Hand Proof

Quiz Results and Comments: Moses and Exodus and Kings of Egypt and Judah

2010-04-04T00:41:00.000+03:00

Quiz Results and Comments: Moses and Exodus and Kings of Egypt and Judah

The key to astronomy has often been serendipity

2010-01-04T01:54:00.000+02:00

The key to astronomy has often been serendipity

We tweeted at Twitter:

The key to #astronomy has often been serendipity http://bit.ly/4PVX3x ars technica John Timmer #astronomical #discoveries #history #science

Sign Petition for Libel Law Reform in the United Kingdom (UK)

2010-01-04T01:45:00.001+02:00

See the Law_Pundit tweet at Twitter:

Sign #Petition for #Libel #Law #Reform in the #United #Kingdom #UK http://bit.ly/8T5NFd Index on #Censorship #PEN Sense about #Science

Truth in Science : C. John Holcombe at TextEtc.com

2010-01-04T01:17:00.001+02:00

Truth in Science by C. John Holcombe at TextEtc.com:

"What is science, and what are its intellectual underpinnings?

This is a short article which covers "truth in science" from the standpoint of the works of Thomas Kuhn, Karl Popper, Imre Lakatos, and Paul Feyerabend.

Theories of Truth at the Encyclopedia.com

2010-01-04T01:08:00.000+02:00

Theories of Truth at the Encyclopedia.com:

Theories of Truth

Whoppers of 2009 | FactCheck.org

2010-01-04T01:03:00.000+02:00

Whoppers of 2009 | FactCheck.org:

"Whoppers of 2009
We review the choicest falsehoods from a year that kept us busy."

snopes.com: Urban Legends Reference Pages

2010-01-04T00:49:00.000+02:00

Rumor Has It at Snopes.Com: Urban Legends Reference Pages, which is:

"a searchable database of urban legends and myths, email hoaxes, computer virus warnings, and folklore."

FactCheck.org

2010-01-04T00:41:00.000+02:00

FactCheck.org

"monitor[s] the factual accuracy of what is said by major U.S. political players in the form of TV ads, debates, speeches, interviews and news releases. Our goal is to apply the best practices of both journalism and scholarship, and to increase public knowledge and understanding."

Facts and Theories

2010-01-04T00:36:00.000+02:00

Facts and Theories

Theories versus facts : V. Turchin : Principia Cybernetica Web

2010-01-04T00:34:00.000+02:00

Theories versus facts

"Top-level theories of science are not deduced from observable facts; they are constructed by a creative act, and their usefulness can be demonstrated only afterwards. Einstein wrote: 'Physics is a developing logical system of thinking whose foundations cannot be obtained by extraction from past experience according to some inductive methods, but come only by free fantasy'."

The Enchanted Glass: Scientific American by Michael Shermer

2010-01-03T23:19:00.000+02:00

The Enchanted Glass: Scientific American by Michael Shermer

"Francis Bacon and experimental psychologists show why the facts in science never just speak for themselves."

"Cognitive barriers that color clear judgment presented a major impediment to Bacon's goal. He identified four: idols of the cave (individual peculiarities), idols of the marketplace (limits of language), idols of the theater (preexisting beliefs) and idols of the tribe (inherited foibles of human thought)."

FactCheck.org

2009-12-10T23:04:00.000+02:00

These people check the facts. Great site.

FactCheck.org

Looking over the Shoulder of the Creator of “A Christmas Carol” - The New York Times

2009-12-02T02:08:00.000+02:00

Looking over the Shoulder of the Creator of “A Christmas Carol” - The New York Times

Hand Proof - Just a Lot of Handwaving - Psychoanalysis and Socratic Education

2006-09-08T12:12:00.000+03:00

There are advantages, disadvantages and pitfalls both in the exercise of judgment as well as in the exercise of intuition. In the Abstract to Psychoanalysis and Socratic Education*** by Trevor Pateman (article available as a .rtf document), it is written that:

"A range of concepts are introduced to argue similarities between Socratic Education and Freudian psychoanalysis. The concepts are these: the talking cure; floating attention; knowledge and acknowledgment; judgment and intuition; (prior) theoretical understanding; attending for truth; acting in role; play; negative dialectics; the training of the self ... "

What interests us particularly to describe the content of this blog in the future is Bateman's discussion of judgment and intuition, the former - in his definition - involving what we know or think to to know in an appeal to shared knowledge and the latter - in his definition - involving the subjective expression of how things look or feel to us as individuals. Bateman writes:

"The exercise of judgment involves appeal to what I know or think I know at some articulate level of consciousness. Typically, judgment appeals to shared knowledge: what everyone knows or thinks. So rationalization and self-deception find ready-made support in all kinds of conventional wisdom...."

In contrast, intuition is the expression of a personally experienced connection, drawing on a reservoir of inarticulate consciousness. Intuition is the expression of how things look or feel to me.... [I]ntuition will get us to a (correct) result well before we have the means to judge its correctness ... [M]athematicians have the concept of a hand proof. In a hand proof, there is no (real) proof, just a lot of handwaving. But it gestures to an intuition that if we set out in the general direction indicated by the hand proof, we will get to the proof we want to reach. Intuition is then like a compass. [emphasis added]

But intuition does not always work like this; sometimes it leads us astray. Shown the Muller-Lyer lines, I may intuit that one is longer than the other, but I am actually wrong; judgment is against me. But it still remains that the lines look that way. (The Muller-Lyer lines are the ones placed parallel to each other, but with arrow-heads pointing in opposite directions)...."

To see a graphic of Muller-Lyer lines, see the Epistemology of Perception at The Internet Encyclopedia of Philosophy.

*** "Website version 2004. A first version appeared, under the same title, in a 1993 issue of Aspects of Education (University of Hull, England), number 49, pages 76 - 80. A second version, again under the same title, appeared in S.Appel, editor, Psychoanalysis and Pedagogy (Bergin and Garvey: Westport, Connecticut), pages 45 - 51. Copyright material used by permission."

The basic problem with "hand" proofs as opposed to "mechanical" proofs is that, as noted by Neeraj Suri, Michelle M. Hugue, and Chris J. Walter in Synchronization Issues in Real-Time Systems:

"As hand proofs are sensitive to the skills of the prover, mechanical proofs are sensitive to the correctness of the theorem prover and its underlying logic. "

In other words, to employ a phrase used by Thomas Kuhn (The Structure of Scientific Revolutions), if the paradigms (viz. "mechanical" proofs) underlying a given view of "shared knowledge" are wrong, then that knowledge is likely also wrong. What this means is that someone along the way has done an intuitive "hand proof" which does not conform to the judgmental mechanical proofs in vogue. A hand proof made by a skilled prover is thus always at the root of scientific progress, in any academic field.

In this regard, Thomas Kuhn's theory of scientific revolutions is more accurate than Karl Popper's ideas concerning scientific thought as the falsifiability of mainstream statements because "hand proofs" - also in fields other than mathematics - are generally made to conform to the observations at hand, often initially ignorning completely any presumed attempt to "falsify" existing mainstream ideas.

Only after an observation-fitting hand proof is made and then compared with the mechanical proofs in vogue does the battle with the inertia of existing paradigms begin.

Mainstream scientists want the ensuing discussion to proceed under their terms and thus demand that their theories be proven false. This, however, does not accurately describe the process of scientific discovery - this constitutes Popper's main error in analysis. Popper, by concentrating on mainstream science, does not actually describe the actual process of scientific advance - rather, he describes the process of mainstream resistance to advance and the mechanisms by which that resistance is broken.

The true pioneers in science, on the other hand, and this is where Kuhn's analysis is the more accuracte, have no interest to waste their time on developing proofs to falsify the erroneous theories in vogue, but rather, prefer to be busy building up their own systems which correspond to the evidence at hand. The falsification process of the erroneous prevailing theories is then later carried out by others, i.e. the innovators and early adopters of new theories.

A good example here are the "hand proof" works of Isaac Newton, which present new interpretations of observed phenomena and spend as little time as possible wasting time in disproving the erroneous ideas of others.