Technical Note: Sorry for any recent performance issues. We are working on it.
This month’s open thread – for appetizers we have: William Nordhaus’s extremely impressive debunking in the NY Review of Books of the WSJ 16 letter and public polling on the issue of climate change. Over to you…
Some links on planetary motion and climate — this stuff isn’t big news; the effects are extremely small and change very slowly, compared to the rate of CO2 increase from fossil fuel use.
It’s like the effect of lighting a candle inside a house. Yes, if the candle lasted long enough over enough time it would warm the house. But the house is on fire at the moment.
Cloud solutions to the Faint Young Sun paradox are not compelling. There’s been different flavors of how this could work, either by reducing the albedo in the early Archean (e.g., Rosing et al 2010) or increasing the greenhouse effect (Rondanelli and Lindzen, 2010).
The latter paper involves an unwarranted extrapolation of the IRIS hypothesis to early Earth (i.e., a negative feedback between temperatures and high clouds), a hypothesis which is highly controversial even in the modern day and has convincingly been shown to be highly exaggerated. For the early Earth, Goldblatt and Zahnle have done a good job showing that you need a number of implausible changes to clouds (such as 100% tropical cloud cover, thicker, and higher/colder clouds to make this solution a plausible one). This might be important, but there is no robust physical explanation as to why this should be a dominant factor, though I think anyone in the early Earth community would agree that a much better handle of cloud dynamics is necessary to answer these questions with high confidence.
The other problem for an Earth with 0.75-0.8x modern solar irradiance is that it is extremely prone to a snowball state because of ice-albedo and water vapor feedbacks (and not trivial to escape from that state, this is a problem even for the Neoproterozoic global glaciation, let alone an earlier one). The Lindzen solution would suggest it is more practical for temperatures only exceeding the freezing point by small amounts (or having only tropical areas ice free). I do not believe this is a tenable solution to a faint young sun at Earthlike orbit. There’s some more compelling negative feedback relations between temperature and CO2 (via silicate weathering) over geologic time.
I should also mention that there is still debate between geologists and planetary scientists concerning ancient (Archean) CO2 levels. No one has unequivocally shown that CO2 couldn’t have been much higher than today, though it’s probably not the only think going on. Methane, or even a different background pressure of gases like N2 (which are not GHGs in the modern atmosphere) that helps broaden the absorption features of the other GHG molecules may have been important.
Regarding the equation dT being proportional to 1/1-f, you can find this in a number of papers (see Roe, 2009 for a more recent mathematical overview of feedback analysis). With regard to the argument that there is a low probability that feedbacks could be strongly positive and yet somehow never having exceeded f=1 in 4+ billion years, this really isn’t true either. f almost certainly did exceed one in the transition into or out of snowball states, and it’s possible Earth had other such bifurcations in its history. This could also happen locally, such as with the the demise of a Greenland ice sheet after it reaches a certain critical volume. See here for an overview of positive feedbacks and how this doesn’t imply a runaway scenario.
Chris Crawford #96, no, you have to look at the relative size of the Earth orbit and the orbits of Jupiter and Saturn — over five times larger. It’s the latter planets that are mostly responsible for the difference between Solar centre and barycentre. And their periods are over ten times longer than the Earth’s.
This means that it is approximately correct to model the motion of the Earth and inner planets as “satellites of the Sun”, where the differential attraction of Jupiter and Saturn on the Sun and its satellites can be modelled as tidal perturbation. And there are no large long-periodic perturbations of the semi-major axis — if there were, you would see variations in the length of the year according to Kepler’s third law :-)
I have some difficulty finding documentation of that on the Internet, but here is one place. The first column is time before present in kyrs, the second, Earth orbit semi-major axis. As you see, variations of order 1:100000. Time resolution is poor, but it makes the point. Documentation in the README here.
> as do all other objects in the solar system, including the sun
Eh, the moons of Jupiter? Just being facetious :-)
Florrie @84 — I recommend reading “The Discovery of Global Warming” by Spencer Weart, first link in the science section of the sidebar here.
Martin, you’re certainly right when you write: it is approximately correct to model the motion of the Earth and inner planets as “satellites of the Sun”. However, it is more correct to model the motion of the Earth and inner planets as orbiting around the barycenter of the solar system. The difference really is tiny, but it’s real. In any case, the significance of this to climatology is, as I pointed out, tiny.
Further to Phil Clarke, it also goes without saying that those complaining of Heartland’s documents being wrongly leaked have of course not actually read those documents themselves.
We wouldn’t knowingly buy goods from a fence.
To Vince Belovich (#18). I’ve recently started reading the textbook Climate Change and Climate Modeling by J. David Neelin. He addresses cell and time step size and handling sub-grid processes at the beginning of Chapter 5. I highly recommend this book for learning about how fiendishly difficult it can be to predict what a stratified rotating spherical fluid sitting over a mixture of land and sea will do over time.
A father-son team has recently authored Global Climate Change: A Primer. The father, Orrin Pilke has been co-editor or co-author of 43 books. Reviews of many may be found @
85 CM is correct. Congratulations are due to Mike Mann from all at RC on winning in the Virginia Supreme Court with prejudice. An article in celebration is recommended.
Hank 3 Mar 2012 at 11:45 AM
Yes obviously I realise there are ups and downs. You’ve somehow missed the essential point though, which is that over 30+ years, the current theory says the trend should be up.
To qualify as being scientific, it must be clear how a theory would be falsified. So how many years of a non-increasing trend would it take to prompt a rethink? Or is the theory not quite scientific yet?
(The sideways trend of the last ~10 years I’ll leave for another time).
The president of the AGU needs to write another sternly worded message, this time to the Heartland Institute, firmly yet politely asking them to stop helping to sue climate scientists in New Zealand.
As we know– despite the unnecessarily desperate tactics of a few– a simple but clear request is all that is needed to help the Heartland Institute remember that they live in a world of full transparency and that eagle-eyed politicians ever on the lookout for the public welfare will put a swift stop to Heartland’s activities if they don’t do so themselves.
Besides, the Heartland Institute is just naturally good-hearted. Indeed, Bob Carter’s sworn affidavit to the court in which he’s testifying against the NZ climate scientists that the $1667/month he receives from Heartland is not related to his testimony and that in fact he doesn’t actually receive that money at all despite what our lying eyes and Heartland’s own documents* may tell us is proof that this is all some sort of innocent mistake.
We have only to look to our C02 concentration successfully stabilized at less than 400ppm to know that Heartland will instantly heed and obey the AGU president.
Any thoughtlessly rude, insensitive and completely pointless acts committed against Heartland will be punished to the full extent available to the AGU.
*If you do not like acts of desperation, just pretend you didn’t read about any $1667/month paid to Bob Carter by the Heartland Institute. And don’t think of an elephant.
Looking for input: two recent papers on cloud effects.
talks about a negative feedback based on reduced cloud heights.
Graeme Stephens talks about low cloud feedback here:
and suggests that models overestimate the albedo of low clouds by a factor of two.
Can someone who knows this area come up with a synthesis?
#109 Florrie. As a layman I suppose a commonsense answer might be “Every year have a look at the most recent 30-year trend and ask your question again if and when it goes negative”. Maybe that will be soon; but again, maybe it won’t. Time will tell.
Do the Galilean moons of Jupiter orbit the Solar system barycentre too?
I’d like to see the reference for that too. I’ve seen anecdotal / web stories about this, and it appears that its _weather_presenters_, primarily in the U.S., that are sceptical, rather than professional forecasters.
But a solid reference would be good.
Basically, professional meteorologists typically have a background in science, and a fuller understanding of the science; either a BSc/ MSc in meteorology. Weather presenters, in the US at least, are more likely to have a shorter few-week course, being primarily presenters rather than scientists. They are taught to not trust the (NWP) models after a few days, rather than having a background in the difference between weather and climate models and the science involved (this is less so in Europe where the presenters are more likely to be meteorologists from the national weather services than being hired as presenters.
#109–Florrie, as I expect you know, the 30-year trend IS up. If I’m not mistaken, the trend for every span ending at the present and beginning with a year prior to 1998 is up. And the trend, last I heard, is statistically significant to 95% confidence from 1995 on back.
There is no set number of years automatically “falsifying the theory”–after all, the laundry list of radiative forcings has about a dozen terms, so the hypothetical lack of warming you propose would raise the question of just which factors were involved. However, I recall reading recently–but was unable to find the reference, unfortunately–that it generally takes about 17 years of global temperature data to reach that 95% level.
If you’d like a more in-depth reference looking at this question, there’s this:
I really don’t think that IS what I’m asking.
Watch this 2min video of Peter Cox and David Attenborough.
All I’m really saying is why not re-do what peter cox has done, and ,in fact, re-do it every single year?
We’ve plotted the trend from 1967-1977, 1977-1987, 1987-1997 and 1967-1997. So three contiguous negative trends give rise to a positive trend. Clearly seeing fluctuations in noisy data is not all that exceptional.
Your idea of falsification is somewhat oversimplified. You have to look at all the data and pick the theory that best explains it. If you have something you don’t understand, that is certainly an opportunity to improve the theory. However, when the theory explains a mountain of data, it is unlikely that you will radically alter it based on a single discrepancy of questionable statistical significance. Tweaking is a lot more likely than radical alteration.
And Florrie has somehow missed the essential point that CO2 is not the only forcing of climate, and that CO2 is not the only thing that has varied over the last x years (pick what ever time period you like for x).
The book is not out where I am until this week. As a student of some luminaries in the fields of cognitive psychology and modern factor analysis, I have some exceptions to Gould’s “takedown” depending on how this takedown is described. Gould had some points that were sensible and cogent but a number of others that absolutely were not in his 1981 book. He really didn’t understand how the rise of cognitive psychology and related fields changed some of his arguments with respect to the measuring cognitive abilities, in my opinion.
Florrie wrote: “… it must be clear how a theory would be falsified …”
My theory is that you are here to recite talking points, and not to learn about climate science.
That theory can be falsified by evidence that you are studying the material to which other commenters have helpfully referred you, and gaining thereby a better understanding of the science involved — rather than ignoring that information and continuing to repeat the same ill-informed talking points.
Also for Florrie:
As I and several others pointed out, you came in with bad information (I am curious where you read the things you assumed were true that are wrong). If you come back and read any of this, please do say more. There’s nothing wrong with being fooled — there’s lots of bad info out there. What matters is learning how to check this stuff for yourself.
As Jim Eager points out, there are other factors besides CO2 that affect climate. Those can be dropped out statistically, as is done in this paper:
“increased precision enables us to establish the statistical significance of a warming trend using a shorter time span than with unadjusted data. All five data sets show statistically significant warming since 2000.”
Also for Florrie — here’s the paper that found “17 years” needed — looking at several different data sets, figuring out how variable they are and so how many years you need to look at to drop out the natural variability, and see if there’s a trend over time.
Separating signal and noise in atmospheric temperature changes: The importance of timescale
View as HTML
8 John said, “Of the 62% of people that aren’t completely isolated from reality: 28% believe scientists are overstating the evidence about “Global Warming” ”
It’s worse than that, John. They said “scientists are overstating the evidence about Global Warming for their own interests”. Perhaps the respondents didn’t think the question through, but at first glance it seems that 44% of the USA believes climate scientists as a group are not just wrong or biased, but committing grievous scientific misconduct which if revealed would devastate or end a career.
22 David Miller asked, “how we can tell that no ring was generated some particular year?
I’m no expert, but I’d guess that they use rings from different species and/or locations to cross-check. For example, since they often use trees near the cold edge of their range, they could sample trees from warmer areas, where missed rings should show up. It would take minimal sampling, as detection would be the only goal.
Jim beat me to it.
Florrie, your mischaracterization of climate science is immediately falsifiable, no need to wait. You’re right that your mischaracterized theory “isn’t quite scientific”, because it’s not a theory that exists in science at all.
Climate science does not posit that CO2 and only CO2 affects climate.
So I suggest you go away and learn what climate science tells us before posting again. None of us want you to look foolish in public, after all.
#113 Martin Vermeer “Do the Galilean moons of Jupiter orbit the Solar system barycentre too?”
The barycentre of the solar system varies “slightly” with changing planetary positions. I should say that the Galilean moons of Jupiter can indeed be said to orbit the solar system barycentre (while simultaneously orbiting the barycentre of the Jupiter+moons system) just as the earth’s moon does if we consider it as part of the earth+moon system (and around whose barycentre the moon also orbits). If our moon had been sufficiently large (so that the earth+moon barycentre was in space rather than within the earth itself) we could have said that the earth orbited the earth+moon barycentre while orbiting the solar system barycentre. I imagine the barycentre of the solar system is well within the sun itself and not far removed from the sun’s centre of mass, but I don’t know this for sure. But if so the point about whether the planets orbit the sun or the solar system barycentre is pedantic for most purposes. BTW I’ve never understood why the the angular momentum of the solar system is possessed mainly by the orbiting planets while its mass is concentrated in the sun. How can this have come about?
Do the Galilean moons of Jupiter orbit the Solar system barycentre too?
If you set out to model the climate of any of those moons, you would need to get their movement with respect to the sun nearly correct, and motion around the solar system barycentre would be part of that. Approximating the solar system barycentre as the center of the Sun would not be exactly right, but it make a smaller difference than it does for Earth. Of course they also move around the Jovian system barycentre.
Martin Vermeer: Do the Galilean moons of Jupiter orbit the Solar system barycentre too?
Indeed they do. They If you plot their positions in the solar system’s frame of reference, you’ll find them tracing an ellipse around the sun, with tiny epicycloids representing their motion around Jupiter. If you plotted them even more closely, you’d see perturbations from Saturn, and if you increased the resolution even more, you’d see perturbations from all the other planets.
But the big question is, how bad was Michael Mann’s hangover yesterday? ;) Many congratulations. And how many hockey sticks are there out there, now?
thank you for hanging in there.
I’m prepared to be put straight on that, but I didn’t mean to start an off-topic discussion of IQ and such. Perhaps you should comment here when you’ve read the book, if you think (i) that Gould’s argument is flawed and Mike Mann’s own argument suffers from the same flaws, or (ii) Mann’s is valid but he doesn’t do it any favors with the Gould comparison, or (iii) both are valid as far as the comparison goes and I can relax.
The book is available on Kindle (I was being metaphorical about the shelf).
Simon Abingdon (#124), the barycenter of the solar system is usually outside the sun, but by only by about the radius of the sun. Because the planets are constantly shifting their relative alignments, the distance of the sun from the barycenter is variable. I believe that in an earlier post, Martin provided a link to a map of the solar motions for the next few decades.
The angular momentum of the solar system is carried mostly in the planets because angular momentum equals mass times distance times linear velocity. Thus, Jupiter has more of the solar system’s angular momentum because the product of its values is 2*10^27 kg * 8*10^11 m x 1*10^4 m/s, or about 2 *10^43 kg-m^2/s.
Even if we assume that all the mass of the sun is at its surface on the equation (I’m too lazy to carry out the 3-dimensional integration over variable density), the solar angular momentum is 2*10^30 kg x 7*10^8 m * 1*10^3 m/s, or about 1.5*10^41 kg-m^2/s — about a hundred times less than Jupiter’s.
Florrie, you’re getting bad info somewhere. What source are you relying on for the statements you’re making?
Spencer Weart’s book (right sidebar) will get you past the “falsified” problem with radiation physics. The physics explains lasers, the greenhouse effect, and a lot about how stars work.
People know a lot of stuff that’s wrong about this area.
Seriously — ask yourself where you’re getting your information, and if it’s a reliable source. Test it. Do a simple search, look at the results.
Let us know what you find where you’ve been looking, if you care to.
For example: https://duckduckgo.com/?q=climate+change+radiation+physics
Take the same key words and search with Scholar and see how different the results are.
For example: http://scholar.google.com/scholar?q=climate+change+radiation+physics
Think about the difference in the results.
You won’t learn anything if you just take stuff that looks clever from someone else’s blog and paste it in here as a challenge. There’s a lot of bad info out there — work on it, think about it, see what the science says.
People here will try to help. But show you’re making the effort.
We get a lot of visitors in here who just act like tubes, carrying stuff from elsewhere they haven’t thought about at all. Regular readers like me and some of the others try to answer the often repeated stuff to save the real scientists the bother of repeating the same answers over and over.
You’ll also see some short-tempered responses; some people don’t pretend to be patient with the tubes. Some of us try to.
Spencer Weart’s ‘Discovery of Global Warming’ book
is this link in the right sidebar:
AIP:Discovery of Glob. Warm.
Richard Alley was quite funny when he told Rohrabacher, “Your brightness is the sun…”
#129 Chris Crawford. Thanks for your response.
My puzzlement over the solar mass v. angular momentum question is not that I didn’t know the meaning of the terms but that I had always understood it had been accepted that the solar system must have condensed from a rotating mass. Your figures only confirm the mystery of why the solar angular momentum is so much less than its mass would suggest were the condensing rotating mass theory correct.
I really don’t get it…the Brookings Report seems trivial. By my understanding, very few scientists and those who follow the issue closely will deny that the planet is getting warmer. And that’s all they asked. all the detail is related to “belief”, nothing else. Nice for a political scientist, but hardly helpful for someone wanting to make an informed judgement about the science.
the real issue is cause-effect relationships and differences over policy issues. Right?
i’m left thinking “so what?” after looking over the Brookings Report.
what am i missing?
For Simon Abington:
“It has long been known that angular momentum must be lost.”
“Many folks know from history that Arctic Ice was as low if not lower than it is today in the early part of the 19th century. Russia built ports on the northern coast of Siberia and established shipping up until the early 1950′s when the freeze returned and the routes and ports were closed.
How do I know?
I was around at the time.” Titus — 1 Mar 2012 @ 4:16 PM
Unprecedented low twentieth century winter sea ice extent in the Western Nordic Seas since A.D. 1200, Fauria et al, Climate Dynamics, DOI 10.1007/s00382-009-0610-z
“3. The twentieth century sustained the lowest maximum sea ice extent values since A.D. 1200.
4. Low maximum sea ice extent also occurred over periods of some decades (e.g., mid-seventeenth and mid-eighteenth centuries, early fifteenth and late thirteenth centuries), with absolute values in some cases as low as the twentieth century ones, but these periods were in no case as persistent as in the twentieth century.
10. The presently low maximum sea ice extent in the Western Nordic Seas is unique over the last 800 years, and results from a sea ice decline started in late-nineteenth century after the Little Ice Age.”
Reconstructed changes in Arctic sea ice over the past 1,450 years, Kinnard et al, Nature, doi:10.1038/nature10581
“Two episodes of markedly reduced sea ice cover also occurred in the late sixteenth and early seventeenth centuries (T2 in Fig. 3). However, by the mid-1990s the observed decrease in sea ice cover had exceeded the lower 95% confidence limit of these prehistorical minima. Our findings support a previous study suggesting that the impact of anthropogenic climate warming on Arctic sea ice became detectable from the early 1990s onwards(19). The present decline in sea ice is occurring at a pace seen in earlier episodes, but the sustained trend (now nearly 50 years long) is unprecedented in the 1,450-year reconstruction period presented here.”
There is a difference between peaks and valleys in noisy processes (1998 surface air temperature, 2007 record minimum ice, or shipping at a few small areas on the edges of the Arctic ocean) and CO2 forcing driven trends, especially when different measures. proxies, and baselines introduce other variability
I use kobo in Canada and have to wait till Tuesday.
Re. where Gould goes wrong from a psychologist’s POV, an article by John Carroll shows some of the problems.
“…make an informed judgement about the science.” “the real issue is cause-effect relationships…”
Unfortunately, if you are setting policy, or voting for those who set policy, based on your belief that the cause-effect relationships between CO2 and AGW are debatable, or that science is irrelevant to policy decisions because we can “make our own reality”, actual reality will eventually prove you foolish. And the impacts of foolish decisions (about tar sands, or “clean coal”, or offshore drilling, or whether AGW driven weather extremes will have trivial impacts on Texas & Australian droughts, Mississippi & Mekong floods), don’t just adversely affect the policy makers.
#135 Hank Roberts. Thanks for the interesting reference. The complete quote is “Were angular momentum conserved this would lead to ridiculous spin rates, so it has long been known that angular momentum must be lost”(!) One can’t help wondering where it went.
Isolating the relevant responses from the noise, it would appear that 17 years of non-increasing temperature data trends would be enough to prompt a rethink of the current CO2-knob temperature theory. And perhaps 30 years would be needed for a more thorough falsification.
> simon … where it went
Personally, I think the missing angular momentum migrated to the Internet as spin. But that’s just a guess based on the quantity observed.
Nope. “It would appear” and “perhaps” aren’t used in statistics.
Specify a data set; look at the natural variability in the data; remove what can be explained. Do the math. You haven’t specified a data set yet. Did you look at Robert Grumbine’s page yet? He’ll walk you through how the arithmetic is done.
Chris Crawford #126, I see. We want to split hairs now, do we? But, don’t you agree that the primary orbital motion of the moons of Jupiter is around Jupiter, and the rest is perturbations — in a common-sense sense? And don’t you agree that the same applies for the Earth orbit around the Sun?
My point is that the choice of origin relative to which to describe the equations of motion is arbitrary — and transformation between them readily possible –, but some choices are “nicer” than others. If all you’re interested in is the motions of the Galilean moons, you choose the Jovian barycentre for origin, because then everything will be nice. Numerically, but certainly from a conceptual-understanding viewpoint.
In the description of the DE200 planetary ephemeris, it is pointed out that, contrary to all the other objects in the computation which use the Solar system barycentre, the orbit of our own moon is computed relative to the Earth-Moon barycentre, because then, the orbit integration will behave nicer numerically — which is good, as the Moon is an object of special interest. I would add that this also corresponds better to our conceptual understanding.
Looking at computing the orbits of the inner planets heliocentrically vs. barycentrically, you don’t see any difference in numerical behaviour. This is because orbit integration is nowadays done using advanced integrators (like Adams-Moulton) in rectangular state-vector components. These orbital elements change rapidly all the time anyway, no matter where you place the origin.
Now, if you were to transform these to Keplerian elements, you would see that the heliocentric elements are almost constant: they change at most slowly, with secular changes over tens of thousands of years. If, instead, you would look at barycentric Keplerian elements, you would see them change hundreds of times faster, but most of that would be oscillations at the orbital periods of the outer planets like Jupiter and Saturn. And if you were to remove these oscillations, you would be back at the slowly changing heliocentric Keplerian elements.
This is also easy to see by evaluating the dominant perturbations in each case:
* in the heliocentric frame, the dominant perturbation is due to Jupiter. Say, it has a mass of 1/1000 of that of the Sun, and is at a distance of 5x that of the Earth. Then, its attraction will be 1/25000 of that of the Sun; its differential attraction between Sun and Earth, i.e., perturbing acceleration, will be 1/125000 of the Solar attraction.
* In the barycentric frame, the dominant perturbation is that of the Sun not being in the origin: 1/200 of the Solar attraction, i.e., over 600 times as strong.
My concluding point: in explaining things to people, use the heliocentric viewpoint. It is “nicer”. Don’t bring up the barycentric viewpoint unless you’re in the company of aspiring celestial mechanicists — or if you (not you, but you know who I mean) want to obfuscate things.
Florrie #140: how many seconds of bird flight would make you re-think gravitation? How many more to falsify it more thoroughly?
#140–It is also relevant that “Climate science does not posit that CO2 and only CO2 affects climate.” (Dhogaza @ #123.)
So it concerns me to hear the phrase “the current CO2-knob theory”–a control knob usually exerts a unique ‘forcing’ on whatever it may control. CO2 does not; the continuous increase in concentration, driven by human emissions, is powerful because it is unidirectional. But it is far from the only forcing.
So if you are looking for climate ‘control knobs,’ you need a bunch more than just one for CO2. (For instance, Gavin just gave 14+ as a common number of ‘knobs’ used in modeling 20th century climate.)
Flossie, I apologize if this was already clear to you; but it didn’t seem to be from your comment.
@ 140 Florrie
What non-increasing 17 year temperature trend?
It appears that you are not reading the responses. Seventeen years would be sufficient to indicate a problem with the theory–that certainly would not mean that we abandon the idea of CO2 as a greenhouse gas, and it likely would not mean that we abandon the idea of substantial positive feedback in the climate energy balance. The changes would depend on precisely HOW the theory failed.
I’ve been told by a friend that James Hansen once said that albedo changes from melting the arctic sea ice would capture as much additional heat as doubling CO2.
That sounds very high to me, even before discounting for the seasonality of missing ice and heavy cloud cover. He can’t provide a reference and I couldn’t get a straight answer out of google.
Does this ring any bells with anyone?
Isolating the relevant responses from the noise, it would appear that 17 years of non-increasing temperature data trends would be enough to prompt a rethink of the current CO2-knob temperature theory.
But of course, when known sources of natural variation (“noise”) are removed, the trend becomes even more, not less, apparent. Come back when we hit a 17 year stretch where this isn’t true, and you may be on to something.
heck, even if you don’t remove known sources of natural variation, the trend is obvious
Again, I beg of you, quit making a fool of yourself in public.
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