Climate tipping might be predicted using algebraic topology

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Theoretical progress in climate science indicates algebraic topology applied to reduced climate models might help predict if and when the Earth system will tip

Peer-Reviewed Publication



The Earth’s climate system seems to have shifted abruptly between colder and warmer modes in the past. Do we risk the same today from anthropogenic climate change? Frankly, climate models cannot answer that question yet. But a result in the journal Chaos by Gisela D. Charó, Mickaël D. Chekroun, Denisse Sciamarella and Michael Ghil suggests a way to resolve the matter. Analyzing a model that combines the two leading theories for climate change with algebraic topology tools, the authors show that the climate system indeed progresses through abrupt transitions, also known as tipping points. These tools are applicable to reduced climate models and they well might help assess whether the Earth’s climate system on a whole is about to tip due to global warming. The work is part of the TiPES project, a European science collaboration on tipping points in the Earth system.

How does the climate evolve?

”It is one of the truly unsolved mysteries about the climate sciences, that we are trying to get at,” explains Michael Ghil, École Normale Supérieure, Paris, France.

There have been essentially two complementary views of what makes climate evolve. One is the deterministically chaotic view of Edward Lorenz. This is the chaos theory that is widely known through the idea that a butterfly flapping its wings on one continent can be the origin of a raging storm on another continent.

The other view is that of Klaus Hasselmann, the recent Nobel Prize winner, who said the climate system is stochastic and everything fluctuates but regresses to the mean.

The combination looks strange

”We have earlier, in 2008, brought these two theories together and shown that things get a lot more interesting if you have both deterministic chaos and stochastic perturbations,” says Michael Ghil.

The result from 2008, a so-called random attractor, can be seen in a video here,

This random attractor changes with time. The shape it takes at a given instant, called a snapshot, determines where the climate system is most likely to be. It has not been clear, however, how to interpret the random attractor’s changes in time. What does its changing path mean for our understanding of the climate? Algebraic topology now helps with that.

Abrupt changes

Algebraic topology is quite abstract but its results are easy to understand. If two systems’ geometric objects are qualitatively similar, they contain the same number of holes.

The analysis in Chaos of the climate’s random attractor reveals that, over time, holes appear and disappear. This means the system shifts between different regimes. The transitions seem to be instantaneous. And because the analysis in effect reveals changes in the most fundamental properties of the physical system being analysed, the results suggest that the nature of Earth’s climate indeed is to evolve through abrupt transitions – commonly known as tipping points.

Early warning

The method might have implications for predicting an eventual tipping of the climate system. Today, such a tipping of the entire climate system is much too complicated an occurrence to establish an early warning system for. However, algebraic topology could be the answer.

”This is a fairly robust method of establishing critical conditions in very complex situations. So I think that it should be possible to use these tools in order to really foreshadow transitions in a system that is as complex as the climate system,” says Michael Ghil.

Success in carrying out this program, however, will depend on whether climate models can be reduced to manageable sizes for analysis with the algebraic topology tools used in this work.

Contributors to this work.

Gisela D. Charó, CONICET – Universidad de Buenos Aires (UBA), Argentina; and the CNRS – IRD – CONICET – UBA. Institut Franco-Argentin d’Études sur le Climat et ses Impacts, Argentina. Mickaël D. Chekroun, the Weizmann Institute of Science, Rehovot, Israel. Denisse Sciamarella, CNRS – Centre National de la Recherche Scientifique, Paris, France, and CNRS – IRD – CONICET – UBA. Institut Franco-Argentin d’Études sur le Climat et ses Impacts, CABA, Argentina. Michael Ghil, Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), École Normale Supérieure and PSL University, Paris, France, and Department of Atmospheric & Oceanic Sciences, University of California, Los Angeles, California, USA.

The TiPES project is an EU Horizon 2020 interdisciplinary climate science project on tipping points in the Earth system. 18 partner institutions work together in more than 10 countries. TiPES is coordinated and led by The Niels Bohr Institute at the University of Copenhagen, Denmark and the Potsdam Institute for Climate Impact Research, Germany. The TiPES project has received funding from the European Horizon 2020 research and innovation program, grant agreement number 820970.


Chaos An Interdisciplinary Journal of Nonlinear Science




Computational simulation/modeling


Not applicable


Noise-driven topological changes in chaotic dynamics



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Ed Hanley
October 21, 2021 10:16 pm

From the article: “Success in carrying out this program, however, will depend on whether climate models can be reduced to manageable sizes for analysis with the algebraic topology tools used in this work.”

Is a smaller model more likely or less likely to match the real-world climate?

For that matter, do we yet have ANY model that matches the real-world climate?

Wouldn’t all this mathematical talent be put to better use solving some conjectures scribbled into book margins?

Reply to  Ed Hanley
October 21, 2021 10:57 pm

Didn’t Steven McIntyre develop a simplified model that proved to be more accurate than the hotchpotch climate ensemble ?

Reply to  Streetcred
October 24, 2021 9:01 am

Didn’t Steven McIntyre develop a simplified model that proved to be more accurate

No, he didn’t.

Ron Long
Reply to  Ed Hanley
October 22, 2021 3:46 am

“…do we yet have ANY model that matches the real-world climate?” No, and therefore no math manipulation of something that is wrong cannot produce truth. The math manipulation can, however, produce more fodder for our fruit-loop friends to wave around.

Reply to  Ron Long
October 25, 2021 7:57 am

There’s one model that works, which is that on average, each w/m^2 of forcing will produce about 1.62 w/m^2 of surface emissions and that on average it takes 1.62 w/m^2 of surface emissions for 1 w/m^2 to leave TOA. This average ratio has remained virtually unchanged since we have had data that can measure it with sufficient precision. Specifying the effect of forcing as a temperature change, rather than an emissions change, is a purposeful deception to disconnect the analysis from the requirements of COE.

The IPCC claims the next w/m^2 will nominally increase the surface temperature by 0.8C corresponding to an emissions increase of 4.4 w/m^2. They claim feedback is what increases the 1.62 up to 4.4, but based on the theory they applied, this extra emitted power can only be replaced by the implicit power supply required by the feedback model that doesn’t actually exist.

The claim that the average forcing not accounted for by the incremental analysis is the power supply is absolutely wrong, since the average forcing not accounted for by the incremental analysis is already completely consumed maintaining the average temperature which is also not accounted for by the incremental analysis.

Reply to  Ed Hanley
October 22, 2021 12:12 pm

The very lowest estimates of the CMIP models appear to track fairly closely with recent warming; the ones that estimate a benign +1.4° C per century, which is the 40-year linear trend Dr. Roy Spencer has derived from his monthly UAH global temperature measurements. That’s a far cry from the crazy scary numbers screamed by hysterical climate scientists alarmists.


That doesn’t mean the CMIP models are accurate. In fact it demonstrates how wrong they are because those estimates are for the low CO2 of the RCP2.6 scenario where all the nations of earth hold hands together and jump off the cliff into economic collapse by rapidly ending fossil fuel use (like, right now) while singing kumbaya. But CO2 levels are tracking nicely with the apocalyptic RCP8.5 scenario while temperatures and sea levels remain in the benign RCP2.6 range.

We are currently at about 413 ppm CO2 (0.0413%), which is about 47% higher than the estimated 280 ppm at the end of the Little Ice Age. At current rates, we may double to 560 ppm (0.056%) sometime in the next 50 years. So what?

According to estimates, CO2 was ~1000 ppm (0.1%) during the Paleocene-Eocene Thermal Maximum (PETM) 55.5 million years ago and even at 1000 ppm there was no “runaway greenhouse”. Clearly there is no imminent “tipping point” now. In the immortal words of Rock n’ Roll Detective Ford Fairlane, “this case is getting cuh-losed!” Or in sciencese, QED.

Also, one of the intriguing events of the PETM is the dramatic increase and spread of mammals. So the higher CO2 appeared to be especially good for mammals, which is also true today, a fact anyone can appreciate if they pull their heads out of their doomsaying CO2 abyss and look around.

Last edited 1 month ago by stinkerp
The Saint
Reply to  stinkerp
October 22, 2021 6:21 pm

I think the only climate tipping in our future will be from the inter-glacial to the glacial. Rising CO2 might bring that about in this orbital long cycle.

Reply to  stinkerp
October 23, 2021 2:59 pm

And as I recall, CO2 levels determined from proxies seem to indicate as much as 20,000/million sometime billions of years ago. Another researcher has concluded that with today’s atmospheric make-up a pterodactyl can’t fly, it would need at least 8,000 ppm CO2 to get aloft. So anyplace we are, whether it’s the static condition of right now, or the rate of change of the last anytime, this old Earth has been there before and survived just fine. If there was a “tipping point” in our climate, it would have tipped loooooooooong ago, and none of us would exist now to even argue about it. We do, so it doesn’t.

October 21, 2021 10:23 pm

It would be simpler to use the Ouija Board with all the committee assembled around it. It would be just as accurate too.

Reply to  nicholas tesdorf
October 21, 2021 10:53 pm

In a pinch, the Magic 8 Ball of climate projection forecasts would work well in a COVID world of social distancing.

my fav: “Signs point to yes.”

Reply to  Joel O'Bryan
October 23, 2021 3:00 pm

Doesn’t that Magic 8 Ball have about 11 ways to say, “I don’t know”?

oeman 50
Reply to  nicholas tesdorf
October 22, 2021 6:04 am

I like the Magic 8 Ball’s “The future is cloudy.”

October 21, 2021 10:45 pm

“applied to reduced climate models”

Didn’t these folks ever get a proper CompSci class lesson in GIGO?

Clyde Spencer
Reply to  Joel O'Bryan
October 22, 2021 7:39 am

Furthermore, mathematicians notoriously ignore measurement uncertainties in conjectures of this type!

Reply to  Joel O'Bryan
October 22, 2021 2:23 pm

It’s a real struggle for wordsmiths when they have to make ordinary words like ‘simplified’ sound strong and controlled. To somehow convey smaller yet remain whole.

When the reality is actually a sparse echo of a climate model. That is, restricted inputs, limited run program.

Reply to  ATheoK
October 23, 2021 3:02 pm

Wasn’t it Monkton that produced a “model of a model”, that pretty closely replicated the results obtained from the model? And the model-of-a-model was little more than a y = mx + b equation?

Tim Gorman
Reply to  Red94ViperRT10
October 24, 2021 9:36 am

I believe you are talking about Dr. Pat Frank.

Alexy Scherbakoff
October 21, 2021 11:00 pm

I think they should have written a paper titled:
The tipping points of the psychosexual behaviour of girl children.
Now we have Maths majors sucking on the teat of Climate Change.
Where and when will this nonsense end?

Reply to  Alexy Scherbakoff
October 22, 2021 4:01 am

Little people… persons, and girl as in boy.

Clyde Spencer
Reply to  Alexy Scherbakoff
October 22, 2021 7:41 am

… psychosexual behaviour of girl children.

That should be “People who can become pregnant, when they get older.”

Reply to  Alexy Scherbakoff
October 23, 2021 3:04 pm

It would be equally worthless. Because every man knows you can never figure out a woman, not even when they’re still little girls!

October 21, 2021 11:08 pm

The “climate system” of Earth is actually pretty stable. The atmosphere effect is only about 8K, and largely ruled by the mass of the atmosphere. Though there is certainly some room for alteration, it is important so see that Earth is mostly as warm as solar irradiance allows it to be. If people talk about the “complex” climate system, it just means they have not understood it. Rather it is relatively simple.

Richard S Courtney
Reply to  E. Schaffer
October 22, 2021 12:00 am

E Schaffer,
You assert,
“If people talk about the “complex” climate system, it just means they have not understood it. Rather it is relatively simple.”
No, that could not be more wrong.
The climate system is extremely complex. Indeed, the climate system is more complex than the human brain (the climate system has more interacting components – e.g. biological organisms – than the human brain has interacting components – e.g. neurones), and nobody claims to be able to construct a reliable predictive model of the human brain. It is pure hubris to assume that the climate models are sufficient emulations for them to be used as reliable predictors of future climate when they have no demonstrated forecasting skill.

Reply to  Richard S Courtney
October 22, 2021 1:19 am

Absolutely right, Richard.
(And nice to see your name again.)

But if “algebraic topology” needs to be added into the witches’ brew of X-box prognostications of Glowbull Warming “Science”, in order to burnish its threadbare shroud waving conclusions, I do wonder if Boris actually needs to drive the economy off the cliff, pedal to the metal.

Perhaps we’d all be better if he concentrated his talents on sorting out those naughty fairies at the bottom of his garden.

Richard S Courtney
October 22, 2021 3:10 am

Martin Brumby,

Thank you for your kind words.

My pain relief inhibits thought so I need to stop it when making contributions and, therefore, I contribute to here and elsewhere in infrequent bursts.

I have recently decided not to cope with side effects of the hormone treatment that has been slowing progress of the cancer that has spread to my bones (having destroyed my prostate it is now active in my skull, my neck, four other places in my spine, my left shoulder blade, my rib cage and my left hip).

So, having stopped the hormone treatment I intend to make more frequent contributions where I can and while I can (experts say the cancer will finish me but I think it will be the emphysema which combines with the disease of my ribs to make breathing difficult although, of course, we may all be proved wrong by my heart condition).


Reply to  Richard S Courtney
October 22, 2021 5:41 am

Sigh, there’s nothing to say except “Yikes!” and offer very sincere thanks for your comments over the years.

Reply to  Richard S Courtney
October 22, 2021 7:58 am

Good grief Richard! What (a) horrible condition(s) to have. Please post as much and as often as you can contribute.


Reply to  Richard S Courtney
October 22, 2021 9:24 am

Oh my gosh!

That is distressing news to read, thank you for educating us of your current conditions which I can’t express in words of understanding but to say thank you for your bravery and willingness to contribute here with your valued comments of which I have missed greatly.

My regards to you,


Tom Abbott
Reply to  Sunsettommy
October 22, 2021 4:07 pm

“your valued comments”

Yes, they are valued because they are always well considered.

God Bless you, Richard.

Reply to  Richard S Courtney
October 22, 2021 3:18 pm

Bless you Richard.

You assisted me a great deal with honest and genuinely expert advice on several occasions when you were one of the main boffins at CRE and I was a Group Civil Engineer.

My most sincere thanks for your assitance and my v8ery best wishes.


Reply to  Richard S Courtney
October 23, 2021 3:08 pm

Never mind. That might have been in poor taste.

Last edited 1 month ago by Red94ViperRT10
Reply to  Richard S Courtney
October 22, 2021 4:11 am

The chaos stems from incomplete or insufficient characterization, and unwieldy problem sets. The models have demonstrated neither forecast nor hindcast skill outside of a limited frame of reference.

Reply to  Richard S Courtney
October 22, 2021 8:33 am

Weather is complex, climate is not. I can not give you the numbers of the next lottery, but predicting how often numbers get drawn in the long run, how many wins there will be and so on, that is possible. There are invisible strings such systems obhere to, and if you know them, despite the random walks, things become predictable.

The problem with climate models is, they get all the basics wrong from the get go. I mean if you don’t know what the GHE is, what size it has and what contributes to it, “climate modelling” will turn extremely hard. However, if you have this knowledge it becomes simple.

Here is a little hint..

comment image

Reply to  E. Schaffer
October 22, 2021 8:49 pm

“There are invisible strings such systems obhere [sic] to, and if you know them….”

But how does one know that one knows all that’s necessary to know?

I would submit that it’s easier to learn English than to model the Earth’s climate, and some have not mastered the easier task.

Reply to  damp
October 22, 2021 9:11 pm

Interesting! I was pretty certain “to obhear”, which I mistyped anyhow, was an english word, in the sense of “to obey”. Seems like it does not exist at all. Such things happens if you are multilingual. Then I am still confusing Italian and Spanish terms..

Then I think it is not about knowing it all, but about knowing enough. Sure, that will be relative to the question asked. But in terms of “climate science” I do know enough, and that is a different dimension relative to “consensus” and “critical”..

The odd thing is, we should be discussing my revolutionary insights, rather than this bullshit. But hey, that would require you to read and comprehend, and we both know that’s more than you can do 😉

Reply to  E. Schaffer
October 23, 2021 3:17 pm

I think the word you meant to use was “adhere”, but the best definition given that context is marked Obsolete. And I had to look it up to see if the word you used was a real word, so no one can have a 100% grasp of any language.

But to your larger point, I agree the climate follows certain rules. It has not only response to inputs and feedbacks, it has safeties and limits and all kinds of stuff. I don’t think it will be possible to ever grasp all of them well enough to predict even a year out, let alone 50 or 100 years.

Sceptical Sam
Reply to  Red94ViperRT10
October 25, 2021 7:59 am

Now, just remind me, which amazingly obtuse Intergovernmental Panel was it that concluded climate was a non-linear chaotic system and as such could not be reliably modelled?

But on and on, ad infinitum, they go, like some unthinking perpetual motion machine.

Reply to  Richard S Courtney
October 22, 2021 10:01 am

In addition to the total number of interacting elements, neurons are more or less similar to each other.
Each of the interacting elements in the climate is unique. The response characteristics of a moose, will be radically different from the response characteristics of a red wood.

Mike Edwards
Reply to  E. Schaffer
October 22, 2021 5:37 am

Mr Schaffer,

You claim “The “climate system” of Earth is actually pretty stable.”

Have you seen graphs for Earth’s temperature over the past couple of million years? The regular flipping between glacial conditions and interglacial conditions, currently every 100K years or so, previously every 40K years or so?

That does not meet my definition of “stable”. Anything but.

I also consider the climate system as an especially complex system made up of several co-interacting subsystems. If you consider such a system as “simple”, you have a very strange definition of “simple”. If the climate system really were simple, it would be straightforward to model it. We know very well that modelling the Earth’s climate system is a major challenge.

Tim Gorman
Reply to  Mike Edwards
October 22, 2021 7:44 am

The fact that the climate has oscillated between two two points (i.e. cold and warm) indicates a certain stability. If it was *not* a stable oscillation then the climate would have long ago gotten stuck at one extreme or another, either a frozen ball or a molten ball. Of course both of those extremes would be “stable” as well I suppose.

Clyde Spencer
Reply to  Mike Edwards
October 22, 2021 7:45 am

So, it you have a 12V DC system with some noise you would call that “unstable?”

Reply to  Mike Edwards
October 22, 2021 7:53 am

I am not just saying THAT it is simple, but also WHY it is simple. Though since it takes me more than just a few lines to explain, I can only invite you to read the link.

Rud Istvan
Reply to  E. Schaffer
October 22, 2021 1:56 pm

I did. Been at this game since 2011. And, like I disagree with Monckton in certain respects, I also disagree with you in certain respects. Start over at Judith’s by reading my longish comments on his ‘irreducibly simple equation’ paper when it first came out. Then, if you want me to critique your Site’s stuff with math and references, I will provide it. Caveat Emptor is provided by the Monckton reference.

Reply to  Rud Istvan
October 22, 2021 2:20 pm

“Then, if you want me to critique your Site’s stuff with math and references, I will provide it”

You are invited to do your worst, or best respectively.

Reply to  Mike Edwards
October 23, 2021 3:27 pm

It is exceptionally stable! I once perused the ASHRAE tables and found the place in the United States with the greatest difference between winter design day and summer design day was a place in Montana with a difference of 134º F, ranging from a summer design of 97º F all the way down to a winter design temperature of -37º F. Change that to ºR, it becomes a variation of <25%. Year round. On a daily basis, the largest daily average swing from nighttime to daytime (used for design purposes) is <30º F, which is what I experienced in Phoenix. Summer highs could average 117º F for weeks at a time, so I’ll use that to start, in ºR that’s <5% variation. Now, have you ever designed controls systems? How good, and expensive, does your design have to be to maintain ±2.5% for an extended period? Yeah. That’s how stable it is.

Reply to  E. Schaffer
October 22, 2021 10:34 am

I think E. Schaffer has it about right. Climate (long-term weather) is pretty simple in the sense that there has never NEVER been a “tipping point” in known/inferred Earth history. Big changes in ocean temperature? – YES. Big changes in ice cover? – YES. Big changes in forest cover and extent of deserts? – YES. Have some of these changes been “fast” in geologic terms? – YES, but many more have been quite gradual

But no tipping points.

What is clearly chaotic and complex and impossible to forecast is WEATHER.

To say that “climate is really pretty simple” is not the same as saying we understand it very well. We don’t. But it is nevertheless quite stable over geologic time periods – so “simple”

Reply to  GeologyJim
October 22, 2021 10:46 am

Sorry, but I do understand it and I am sharing my knowledge. If you can tell the difference between climate fiction and climate facts, which you find nowhere but on my site, it is simple after all.

Reply to  E. Schaffer
October 22, 2021 7:52 pm

E Schaffer – I was agreeing with you that Earth climate is stable/simple in that it has vacillated between hothouse and icehouse conditions – but has never “tipped” and runaway

Nonetheless we don’t really understand why hothouse conditions persist for as long as they do(same for icehouse) nor why there seem to be periodic patterns as well as non-periodic. Not even short-term phenomena like Younger Dryas cooling/heating are well characterized let alone comprehended.

What causes long steady cooling to switch to rapid heating? And why does this quite rapid heating switch rather suddenly to another long slow cooling phase? Don’t really know

In any event, the claim of alarmists that human activity drives long-term climate change, I’m sure we agree, is preposterous

Best regards

Reply to  GeologyJim
October 23, 2021 6:19 am

In one phrase: They forgot to account for overlaps and accurate surface emissivity. They suggest surface emissivity would not matter, so they set it to 1 for simplicity, and use clear sky base scenarios, which of course rules out any overlaps between GHGs and clouds at the get go. Eventually they even manage to deny intra-GHG overlaps, like CO2/vapor.

These omissions are responsible for about 50% of CO2 forcing, and about 70% of vapor (primary) feedback. Also they stick to an erroneous Lambda of 0.3, which should be 0.27.

With 1.1K for 2xCO2 and 1.8W/m2 vapor feedback, with a Lambda of 0.3 you get..

1.1 / (1-1.8 x0.3) = 2.4K ECS, excluding other feedbacks.

With 0.53K for 2xCO2 and 0.5W/m2 vapor feedback, with a Lambda of 0.27 you get..

0.53 / (1-0.5×0.27) = 0.61K ECS, excluding other feedbacks.

On top of that lapse rate feedback (which is not really a “feedback”) is strongly negative, mitigating surface temperature by about 30%, thereby making vapor feedback negative all over.

That is why GHGs have no potential of destabilizing the climate of Earth. Whatever causes ice ages and so on, must be something else.

Gary Pearse
Reply to  E. Schaffer
October 24, 2021 12:30 pm

E. Schaffer, all in the climate science field, including you, seem unaware of the Le Châtelier principle. LCP is well known to chemists and chemical engineers, less so to physicists – it is employed to optimize product producion. LCP as applied in chemistry states that in a system of several interacting components, if you change one of components (chemical concentrations, pressure, temperature), the entire system inter-reacts to resist the change. The result is a new equilibrium with a more moderate change than one expected.

Climate is a perfect fit. The delta ‘T’ you get by summing the “simple” elements of climate change of the added nuts and bolts of the changing mixture of greenhouse gases and their emissions, will yield a result that is less(!) than your simple calculations because of LCP. Unnoticed will be the subtle changes to all other components of the system, pressure, atmospheric composition, enthalpy, albedo, biological agents, etc. etc., that act to resist the change in ‘T’!

Consensus climate science calculated temperature change which 20yrs later proved to be 300% too high when measured against two independent T observation sets. Ignoring their biases and natural variation contributions for the sake of demonstration, one could say they should have multiplied their result by an LCP coefficient of 0.33. With much experimentation, perhaps we will one day be able to estimate a reasonable coefficient.

Reply to  GeologyJim
October 23, 2021 3:35 pm

Let me be the devil’s advocate at this point, and say the climate does seem to exhibit step changes. They, at least during the time I have been alive, typically are less than 1.5º C, so they’re not Earth shattering, on a day to day basis neither you nor I would notice them, not even if we have a thermometer in our own back yard, but in hindsight analyzing the data, we do find them. My question is, what causes them? Can you predict the next one? Will it go up or down? See, these things could be researched, but I don’t know that anyone is. Even if we know what causes them well enough to predict the next one, can we control it? (My opinion is an unequivocal “NO”!). And even if we could, do we want or need to? (Again, my opinion is “NO!”) And I don’t think step changes, and the inability to predict or model them, fit the definition of “real simple”. So chew on that for awhile.

October 21, 2021 11:12 pm

The ocean surface temperature determines global air temperature and temperature of entire ocean determines global climate.
We have been in icehouse global climate for 34 million years and we going to stay in this
icehouse global climate. We are in this icehouse climate because we have a cold ocean.
The average temperature of the entire ocean is currently about 3.5 C.
During peak interglacial temperature the ocean can warm to more than 4 C.
If our entire ocean increases to 4 C, it with have significant “climate change”.
Such significant climate change is greening of Sahara Desert and tree line moving poleward resulting the “largest forest in world” becoming larger. And arctic summer ice free polar sea ice.
For about the last 5000 years, global air temperature been treading downward, though for centuries of time, global air temperature increased and decreased, but entire ocean has remained around 3.5 C.
Before this we had the warmest period of our Holocene, which is called Holocene Climate Optimum: Holocene climatic optimum – Wikipedia
And during time sahara desert was grassland, and rivers and forests, the treeline was higher and had summer arctic ice free polar sea ice. And our largest forest, was larger.

There is no evidence we going to return to such a warm period- any time soon.
But would nice if we did.

Bjarne Bisballe
Reply to  gbaikie
October 22, 2021 2:01 am

0.5 C requires 2750 zettajoule more energy in the oceans. They get approx 9 zettajoule extra each year.

Mike Dubrasich
October 22, 2021 12:06 am

The Climate is really a suite of climates. None of them are chaotic or stochastic but instead are relatively stable. There are no “tipping points”. Tipping point theory is bogus. The TiPES Project is klepto-quackology. The participants are fools, knaves, thieves, or worse.

I’ve had enough of the warmunist alarmobots screeding fear porn about the climate. We have some real problems that need addressing. One of them is The Great Climate Hoax™ which is a weapon of mass destruction aimed at humanity. History will not be kind to these jackalopes.

Reply to  Mike Dubrasich
October 22, 2021 2:20 am

I agree with most of what you wrote, except “None of them are chaotic…“. Have you any evidence for that?

Tim Gorman
Reply to  Disputin
October 22, 2021 7:47 am

summer follows spring, fall follows summer. Winter follows fall. spring follows winter. That’s not very chaotic at all. It’s been that way for a looooong time.

Reply to  Tim Gorman
October 22, 2021 10:33 am

These monster forcing changes in no way rule out a chaotic climate. Weather is chaotic and climate is average weather so it exhibits what in chaos theory are called strange statistics. This means the averages oscillate over time, which we do observe. Take any two periods of say 30 years and find the average for each of temperature, precip, etc. and the averages will differ.

Reply to  David Wojick
October 23, 2021 3:41 pm

Maybe it is non-chaotic, but we don’t know all the inputs (*sigh*, forcings, if you must) to fully measure it?

Mike Dubrasich
Reply to  Disputin
October 22, 2021 11:52 am

The love affair with “chaos theory” is blinding and indicates that the aficionado doesn’t understand it at all.

IN NO WAY do butterflies flapping wings in China cause tornadoes in Kansas. IN NO WAY does weather bifurcate into runaway global storms. IN NO WAY do the initial condition of last Thursday fractal into continental mega droughts next month. IN NO WAY is The Climate about to chaotically tip over into a ocean-boiling Hotpocalypse.

Math is fun. I like math. But Lorenzian deterministic randomness IS NOT the way the real world works.

You want me to prove it? Sorry Charlie, it’s your dumb theory so it’s on you to prove that Chaos Theory makes the sun rise, little green apples, and puppies. And tornadoes in Kansas. Sheesh. Catch a clue. The End Of The World is not pending.

Reply to  Disputin
October 23, 2021 3:40 pm

Weeeeeell, in the simplest definition of “chaotic”, an input (forcing, if you must) will not always result in the same variation of the atmosphere. I don’t know if we can accept without question that our atmosphere always behaves in a consistent manner. So, Mr. Tim Gorman, I call your bluff, and ask again, can you prove that?

Tim Gorman
Reply to  Red94ViperRT10
October 24, 2021 9:53 am

Call my bluff? Have you ever seen spring transition into fall without passing through summer? Or winter transition into summer without passing through srping?

A transition from spring into fall with no summer would mean many of the growing things we take for granted would have never evolved – tomatoes, wheat, prairie grasses, etc.

I can prove that the earth’s tilt is a gradual transition and not an instantaneous one – and that is what drives the seasonal transitions. It is the angle and distance of the sun with the earths surface that drives the entire environment, including the atmosphere. It is the sun and the orbit of the earth that is the ultimate input (forcing if you must).

Joseph Zorzin
Reply to  Mike Dubrasich
October 22, 2021 4:40 am

“I’ve had enough of the warmunist alarmobots screeding fear porn about the climate.”

Here in Massachusetts, this alarmist insanity is as bad as CA and Britain. It’s all day every day in every newspaper, radio, TV. Almost every news item on every subject- they bring back to climate lunacy. I’ve worked outside for 50 years and see no reason for such panic. This past year my garden, lawn and especially my fruit trees had their best year ever. My fruit trees’ branches are bent to the ground overloaded with fruit. I should invite some of the local alarmists here to see them. They’ll probably say, “your fruit trees are not behaving normally with such abundance of fruit- there’s something wrong with them- clearly it’s due to drastic climate change”.

Mike Dubrasich
Reply to  Joseph Zorzin
October 22, 2021 12:08 pm

Ditto, Joe. Best garden year ever. And we live in Heat Wave Central in W. Oregon. All that warmth yielded bumper crops of everything. The pumpkins are so big I can’t lift them into the cart. Nobody wants them anyway. I planted two mounds, three seeds each, of butternut squash and harvested 75. Yikes. They keep, but we’ll be eating them for the next six months — that’s 3 per week. The freezers are full to bursting. I pressed 200 gallons of apple juice, and dried another 4 bushels. Et cetera plus 42.

Tipping Point Theory predicts stochastic chaotic disaster. Oh no, run for your life. Or huddle in the cold and dark while the Planet burns! Balderdash poppycock baloney. The absolute total disconnect between Warmunist Garbage Models and the Real World is a chasm of galactic proportions.

October 22, 2021 12:29 am

Nah’ – researchers can’t use algebra since that’s math. And the bright light of evolved American wisdom, as long ago as 2020, revealed that math exemplifies white privilege.

Robert of Texas
Reply to  gringojay
October 22, 2021 12:54 am

Math is racist. I don’t know why, or how, but that is what the wokes are screaming.

Reply to  Robert of Texas
October 22, 2021 8:24 am

Anything that black people find difficult is racist. What is clear is that white people have just as much difficulty with Sums’n’Stuff™…

To paraphrase, I think, Macmillan:

“We all identify as black. now”

Reply to  Leo Smith
October 23, 2021 3:51 pm

…just like I identify as vaccinated!

Gary Pearse
Reply to  gringojay
October 24, 2021 12:50 pm

The new math will be easier and more flexible for everyone.

H. D. Hoese
October 22, 2021 12:49 am

“Algebraic topology is quite abstract but its results are easy to understand….This is a fairly robust method of establishing critical conditions in very complex situations.”

There is still some old school statistics going on. Part of abstract. Strimbu, B. 2012. (Louisiana Tech University) Challenges in environmental modeling. Louisiana Scientist. (Abstract) 2(1):7 “Algebra and regression analysis are two major tools used in environmental sciences to build models. This paper identifies and discusses some of the major mathematical pitfalls that could lead to wrong models. Some common mistakes in the environmental models based on regression are: (1) back-transformation of the dependent variable (performed to obtain a better fit, a significant relationship or to increase the prediction‘s confidence interval) – generally, this is not possible because it leads to a logic violation: part is larger than the whole (e.g., terrain stability models, biomass-nutrients models); (2) the set of independent variables contains variable(s) equivalent with the dependent variable (tautology); (3) the relationship between the dependent variable and the set of independent variables is not significant even if R2 is close to 1 (e.g., exploratory studies). Abstract algebra creates problems mainly involving ordered sets (e.g., habitat suitability index models and plotting positions in hydrology).”

Could they be tipping the glass too much, leads to chaos.

Jay Willis
Reply to  H. D. Hoese
October 22, 2021 1:19 am

Thanks, that looks like a very interesting paper, I shall read it.

Tim Gorman
Reply to  H. D. Hoese
October 22, 2021 7:55 am

It looks to me like all of this climate analysis totally ignores the fact that it is all time dependent. Regression analysis of time functions is fraught with problems and leads to false conclusions.

You would think some of the climate scientists would figure out how to remove the time dependency to turn a non-stationary data set into a stationary data set more conducive to regression analysis but that never seems to be the case.

Even just a simple integration of the temperature profile on a daily basis leads to a stationary data set [i.e. the integral of (temp/time) * (time)] but that never seems to get done by the climate scientists. We’ve had the ability to get minute or five minute temp data from modern temp measuring stations since the 80’s. This should be enough to get some kind of an integral of the temperature profile, admittedly with some measure of uncertainty but at least a stationary data set more amenable to regression analysis.

Robert of Texas
October 22, 2021 12:53 am

The models might have tipping points because that is how they were programmed – the more complex the equations used the less predictable behavior will become. This has NOTHING to do with how real climate works, other than it too might also have tipping points completely unrelated to the models.

People need to stop treating models as reality and start looking outside the window at real weather, or talking to geologists and paleobotanists about the past. They need to STOP all this other nonsense.

Jay Willis
October 22, 2021 1:21 am

Great stuff. The department for tipping points went out to look for tipping points as part of a larger tipping point project…..and they found some.

Derek Wood
October 22, 2021 1:26 am

“Might”. I came straight from there to here.

Geoff Sherrington
October 22, 2021 2:34 am

Surely our present climate is composed of an infinite series of chaotic systems from atomic to interstellar size, all whirring away in unpredictable ways but mostly with with so little individual effect that we are always near to a regressed mean. A disaster change might happen, in concept, if a number of these by chance operated in some form of synchrony to create a discernable tipping point; but because we have not observed this in the past, we need not expect it in the future. Geoff S

Reply to  Geoff Sherrington
October 22, 2021 8:32 am

I think in toplogical terms, the state map of a chaotic climate is a series of hollows representing various ‘attractors’ at various different approximate ‘mean temperatures’ and from time purel;y by chance or assisted by extrenalities the climate can cease to wander around one attrractor randomly and start to wander around another.

That isn’t a tipping point in my book, but might be considered such. The problem is we have no tools to analyse chaotic systems with. At best we can identify regions of such strong negative feedback – attractors – that it is unlikely climate could exist much outside their spheres of influence, so to speak…

And unless you find out what the underlying patterns are, a chaotic system looks pretty stochastic.

Reply to  Leo Smith
October 23, 2021 3:55 pm

That would be what I called just a step-change (see my comment above). We can’t explain them, either.

Joao Martins
October 22, 2021 2:43 am

We are spending too much money on all those clowns who do nothing but to spend all their “working” hours playing with “models”.

All that production is useless but to feed the msm so that they continue their terrorizing campaign againts the peoples of the wold.

Last edited 1 month ago by Joao Martins
Geoff Sherrington
October 22, 2021 2:47 am

To philosophize, climate research has long been fixated on temperature, partly because temperature seemed important and partly because academia had some measurements with which to commence. Models that have core concepts based on temperature might be fundamentally invalid if, for example, the key ingredient of climate change has nothing to do with temperature as an input. Maybe some minute marine organism decides now and then that a breeding frenzy would be fun, so it produces more of some substance than the earth can digest. Sounds like a tipping point? When the parent organisms tell their kids to stop the frenzy, give it a rest, the tipping point reverts to the old mean.
Philosophically, there is no difference between using this organism or using temperature as the key input, because at this stage of human comprehension we simply do not know if either is right or wrong.
Nothing in science says that temperature is THE key determinant.
Back to the drawing boards. Geoff S

Jim Gorman
Reply to  Geoff Sherrington
October 22, 2021 5:41 am

Temperature is a dependent variable. It is fundamentally driven by one thing only, the sun’s radiation. The key is to find what independent variables result in temperature variations. Models are nothing more than throwing darts at a map trying to find the right combination. It reminds me of what alchemists did when trying to find what might be done to synthesize gold. Just look at the plethora of models, each with different outputs. Just like alchemy, throwing together all the combinations of what they tried would not have resulted in the correct process. Heck, temperature might not even be the correct dependent variable to be using. It may be a side effect. Maybe average wind speed is the correct dependent variable. Has anyone ever considered that temperature is NOT the correct variable to be shooting for?

Clyde Spencer
Reply to  Jim Gorman
October 22, 2021 8:35 am


But, temperatures are important because they control freezing of water, heat death in organisms, cooling of sweating humans, rates of chemical reactions, they are a significant factor in phase transformations in general. Plus, they are easily measured directly.

They are clearly dependent variables of the rate of absorption and emission of energy, the specific heat of the material, and to a lesser extent the thermal conductivity of the material. We know a lot less about specific heats and net energy exchanges at specific points on the surface and in the air than we do about the more easily measured temperatures.

The question, as I see it, is whether temperature can be a reliable proxy for the poorly known things that cause temperature changes. I suspect not because changes in pairs of independent variables, resulting in net temperature changes, tells us little about how the individual independent variables are actually changing — especially when we deal with average temperature changes!

Tim Gorman
Reply to  Clyde Spencer
October 22, 2021 2:38 pm

Think enthalpy. Enthalpy depends on temperature, pressure, and absolute humidity. Humans survive in the heights of the Andes to the inner-Sahara. It is the heat content, i.e. enthalpy, of each that would give a far better proxy for climate than does temperature alone.

Reply to  Tim Gorman
October 23, 2021 4:04 pm

So you already got to what I just stated above. But I’m going to leave mine, just the same.

Reply to  Geoff Sherrington
October 23, 2021 4:02 pm

I always knew temperature alone did not describe the climate. 90º F in Houston is not the same as 90º F in Phoenix. Because it leaves out moisture, and it ignores what comes before and after it. In Phoenix, 90º F is pre-dawn July temperatures. In Houston, that’s approaching noon in August. But guess which one you can put up with longer? That’s moisture. I would more believe a model based on total heat of the atmosphere, but they lack that data for any extensive period of time, and then they might have to know some math and even have to use empirical data (a psychrometric chart is produced from empirical data, and dates back to the 1930’s). But, while I think total heat of the atmosphere tells us more about the overall climate, it still is far from a complete picture of climate. Especially if you “average” it and eliminate all variability.

Let’s use some old fashioned common sense, you know, the kind that says, if you don’t like the weather just wait awhile, it will change. We will never be able to predict a future climate, all we can do is wait and see.

Tim Gorman
Reply to  Red94ViperRT10
October 23, 2021 5:14 pm


October 22, 2021 2:49 am

In the Church of Warming the climate models are the equivalent of the Oracle of Delphi.

Richard S Courtney
Reply to  Billyjack
October 22, 2021 3:18 am


I am sure the Oracle of Delphi was much better than that.


Reply to  Richard S Courtney
October 22, 2021 10:40 am

Indeed, the models cannot explain past abrupt events, which look to have included several degrees of warming in a few decades or less, because in the models only human activity can cause climate change. See Figure 2 of the AR6 SPM which supposedly lists all the known drivers of climate change. All are human! No science here, right?

October 22, 2021 3:22 am

Prediction is hard … especially about the future.

Reply to  Speed
October 22, 2021 3:48 am

And the past. In fact, outside of a limited frame of reference from the observer.

Reply to  Speed
October 22, 2021 3:52 am

“It’s hard to make predictions- especially about the future”- attributed to Yogi Berra.
But he also said, “I never said most of the things I said”, and “if you don’t know where you’re going, you will end up someplace else”.

October 22, 2021 4:01 am

“The method might have implications for predicting an eventual tipping of the climate system. ”

Or not. Scary Speculation of the vaguest possible sort.
Or this:

Clyde Spencer
Reply to  David Wojick
October 22, 2021 8:37 am

It seems that a common characteristic of alarmists is equating possibilities with probabilities.

Reply to  Clyde Spencer
October 22, 2021 11:21 am

Yes, high probabilities. Speculation reported as established fact.

October 22, 2021 4:09 am

Climate tipping might be predicted using algebraic topology

Well I suppose that is an improvement on dead chicken entrails.

very old white guy
October 22, 2021 4:33 am

All the math on the planet will not alter the climate. If every living being on the planet ceased to exist today the climate will remain as it always has.

Last edited 1 month ago by very old white guy
October 22, 2021 5:14 am

Frankly, climate models cannot answer that question yet.” And they never will, climate models are purely a tool to push leftist political agenda. Until anti-human leftist sh*t is removed from science it is all corrupted.

October 22, 2021 5:38 am

So they’re making even more complex models with zero understanding of the underlying population of things they’re modeling.

More cowbell!

The climate system is extremely complex and is not likely to be modeled correctly any time soon, if ever.

Also, if there is a tipping, geological history proves that is is the shift to a cold cycle is far shorter and more dramatic, occurring over hundreds of years … while shifts to warming cycles are far more long and drawn out, over tens of thousands of years .. such as the warming cyle we are in right now since the end of the last glaciation. If they’re worried about “tipping” they need to be worrying about not global warming caused by humans but global cooling caused by natural phenomena.

Clyde Spencer
Reply to  Duane
October 22, 2021 8:46 am

… geological history proves that is is the shift to a cold cycle is far shorter and more dramatic, occurring over hundreds of years … while shifts to warming cycles are far more long and drawn out, over tens of thousands of years, …

I think that you have that backwards, even if it is asymmetrical. However, looking at the constructive interference of the Milankovitch Cycles, I think a case can be made that either cooling or warming can be abrupt, depending on the phase and amplitude of the particular MC components.

I’m not going to take the time to chase it down, but there has been at least one study that suggested that the last glaciation may have ended in a matter of decades, as suggested by “First meltwater pulse” in sea level reconstructions.

Reply to  Clyde Spencer
October 22, 2021 2:05 pm

You have it backwards. We have been warming for the last 16 thousand years, with some minor fluctuations from time to time.

Clyde Spencer
Reply to  Duane
October 23, 2021 9:01 pm

Do you see any evidence for your claim in the following graph?

Mike Edwards
October 22, 2021 5:49 am

I couldn’t see a link to the paper underlying this story. It is freely available here:

“Noise-driven topological changes in chaotic dynamics”

The video linked in the article here is very pretty, but it isn’t clear what it is meant to represent and I don’t see an explanation for it in the paper itself.

Reply to  Mike Edwards
October 22, 2021 11:25 am

Thanks Mike. I used to lecture on the role of chaos theory in science. Very interested to see what a hole in the strange attractor looks like.

October 22, 2021 5:54 am

How about a cycle turning point……down in this case.

October 22, 2021 6:22 am

Remember, there are 10s of thousands of professors, grad students and post-docs looking desperately for dissertation topics in order to get funding, graduate, or get a permanent academic position. The whole enterprise is a big-kids version of K-12 science fairs. Every year, millions of kiddos have to come up with science fair topics out of a proportionately small list of options in order to get a good grade that counts heavily toward their final average.

Next year, it is “wash, rinse and repeat” with the next crop of kiddos, grad students and post-docs. Using algebra to study tipping points is just another “science fair” topic. It may not prove anything (any more than a 3rd grader growing crystals on a string in a jar), but it might get someone a good “grade.”

Clyde Spencer
October 22, 2021 7:36 am

– commonly known as tipping points.

The most overused word-pairing of the 21st century!

Andy Pattullo
October 22, 2021 7:42 am

I fully accept the tipping point model both in theory and practice. In theory a two energy state model with an energy barrier between the two states is understandable. Anyone who wears contact lenses knows there is a right way and wrong way for them to be and there is a small energy push needed to turn contacts the from the wrong way to the right way so as to feel comfortable on the eye. In practice we know the earth system has oscillated between cold glacial conditions and warmer interglacial for several hundred thousand years and the transitions appear to be those tipping points which we don’t fully understand.

We also know with certainty that my Jeep did not cause those tipping points. Applying theory of tipping points to demonstrably useless climate models is clearly a work that belongs to chaos theory. I don’t intend that as complement.

Andy Pattullo
Reply to  Andy Pattullo
October 22, 2021 7:47 am

Also I don’t need Herculean math skills to know that the forces involve in a butterfly flapping it’s wings can never, in the known universe, be causative of a hurricane. The idiot who tracks the series of events beginning with butterfly flying and ends with a hurricane, and then concludes the former caused the latter has a problem with thinking.

Reply to  Andy Pattullo
October 22, 2021 11:29 am

The butterfly effect is a misnomer. Chaos is a math property exhibited by certain nonlinear equations. Infinitesimal differences in initial conditions quickly lead to divergent behavior. No butterflies are involved. The proper language is extreme sensitivity to initial conditions.

Rud Istvan
Reply to  David Wojick
October 22, 2021 2:03 pm

True, but is only one manifestation. Others include bifurcations (see my peer reviewed paper on same in a manufacturing setting in Journal of Strategy, if I recall correctly 1991) and strange attractors in N-1 Lorenz space. An example of bifurcation between strange attractors is ice ages alternating with warm periods. What we don’t know is why the ice period shifted from about 40ky to about 100ky about 1000ky ago.

Andy Pattullo
Reply to  David Wojick
October 22, 2021 3:36 pm

I agree but as it is commonly used the implication that a very tiny force or action can lead to a massively energetic action is often made simply with the observation of one following the other.

October 22, 2021 8:04 am

Ah… the solution! When all the existing models don’t work, cobble up another BS model combining all previous BS models.

Rud Istvan
October 22, 2021 9:12 am

My nephew has a recent PhD in mathematics from LSU. His specialty is algebraic topology. So I called and asked him if it could be applied to the output of mathematically chaotic climate models to predict shifts between their strange attractors. His emphatic answer was no. Nuff said.

Reply to  Rud Istvan
October 22, 2021 12:53 pm

Guess I do not have to look at the article. Of course the authors likely disagree. I still want to know what a hole in an attractor looks like? Is it a place the system trajectories do not go? Or do they go in and disappear? Are we in danger of hitting a hole? That would be worse than a tipping point! Can we get tipped into a hole? Just kidding but still wondering about them holes. Maybe your nephew could look at the paper.

Rud Istvan
Reply to  David Wojick
October 22, 2021 2:13 pm

He did not want to waste his time—I tried.
IMHO, a hole in an attractor is actually a hole in the paper and it’s premises. Attractors are like gravity wells. They have a bottom, but the bottom cannot be a hole.

October 22, 2021 9:13 am

The last major perturbation of the climate was the closure of the Isthmus of Panama some 3.5 million years ago. That stopped the circulation of a global current and more or less split the equatorial circulation into Atlantic and Pacific. The split appears to have caused the newest ice ages, and several greatly different weather effects- the el Nino-la Nina circulation, redirection of the Gulf Stream and the formation of a cold counter current, a huge change in the South American fauna due to the infiltration of North American species and more.

While it may eventually be possible to predict the climate behavior many mathematician/scientists have pointed out how difficult the idea is. The primary limitation is computing power. Digital computers have serious limitations since it is very difficult to solve differential equations on them. Due to digital limits, differential equations have to be solved by procedures. But the procedures are limited in accuracy by the same limits in the machine. Over the millions of repetitive calculations the error in the results can balloon out of control.

Other limitations, specifically the smallest difference the computer can generate is still to big to make useful modelling calculations, particularly since all the calculations build up errors as the calculations interact with each other. Perhaps quantum computing will solve the problem some day. Until it does, the machine error, the machine epsilon, will continue to limit digital computers for climate models.

The other major problem is with the climate models themselves. The climate responds, such as a droplet forming, at tiny levels. When a drop of water hits the ocean surface it makes a vortex that can take some seconds to die out while its energy is spreading out. Both the droplet formation and its dissolution are both the source and the generation of the storm’s power.

Until the calculation problem is solved it won’t be possible to calculate useful results. They can’t just be lumped into averages because the effects don’t act on averages. For example, how does one determine the behavior of clouds on a rainy day. Which one is going to rapidly grow and generate a tornado. What limits an incipient tornado from dropping down and devastating a town or simply lets it fold back into the storm?

Reply to  Philo
October 22, 2021 12:56 pm

If it is chaotic no amount of computing power will make it predictable because we cannot know the state of the system to the degree needed to rule out the sensitivity that makes it unpredictable.

I would think the last perturbation of the climate was coming out of the last ice age, which is very recent.

Rud Istvan
Reply to  Philo
October 22, 2021 2:17 pm

See my post here some years ago for illustrations of your basic points. Titled, “The Trouble with Climate Models”. The present climate model computational intractability (thanks to the CFL constraint on numeric solutions to PDEs) is 6-7 Orders of Magnitude!

October 22, 2021 9:56 am

90% of the last 10 to 15 thousand years was at a minimum 1 to 3C warmer than today, and no tipping points were hit.
Anyone who believes a few tenths of a degree is going to kill us all is delusional.

Rud Istvan
Reply to  MarkW
October 22, 2021 2:18 pm

We know they are. Examples: Mann thinks he is a scientist, and Kerry thinks he thinks.

October 22, 2021 10:11 am

The only possible tipping point is towards a colder climate.

October 22, 2021 11:28 am

 A European science collaboration on tipping points in the Earth system found that the tipping points MIGHT be predicted. What a nice result. May their lunch plates be always full.

October 22, 2021 11:59 am

Eventually, after much improvement, the models might be able to predict the positions of chicken entrails on a table.

October 22, 2021 2:01 pm

Theoretical progress in imaginary climate science indicates algebraic topology misapplied to reduced imaginary climate models”

This one sentence is filled with specious assumptions surrounded by sophistry words.

e.g., how does one theory progress? Any change makes it a new theory.

Or, how does theoretical anything progress?
Theoretical basically means hypothetical. If theoretical happens to relate to reality, it loses that bit of theoretical. Theoretical undergoes a irrational change remains firmly theoretical. That is, theoretical does not “progress”. That pure sophistry.

Eventually, it begs the question exactly why do algebraic functions relate to inaccurate climate models in any predictive sense?

October 22, 2021 7:33 pm

I think Niels Bohr is spinning in his grave at the abuse, by reference, of his name.

October 23, 2021 2:53 pm

Only 2 things wrong with this paper: 1) Tipping points, 2) models. Need I say more?

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