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Posts Tagged ‘**hypothesis**’

**“Abduction field” or a priori “stealing” program; (Jan. 23, 2010)**

I am coining the term “abduction field” to describe and explain how people manage to function in their daily routine. People move and act as if executing an “a priori program”: they seem to mentally “pick up” objects and event as they go about. People seem to know in advance what they want to do. Hazards are just obstacles that the “abduction field” in the brain failed to adjust in a timely manner to redesign the plan. It might be a good idea to explain what abduction reasoning means before I venture into this topic.

Human mind uses many reasoning methods such as deduction, induction, and abduction. Deductive reasoning is a process that starts from a set of basic propositions (proved or considered the kind of non provable truths) and then prove the next propositions based on the previous set. In general, a law, natural or social, or a theorem in mathematics guides the demonstration. Practically, it is like using a function to find the appropriate pieces of data or information that are available on a well drawn path or trend.

Inductive reasoning is a process of selecting samples from a phenomenon or a basket of items and then studying the samples. If the items are the “same” in each sample then the individual is prone to recognize that a law is guiding that phenomenon. The sample taker is ready to form a law, though he knows that logically, if in the future one sample is wrong, then the law is logically invalid. In the mean time, the sample taker can resume his life as if the law is valid, as long as it is working (more frequently than not).

We call a “paradigm shift” the period when accumulated samples or observations are showing to be “false” and that the law has to be dropped for a better performing law. The process needs time before the scientific community reaches a consensus for a change in venue, simply because it was comfortable using well-known mental structures. The paradigm shift period is shortened if a valid alternative is demonstrated to work far better, not just slightly better, than the previous theory.

Abduction reasoning is an “intuitive” process such as having a few facts or data and we manage to find a connection among these facts. In a way, we got an idea that the facts follow a definite trend. For example, the astronomer and mathematician Kepler started with the notion that planets move in circles around the sun; his observations of Mars detected two positions that didn’t coincide with any circle. Kepler selected another trajectory among those mathematically described in geometry that might be appropriate. The elliptical shape accounted for the two observed positions of Mars. Kepler got convinced that planet trajectories are elliptical, but he needed to convince the “scientific community”. Thus, Kepler worked for many years waiting for Mars to cross different positions that he knew would inevitably be on the ellipse anyway.

Most scientific discoveries are fundamentally of the abduction kind reasoning. Usually, in order to describe the discovery process, scientists prefer to introduce as many deductive or inductive reasoning in the explanation so as to avoid sounding that the discovery was a pure fluke of intuition and not hard mental work.

People use the abduction reasoning technique as routine behavior to decide, move, or act. People have implicitly a priori (idea, plan, concept, hypothesis, path, or line of actions) before they get moving. People move as if they already know what will happen next; they adjust their plan as frequently as obstacles occur. Thus, abduction reasoning is the rule instead of the exception in most commonly used strategies.

A good way to explaining the abduction field theory is by observing someone who is familiar with a particular supermarket. The customer moves around and pick up items in a determined manner. A few times, the customer stops and study particular varieties of the “same” items for prices, weight and chemical contents. The customer might look as if he just woke up or is disoriented, but his action is kind of planned: he behaves pretty “sober” in his decisions.

People move and act within abduction fields of reasoning, otherwise, how can we imagine extending a step forward without advanced planning? The initial schemas of abduction fields are not that well oiled, and many errors and pitfalls occur during the abduction plans. By the by, the human brain gets adjusted and trained to secure better fit in forecasting next steps and moves.

Highly intelligent people differ from normal intelligence in that, more frequently than not, they consciously apply deductive and inductive reasoning on their initiated abduction fields. The implicit purpose is to optimize the “abductive field” performance by supporting it with better formal or coded laws among the working laws.

With conscious training and application of the other two reasoning methods, the individual acquire higher intelligence reasoning choices or diversified perspectives to viewing and resolving a problem.

Brainwashing is an application phenomenon of abduction field distortion. Brainwashing is not so much a process of feeding misinformation or disinformation as in ideologically and dogmatic State-controlled government. Brainwashing is the process of altering the abduction field so that an individual lacks the objective flexibility to pick up the appropriate objects, tools, or events to place on his “abduction path”: The individual is picking what is available on his path, including ready-made terminology and definitions, and not what his brain was more likely to select in normal conditions.

When we say “this guy is a one track mind or one-dimensional mind” then we basically means that his abduction field has been restricted by habit: his brain ended up lacking the potential flexibility and versatility to train and develop his abduction field reasoning.

Note: I am under the impression that Spinoza had the same philosophical theory when he wrote: “The movements of our investigative spirit obey real laws”. If we think well then we are bound to think according to rules that link things one to another. Kant adopted this reasoning and offered the “a priori” dispositions of the mind. I think Einstein misinterpreted Kant’s “a priori proposal” because Einstein was engrossed with the deductive processes in resolving the restricted relativity theory. Einstein was not concerned of how people behave in their daily routines.

Note 1: The abduction field explains the contradictory feeling we have that our actions are determined frequently or following a free-will course of action, occasionally. For example, if we consciously start with a thief program that is pre-programmed to suit what we want today, we tend to steal objects, events, opportunities on our way. Otherwise, the default value is the “habit thief program”, and we feel that the day is pretty much determined.

Note 2: The individual “I” is spread all over our organism, physical, genetics, and mental (brain). Decisions are delayed until all the different varieties of “I” reach a working consensus, or a particular I override the other I, depending on which thief program we launched at the start of the day.

**Idiosyncrasy in “conjectures”; (Dec. 21, 2009)**

Idiosyncrasy or **cultural bias** relates to “common sense” behavior (for example, preferential priorities in choices of values, belief systems, and daily habits…) is not restricted among different societies: it can be found within one society, even within what can be defined as “homogeneous restricted communities” ethnically, religiously, common language, gender groups, or professional disciplines.

**Most disciplines have mushroomed into cults**.

A cult is any organization that creates its own **nomenclature** and definition of terms to be distinguished from the other cults in order to acquiring recognition as a “**professional entity**” or independent disciplines that should benefit from laws of special minorities (when mainly it is a matter of generating profit or doing business as usual).

These cults want to owe the non-initiated into believing that they have serious well-developed methods or excellent comprehension of a restricted area in sciences. The initiated on multidisciplinary knowledge recognize that the methods of any cult are old and even far less precise or developed; that the terms are not new and there are already analogous terms in other disciplines that are more accurate and far better defined.

Countless experiments have demonstrated various kinds of idiosyncrasies. This article is oriented toward “cult” kinds of orders, organization, and professional discipline. My first post is targeting the **order of mathematicians**; the next article will focus on experiments.

Mathematics, meaning “sure study” (wisekunde), has no reliable historical documentation. Most of mathematical concepts were written many decades or centuries after they were “floating around” among mathematicians.

Mathematics is confusing with its array of nomenclature. What are the differences among axiom, proposition, lemma, postulate, or conjecture? What are the differences among the terms, theorem, questions, problems, hypothesis, corollary, and again conjecture? For example, **personally, I feel that axiom is mostly recurrent in geometry, lemma in probability, hypothesis in analytical procedures, and conjecture in algebraic deductive reasoning.**

Hypothesis is in desuetude in mathematics. For example, Newton said “I am not making a hypothesis”.

**Socrates** made fun of this term by explaining how it was understood “I designate hypothesis what people doing geometry use to treating a question. For example, when asked for their “expert opinion” they reply: “I still cannot confirm but I think that if I have a viable hypothesis for this problem and if it is the following hypothesis… then I think that we may draw a conclusion. If we have another hypothesis then another conclusion is more valid.”

**Plato** said: “As long as mathematics start from hypothesis instead of facts then we do not think that they have true comprehension, since they are not going back to fundamentals”

Hypothesis is still the main term used in experimental research. Theoretically, an experiment is not meant to accept a hypothesis as true or valid, but simply “Not to reject it” if the relationships among the manipulated variables are “statistically significant” to a pre-determined level, usually 5% in random errors.

Many pragmatic scientific researchers don’t care about the fine details in theoretical mathematical concepts and tend to adopt a hypothesis that was not rejected as law. This is one case of idiosyncrasy when the researcher wants badly the “non-rejected” hypothesis to represent his view. Generally, an honest experimenter has to repeat the experiment or encourage someone else to generalize the results by studying more variables.

Conjecture means (throwing in together) and can be translated as conclusion or deduction; basically, it is an opinion or supposition based on insufficient proofs.

In the last century, conjectures were exposed in writing as promptly as possible instead of keeping them floating ideas, concepts, or probable theorems. This new behavior of writing conjectures was given the rationale that “plausible reasoning” is a set of suppositions thrown around as questions mathematicians guess they have answers to them, but are unable to demonstrate temporarily.

The term conjecture has been used so freely in the last decades that **Andre Weil** warned that “current mathematicians use the term conjecture when they fail after a few attempts to verify a concept, even if the problem is of no importance.” **David Kazhdan** ironically warned that this practice of enunciating conjectures might turn out like a 5-year Soviet plan.

At first, a set of conjectures was meant to be the basic structure for a theorem or precise assertions that were temporarily used in the trading of logical discussions. Thus, conjectures permit the construction of rigorous deductions that are accessible to direct testing of their validity. A conjecture was a “research program” that move ahead in order to foresee the explored domain.

Consequently, conjecture is kind of extending a name and an address to a set of suppositions and analogies for a concept, long before tools and methods are created to approach directly the problem.

A “Problem” designates a mental task submitted to the audience or targeted for research or project; usually, the set of problems lead to demonstrating a general theorem. Many problems are in fact conjectures such as the problem of twin primary numbers that consists of proving the existence of an infinity of coupled numbers such that p-q = 2.

One of the explanations for using freely the term conjecture is the modern facility of mathematicians of **discriminating aspects of uncertainty at the theoretical level.** It is an acquired habit, an idiosyncrasy. Thus, for a mathematician to state a conjecture he must have solved many particular cases and recognize that a research program is needed to developing special tools for demonstrating the conjecture. **This is a tough restriction in this age where time is of essence among millions of mathematicians competing fo**r prizes.