"The meaning of the world is the separation of wish and fact." - KURT GÖDEL

"According to Peirce's doctrine of fallibilism, the conclusions of science are always tentative. The rationality of the scientific method does not depend on the certainty of its conclusions, but on its self-corrective character: by continued application of the method science can detect and correct its own mistakes, and thus eventually lead to the discovery of truth".

A guiding principle for accepting claims of catastrophic global events, miracles, incredible healing, invisible friends, or fill in the blank is:

“extraordinary claims require extraordinary evidence.” - Carl Sagan

"Faith may be defined briefly as an illogical belief in the occurrence of the improbable." - H. L. Mencken

I would add irrational and highly delusional to the mix when faith requires one to accept magical violations of the well known, well tested or easily demonstrated laws of Nature. - PWL

"Science is Progress and the Future. Faith is regression to the Dark Ages." - PWL

“It pays to keep an open mind, but not so open your brains fall out.” - Carl Sagan

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring." - Carl Sagan

"Two important characteristics of maps should be noticed. A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness." - Alfred Korzybski

"Science is a search for basic truths about the Universe, a search which develops statements that appear to describe how the Universe works, but which are subject to correction, revision, adjustment, or even outright rejection, upon the presentation of better or conflicting evidence." - James Randi

"Hypotheses are nets: only he who casts will catch." - Novalis

"Nullius in verba. Take no one's word for it." - Motto of the Royal Society

"I'm trying to find out NOT how Nature could be, but how Nature IS." - Richard Feynman

"The improver of natural knowledge absolutely refuses to acknowledge authority, as such. For him, scepticism is the highest of duties; blind faith the one unpardonable sin." - Thomas Henry Huxley

“A foolish faith in authority is the worst enemy of truth.” Albert Einstein

"Science is empirical. Knowing the answer means nothing. Testing your knowledge means everything." - Lawrence Krauss

"Skepticism is the agent of reason against organized irrationalism - and is therefore one of the keys to human social and civic decency." - Stephen Jay Gould

"Science is best defined as a careful, disciplined, logical search for knowledge about any and all aspects of the universe, obtained by examination of the best available evidence and always subject to correction and improvement upon discovery of better evidence. What's left is magic. And it doesn't work." - James Randi

Looking back in time at the Mean Sea Level graphs from the University of Colorado I noticed some things that bother me about their graphs and the manner of their presentation. Some serious questions where raised.

I made this slow 2 second blink comparison movie (it speeds up at the end) of two graphs from sealevel.colorado.edu to visually compare a noticeable change in plotting and data from 20041119 and about a month later on 20041223. The graph format changed and possibly the data points where changed or deleted.

Very cool tool from visualizing data from NASA satellites in 3d in a web browser.

What I’m interested in is not just the visualization aspect but the actual data behind the visualizations since as we know from the Climategate confirmations of scientific fraud in climate science visual images can be highly misleading towards the alleged scientists point of view. Raw data please. All manipulations MUST be FULLY documented with the software source code that made the changes and detailed reasons listed for all adjustments.

If we are to raise our knowledge, skills and competence in using the scientific method to study the Earth, Moon, Sol and other relevant systems we must do some basic learning. Hard science requires making use of hard data without cheating and with showing ones data and any adjustments with justifications and open source code for auditing and proper open peer reviews!

Now let’s see what we can learn from this 3d puppy. My favorite is the GRACE Gravity satellites.

I’ve often wondered what impact the uneven gravity has on the Earth’s climate systems and if the gravity effects are taken into account in the so called climate models. As you can see from the above video the Earth isn’t even an oblate spheroid, it’s a really bumpy place when it comes to gravity. This must impact the weather and thus the climate systems as the atmosphere and water and ice move about.

Two excellent video series by Norman J Wildberger. Very well done and designed to be easy to comprehend. While they start out very simple and basic they get quite deep yet remain as simple as possible. (The bonus series even gets into Relativity, very cool). Wildberger is the math teacher I wish I had all through high school and since, and now through his videos he can be our math teacher! Gotta love online education.

The first series is on the amazing new (and very old) way of doing Rational Trigonometry without using sin and cosine of Classical Trigonometry. It’s Fantastic.

“The new form of trigonometry developed here is called rational trigonometry, to distinguish it from classical trigonometry, the latter involving [cosine, sin and their fellow] functions and the many trigonometric relations currently taught to students. An essential point of rational trigonometry is that quadrance and spread, not distance and angle, are the right concepts for metrical geometry (i.e. a geometry in which measurement is involved).

Quadrance and spread are quadratic quantities, while distance and angle are almost, but not quite, linear ones. The quadratic view is the more general and powerful one. At some level, this is known by many mathematicians. When this insight is put into practice, as it is here, a new foundation for mathematics and mathematics education arises which simplifies Euclidean and non-Euclidean geometries, changes our understanding of algebraic geometry, and often simplifies difficult practical problems.

…

Rational trigonometry deals with many practical problems in an easier and more natural way than classical trigonometry, and often ends up with answers that are demonstrably more accurate. In fact rational trigonometry is so elementary that almost all calculations may be done by hand. Tables or calculators are not necessary, although the latter certainly speed up computations. It is a shame that this theory was not discovered earlier, since accurate tables were for many centuries not widely available.”

Exerpt from the Introduction to “Divine Proportions: Rational Trigonometry to Universal Geometry” by Associate Professor Norman J Wildberger

Here are a few videos from the Rational Trigonometry series with the full series of 46+ episodes here. These first episodes lay the corner stone of Rational Trig, and it only gets better from there!!! Watch them all a number of times and do the examples. Amazing!

“Why classical trigonometry is hard:

The problem is that defining an angle correctly [in Classical Trigonometry] requires calculus [whereas Rational Trigonometry doesn’t]. This is a point implicit in Archimedes’ derivation of the length of the circumference of a circle, using an infinite sequence of successively refined approximations with regular polygons. It is also supported by the fact that The Elements [Euclid] does not try to measure angles, with the exception of right angles and some related special cases. Further evidence can be found in the universal reluctance of traditional texts to spell out a clear definition of this supposedly ‘basic’ concept.” – NJ Wildberger

“Quadrance measures the separation of two points. The easiest definition is that quadrance is distance squared.

… quadrance is the more fundamental quantity, since it does not involve the square root function. The relationship between the two notions is perhaps more accurately described by the statement that distance is the square root of quadrance.

In diagrams, small rectangles along the sides of a triangle indicate that quadrance, not distance, is being measured … .” – NJ Wildberger

“Spread measures the separation of two lines. This turns out to be a much more subtle issue than the separation of two points.” – NJ Wildberger

The spread s between the two lines is the ratio of quadrances. The spread also works out to “square of sine of angle”.

“The spread between two lines is a dimensionless quantity, and in the rational or decimal number fields takes on values between 0 and 1, with 0 occurring when lines are parallel and 1 occurring when lines are perpendicular. Forty-five degrees becomes a spread of 1/2, while thirty and sixty degrees become respectively spreads of 1/4 and 3/4. What could be simpler than that? Another advantage with spreads is that the measurement is taken between lines, not rays. As a consequence, the two range of angles from 0◦ to 90◦ and from 90◦ to 180◦ are treated symmetrically.” – NJ Wildberger

You can find a couple freely available pdf chapters of the book “Divine Proportions: Rational Trigonometry to Universal Geometry” here. Make sure to check out Divine Proportions Overview Chapter 1 as it covers the basics with examples.

You will find some additional pdf papers by the professor here.

The second series is on the Foundations of Math. An excellent review and introduction for everyone at any age.