The popular idea of "other ways of knowing" promotes intuition not only as a source of new ideas, but also as a way of checking ideas. Ray Hyman used the following example to illustrate how poor our intuition can be for solving problems.
Imagine folding a .004 inch thick paper in half one time. Its thickness doubles to become .008 inches. Fold it in half again and it becomes .016 inches thick. In your imagination continue folding the paper until you have done so 50 times. Now, without doing the numerical calculations and using only your intuition, imagine how thick the paper will be. The answer is given below...
In 1892 Henry Slade, commonly credited with bringing slate writing into popularity, was exposed by John Truesdell in his book The Bottom Facts Concerning the Science of Spiritualism. Slade's exposure had little effect. He continued to gain popularity and became rich through gifts from the European royalty. Truesdell, himself, later became a slate writer, using methods he had not revealed in his book.
The entry for "Spiritualism" in the 1994 edition of Encyclopedia Americana states, "Experimental studies in extrasensory perception ... have shown that the mind can, in certain instances, reach out across space and time and physical barriers to acquire information that the senses and the reason could not obtain. If the medium has such powers ... we need only suppose that he can draw upon a wider than normal range of circumstances to acquire the information that he embodies in his messages." This entry was written by Joseph B. Rhine, parapsychology researcher at Duke University. What other "facts" might children find in this common source of information for school reports?
The September 17, 1994 Oregonian ran an article from the Knight-Ridder News Service describing a company called Advisor Associates, a corporate psychic service which advises employers on hiring decisions. After a few testimonials from the psychics themselves and some satisfied, but anonymous (they feared they might get sued if they gave their business name) customers, the reporter asked the psychics how they did it. "We just sit here the way we are now and start talking about the person or situation. The information just comes to us," was their response.
Oregon has its own Centre for Crop Circle Studies (CCCS) located in Aloha. The center reported three crop circles occurred in Oregon this past summer. A Celtic cross design appeared in a field adjacent to Sunset Highway in Hillsboro on June 15th. A MUFON spokesperson told KOIN-TV news he thought the circle was man-made because of tracks leading into the site. Carol Pedersen, CCCS Oregon coordinator, also appearing on KOIN news, believed it to be "genuine."
The November 11th Oregonian editorial page ran an opinion piece by Pedersen under the headline "Investigation shows state had genuine crop circles." In it Pedersen says CCCS sent samples from the circle to W. C. Levengood, a biophysicist at Pinelandia Laboratories in Grass Lake, Michigan. Pedersen tells us Levengood's analysis "showed significant alterations in the crop samples and seed germination not apparent in the controls." She concluded saying, "This mystery must continue to be scientifically and metaphysically explored by imaginative minds open to the possibility of the discovery of new dimensions in time and space."
W. C. Levengood, the biophysicist analyzing samples from the Oregon crop circles, has published his results in the Danish research journal, Physiologia Plantarum (92:356-363, 1994). Plant samples used in these studies were collected from circles in Canada, UK, USA and Australia from 1990 to 1992. Levengood reports changes in macroscopic and microscopic plant structures, abnormal flower development, and reduced seed germination. He attributes the abnormalities to "transient high temperatures" and proposes ion plasma vortices "guided by variations in the earth's magnetic field" could produce plant abnormalities and complex, symmetrical field patterns, including the Mandelbrot formation.
The author, however, exhibits a poor knowledge of plant development and of plants' complex responses to stress and varying field conditions. For example, he was apparently unaware, until it was explained to him by the farmer, that an excessive application of nitrogen fertilizer would produce darker colored plants and weak stems that could cause the plants to lay over in the field. Is there something genuine here to be explained or is this another case of expertise being applied in the wrong field?
The paper's thickness does not increase linearly with folding, but exponentially. A graphic representation of its increasing thickness shows almost all the increase will occur in the last fe folds.
After 50 folds the paper is about 72 million miles thick. That is a little more than 3/4 of the way to the Sun from Earth!