"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
“Wonders of the Universe is a 2011 television series produced by the BBC, Discovery Channel, and Science Channel, hosted by physicist Brian Cox. Wonders of the Universe was first broadcast in the United Kingdom on BBC Two on 6 March 2011. The series comprises four episodes, each of which focuses on an aspect of the universe and features a ‘wonder’ relevant to the theme. It follows on from Cox’s previous series for the BBC, Wonders of the Solar System, which was first broadcast in 2010.” [1] Read the rest of this entry »
The benefits of carbon dioxide supplementation on plant growth and production within the greenhouse environment have been well understood for many years. Carbon Dioxide (CO2) is an essential component of Carbon Based Life on Earth.
There would be NO GREEN without the ESSENTIAL NUTRIENT CO2. MORE CO2 = MORE PLANTS. Inconvenient FACTS of PLANT BIOLOGY. More CO2 = More Plants = Cleaner Air. More CO2 = Plants = More Food For Humans. More CO2 = A Good Thing.
GROWING MORE PLANTS WITH CO2 IN GREENHOUSES TODAY
“The benefits of carbon dioxide supplementation on plant growth and production within the greenhouse environment have been well understood for many years. Read the rest of this entry »
Let’s explore this by way of two very interesting conversations, one from philosopher and physicist Paul Davies and the other from Stephen Wolfram.
Philosopher and physicist Paul Davies give a fascinating and thought-provoking talk on the possibility of an ultimate explanation for our universe. Dismissing the multiverse and God, he outlines an idea for finding an explanation for the universe and physical laws within the universe itself.
“It’s said that science will dehumanize people and turn them into numbers. That is false and tragically false. Look for yourself, this is the concentration camp and crematorium at Auschwitz. This is where people where turned into numbers. … It was not done by gas… It was done by arrogance… it was done by dogma… it was done by ignorance. When people believe they have absolute knowledge with no test in reality this how they behave. this is what men do when they aspire to the knowledge of the gods. … Science is a very human kind of knowledge… we are always at the brink of the known… every judgment in science stands on the edge of error and is personal. Science is a tribute to what we can know although we are fallible. We have to cure ourselves of the itch for absolute power.” – Bronowski‘s The Ascent of Man
Continuing Dr Bronowski’s personal view of mans major discoveries and the evolution of his thought; this programme highlights the achievement of twentieth century physics in proving that absolute certainty inside or outside science is beyond our grasp.
1) The Method of the Artist.
2) The Invisible Waves.
3) Karl Friedrich Gauss and Göttingen.
4) Max Born and Heisenberg.
5) The Principle of Uncertainty.
6) Leo Szilard.
7) The Tragedy of Scientists.
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.
“Sometimes we forget that not all numbers are the same. This becomes very apparent in dealing with floating point numbers in parallel computing. … Floating numbers are not associative or distributive. … The more cores programmers run their parallelized code on, the more ways operations can be interleaved and the more challenges programmers face.” – Tim Mattson and Ken Strandberg, Intel
As if it’s climate science is not bad enough with intentionally corrupt or incompetently done statistics it turns out that climate models may be based upon computer programs with serious math flaws: the limits of the floating point and double precision floating point data types can produce incorrect results since “Floating Point Numbers Aren’t Real Numbers!” they are data types with limited precision. It gets even worse than that, when supposedly good programs are transformed into massively parallel programs with N threads of execution the results can vary with the number of threads chosen to run the program! Of course in climate science N can be 2 or 4 threads on a single multi-core machine but it can also be 1,000+ using GPGPUs or server compute farms.
Have the climate model programs been vetted to ensure mathematical accuracy? Is there a set of test cases that validate it after new changes have been made to the climate models? Do the test cases cover all the calculations in the climate model software? How do we know the answers are even accurate mathematically? (Of course that’s not even asking how do we know the model is relevant but this inquiry is not into relevancy it’s into accuracy of the calculations, whatever they happen to be, in climate models).
“The more cores programmers run their parallelized code on, the more ways operations can be interleaved and the more challenges programmers face. Parallel programmers must deal with a host of issues peculiar to parallel programs such as synchronization, protecting shared variables, and finding thread safe versions of common math routines (such as random number generation). One of the most subtle problems faced by the parallel programmer, however, arises from the properties of floating point numbers. Floating point numbers are the same in serial and parallel computations, of course, but when a program executes in parallel, special features of these numbers are more likely to impact your results.” – Tim Mattson and Ken Strandberg, Intel, in “Parallelization and Floating Point Numbers“
One aspect of models in science and engineering that involve calculations using the “floating point number format” is that Floating Point numbers are NOT REAL NUMBERS they are limited precision approximations of Real Numbers and as such they have their limits often caused by rounding which results in Floating Point numbers not being associative, in other words the order matters!!! What happens in science and engineering calculations on computers using Float 32 or Double floats (64 bits) especially when scaling massive numbers of computations to multiple threads on your multiple cores or on thousands of processor nodes in super computers or on GPGPU (general purpose graphics processing units) is that you get the wrong answers due to the miss use of these floating point data types.
You can easily generate numbers that don’t fit into the floating point format, and thus you produce answers from the basic arithmetic operations that don’t fit into a floating point format. In other words, the floating point numbers when operated on by the basic arithmetic operations do not constitute a closed set.
The impact of this is significant. Floating numbers are not associative or distributive. So,
A * (C * B) ≠ (A * C) * B and
A * (B + C) ≠ A * B + A * C
[Obviously the sentence is missing something here, most likely the two equations do not produce the same answers! -pwl]
This means that as you change the order of a long sequence of arithmetic operations, you can generate different answers. Mathematically with real numbers, the answers can’t depend on the order of the operations (for commutative operations) or the way they are grouped together (associatively). But with floating point numbers, if you interleave the operations in different ways, you get different results.
Here’s a good test to demonstrate the implications of this behavior by floating point numbers:
1. Fill 2 arrays each with 10000 random values between 0.0 and 1.0.
2. Shift one up by 100 and shift the other down by 0.001.
3. Mix the arrays together, sum them, and subtract a large number (500000).
Here are the results run on 1, 2, and 4 threads.
1 thread computes 170.968750
2 threads computes 171.968750
4 threads computes 172.750000
Which one of these numbers is correct, the 1-thread, 2-thread, or 4-thread value? Are any of these the true value? Would you consider that with 4 threads, the answer is correct and the others wrong? Or with 1 thread?
This is not a trick question, nor is its goal to make programmers look silly. Developers are smart people. But, many programmers steeped in sequential programming for so many years make the assumption that there is only one right answer for their algorithm. After all, their code has always delivered the same answer every time it was run. When you consider the above example, however, all the answers are equally correct. To pick one arbitrarily and call it right and the others wrong is completely unjustified.
Wait there is more! This is quite shocking isn’t it? What you were taught in math class isn’t the way that computers do math! Yikes. Most computer scientists are not aware of this problem as most never encounter it in their careers, or don’t know that it’s a problem that is happening right under their noses. Scary.
By mixing the numbers as this example does, it creates a pathological situation designed to maximize problems due to round off error. The test mixes very large and very small numbers together. The arithmetic unit aligns the numbers before adding them, which, given the large difference in their absolute magnitudes, all but guarantees that we’ll loose bits of precision in the process.
As the number of threads changes, the combinations of numbers being added also changes. With all the roundoff errors, as the way these numbers are combined changes, the way roundoff error is accumulated also keeps changing. Thus, the answers change.
So which answer is correct? The algorithm for adding them together is unstable. If you carefully add the numbers together so large numbers add with large numbers and small numbers add with small numbers, and then add the “large_set_sum” to the “small_set_sum”, you get a numerically stable result. The answer in this case is 177.750. Note that the test answers in every case considerably vary from the stable method of obtaining the answer.
Note also that, with a serial algorithm, you’d never know there was a problem. Only as the thread count grows and the answers change, does the instability of the algorithm become obvious. It’s apparent the problem is not in the compiler or even the program. The problem is with the numerical instability of the algorithm. And it’s only revealed by going to multiple threads.
The video with Tim Mattson explains it well.
Are you getting different numbers for calculations as you vary the number of threads? Your algorithm may be incorrect. Real numbers are nice; floating numbers are not nice. Floating numbers are not a closed set, the overflow bits need to be rounded and that can change the results of a calculation. Tim discusses how to work with floating point numbers and resources available to help in the Intel Math Kernel Libraries.
In the engineering applications that I’ve worked on for civil engineering of bridges we found that Double Precision Floating Point Numbers at 64 bits was simply not enough accuracy. We were able to use 80bit Extended Double Precision Floating Point numbers supported by the 8087 math coprocessor in the Intel line of chips. Even though the extended precision covered most of the cases that Double Precision didn’t there were a few cases where we had to adjust the order of our computations to ensure that we didn’t overflow the precision limits of the computation of the extended 80bit math! As you can imagine errors in bridge calculations are rather critical to life and limb.
The same is true in the Climate Models, lives and treasure both depend on correct math. The science fails when the math is wrong. Have they been vetted for numeric accuracy? How do we know that? Have test cases been written that test these limits in the climate model programs?
The same applies to random numbers in computers, they are not real random numbers either. As Tim Mattson says “We now know that god does play dice but that computers can’t!” (paraphrased). Random numbers are important in climate models since the climate is in inherently a system with randomness being generated from within. See Wolfram’s A New Kind of Science.
Computers cannot make truly random numbers. For statistical algorithms requiring random numbers, developers need to be careful in parallel code to avoid overlapping sequences from random number generators. Tim discusses different methods to use random number generators – including using independent generators for each thread and the “leap frog method” – to produce “pseudo random numbers” for statistical algorithms that work in parallel code.
Very interesting and important topic to any system that depends upon parallel computations being correct to protect limb, life and treasure.
Thanks to Intel, Tim Mattson and Ken Strandberg for this important information.
A team of scientists explore a Mexican cave filled with giant crystals; some of the largest ever discovered. With temperatures near 120 degrees and over 80 percent humidity, the cave [, in the Naica Mine,] is one of the deadliest environments on earth.
The movie “The Core” got it right!!! Giant underground crystal caves!!! Ok, well sort of… heat… space suits… lava… not a geode but close enough for fun…
Favorite lines from The Core: “What would it take you to get it done in three months?” … “Oh, 50 Billion dollars, I don’t know…” … “Will you take a cheque?” … “Why don’t you use a credit card, you’d get miles?” … “hmmm.”
The sun is the superpower of our solar system, a thermonuclear blast furnace, erupting with massive explosions. At 93 million miles away it would seem that we are safe from the suns wrath. But are we? With some experts predicting the most violent outbreak of solar activity in modern history its never been more important to understand the secrets of the sun.
Another course in linear algebra and matrix theory, which is needed in many fields of science including computer science, climate science, physics, statistics, etc…. It has 35 lectures! They are excellent!
The Hominidae (anglicized Hominids, also known as great apes[notes 1]) form a taxonomic family, including four genera: humans, chimpanzees, gorillas, and orangutans.
(To watch this video you’ll have to click through to the youtube site… since they diabled embedding).
Should we abandon dark matter as a theory to explain the missing element in the universe? Watch this clip to hear some interesting arguments for and against in this video from BBC science show ‘Most of Our Universe in Missing’.
Yikes, most of the universe is missing? Where the heck did it get put? Where did it go? Was it even there to begin with?
