Paths To Knowledge (dot Science)

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Archive for the ‘Graphics’ Category

Questions about the Historical Global Mean Sea Level Graphs from the University of Colorado

Posted by pwl on April 25, 2011

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.

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Posted in Bad Science, Bad Science Attitude, Climate Science, Complex Systems, Ethics in Science, Get some perspective people, Graphics, Hard Science, Hard Science Required, Holding those who run the world responsible for their crimes against humanity, Humbled by Nature, Learning about Science Organizations, Proofs Needed, Rational Thinking, Reality Based Environmentalism, Science over Propaganada, They got the math wrong!, Video | 6 Comments »

NASA JPL Satellite Eyes On the Earth 3D – Gravity Balls and Friends

Posted by pwl on December 10, 2009

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.

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Posted in Adventure, Awesome, Big Brother Planetary Control System, Climate Science, Climategate, Complex Systems, Evil Walks the Earth and Carries a Big Stick, Exercise for the Reader (that's you), Get some perspective people, Graphics, Gravity, Hard Science, Hard Science Required, Humbled by Nature, Ignorance to Knowledge, It's weather AND climate!, Learning about Science Organizations, Majestic Universe, Math, Proofs, Proofs Needed, Rational Thinking, Reality Based Environmentalism, Science Ficition, Science Missions, Science over Propaganada, SkyNet Battlefield Earth, Total Control Over Our Lives, Video, WOW!!! | 4 Comments »

Rational Trigonometry and a new Foundation For Math

Posted by pwl on August 11, 2009

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.

Here are a few videos from the Foundations of Math series with the full series of 35+ episodes here.


There is also a series of advanced Math Seminars on the topic of Hyperbolic Geometry is Projective Relativistic Geometry.

Posted in Awesome beyond awesome, Exercise for the Reader (that's you), Graphics, Hard Science, Humbled by Nature, Ignorance to Knowledge, Math, Norman J Wildberger, Proofs, Rational Thinking, Science Education, Science Info Educational Videos, Science Shows, Video, WOW!!! | 12 Comments »

The Terminators Continue doing their thing

Posted by pwl on May 18, 2009

Posted in Evil Walks the Earth and Carries a Big Stick, Film, Fun, Graphics, SkyNet Battlefield Earth, The End is Nigh, The Sky Is Falling, Total Control Over Our Lives, Video, Violent | Leave a Comment »

Painting The Mona Lisa Really Really Fast

Posted by pwl on April 11, 2009

Very cool stuff. The resemblance isn’t too bad either!


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Posted in Adult Supervision Required, Business, Graphics, Ideas Crazy Enough to Have a Chance, Intel Larrabee, NVidia, Painting Elephants, Parallel Computing, Science Education, Science Shows, Tesla, Video | Leave a Comment »

 
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