Guest Post by Willis Eschenbach
Figure 1. The Experimental Setup
I keep reading statements in various places about how it is indisputable “simple physics” that if we increase the amount of atmospheric CO2, it will inevitably warm the planet. Here’s a typical example:
In the hyperbolic language that has infested the debate, researchers have been accused of everything from ditching the scientific method to participating in a vast conspiracy. But the basic concepts of the greenhouse effect is a matter of simple physics and chemistry, and have been part of the scientific dialog for roughly a century.
Here’s another:
The important thing is that we know how greenhouse gases affect climate. It has even been predicted hundred years ago by Arrhenius. It is simple physics.
Unfortunately, while the physics is simple, the climate is far from simple. It is one of the more complex systems that we have ever studied. The climate is a tera-watt scale planetary sized heat engine. It is driven by both terrestrial and extra-terrestrial forcings, a number of which are unknown, and many of which are poorly understood and/or difficult to measure. It is inherently chaotic and turbulent, two conditions for which we have few mathematical tools.
The climate is composed of six major subsystems — atmosphere, ocean, cryosphere, lithosphere, biosphere, and electrosphere. All of these subsystems are imperfectly understood. Each of these subsystems has its own known and unknown internal and external forcings, feedbacks, resonances, and cyclical variations. In addition, each subsystem affects all of the other subsystems through a variety of known and unknown forcings and feedbacks.
Then there is the problem of scale. Climate has crucially important processes at physical scales from the molecular to the planetary and at temporal scales from milliseconds to millennia.
As a result of this almost unimaginable complexity, simple physics is simply inadequate to predict the effect of a change in one of the hundreds and hundreds of things that affect the climate. I will give two examples of why “simple physics” doesn’t work with the climate — a river, and a block of steel. I’ll start with a thought experiment with the block of steel.
Suppose that I want to find out about how temperature affects solids. I take a 75 kg block of steel, and I put the bottom end of it in a bucket of hot water. I duct tape a thermometer to the top end in the best experimental fashion, and I start recording how the temperature changes with time. At first, nothing happens. So I wait. And soon, the temperature of the other end of the block of steel starts rising. Hey, simple physics, right?
To verify my results, I try the experiment with a block of copper. I get the same result, the end of the block that’s not in the hot water soon begins to warm up. I try it with a block of glass, same thing. My tentative conclusion is that simple physics says that if you heat one end of a solid, the other end will eventually heat up as well.
So I look around for a final test. Not seeing anything obvious, I have a flash of insight. I weigh about 75 kg. So I sit with my feet in the bucket of hot water, put the thermometer in my mouth, and wait for my head to heat up. This experimental setup is shown in Figure 1 above.
After all, simple physics is my guideline, I know what’s going to happen, I just have to wait.
And wait … and wait …
As our thought experiment shows, simple physics may simply not work when applied to a complex system. The problem is that there are feedback mechanisms that negate the effect of the hot water on my cold toes. My body has a preferential temperature which is not set by the external forcings.
For a more nuanced view of what is happening, let’s consider the second example, a river. Again, a thought experiment.
I take a sheet of plywood, and I cover it with some earth. I tilt it up so it slopes from one edge to the other. For our thought experiment, we’ll imagine that this is a hill that goes down to the ocean.
I place a steel ball at the top edge of the earth-covered plywood, and I watch what happens. It rolls, as simple physics predicts, straight down to the lower edge. I try it with a wooden ball, and get the same result. I figure maybe it’s because of the shape of the object.
So I make a small wooden sled, and put it on the plywood. Again, it slides straight down to the ocean. I try it with a miniature steel shed, same result. It goes directly downhill to the ocean as well. Simple physics, understood by Isaac Newton.
As a final test, I take a hose and I start running some water down from the top edge of my hill to make a model river. To my surprise, although the model river starts straight down the hill, it soon starts to wander. Before long, it has formed a meandering stream, which changes its course with time. Sections of the river form long loops, the channel changes, loops are cut off, new channels form, and after while we get something like this:
Figure 2. Meanders, oxbow bends, and oxbow lakes in a river system. Note the old channels where the river used to run.
The most amazing part is that the process never stops. No matter how long we run the river experiment, the channel continues to change. What’s going on here?
Well, the first thing that we can conclude is that, just as in our experiment with the steel block, simple physics simply doesn’t work in this situation. Simple physics says that things roll straight downhill, and clearly, that ain’t happening here … it is obvious we need better tools to analyze the flow of the river.
Are there mathematical tools that we can use to understand this system? Yes, but they are not simple. The breakthrough came in the 1990’s, with the discovery by Adrian Bejan of the Constructal Law. The Constructal Law applies to all flow systems which are far from equilibrium, like a river or the climate.
It turns out that these types of flow systems are not passive systems which can take up any configuration. Instead, they actively strive to maximize some aspect of the system. For the river, as for the climate, the system strives to maximize the sum of the energy moved and the energy lost through turbulence. See the discussion of these principles here, here, here, and here. There is also a website devoted to various applications of the Constructal Law here.
There are several conclusions that we can make from the application of the Constructal Law to flow systems:
1. Any flow system far from equilibrium is not free to take up any form as the climate models assume. Instead, it has a preferential state which it works actively to approach.
2. This preferential state, however, is never achieved. Instead, the system constantly overshoots and undershoots that state, and does not settle down to one final form. The system never stops modifying its internal aspects to move towards the preferential state.
3. The results of changes in such a flow system are often counterintuitive. For example, suppose we want to shorten the river. Simple physics says it should be easy. So we cut through an oxbow bend, and it makes the river shorter … but only for a little while. Soon the river readjusts, and some other part of the river becomes longer. The length of the river is actively maintained by the system. Contrary to our simplistic assumptions, the length of the river is not changed by our actions.
So that’s the problem with “simple physics” and the climate. For example, simple physics predicts a simple linear relationship between the climate forcings and the temperature. People seriously believe that a change of X in the forcings will lead inevitably to a chance of A * X in the temperature. This is called the “climate sensitivity”, and is a fundamental assumption in the climate models. The IPCC says that if CO2 doubles, we will get a rise of around 3C in the global temperature. However, there is absolutely no evidence to support that claim, only computer models. But the models assume this relationship, so they cannot be used to establish the relationship.
However, as rivers clearly show, there is no such simple relationship in a flow system far from equilibrium. We can’t cut through an oxbow to shorten the river, it just lengthens elsewhere to maintain the same total length. Instead of being affected by a change in the forcings, the system sets its own preferential operating conditions (e.g. length, temperature, etc.) based on the natural constraints and flow possibilities and other parameters of the system.
Final conclusion? Because climate is a flow system far from equilibrium, it is ruled by the Constructal Law. As a result, there is no physics-based reason to assume that increasing CO2 will make a large difference to the global temperature, and the Constructal Law gives us reason to think that it may make no difference at all. In any case, regardless of Arrhenius, the “simple physics” relationship between CO2 and global temperature is something that we cannot simply assume to be true.
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One of the mysteries, to me at least, of the entire debate is why the ‘experts’ are even bothering to use air temperatures to determine whether or not we are heating or not. Isn’t it the energy budget (heat) of the entire earth that is important in the big picture? Don’t you really want to know whether the earth is gaining or losing energy to space?
By using air temperature as a proxy for an energy budget you are using the very low specific heat and chaotic sensory regime of air to ascertain the inner workings of the relatively enormous dense, high specific heat of the planet which is also chaotic.
It’s like waving a thermometer over your baby’s butt to see if he has a temp isn’t it? The first rule of measuring anything is to remove the potential variables that introduce error. By using air temps you are using the worst possible indicator aren’t you?
Thinkingbeing(15:08:16):
“RJ (14:18:54) :
“Can you please point me to an article or study that demonstrates the backcast capability of models?”
TB:”Implying what, that I was lying? Do your own work. Use google. Read. Learn. Stop parroting things without thinking. This information is readily available, in abundance. I’m not going to hold your hand.”
“lying”? Sheesh! Of course I went to google first. Nothing I’ve found supports accuracy of backcasts. My request was polite, yours condescending and weirdly macho.
Your claim of backcast reliability was almost a throw-away line made with great confidence. Surely, in the time it took you to insult me, you could have referenced a study done on the accuracy of backcasts.
I am sincerely looking at both sides of climate change, folks with your attitude do nothing to inspire confidence in the science supporting AGW. Yeah, yeah I know, you don’t care what inspires my confidence. Then why are you here?
Give me a link, please.
kevoka (21:43:23) :
Last I looked we are still using 101,325 Pa as the standard pressure at sea level. If we are dumping Billions and Billions of tons of C02 into the air, should this not go up just a bit? Who should I call to get this adjusted? Would Al Gore know?
Not sure if that is sarcastic or not, but if not, adding 0.01% or even 0.02% to the atmosphere will not change pressure in any measurable way. The minute to minute fluctuations of pressure and humidity would mask that.
Hang on … perhaps it won’t change the heat trapping properties either? There’s a thought.
In fact:
Global climatologists claim that the Earth’s natural greenhouse effect keeps the Earth 33C warmer than it would be without the trace gases in the atmosphere. About 80 per cent of this warming is attributed to water vapor and 20 per cent to the 0.03 volume per cent CO2. If such an extreme effect existed, it would show up even in a laboratory experiment involving concentrated CO2 as a thermal conductivity anomaly. It would manifest itself as a new kind of `super insulation’ violating the conventional heat conduction equation. However, for CO2 such anomalous heat transport properties never have been observed.
Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics:
http://www.schmanck.de/0707.1161v4.pdf
The spectrum CO2 gass can absorb and radiate is the independent of temperature. The intensity of the radiation depends on the temperature. The higher the temperature the more intense the radiation. So the colder at the top the less is radiated out. If it were warmer at the top then at the ground, greenhouse gasses would have a cooling effect.
Surely this is wrong, not to say contradictory. If cold CO2 has the same absorption band as warm CO2 (which I would expect) how does it suddenly become less transparent? It is either absorbing more energy and radiating it back (i.e. greenhouse effect) or it is absorbing the same amount. Its temperature is irrelevant unless it implies less transparency.
I don’t see why a cold CO2 molecule in the upper atmosphere radiates out less energy than an equally cold O2 molecule. A black box is not dependent on its make-up after all. If having extra CO2 makes the upper atmosphere colder it would it make any difference, but I don’t see how that would work.
This “extra layer of cold CO2” sounds likely total techno-waffle to me.
vukcevic (02:43:56) ” http://www.vukcevic.talktalk.net/LOD-GMF.gif http://www.vukcevic.talktalk.net/SSN-GMF.gif “
vukcevic, is it the same 90N GMF curve in both plots? (i.e. one is the negative of the other?)
Paul B (16:12:17)
I believe you are beating on Pielke, Sr.’s hobby horse there.
“In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
– Life on the Mississippi
ohn M (15:31:51) :
ThinkingBeing :
I understand it, and the ramifications of everything involved, more than enough for my own satisfaction.
THE GREAT OZ HAS SPOKEN!
—
LOL!
Wow – this thread really went nuts! I suppose Mr. T-B is off to do a numerical stability analysis of his GCM so that he can prove to us commoners that the highly coupled, non-linear system of PDEs that comprise the average climate model is well-posed…LOL
“”” Mooloo (16:37:20) :
The spectrum CO2 gass can absorb and radiate is the independent of temperature. The intensity of the radiation depends on the temperature. The higher the temperature the more intense the radiation. So the colder at the top the less is radiated out. If it were warmer at the top then at the ground, greenhouse gasses would have a cooling effect.
Surely this is wrong, not to say contradictory. If cold CO2 has the same absorption band as warm CO2 (which I would expect) how does it suddenly become less transparent? It is either absorbing more energy and radiating it back (i.e. greenhouse effect) or it is absorbing the same amount. Its temperature is irrelevant unless it implies less transparency.
I don’t see why a cold CO2 molecule in the upper atmosphere radiates out less energy than an equally cold O2 molecule. A black box is not dependent on its make-up after all. If having extra CO2 makes the upper atmosphere colder it would it make any difference, but I don’t see how that would work.
This “extra layer of cold CO2″ sounds likely total techno-waffle to me. “””
Actually, cold CO2 does not have the same absorption band as warmer CO2, so there is a difference. The hotter the CO2 molecule is, the greater its random molecular motion is (i.e. more “heat”) That higher velocity molecular motion, means a greater Doppler effect, which will shift the wavelength range of LWIR which the CO2 can efficiently absorb, so hotter the CO2 is, the wider range of wavelenghts it can intercept, or conversely, the less effective colder CO2 becomes. Also the colder CO2 is generally at higher altitudes, where the atmospheric pressure, and density is lower, so there is a longer mean free path between molecular collisions, and once again the “pressure broadening” of the absorption spectrum is narrower at lower densities.
So at higher altitudes, CO2 will absorb less of the radiation spectrum, so more of it will escape.
The energy of the excited CO2 molecule will usually be lost in collisions with nitrogen or oxygen molecules, and it is they that will generally re-emit thermal radiation due to the air temperature. And the colder the air temperature and the lower its density, the less energy is emitted as LWIR in all directions, both up and down. The up radiation will tend to encounter even colder less dense CO2 and so be absorbed even less, allowing more to escape, while the downward LWIR will run into denser warmer CO2, so be more likely to be re-absorbed.
Since the probablitity of downward radiation, and upward should be about equal, the downward faces a greater probability of re-absorption by another CO2 molecule, compared to the upward, and the re-emission from the lower atmosphere due to that secondary absorption, will once again be split into about half up, and half down. The result is the up path is favored over the down path as far as transmission, so escape to space is facilitated, while the probability of reaching the surface is reduced.
Another simplistic science idea is that global warming is heating up the oceans and damaging coral reefs, etc. It isn’t! I have read that a one degree rise in air temperature will take 150 years to warm the oceans by one degree. I do not know the source so I can not say what scientific basis there is to it, but it sounds right. [I do remember the original article – it was written by someone who firmly believed in global warming and then realised he had been ‘mislead’. He was really, really unhappy at being conned!]
A question I have is about the distribution of CO2 : CO2 is heavy! I recently watched a program about a volcanic lake where a rock slide released huge quantities of CO2 trapped in the sediment, which then rolled down the side of the volcano and suffocated 2000 people to death. There are gulleys in South America where any animals which enter die – the gulleys have filled with CO2 from a nearby volcano and created a bizarre death trap.
Every molecule of CO2 is trying to fall to sea-level. Does the concentration of CO2 vary with height, or does the mixing of the wind keep the mix even? A greenhouse is only useful if the glass is above you, not on the ground!
So, are we adding molecules to the atmosphere, or are we just changing the type of molecules in the atmosphere?
Paul B (16:12:17) :
By using air temps you are using the worst possible indicator aren’t you?…………
For climate studies this is possibly true, and a good scientific competition would be to ask for a listing of the worst to the least temperature indicators, now that would help to qualify temperature measurement.
The problem is to extrapolate what was designed as a human related measurement (Stevenson screens 1.2 above ground level) system into a climate model. As has been discussed here many times, this is a major problem. Some have suggested caves, others ocean temp, but what depth is ‘stable’, what about upwelling currents?. Bucket readings from the surface seem to be the most stable and correlate well with satellite readings and again there is disagreement with engine intake readings preferred.
Buried earth sensors have been mentioned. I use a natural gas instant water heater and, out of curiosity, a few tears ago I measured the cold water input temperature range. It went from 11degrees C in winter to 19degrees C in summer. These buried pipes are measuring water flowing through the ground surrounding the pipe and are not restricted to one area of ground(I kept the water flowing until the temp stabilised) and may be one answer.
Michael Maxwell (17:01:36) :
“In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That…”
Major coup post on Twain. Could it be there was some small semblance of sarcasm in his manner?
Fantastic article Willis, much needed education! The acceptance of non-equilibrium chaos dynamics in climate is a paradigm shift no less significant than astronomers accepting the earth rotated around the sun (not vice versa).
“The IPCC says that if CO2 doubles, we will get a rise of around 3C in the global temperature.”
Lets go briefly to an analogy that I like, the Ordovician era, 450 odd million years ago. Here atmospheric CO2 concentration was 8-20 times higher then the present level. According to the IPCC this would mean 12-30 degrees C (K) of warming. This would have killed all life except maybe some microbes; however the reality was a temperature difference of only one or two degrees compared to the present. And a global climate which allowed life to thrive and radiate, with among other things the first evolution of corals – the very organisms supposedly threatened by tiny increases in CO2 now. (Utter nonsense.) The funniest part is that the Ordovician ended not in IPCC-compliant run-away warming but in an extremely severe “snowball earth” ice age with glaciers over the present-day Sahara. What was CO2 greenhouse warming doing during this era? It is hard to imaging a more comprehensive failure of a scientific hypothesis than that of CO2 greenhouse warming (and attendant coral-killing ocean acidification) in the Ordovician era.
As Willis has explained, non-equilibrium dynamics and the Constructal Law instead show the earth’s climate system to enforce a certain climate regime as an attractor with considerable robustness to so-called “forcings” which really don’t do much forcing at all, but rather participate in a sort of dance.
CodeTech (15:04:41) :
ThinkingBeing:
Please provide links to your posts on this, but off the top of my head, your argument above is silly. The ocean is no where close to absorbing all of the heat it is capable of absorbing, but it has absorbed an incredible amount of additional heat in the last twenty years. Comparing the oceans to a pot of water that has reached boiling point? Are you serious? This is such a weak understanding of physics and science that I am now appalled that I ever bothered to post a comment on your post. It’s beneath me.
Excuse me?
Where, then, is this heat?
————–
It’s in Jim Hansen’s sock drawer.
Paul B (16:12:17) :
The “experts” are using air temperatures as measured at airports, a fact that is easily documented with a cursory scan of the stations listed in the current GHCN v2 mean file. These sites, the airports, are contaminated with UHI, especially those in areas with consistently high humidity.
Furthermore, as airports become larger and as cities grow, the contamination steadily increases over time. No physicist in his/her right mind is going to argue these points.
Water vapor is a much “stronger” greenhouse gas than CO2. Nights are going to be significantly warmer near huge runways in areas with lots of moisture in the air.
Assuming that air temperature is even a valid way to gauge climate change, there are substantial issues with regard to the actual collection of the air temps.
Of course, the Team scientists all believe that their adjustments can properly eliminate the UHI signal, but every adjustment increases uncertainty so the final product is more uncertain. The adjustments also provide an opportunity (I’d call it an open barn door) for the more unscrupulous Team members a chance to make mischief with the data. Bodge the data, hide the decline.
For the record, I would no more trust Phil Jones and his ilk any farther than I could spit.
I found this in the Physics Factbook:
“So even though surface waters can be a comfortable 20 degrees Celsius (good for swimming in!), the majority of our ocean water has a temperature between 0-3 degrees Celsius (32-37.5 degrees Fahrenheit).”
So if the ocean is close to absorbing all of the heat it is capable of absorbing, we’re in BIG trouble! However, ocean water can absorb heat (and still stay in the ocean) until it starts to boil, which is around 100C, depending on salinity. I think we have a long, long way to go before the oceans are anywhere near their maximum heat capacity.
Another example of some people being educated but never learning to think. No wonder they’re called sheeple.
Mooloo (16:37:20) :
Surely this is wrong, not to say contradictory. If cold CO2 has the same absorption band as warm CO2 (which I would expect) how does it suddenly become less transparent? It is either absorbing more energy and radiating it back (i.e. greenhouse effect) or it is absorbing the same amount. Its temperature is irrelevant unless it implies less transparency.
The absorption depends on temperature broadening the absorption lines, the colder the CO2 the narrower the lines (and since there is pressure broadening too, at high altitudes the lines are narrower due to that too).
The temperature is very relevant.
I don’t see why a cold CO2 molecule in the upper atmosphere radiates out less energy than an equally cold O2 molecule.
The O2 molecules don’t radiate at all in the IR.
ThinkingBeing:
In your opinion maybe. So far all we have to show for the tens of billions of public funding wasted on this nonsense is a hypothesis that doesn’t hold up. There is no observable correlation between CO2 concentration and global temperature in the atmosphere, directly or indirectly. Climate scientists are doing politics.
First you need to define what a “Climate Scientist” is. What’s wrong with traditional disciplines, where has this sorry term come from all of a sudden? The main proponents seem to be a mixture of second rate mathematicians, wannabe philosophers with some left-leaning political agenda and the odd divinity student. A PhD of itself means nothing, I see no real scientists amongst this motley bunch at all. The correct term for them is “Climate Propagandists”.
The first thing all of them sign up to is wholesale displacement of time honoured, normal scientific principles by vague, dangerous philosophical nonsense put about by the likes of Mike Hulme. You might as well believe in fairy stories. This isn’t science at all, it’s an exercise in self-delusion with a view to imposing pseudo-intellectual tyranny. The word for that is bull$hit.
The whole scam is now just a self-perpetuating celebrity cult with all the hallmarks of indoctrination and massive media hysteria. Just the sort of thing politicians (and NGOs that live in their wake) latch onto until it inevitably turns sour. But take care, this enormous overripe fruit salad has a long way to fall and will make a much bigger mess than a few polar bears with no parachute.
1. Very well put.
2. I wish that we could get rid of the term “forcings.” It prejudges the case. Why not revert to the term used in the rest of science: factors?
Or “variables” would be better. You know, the putatively independent and dependent varieties, which variety, if either, remaining to be determined by experiment?
huh? (09:44:58) :
Phil. (07:21:49) :
“Water flowing downhill tries to get there as fast as possible which would mean following a brachistochrone and this is supposed to tell us something about the response of the climate to CO2?”
Phil, since you seem to know so much about everything, can you please explain why cutting through an oxbow is not a stable approach to making a river’s path shorter? Or is the whole claim about the river wrong?
In making the path shorter you slow down the rate of flow so any further perturbation which tends to increase the length will increase the flow rate and so the path will lengthen again. The Bernoullis, Newton, Liebniz and l’Hôpital had it worked out about 3 centuries ago.
I await your enlightening response.
ON UNCERTAINTY
ThinkingBeing: I accept the point that H2O is itself a greenhouse gas, I can’t think though that H20 in the atmosphere in the form of clouds doesn’t have some proportion of cooling effect. I am satisfied that we agree that whatever one calls climate sensitivity (with or without fast feedbacks and with or without slow feedbacks) the system won’t be fully modeled until all factors and feedbacks are imagined, studied and accounted for. I have to add here that negative feedbacks should be wished and hoped for if we are truly alarmed that global warming is a dire condition. Is the proposition that warmer global temperatures would result in an increase in cloud cover such an outlandish a proposition? It seems like a topic ripe for study. I’m quite confident that the IPCC and other large scale studies of the climate question discuss the difficulties clouds present to modelers. I also note that Kevin Trenberth feels that uncertainty due to clouds is important enough to discuss in his emails. It is the context for his famous statement that “it’s a travesty that we can’t” [account for the lack of warming].
“The CERES data are unfortunately wonting [sic] and so too are the cloud data.” – Kevin Trenberth, communication as public official.
“The CERES data published in the August BAMS 09 supplement on 2008
shows there should be even more warming: but the data are surely wrong. Our observing system is inadequate.” – Kevin Trenberth.
[snip – juvenile missive]
George E. Smith (10:30:42) :
On the other hand for the very small changes in CO2 that are closely monitored these days, at places like Mauna Loa, the logarithm of the CO2 change would seem to be very little different from unity; and given that Ln(1+x) is approximately x, that would seem to make the relationship at least as close to linear, as it is to logarithmic.
Yes George that’s true for small x such as a few years growth, it’s far from true when we’re talking about doubling (x=1)
May I suggest Phil, that the presumed logarithmic connection between CO2 abundance in the atmosphere, and global mean temperature, is more a figment of the presumption of the reality of the concept of “climate sensitivity”, than it is of any operating physics.
You can suggest it but you’d be wrong. The log dependence arises from line broadening (see Voigt profile), it’s a well known phenomenon in spectroscopy.
The relationship is evidently logarithmic, because the inventor of “Climate sensitivity” (izzat Steven Schneider of Stanford?) said so;
Nope, see above.
Happy New Year George.