abbott 2004:126)

A final argument heuristic is reconceptualization . . . taking a familiar or taken-for-granted phenomenon and treating it as if it were an example of something quite different. . . . Sometimes reconceptualization is almost forced on one by data. (Abbott 2004:134)

Reconceptualization is always easier when one is working with . . . lists of topics or commonplaces . . . A seasoned social scientist always keeps [such] kinds of lists in mind. He or she is always rethinking things of interest. (Abbott 2004:135)

Abbott draws on lists of attributions (qualities), motives and causes. Aristotle, Kant and Kenneth Burke each contribute. (Abbott 2004, Chap. 3, passim)

Now you can go ahead and master more of the art of heuristic as you like.

Food for thought

Sleep thinking . . . is your brain continuing to work on the issues and problems that matter to you while you sleep. - Eric Maisel, 2006, 10.

[An] extraordinary thing that your brain can do while you sleep is THINK. - Eric Maisel, 2006, 11.

During NREM sleep . . . a terrific amount of high level activity happens . . . including thinking and problem-solving. David Foulkes . . . showed through his accounts of sleep subjects that people awakened during NREM sleep often reported that they were thinking. - Eric Maisel, 2006, 11.

Some dreams are meaningful while most aren't. - Eric Maisel, 2006, 22.

Record dreams and assess their meaningfulness. - Eric Maisel, 2006, 35.

Scientists, inventors, and artists . . . had solutions to their intellectual problems arrive in a dream. - Eric Maisel, 2006, 35 ff.

The world comes to meet me as a multiplicity . . . We call this form of the world simply the given and - insofar as we do not develop it through conscious activity but find it ready-made - we call it percept . . .

We do not relate percepts to ourselves only through concepts, but also through feeling. - Rudolf Steiner, 1995, 127-8.

We are so organized that the full, total reality (including that of ourselves as subjects) initially appears to us as a duality . . . and cognition assimilates it into a (monistic) unity. - Rudolf Steiner, 1995, 104.

If we consider the sum of all percepts as one part of the world, and then oppose to these percepts a second part, the "things-in-themselves," we are philosophizing into thin air. We are just playing a game with concepts. - Rudolf Steiner, 1995, 105.

From a sufficient number of perceptual facts we can infer the character of the thing-in-itself underlying those facts. . . . [But] the form that we thus give to the metaphysical can be called only relatively correct. It is subject to correction by future cases. - Rudolf Steiner, 1995, 120.

I hope my writing contrasts with the standard academic style, which 'seeks precision by total mind control, through issuing continuous and rigid interpretative directions' . . . I have tried to avoid this. - Julian Baggini 2016, Introduction.

Assuming that the dead do not have a hand in automatic writing, what are we to make of this curious phenomenon? - Richard Wiseman 2011, "Mark Twain and the Grand Illusion".

My store of mental pictures is determined . . . by the sum of concepts that have come into contact with percepts in the course of my individual life, that is, by the concepts that have become mental pictures. These, again, depend on my greater or lesser capacity for intuition and on the range of my observations - that is, on the subjective and objective factors of my experiences, on my inner character, and on my lifesetting. - Rudolf Steiner, 1995, 140.

[A] skill, called induction, enables us to summarise our knowledge of the world and use it to predict, decide and act in novel situations. - Mark Darren Reid, 2007, 3.

We think for a purpose within a point of view based on assumptions leading to implications and consequences . . . to interpret data, facts, and experiences in order to . . . solve problems, and resolve issues. - Elder and Paul, in Lennon 2014, 48.

A 2006 Reader's Digest survey of 1,006 adult Britons reported that 43 percent said they could read other people's thoughts or have their thoughts read, more than half said that they had had a dream or premonition of an event that then occurred, more than two-thirds said they could feel when someone was looking at them, 26 percent said they had sensed when a loved-one was ill or in trouble, and 62 percent said that they could tell who was calling before they picked up the phone. A fifth said that they had seen a ghost, and nearly a third said that they believed that near-death experiences are evidence for an afterlife. - Michael Shermer 2013, 1-2.

Belief systems are powerful, pervasive, and enduring. - Michael Shermer 2013, 2.

We form our beliefs for a variety of subjective, personal, emotional, and psychological reasons in the context of environments created by family, friends, colleagues, culture, and society at large; after forming our beliefs, we then defend, justify, and rationalize them with a host of intellectual reasons, cogent arguments, and rational explanations. . . . our understanding of it [reality] depends on the beliefs we hold at any given time. - Michael Shermer 2013, 2-3.

A popular notion holds that skeptics are closed-minded or cynical, but in principle, they aren't. - Michael Shermer 2013, 4.

Many smart people believe weird things, and they do so because they are skilled at defending beliefs they arrived at for non-smart reasons. - Michael Shermer 2013, 6.

The critical thinker does not have to give up hope. - Tracy Bowell and Gary Kemp 2002, 246.


Heuristics, IDEAL PUPILS, from the art of finding out, Literature  

Abbott, Andrews. 2004. Methods of Discovery: Heuristics for the Social Sciences. New York: Norton and Company.

Aronsen, Elliot, Timothy D. Wilson, Robin M. Akert and Samuel R. Sommers. 2016. Social Psychology. 9th ed. Boston, MA: Pearson Education.

Baggini, Julian. 2016. The Edge of Reason; A Rational Skeptic in an Irrational World. London: Yale University Press, 2016.

Bowell, Tracy, and Gary Kemp. 2002. Critical Thinking: A Concise Guide. London: Routledge.

Bruner, Jerome: 1974. Beyond the Information Given: Studies in the Psychology of Knowing. Selected, edited, and introduced by Jeremey Anglin. Allen and Unwin, London.

Bruner, Jerome: 1966. The Process of Education. Harvard University. Cambridge.

Calaprice, Alice, coll. 2011. The Ultimate Quotable Einstein. London: Princeton University Press.

Cayce, Edgar. 2006. The Psychic Sense: How to Awaken Your Sixth Sense to Solve Life's Problems and Seize Opportunities. Virginia Beach, VA: A.R.E. Press. Gilovitch, Thomas, Dale Griffin, Daniel Kahneman. 2002. Heuristics and Biases: The Psychology of Intuitive Judgment. Cambridge: Cambridge University Press.

Kerlinger, Fred Nichols, and Howard Lee. 2000. Foundations of Behavioral Research. 4th rev. ed. Andover, Hampshire: Cengage Learning.

Lennon, Nancy K. 2014. How Professors Infuse Critical Thinking into College Courses. South Orange, NJ: Seton Hall University Dissertations and Theses.

Maisel, Eric. 2006. The Power of Sleep Thinking. Np: Singingwood Press.

Myers, David. 2004. Intuition; Its Powers and Perils. London: Yale Nota Bene / Yale University Press.

Reid, Mark Darren. 2007. Deft Guessing: Using Inductive Transfer to Improve Rule Evaluation from Limited Data. Doctoral thesis. Sydney: The University of New South Wales.

Schunk, Dale: 1996. Learning theories. An Educational Perspective. 2nd ed. Englewood Cliffs, NJ: Merrill/Prentice-Hall.

Schunk, Dale. 2012. Learning Theories: An Educational Perspective. 6th ed. Boston, MA: Pearson Education.

Shermer, Michael. 2013. Skepticism 101: How to Think like a Scientist. Skepticism 101: Chantilly, VA: The Great Courses.

Steiner, Rudolf. 1995. Intuitive Thinking as a Spiritual Path: A Philosophy of Freedom. Tr. Michael Lipson. Hudson, NY: Anthroposophic Press.

Wiseman, Richard. 2011. Paranormality: Why We See What Isn't There. London: Macmillan.

Zukav, Gary. 1979. The Dancing Wu Li Masters: An Overview of the New Physics. London: Rider.

Harvesting the hay

Symbols, brackets, signs and text icons explained: (1) Text markers(2) Digesting.

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