A mathematical joke asks, “What do you get when you cross a mountain-climber with a mosquito?” Answer: “Nothing: you can’t cross a scalar with a vector.”
Non-mathematically minded readers may not get the ‘joke’ until later in this article. But when you do, you may feel it’s the most expensive ‘joke’ told, and it’s being played on you and me.
If you’ve ever followed the heated debate about man-made global warming you will know the cornerstone of that science is the so-called “greenhouse gas effect” (GHE). It is purported that rising human emissions of carbon dioxide (CO2), one of those so-called GHE gases, is dangerously adding to climate change. The chosen remedy of western governments: we must all pay more taxes, cut back our industrial emissions and invest in various questionable alternative energy schemes to avert a planetary crisis.
To this end many a (government) climatologist or Greenpeace activist will regale you with the glib assertion that the GHE makes our planet “33 degrees warmer than it would otherwise be.” But where does this “33 degrees” number come from and is it scientifically valid? Contrary to media hype this number is not “an observation” it is the product of a 30-year-old calculation from a team of researchers led by NASA’s Dr. James E. Hansen. It is a ubiquitous claim that the number “proves” the GHE is real. [1,2]
Putting the Numbers into Context
This thermometer illustration depicts the numbers in degrees Celsius and Fahrenheit. But it is easier to follow this article’s analysis if we instead apply the Kelvin temperatures (in purple) The lower value (minus 18°C) thus becomes 255°K and this is what Hansen raised by 33 degrees to 288°K (15°C).
Now you may be thinking as you let out a yawn,“Oh boy, he’s about to spout math.” But before your finger presses ‘delete’ consider this: what you are about to read has enormous ramifications for our industrialized society and serious implications for you and your family’s personal tax liabilities for decades to come. If it can be demonstrated that Hansen’s “33 degrees” is the product of a bungled calculation then, at minimum, this puts the onus back on climatologists to explain the errors and re-think their “theory” before our economies are exposed to deeper economic travails.
Two Different Number Concepts: One Bungled Meaning
Our story begins in 1981 when Dr. Hansen led a team of researchers who wanted to pin down some simple and iconic numbers. Their quest was to prove to the wider scientific community that carbon dioxide and certain other very efficient infrared absorbing (and emitting) gases make Earth’s atmosphere warmer than it would otherwise be. Lamentably, these scientists chose to ignore the superb energy emitting qualities of these gases.
No rigorous scientific testing was involved – the numbers were obtained from known values. Firstly, Hansen’s team took a measure of average temperatures at the ground (a scalar) and, secondly, they chose a temperature for infrared radiation as it passes out of the top of the atmosphere, (a vector). Both these two numbers are reasonable in themselves. However, in both mathematics and physics vectors and scalars each describe quantities and each is very distinct from the other being differently obtained and proving separate values. A scalar operates in one dimension, a vector in three dimensions.
Now this is where the ‘joke’ comes into play and we need to remember the old saying: “You can’t mix apples with oranges.” Hansen’s team took the 288°K scalar number (the ‘apple’) with a one-dimensional basis and put it alongside the 255°K vector number (the ‘orange’), the product of a flow field in three dimensions.“So what?” you may say. Well, remember what was stated at the top of this article? Hansen had *forgotten* that “you can’t cross a scalar with a vector.” Again, please remember this is an axiomatic principle from Physics 101: “vector and scalar quantities cannot be added together.”
Any high school student, never mind a physicist or climate scientist, can do this disproof of the “33 degrees” number once you understand the rules. So let’s recap starting with an illustrative comparable equation:
The 255°K Number (the ‘orange’)
James Hansen’s ‘orange’ is a measure of the infrared radiation emitted by Earth back into outer space. This he has at 255°K (that’s ok in and of itself). This a vector number, a product of a dynamic process – the sampling of the outward flow of radiation. It has direction and is indisputably a 3-D value. Because of this it is not measured with an ordinary thermometer but with a pyrometer or spectrometer. It is not a measure of the heat of the air, but of the electro-magnetic radiation (EMR) itself, exiting from the top of the atmosphere (TOA).
The 288°K Number (the ‘apple’)
Hansen stated the average thermal temperature at Earth’s surface is 288°K (that’s also ok in and of itself).This is a scalar value number – an average from a set of static temperature readings from weather station thermometers on the ground. It serves as a measure of the heat of the air at our planet’s surface.
The ’33 Degrees ‘ Number (‘Hansen’s fudge’)
The ’33 degrees’ or ‘Hansen’s fudge’ has no validity in mathematics or physics because it is the product of mixing two incompatible metrics: a scalar with a vector. But Hansen used his fudged number to fool fellow climatologists, who in turn misled policymakers and taxpayers, too. While the Intergovernmental Panel on Climate Change (IPCC) propagate the “33 Degrees” fraud with their 2007 Report. 
Only when researchers at Principia Scientific International (PSI) put this “33 degrees” number under the microscope was the error exposed. PSI discussed this problem with several top climatologists and pointed out the errors. But while those climatologists engaged in polite discussion with us they acted unconcerned; as if they understood the message but had a blind spot to the significance of what was being told to them.
You may readily discern the difference between these phenomena yourself if you were stood on a cold, clear winter’s day on a snow capped mountain. On the one hand you may evince a thermometer close by showing a reading of the dry air at -10°C (263°K); naturally you’d shiver with the cold. But place yourself in the radiation of the sunlit sky at 50°C (323°K) and instantly you feel warm despite both temperatures existing within close proximity and time.
Dr. Pierre Latour’s brilliant article, That Bogus Greenhouse Gas Whatchamacallit Effect focused on this issue in January 2012.  Speaking with me last week Dr. Latour added, “We see an intense sunbeam vector with a high radiation temperature that is so powerful at noon you cannot look up at it, but the less intense radiation vectors from clouds, blue sky and green grass are easy to look at because their radiating intensity (temperature) is less. You can detect the different radiation vectors all around you, pointing at you from every direction. So too Earth radiates to space in all directions, day and night. While a laser shines an energy vector in one direction.”
Latour, along with a further 50+ experts at PSI argues that our atmosphere reduces the intensity (temperature) of solar radiation through it by reflecting some, scattering some, absorbing and re-emitting some, and transmitting the rest to the surface. The thinner the atmosphere, the more intense the solar radiation transmitted through it, impinging on the surface. Dr. Latour adds, “That is why you can look at a sunset vector through a thicker atmosphere. And why the surface cools under the shadow of a cloud. One could properly say atmospheres cool planet surfaces rather than heating them.”
PSI researchers like Latour are no lightweights in this debate as Roy Spencer learned to his cost. Dr. Latour is renowned in the field of thermodynamics having worked on the NASA Apollo space mission before embarking on a stellar career as a chemical process control systems engineer to the international oil and chemical process industry. Professor Spencer on his blog addresses the “33 degrees” number and admits he first “became aware of its significance” from reading Professor Richard Lindzen’s 1990 paper, ‘Some Coolness Regarding Global Warming.’ So persuaded is Spencer of it’s validity that he goes on to claim the Hansen junk number offers a ” real-world observed “radiative-convective equilibrium” case.” Thus, both Lindzen and Spencer are completely fooled by Hansen.
Latour and his colleagues are proving to be the more adept numbers analysts. They say a better explanation of our atmosphere’s temperature gradient is adiabatic pressure rather than any supposed GHE – this fact also applies to most planetary bodies in our solar system. So now it’s demonstrated the “33 degrees” claim is bogus what other hard and fast numbers exist to prove the GHE? Well, none actually. All climatologists have left are hand waving assertions that “greenhouse gases” trap or delay the exit of energy from the atmosphere. Some even claim energy gets “back radiated” adding additional heat to the system. But no tests, no observations, no experiments in our atmosphere have adduced any verifiable numbers for those claims. It is all a matter of unproven belief.
Other thermodynamics experts are also hard at work dismantling the GHE. One recent debunk comes from Dr. Jinan Cao. Cao showed Hansen also misapplied the Stefan-Boltzmann equation.  Meanwhile, PSI researchers, Joseph E.Postma and Carl Brehmer are soon to add to such compelling work by publishing more damning evidence disproving the GHE.
Politicized Science Perpetuates a Cover Up
Despite all the above climatologists promoting this chimera stubbornly choose to turn a blind eye. Why is that? Perhaps the answer lies somewhere in the fact that many millions in research grants and jobs for the boys are still riding on this “settled science?” Or, like Lindzen and Spencer, they’re simply too embarrassed to concede they were taken in by Hansen’s sham.
Instead, the diehards dismiss Latour and other PSI researchers as “cranks” claiming the GHE has 150 years of “solid science” backing it. But much of that is from the likes of Arrhenius, Fourier and Tyndall who are often misquoted. Pointedly, these Victorian theorists founded their beliefs on the discredited notion of “luminiferous aether” – which is exposed in a short history of radiation by Dr. Matthias Kleespies. 
To sum up, Principia Scientific International has uncovered a monumental scientific error that no government authority is prepared to address. You may conclude that a clique of charlatans concocted a bogus equation to justify universal “carbon taxes.” Climatologists are not true to the scientific method if they decline to acknowledge these errors. Readers may judge this to be a willful omission to come clean for the sake of prestige and financial rewards. But the price the rest of us pay is enormous. Since 2008 in the UK alone an additional “carbon tax” burden of £18 billion is levied each and every year – all thanks to the Climate Change Act. But that could all be stopped tomorrow if a little common sense and humility was applied.
As it stands, hard-pressed taxpayers now possess a simple and valid scientific argument to say “no more” to greenhouse gas taxes. Instead, these unjustifiable levies should be scrapped and the money invested more wisely elsewhere in public utilities or simply left in taxpayer’s pocket to be used in the fight to resurrect a stagnant global economy.
Unperturbed, the 71-one-year old Hansen still sits in his exalted position as of Head of NASA’s Goddard Institute of Space Studies shamelessly promoting his misguided and politicized global warming agenda. Readers may wish to follow my lead and send an email to Dr. Hansen to politely inquire why he thinks his scalar/vector blunder is ok.
 Hansen, J, Johnson D, Lacis A, Lebedeff S, Lee P, Rind D & Russell G, “Climate Impact of Increasing Atmospheric Carbon Dioxide”, Science, Vol 213, n 4511, pp 957 – 966, August 28, 1981.
 Hansen, J, Fung I, Lacis A, Rind D, Lebedeff S, Ruedy R & Russell G, “Global Climate Changes as Forecast by Goddard Institute for Space Studies Three-Dimensional Model”, Journal of Geophysical Research, Vol 93, n D8, pg 9341 – 9364, August 20, 1988.
., “Chapter 1: Historical Overview of Climate Change Science”, FAQ 1.1, p. 97, in IPCC AR4 WG1 2007: “To emit 240 W m–2, a surface would have to have a temperature of around −19 °C. This is much colder than the conditions that actually exist at the Earth’s surface (the global mean surface temperature is about 14 °C). Instead, the necessary −19 °C is found at an altitude about 5 km above the surface.”
 Cao, J, “Common Errors in the Use of the Stefan-Boltzmann Equation,” www.joannenova.com, (accessed online: October 4, 2012).
 Kleespies, M, “A Short History of Radiation Theories-What Do They Reveal About “Anthropogenic Global Warming?””(November, 2011), www.principia-scientific.org (accessed online: October 5, 2012).