# One Equation to Rule Them All

Written by Stephen Wells

The general public don’t like mathematics. Maths is hard. Maths is boring. Put an equation in a book and you will half its sales for each one you are foolish enough to insert into the pages of it. Nobody want to read a book full of equations.

This is probably why climate scientists fill their academic papers with so many of them. Who has the time to go through all of that stuff and work out if the answers provided are correct after all? Who is even clever enough to do so? If two Nerds are arguing over an equation, who are we mere mortals to say who is right? Best just “trust the experts” and go with “the consensus”.

I’m loathe to even mention a “simple” equation here, much less actually put it in print. I want you to read this article after all, not put it down in favour of a comic book, but the problem is that the whole claimed carbon dioxide effect can be boiled down to one “simple” sum.

I’m going to link the completely peer reviewed totally sciencey paper, so that you can pretend to go and fact check this article, so that you won’t actually have to go through the trauma of seeing an equation in my wonderfully user friendly article itself.

Here is the link (feel free to ignore it if it’s too traumatic):

http://folk.uio.no/gunnarmy/

It’s on page 4 in the table taken from the 1990 IPCC report under CO2

Now, because I’m incredibly heroic, I took the time to actually read this paper look at the equations, suffer the post traumatic stress disorder, and narrow the basics to a single equation for the direct claimed effect of increasing carbon dioxide.

And that’s the thing. There is just ONE equation. I’m sure it got its inspiration from Tolkien: “One sum to rule them all, one sum to find them, one sum to bring them all and in the darkness bind them!”

At 6ft4 I’m a bit tall for a Hobbit but the task of destroying this equation without letting Boromir (or any of you) see it (lest you go mad) is still mine to endure.

All of the other equations ever used in any paper of this nature, are for “feedbacks”, or for other gases, or for calculating a “climate sensitivity” number, or for integrating different areas of the planet to find an average, or, or, or, or…..

What I am saying is this paper (and all of the other ones like it), is a complete paper of obfuscation, that does nothing other than hide the fact that the starting premise for all climate change/global warming alarmism comes down to a simple sum, that anyone could do, if they were prepared to put up with the PTSD afterwards.

It basically says that there is a climate “sensitivity number” for CO2, which it gives as 5.35. Then if you do a sum with this number and the CO2 levels 150 years ago and the CO2 level you are afraid of, you can find out just how much extra warming the surface of the earth will experience from the CO2 alone.

The rest of this paper and all of the other papers discussing “climate forcing” concentrate on whether this 5.35 number is too high or too low and on how many “feedbacks” there might be to make the warming of CO2 be amplified until we all fry in our own body fat. But the foundation is always this equation. Because CO2 is the only gas that humans are actually emitting in any substantial amounts.

The problem is that this equation states that you need to keep doubling the CO2 to get the SAME increase in surface energy.

Let me explain. If you own a small economy hatchback it can probably reach a top speed of 150kmh. If you want to drive at 300kmh you won’t need a car twice as powerful, you will need one about 8 times as powerful and 20 times the price! Each increase in speed requires a much bigger increase in horsepower to achieve it. Because wind resistance grows at every new speed you try and attain.

So it is with the CO2 equation. Each time the gas absorbs some infrared energy there is less infrared energy left to be absorbed by an additional amount of CO2.

You may not like mathematics, but you can follow basic reasoning. There is a hell of a lot of reasoning you can do with this simple bit of knowledge. Let’s take you through a few:

- How can we get a “runaway” effect from a diminishing initial effect? How can “feedbacks” keep increasing if the trigger for these feedbacks keeps getting less?
- The main “feedback” claimed is increased water vapour. If CO2 has a diminishing absorption ability with increasing levels, surely water vapour must adhere to the same rules.
- If feedbacks are greater than the initial effect they must be self perpetuating. If CO2 causes warming which then causes feedbacks, which cause greater warming, then the greater warming must in turn cause more feedbacks which will cause even more warming, which will cause even more feedbacks……. It’s called a perpetual motion machine and it’s a big no no in the world of physics. In fact there is no bigger no no. It’s equivalent to “thou shalt not kill” in the Ten Commandments, it’s called the First Law of Thermodynamics.
- Atmospheric CO2 has increased from 280ppm 170 years ago to 410ppm today and it is claimed that temperatures have risen by about 1C during that time. Even if we assume all of this increase has been due to us driving cars and burning coal (even though much of the rise happened before we burned very much of it) then the nature of the equation and the absurdity of the feedback premise of point 3. means that the next 130ppm rise in atmospheric CO2 MUST have a SMALLER effect than the 1C claimed for the last 130ppm rise! A “runaway greenhouse effect” first popularised by Carl Sagan in 1980 on his show Cosmos about the planet Venus, cannot occur.
- Oh the planet Venus. It takes just 18 doublings of Earth’s CO2 to get us to the amount present on Venus. That’s 96 times more atmosphere holding 96.5% CO2. Do the maths to confirm this if you like, just don’t blame me for the trauma. But if you can do maths then you will also be able to realise if this equation is valid, you need a hell of a lot more doublings of CO2 to get us to the surface temperature of Venus. You need more than 4000 of them. Hopefully you know that 4000 is MUCH more than 18, even if you hate maths! The equation states that each doubling of CO2 will cause an energy increase at the surface of 3.7 watts per square meter. Remember what I said about going faster in a car? I apologise for mentioning a second equation, but the one required to know how much energy you need to get a certain temperature is called the Stefan-Boltzmann equation. Named after the nerds who wrote it. At an average temperature of 15C that translates to an energy of 396W/m2. Venus at 430C requires around 16,500W/m2. That’s a lot of extra 3.7W/m2 per doubling!

What this last point means is that not only is the narrative of catastrophic man made global warming falsified, but so is the Greenhouse Effect premise that the scam is built on. The sums just don’t add up when you take them elsewhere in the solar system. Even if you adjust for the closer proximity of Venus to the sun, there is just no way this equation can be used to predict anything.

I also use the word “scam” very deliberately. Because such a simple equation should never have been there for someone like me to be able to figure out. That behind all of the other complex mathematics was this simple sum, made my blood boil.

Equations to pretend to calculate the climate sensitivity number. Equations to pretend to calculate feedback mechanisms of twenty different trace gases of which only water vapour ends up being used. Equations to pretend to integrate equator and poles, rainforests and deserts, cloud cover, ocean cycles, etc, etc! All dross! All camouflage to cover up the fact that behind it all is just one simple premise based on one simple sum: CO2 absorbs infrared radiation in diminishing amounts with increasing quantity.

An assumption has been made about this observation and a basic calculation has been pushed forward as fact to support that initial assumption. It fails. It fails on every possible level of logic and reasoning that you can subject it to. But because people don’t like mathematics and because we think we should trust people who can do really difficult mathematics, con artists have managed to hide their scam behind it.

We need to stop being intimidated by Nerds. We need to use our basic logic and reasoning to challenge them and hold them to account. We need to force them to stop hiding behind equations and explain themselves in plain language that can be scrutinised for logical contradictions. We need to stop trusting scientists and letting them police themselves. It is our money that pays them. Our taxes. Its time to shine a light on what we have been paying for!

*PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX. Telephone: Calls from within the UK: 020 7419 5027. International dialling: (44) 20 7419 5027. *

## Keith R Snyder

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This was a really good way to write about what is wrong with “the equation.” I’m one of those who don’t really understand the equations even though decades ago I did take some calculus in high school and college. I definitely understand the illogic of what the climate alarmist “scientists” are trying to prove with them. And as much as I like the content, I even more appreciate your style in writing it.

## Gymbo

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I think this treatment from 2008 is better

http://junksciencearchive.com/Greenhouse/forcing.html

## Al Shelton

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Here is a website that has some additional info….

http://nov79.com/gbwm/natl.html

## jerry krause

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Hi Herb,

The problem with your equation is I have no idea of what F, IN, C, or CO are. Delta and 5.35 are the only parts of the equation which I do understand. For any equation to have any meaning the variables must be defined.

Have a good day, Jerry

## jerry krause

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Hi Herb,

Sorry I creditted you with this posting. Have no idea how I screwed up so badly.

Have a good day, Jerry

## Herb Rose

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Hi Jerry,

I was surprised to see my name on the article too. I thought there was another Herb Rose out there because I was sure I didn’t write it.

My argument against the GHT has never been with the behavior of CO2, which I believe is irrelevant, but with the assertion that the surface of the Earth is hotter than the atmosphere and losing heat to it. Your recent articles show that the source of heat for the Earth’s surface is the sun. Energy or heat decreases as a function of the distance from the source so the strange graph of the atmosphere’s temperature decreasing, then increasing, then decreasing, then increasing, shows to me that the temperature readings are not accurate reflections of the kinetic energy of the gas molecules.

When you wrote of having students make thermometer, back when you could teach students by having them do something, you spoke of calibrating the thermometers using ice water and boiling water. How can this calibration be accurate when you are measuring a medium with !/1000 the molecules transferring energy?

Have a good day,

Herb

## John O'Sullivan

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The author name error was my fault – apologies – now corrected.

## John Doran

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Some interesting discussion on this:

http://www.wattsupwiththat.com/2010/03/08/the-logarithmic-effect-of-carbon-dioxide/

& The Gore Roars: “The Science Is Settled.”

What a wonker !!!

## Jim Sternhell

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The original Arhennius experiments did not demonstrate that the infrared bandwidths absorbed were not re-radiated at a different wavelength. They did not demonstrate that the heat stayed there making the gas get hotter and hotter. Note, in reality, the gas in the atmosphere receives almost no radiation at night-how strange that temperatures drop.

How pathetic that these basic re-assesments of the 100 year old experiments has not been performed. Those that profit/ plunder from the “science” refuse to debate the convenient “science.”

Time to wake up- the climate scare is a MASSIVE scam.

## Richard Percifield

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Mr Wells,

Looking at the equations my assumptions are that C0 is the reference concentration of CO2 and the C is the current / modeled concentration. There is also an alpha in all of the equations as well appearing as a linear correction factor. As you state the ln(C/C0) while an increasing function, will limit the effect to cause the thermal runaway predicted. I am an Electrical Engineer and design closed loop feedback systems on a regular basis. No where do I see a gain in the system to be greater than one (meeting Barkhausen criteria for oscillation), and how that feedback with gain can lead to instability. The current empirical data shows the opposite, increasing CO2 but no oscillation or instability. This is even true at the short term level by the annual change in CO2. If this system was this unstable we would expect significant effects on a yearly basis. There is no ringing, oscillation, or significant changes when stimulated by this rapid change in CO2.

I would like to see a control plane analysis of their equations to show where the poles and zeroes lie. Given their lack of understanding and or abuse of the Laws of Thermodynamics, that analysis will be a long time coming….

## Gymbo

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“I keep wondering why it is that PSI people keep on endorsing the false physics that asserts that radiation from “greenhouse gases” like water vapor and carbon dioxide can somehow cause heat transfer from the cold atmosphere to the warmer surface.”

Which PSI articles or papers assert what you write ????? None that I recall.

“The surface temperature is not determined by radiation.”

Then exactly how does the surface temperature of the sand in a desert, for example, increase in temperature by more than 30 or even 50 K in response to the increasingly steep angle of the morning sun striking the ground surface if the solar radiation has nothing to do with it ?

What surface temperature are you alluding to – ground surface or near ground air ???

Just how do the lunar surfaces heat from ~100 K to over ~390 K if the solar radiation has nothing to do with it ?

“thus the base of the troposphere becomes warmer (and so too the surface)”

So let me get this straight – you are explicitly stating that “gravity maximizing entropy”, which can really only have a major effect on the air temperature, is responsible for heating the ground despite the negative mass ratio of ~1.225 kg air per cubic metre versus ~1000 kg per cubic metre of water and ~1800 kg per cubic metre for soils/rocks ??

Aren’t you explicitly stating “there is heat transfer from the cold atmosphere to the warmer surface” “by the effect of gravity maximizing entropy” whilst in the previous paragraph explicitly stating that there isn’t “heat transfer from the cold atmosphere to the warmer surface.”

## geran

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The equation is from Arrhenius. It was his guesswork. There is no derication or proof of the equation. It is pseudoscience.

The equation tries to claim that energy is created just by adding CO2 to the atmosphere. That is, a doubling of CO2 would yield 3.7 Watts/m^2. That would then (supposedly) add to the solar flux, to increase Earth’s temperature!

All bogus, all a hoax, but it has fooled many, for years.