Although wikipedia may be a questionable source due to its consortium authorship I'm going to use it as it's accurate in this case.
- (He uses the calculus term "critical point" and claims that his scale has a critical point at 200. In mathematics a critical point is the point where the derivative of a function equals zero. On a graph, it is the point where the tangent line is flat-the point where you are neither rising nor falling. What Dr. Hawkins didn't realize was that neither logarithmic functions nor exponential functions have critical points. Their derivatives are always positive.) -
This is a false statement. Here's a verbatim quote from wikipedia: [
en.wikipedia.org]
On most logarithmic scales, small values (or ratios) of the underlying quantity correspond to small (possibly negative) values of the logarithmic measure. Well-known examples of such scales are:
Richter magnitude scale for strength of earthquakes and movement in the earth.
bel and decibel and neper for acoustic power (loudness) and electric power;
cent, minor second, major second, and octave for the relative pitch of notes in music;
logit for odds in statistics;
Palermo Technical Impact Hazard Scale;
Logarithmic timeline;
counting f-stops for ratios of photographic exposure;
rating low probabilities by the number of 'nines' in the decimal expansion of the probability of their not happening: for example, a system which will fail with a probability of 10-5 is 99.999% reliable: "five nines".
Entropy in thermodynamics.
Information in information theory
Here's a nice graph: [
en.wikipedia.org]
Notice the blue line is the graph of the logarithm. Also note that the "x" line of the graph would be the critical point - in this case "200" or "Integrity". Therefore the critical point referrence quoted above is false.
wikipedia once again: [
en.wikipedia.org]
Richter magnitude test scale (or more correctly local magnitude ML scale) assigns a single number to quantify the size of an earthquake. It is a base-10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude of the largest displacement from zero on a seismometer output. Developed in 1935 by Charles Richter in collaboration with Beno Gutenberg, both of the California Institute of Technology, the scale was originally intended to be used only in a particular study area in California, and on seismograms recorded on a particular instrument, the Wood-Anderson torsion seismometer. Richter originally reported values to the nearest quarter of a unit, but decimal numbers were used later. His motivation for creating the local magnitude scale was to separate the vastly larger number of smaller earthquakes from the few larger earthquakes observed in California at the time. His inspiration for the technique was the stellar magnitude scale used in astronomy to describe the brightness of stars and other celestial objects.
Richter arbitrarily chose a magnitude 0 event to be an earthquake that would show a maximum combined horizontal displacement of 1 micrometre on a seismogram recorded using a Wood-Anderson torsion seismometer 100 km from the earthquake epicenter. This choice was intended to prevent negative magnitudes from being assigned. However, the Richter scale has no upper or lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.
Here's another great graph: [
en.wikipedia.org]
Factually, both logarithms and exponents deal with geometric progressions; hence my earlier statement that anything that can be expressed exponentially can be expressed logarithmically. A logarithm is the inverse of an exponent expression.
On a side note logarithmic scales are often employed when measuring magnitude - which is exactly what the "scale of consciousness" is or whatever its name is. They are particularly adept for giving fixed increments to evaluate magnitude - therefore the Richter scale.
Review the table under wikipedia's Richter scale entry. The Richter scale is a geometric progression. The plausible correlation to a critical point would be perceptible to human senses. The absolute VAST amount of quakes are below that critical point. The VAST amount of the people are below integrity. Very few quakes occur at the "top" of the scale; very few people are above 900. The VAST majority of quakes cover minute areas; the conscious levels below integrity have little "impact" due to power. As a quake's rating goes "up" the Richter scale it's area covered and devastation increase geometrically; as people ascend the conscious level they counter-balance an increasing area and their "power" grows - each geometrically.
Notice that each of the examples of wikipedia are measuring two quantities simultaneously (as in strength of earthquake and movement in the earth). The consciousness scale, or whatever it is, is measuring power of consciousness and number of those affected by that power.
- (2) Numerous people have pointed out to me that Hawkins completely abuses the mathematics and physics in his book. He consistently refers to his calibration scale as "logarithmic" when it is in fact "exponential"; he uses the term "critical point" when referring to his exponential scales, when an exponential graph by definition cannot have a critical or "flat" point) -
Numerous people are incorrect. The scale is logarithmic, it does have a critical point.
- (He claims that the scale is "logarithmic" and base 10, but in his explanation of what a logarithm is, he confuses logarithmic functions with exponential functions and repeats this mistake throughout the book. Essentially,someone at level 201 has ten times the power of someone at 200, someone at 202 has 10 times the power of someone at 201 and so on.) - I'm uncertain what is being said here but I'm taking it that since each level is 10 times greater than the prededing level that you're stating that this is mistakenly termed "logarithmic" when it should be "exponential". If that is the case then once again this is false. Please see wikipedia once again: [
en.wikipedia.org]
Here is the quote from said link: "In mathematics, the common logarithm is the logarithm with base 10."
In short, Hawkins is straight forward and not confusing in describing the simplest most common logarithm scale. The logarithm scale usage is right on the money as described. It is not confusing or ambiguous. Anyone who says otherwise doesn't know what they're talking about. That makes these statements false:
- (To explain this scale he uses a lot of technical-sounding mathematical terms, but he uses those terms incorrectly- to the point of being gibberish.) -
- (In this case, he just threw in a mathematical term without bothering to find out what it means. ) -
- (In other cases, bad math like this could be overlooked. He is after all a psychiatrist, not a mathematician. In this book, however, the technical terms are used to impress the readers with how scientific the system is, and the claim is that it is based on research. If you can understand what these mathematical terms actually mean, it becomes clear by the gibberish that he is just making this stuff up. If his "mathematical" system was revealed to him through muscle-testing (as opposed to outright fiction), then it shows just how unreliable this system is.) -
- (Are you a student of Hawkins’?) - No.
- (Other laughable statements are that organically grown tobacco is actually healthy, and that taking one gram of vitamin C per day will counter all of the harmful effects of smoking.) - Can you give us the exact quotes on these?