Don’t you love it when a climate scientists thinks he can “clarify” by introducing a methaphor involving dice?
In response to Keith’s post about climate uncertainty, Michael Tobis suggests a betting game that (I guess) is supposed to reveal something about how we should react to climate uncertainty. Let’s look at Michael’s “game”, and then shine some sunlight on an issue that need to be considered before anyone tries to apply the outcome of his betting game to answer the sorts of questions MT poses (e.g. “What does such a long tail mean to risk assessment?”)
Michael’s Game
Suppose you roll a pair of conventional dice. Your median roll, as is well known, is a seven. Now let’s play a game. We make a bet wherein you pay me the dollar amount of two raised to the power of your roll. If you roll a two, you pay me two squared dollars, a three, two cubed, etc. How much would I have to pay you up front to make this worth your while? Half the time you will roll less than a seven, and half the time more than a seven, so I propose 2^7 which is $128. You say you are indifferent to that bet, and suggest $256 instead.
You will be ahead 21 times out of 36, behind 10 times, and break even 5 times. A great bet, right? So what is your expected winning? I summon my magic snake and determine
>>> print 256 – reduce(lambda x,y: x+y,[2**(i + j + 2)
for i in range(6) for j in range(6)]) / 36-185
Your expected winning is negative $185, because the cost goes up rapidly in the tail, which is fat enough to matter. So, even though you win more than twice as often as you lose, it is a bad bet.
Given the context, I think in this dice game is a metaphor: the number showing on the dice is supposed to map into the “climate sensitivity”, the probability distribution function (pdf) for the number showing on the dice is the pdf for climate sensitivity and the amount the bettor wins or losses is the “cost” of climate change.
Under this metaphor, if “we bet $256”, “we” expect to lose– on average– $185 (= $441- $256). Since losing money is worse than winning money, “we” presumably decide not to bet the $256– which moving back to the climate change metaphor, means “we” shouldn’t fail to take action on climate change.
Now for a ray of sunshine
Notice in MT’s game, the probability distribution function (pdf) for the number on the die (i.e. “the climate sensitivity) is taken as given. Treated as a metaphor, there is quite a bit of debate about the appropriate pdf for climate sensitivity. Judy Curry wrote a interesting post discussing that yesterday.
In this post, I’m not going to focus on that issue (feel free to discuss it in comments though.)
Instead, I’m going to focus on the aspect of the problem that has nothing to do with physics; I’m going to focus on the part that has to do with money and values.
Notice that in Michael’s game, metaphorically speaking, if sensitivity equivalent “12 (no units specified) we lose twice as much as if climate sensitivity is “11”. If it’s “11” we lost twice as much as if it’s “10” and so on.
But is the reasonable?
The question that might present itself those pondering the metaphor is: Is the “cost” of climate sensitivity of “12” really twice that of climate sensitivity of 11″, and so on?
Suppose, for example, climate models say there is a 1 in 36 possibility that climate sensitivity “12” (units undisclosed), and suppose further the outcome of a climate sensitivity of “12” is “humanity is doomed to extinction by 2100”. Let’s assume we all accept this (so as to create a rolling the dice metaphor.)
Metaphorically speaking, should the cost of “humanity is doomed to extinction by 2100” be? Should it be $2^12?
Maybe we could discover the cost by asking a 30 year old single-mother hair dresser how much she would pay to avoid “humanity being doomed to extinction by 2100”. We aren’t asking her how scared she is–just how much she’d pay to avoid it. The hair dresser might decide that not going extinct by 2100 is worth paying $384 to avoid, no more, no less. (Why $384? I don’t know. This is metaphor climate-sensitivity dice came metaphor.)
Now, suppose climate models say there is a 2 in 36 possibility that climate sensitivity is “11”. Suppose further the outcome of climate sensitivity of “11” is “we are doomed to extinction by 2150. The hair dresser might decide that not going extinct by 2150 is also worth $384 to her.
Maybe as she ponders all the bad things that happen for each value of climate sensitivity. She learns that an outcome of “2” means her dahlia will over-winter saving her the cost and labor of replanting every year, an outcome of 6 means higher taxes to bring water to her town and so on. She then decides that the “penalty” for each outcome is is the lesser of $2n and $384, where “n” is the climate sensitivity (or number of dots on the two die).
Now, given this view, we “tweak” MT’s dice- as -climate-sensitivity game.
The tweaked game
To reflect the notion that the “cost” associated with high sensitivity hits a cap, let’s put a cap on the bettor’s losses. Instead of losing $2^n where n is the sum of the numbers of the face of the two die, he loses the lesser of $2n and $384.
Once again, as in Michael Tobis’ game, the bettor will play the game if you give him $256 to start. Then, he loses based on the outcome of the die toss and the rule above. At the extremes, he takes home a net of $252 = ($256 – $4) if the die faces sum to 2. On the other hand, he will lose $128 = ($384-$256) if the two die faces sum to 9 or more.
We can do the whole calculation, it will turn out the expected value of the accepting $256 to make the bet is a positive $78.11. So, on average, he wins $78.11 rather than losing $185 as in Michael’s game.
Metaphorically speaking:
- The uncertainty about climate sensitivity (number on the die faces)is the same in both games.
- The odds of winning (21/36), breaking even (5/36) and losing (10/36) are unchanged from the first game.
The only thing that has changed is the penalty or cost one assigns to “high sensitivity”. While economists are able to assign costs to some goods and items rather well, the fact is that in some cases, cost is strongly connected to what individuals value. Individuals each make value judgements everyday; these sometimes include explicit decisions to risk death in exchange for something they value. (Heck, some people volunteer for the military! Others risk death by driving drunk — often risking getting a ticket in the process.)
So Michael setting up a probability game that blithely decrees that the cost or penalty associated with a particular value of “climate sensitivity” increases geometrically without bound amounts to begging the question. After all when deciding on the level of action or choosing the actions to take figuring out the cost or penalty associated with inaction at any particular level of climate sensitivity is a very big part of the question.
Sorry, but Michael and others who like dice metaphors can’t get around discussing substantive questions by discussing dice. Not even if the dice example is enhanced by including lines from scripts:
>>> print 256 – reduce(lambda x,y: x+y,[2**(i + j + 2)
for i in range(6) for j in range(6)]) / 36
You start trying to prove your point that way, and the counter argument is going to be a link to an R script.
security is mostly a superstition
http://www.youtube.com/watch?v=c_OCJyhaJA8&feature=related
this is how an angel flies.. blame it on my ADD
http://www.youtube.com/watch?v=TWfph3iNC-k&feature=related
baby Im a different breed
I thought everybody knew the answer is 42.
Toml-
Is it +42, or -42?
Lucia, when you say “So Michael setting up a probability game that blithely decrees that the cost or penalty associated with a particular value of “climate sensitivity†increases geometrically without bound amounts to begging the question.”.. you’re right on the money.
Have I got this right – we neither know what the probability of a particular outcome is, nor do we know what risk ‘people’ might find acceptable?
Its a good metaphor. Your more sophistaced probability model may be different to Michael T’s probability model, but it still has the same essential property that Michael T is getting at – the average payout is not well predicted by considering the payout for rolling a 7.
I also find it curious that your argument seems to contain the assumption that there is a probability of human extinction large enough to significantly affect the result.
I am pretty sure when Michael starts describing dice and betting that he will point out something either wrong, ridiculous, or obvious. Come to think of it, that pretty much covers most everything he describes…
Michael–
That “essential property” is true of many, many, many games of chance and true in life. I can’t imagine very many people past the age of 5 need to be presented a convoluted dice metaphor learn that. Moreover, where it required, the convoluted lesson would be just as easily taught using an example that has the property where the better “wins” rather than “loses” by betting (or not betting) and where the “lesson” is our out come is “better” than we would expect by seeing what happens if we roll a 7.
Presumably in metaphor space the second example would show that we “shouldn’t” mitigate. I imagine that’s the reason the example were we do “better” on average than if we roll the 7 isn’t used to illustrate this “essential” point.
I don’t think you should find it curious.
I think that it’s important to explicitly discuss what outcomes people are suggesting when they start discussing costs and benefits of action or inaction rather than merely resorting to some sort of metaphor where each thing in the “dice game” supposedly maps into some elements of “reality” in a way that makes people think some tangential thing is implied. Introducing extinction is dramatic enough that it forces people to stop and engage the question: Are we basing our estimates of costs on the possibility of extinction? Do we really think extinction could happen?
Then people can see the elements used in the “cost/benefit” analysis and discover whether they think the foundations make any sense at all. This should always be done before crunching the numbers. But this essential feature — that is discussing the implicit assumptions– is missing for Tobis’s discussion.
Of course, if we start actually discussing our assumptions, we are likely to discover we need to break out of the stupid dice metaphor– but it was a stupid metaphor designed to scramble people thinking and distract them in the first place.
So, I introduced “extinction” into my metaphor because I think it’s to discuss how any cost/benefit analysis — even a metaphorical one– is considering the probability of extinction. Which exists.
There is a non-zero is a probability of humans becoming extinct from asteroids, super volcanoes, nuclear war, sudden new virulent viruses or bacteria and all sorts of things. I should think the “long” in “long fat tail” Michael is arguing about would be bad enough that at it’s tail it involves extinction. I also think that in any cost benefit analysis, if we are considering the cost of extinction due to climate change, then the probability that extinction would occur because by spending so much on climate change, we are unable to detect and intercept the asteroid ought to also be considered and discussed.
So, any game supposedly engaging the notion of ‘the long fat tail’ ought to explicitly state whether they are actually discussing extinction and not leave that entirely unmentioned.
Now that it is brought up explicitly: I don’t think the probability of homo-sapiens extinction due to climate change is remotely close to 1/36, I think it’s well below that. So, clearly, any ‘game’ that used as a metaphor needs a metaphor that permits us to consider things with a lower than 1/36 chance of occurring.
Kohl
It seems to me that’s about right. We aren’t absolutely sure of the probability distribution function for outcomes. (Judy’s engages this.)
We also don’t really know how any individual or collection of individuals find some particular outcome acceptable. My impression is economists grapple with the latter all the time– but some questions are very difficult to put prices on. For example: If some island people have to leave their island and culture because it goes underwater, how much does this “cost”? We know how much it might cost to get ships out there, resettle them etc. But maybe the 2nd generation would think that cost was well worth not being stuck on an island, which they would have been if the island was till above water. Maybe this generation would become so productive after moving to a continent that the cost of moving resulted in a benefit to the rest of mankind.
I have no idea how economists grapple with these things. Zeke is an economist and he knows. But I suspect this sort of problem falls under “making difficult assumptions”.
Lucia – from what I have seen the valuation of risk reduction is fraught with difficulty. Google “willingness to pay” and “compensating differentials” for some starts.
Of the many differences in male and female humans, only one really counts; males can have an unlimited number of children, whereas in females there is an absolute maximum (about 40).
It makes sense for a male to have a harem, impregnating large numbers of females, but it makes no sense for female to have a large number of men impregnating her (beyond the pleasureable aspects).
It makes sense for male and females to have a different types of sexual stratagem. For females the two which work the best are 1) get the best male provider you can and have his children and 2) get the best male provider you can and and have a higher status/better looking/built/more intelligent males children.
Females compete against other females for males who will look after them and the children she bares (not necessarily his).
Males have a huge range of stratagems, but they always have to compete against other males, for example by opportunistically impregnating someone else woman or forming a harem. This last one is a very high risk/high yield tournamental strategy.
Genghis Khan is the quintessential tournamental player. 8% of the worlds males have his Y-chromosome.
So potential fecundity differences in males and females means that different sexual strategies are possible, and leads to different brains and behaviors in the genders.
So males and females have evolved to act in their own best, fecundicial, interest.
Why shouldn’t people behave in their own self interest?
Now, ignore the fat-tail, ignore the metaphor and deal with the real.
Should I live in a modern industrial country, with a high standard of living/health-care/education it means that I can pass all these benefits on to my children.
People on the right who complain about illegal immigrants crossing into the EU or USA are called heartless by people on the left. Normally with the rider “How could any one be so cruel to a group of people just trying to get a better life for themselves and their children?”
Now if my lifestyle means that 100 million people in the third world, who I don’t know and have never met, will die of climate changes caused by my lifestyle, should I give it all up?
Its a no brainer really.
I have a direct responsibility to fight on behalf of my own children and try to make them as high status/financially/physically robust as possible.
In all truth, my feeling toward the wrenched or the third world rank below my feeling to my cat. I know this to be true as I spend far more on her in food/litter and vet bills than I do on my fellow humans.
So, vested interest versus ‘alturism’ is the only math you have to study. The bad news is that humans are not alturistic, they are mutualistic.
You may think that this attitude is wrong for any number of reasons, including moral ones. My burning fossil fuel to support my lifestyle may cause a 6 feet rise in sea levels and kill millions in, say, Bangladesh. Yet, the environmental destruction and massive population growth in Bangladesh is going to kill millions anyway.
The people in the third would aren’t just written off by me, look what the ‘nuclear power no thanks’ and ‘No GM’ have done to them.
“It makes sense for a male to have a harem, impregnating large numbers of females, but it makes no sense for female to have a large number of men impregnating her (beyond the pleasureable aspects).”
Doc – From the UK I don’t recognise this; how does your legal system treat divorce?
curious, how curious. I am from England, now home to more than a 1,000 Polygamous marriage’s.
http://www.religionnewsblog.com/18376/polygamy-britain
Given what we have seen from climate science so far, it would not be a fair game. The dice would be loaded / the editor would have been forced out.
I think 1.5C of warming and 800 ppm of CO2 by 2150 will be a great thing for planet Earth and virtually every single species on the planet. The real dice game is loser for the house and a winner for the player.
How does that compare to the number of divorces?
DocMartyn, “Now if my lifestyle means that 100 million people in the third world, who I don’t know and have never met, will die of climate changes caused by my lifestyle, should I give it all up?”
Even worse, 3 BILLION people in the 3rd world live in poverty and cook their miniscule amount of food over dung fires and millions of them will die every year unless they are allowed to industrialize like India and China are doing now.
Should we deny them that when their is no concrete evidence a minuscule change in temperature will change their lives?
http://www.who.int/mediacentre/factsheets/fs292/en/
Well I had not the patience to go to the original blog for the original “metaphor” because it doesn’t seem to be a metaphor of anything sensible and also because I can’t see what it it is meant to demonstrate.
.
Based on the description given above, what is being done is :
1) Take an iid (die throws) with a variable X over [A,B]
2) Take the pdf of the iid , P(X) which is obviously gaussian
3) Take an arbitrary function F(X) over [A,B]
.
And now ask what I find a really stupid question :
For what C we have : ∫A to C▒F(X)dX= ∫C to B▒F(X)dX
Why is the question stupid ?
Because the answer is trivial : it depends on F
Now the author of the “metaphor” seems to be surprised that for a random choice of F, the C he finds is not equal to (A+B)/2 what is the answer for the gaussian P(X).
What was the probability that by taking an arbitrary F the answer would be (A+B)/2 ?
Well it was 0 and there is nothing to be surprised by.
Moreover if one takes a particular class of F, namely strongly increasing towards B like Exp(X) or even worse, 1/(B-X), then the C will be very near to B.
This is also trivial.
.
Of course even if one can consider that F is a distribution (e.g an arbitrary pdf), this particular class of F has nothing to do with tails fat or otherwise.
The neighbourhood of B for this class of functions is not a tail, it is the dog!
Finally this whole exercice is extremely confusing because there seems to be no relationship with weather or climate.
Why should one bother with a misleading iid when finally the whole trivial point is to show that if I take an arbitrary strongly increasing function, the equality of 2 integrals in the middle of the interval of X will never be achieved ?
A point to add.
.
If one imagines that in the mind of the author X is the climate (let us not worry about metrics, we just play games) and F(X) is the “cost” of the climate X (again let us forget metrics) then it has still nothing to do with “fat tails”.
If, for the purpose of playing games, one postulates that the climate is iid then it has no “fat tail”.
And if one postulates on top that F is a (strongly) increasing function of X, then it has no “fat tail” either. Actually the whole of F’s being is concentrated to one limit of the interval of X.
Whether we do integrals with F alone or with F(X).P(X) changes nothing on the principle.
If I were making a bet, it would be that cholesterol gets Tobis before the climate does. 5 Quatloos.
TomVonk–
It seems to me that Michael Hauber thinks the point you consider trivial is the “essential” one. I agree it’s trivial, and I think that most reasonably intelligent people already grasp the point without writing any integral, sum or reading any specific example.
It seems to me that ‘math’, and the example may have been used by MT to confuse those less comfortable with math into believing that if they knew more math, then they too would be able to have some sort of profound insight. Or maybe it was used to make them think there is something substantive in that post. Or maybe MT has confused himself. He seems to do so pretty often (at least when ever an honest to goodness technical point rears its head.)
But he said he got these numbers by summoning his magic snake. How can they be wrong?
bender–
I didn’t say the numbers were wrong. The numbers are perfectly ok in the sense that they match the rules of the stupid game. It’s the dice game as metaphor that is stupid.
Lucia — MT’s point is essentially correct. You don’t seem to understand that the parameterization of a fully-integrated probability distribution function is constrained by the Erdos effect. In consequence, the skedasticity that is inherent in this rho-to-phi transformation can only be appreciated after a hysteresis de-masking subroutine has been implemented.
.
It seems to me that this sort of framistat discourse is quite common, when the subject turns to Climate.
[To be clear: the first paragraph of this comment was written to sound authoritative, though it lacks meaning.]
he really should call his new blog, the MT Quarter.
http://www.google.com/url?sa=t&source=web&cd=1&sqi=2&ved=0CCAQFjAA&url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRub'_al_Khali&ei=lF6YTpeQGcyTtwfzm4G0Ag&usg=AFQjCNH4ZuKdTc-vng4-hHPwS_XKxyww4w
lucia
I know. I just can’t stop coughing on the choice of language. I had to repeat it for effect.
Re:lucia (Comment #83700)
October 13th, 2011 at 5:40 pm
A number of years ago, I had the pleasure of attending a lecture and lunch with Freeman Dyson. At the time, he was advocating that we increase the resources spent to find and track asteroids, since as he reasoned, an asteroid impact could very well lead to the destruction of our species (or, at the least, the end of civilization as we know it). The chances of this happening being very, very small, but the cost being, for all intents and purposes, infinite.
I think your point is that, if you allow for costs which blow up in the “long tail,” then it’s difficult to understand how one should weigh this particular risk against any other “total disasters” like those you have mentioned. Dice-rolling notwithstanding, we’re still left not knowing quite how to bet.
Oliver–
Also, if a species killing asteroid hits in 2050 money spent to avoid climate change will have been wasted. People could have lived comfortably up to that time spewing as much CO2 as made them comfortable. So, if the remote possibility of species extinction in year ‘x’ due to climate change is included, along with a high cost, then the possibility that extinction will happen anyway needs to be included. That way, we don’t do the climate change equivalent of buying expensive flood insurance and discover we lose the house when we can’t pay the mortgage.
“if a species killing asteroid hits in 2050 money spent to avoid climate change will have been wasted.”
I suspect it would only cost a few billion dollars to inject enough SO2 into the atmosphere to cool it off .8C (or we could wait for a volcano) … but no amount of money would allow us to warm up the earth if we are heading for a Maunder style minimum.
Better to keep the planet as warm as possible until we are sure the Eddy Minimum isn’t coming … so lets not squander any more money on mitigation (unless it has obvious clean air benefits like switching from coal to shale gas).
It is not just asteroids , there are other high cost long tail risks, for example, mutant and novel diseases; anyone up for son of Ebola or AIDS II, or just a deathly-dull porcine/avain influenza epidemic ? The hairdresser need to be asked how much of her $384 extinction pot she allocates to preventing each of these diseases, destroying asteroids, appeasing the Wrath of God et al.
A fun end to consider is the next full ice age – if AGW staves this off, then it might turn out that a 2 metre sea level rise is a very acceptable price to pay.
How I Learned to Stop Worrying and Love Climate Change.
Regardless of how you tweak the game, the real problem with the real climate is that the people placing the bets don’t have to pay off if they lose. Because they’ll be dead by then.
For example, we know that the icecaps are doomed if CO2 goes above 450 ppmv. At the current rate, we will reach 450 ppmv by midcentury if not sooner. But it will take several more centuries for the icecaps to actually melt. Which means that the people driving up CO2 (us) won’t be around for all the negative effects of our actions.
Our parents may have been the greatest generation. Our great-grandchildren will call us the worst.
Strangelove–
For all we know, the hairdresser is willing to pay only $384 precisely because members of her family died in the previous procine/avian flue epidemic, understands how disease can affect the human population and figures that she’s not going to pay $4000 to cover one threat while paying nothing to cover avian flu.
KAP “For example, we know that the icecaps are doomed if CO2 goes above 450 ppmv.”
I’ll make you a deal. If both tide gauges and satellite sea level rises by more than 10mm a year for 10 years in a row, I’ll support mitigation. (This would mean the mythical 1m by 2100 might actually happen).
Right now sea level is dropping so I doubt 450ppm will make much of a difference.
If Tobis is controlling the game, it will be rigged, to be diplomatic.
The very concept of taxing carbon today to prevent a global catastrophe in ~100 years is wrong on every ethical and rational level.
So perhaps it is appropriate that Tobis would use a metaphor utilizing a crooked game with non-sensical rules.
Lucia- sorry, I thought that $384 was for All-Risks (“humanity being doomed to extinction by 2100″ ) – I clearly didnt read the fine print:-)
Presumably the cost of insuring against “humanity being doomed to extinction by 2200″ would be greater but our hairdresser would actually be willing to pay less than she would be willing to pay for insurance against “humanity being doomed to extinction by 2020″
Partly on the basis that while she likes her daughters, their offspring only serve to remind her of the awfull choice in husbands that they made (against her better judgement!).
I can imagine a Cartoon by Josh with the tagline: “It’s metaphorically, exponentially worse than we thought!”
Bruce (Comment #83769)
Pretty much proves my point, Bruce. By the time that happens, you’ll be dead. But you will still have caused it.
Strangelove-
Designing and running a project to ensure humanity will not be extinct before 3000 would cost more than ensuring they will not be extinct by Dec 2012.
But people would likely be more willing to pay for the program that prevents an asteroid we have sighted from hitting us next March– in 2012.
Even people who don’t value the notion of preventing people 1 millenia from now from dying off might pay to avoid their own premature deaths. And, oddly, what they are willing to pay for would cost less to accomplish.
This is, I suspect, one of the difficulties in motivating people to act to prevent harm that will befall those alive sometime in the future.
DocMartyn,
The reason why you should care about those less fortunate than yourself is that there is someone else somewhere in the world who thinks like you but is much much richer than you are and if your children, despite your efforts, should fall on hard times ( and many many millions in the advanced countries have during this recession/depression) they may say well I don’t give a **** about those people, I just look after my own.
And your children will suffer.
Lucia-
Maybe , but then the cost of insuring against extinction in 3000 will be less for our offspring in 2900 than it will be for us today, will it not? [All other things be equal].
We also know that the cost of calculating Pi to 1000 decimal places has declined quite a bit over the last hundred years and so we must also factor in ‘progress’.
As for the difficulties in motivating people: it is the common experience of all (living) people that what we thought was a really big problem last week turns out not to have been such a big deal, on reflection.
We cannot know what their problems will be 2900 – nutcases with pocket antimatter bombs maybe the least of it. if we divert their future wealth into stupid projects they might not thank us for it.
KAP: “Pretty much proves my point, Bruce. By the time that happens, you’ll be dead. But you will still have caused it.”
KAP, satellite sea level is going down. When you try to accuse me of committing genocidal sea level rise … wait until it is actually rising at a level that is even remotely close to the chicken little claims. Otherwise you look kind of dumb.
And KAP, assuming people are standing in place long enough for 2mm a year to drown them … they would need to be really, really short.
Strangelove–
Probably. For one thing if our off-spring are still around in 2900, they don’t need to worry about the hypothetical humanity destroying asteroid that might hit in 2015. If we were going to insure up to 2900, we need to worry about that.
That’s what makes insuring against calamities in the future difficult. Insuring that the past remains as it happened is cheap.
KAP (Comment #83767) October 14th, 2011 at 1:20 pm
Our parents may have been the greatest generation. Our great-grandchildren will call us the worst.
Look up the 1969 Cuyahoga River fire.
Our parents generation faced many challenges..they did better on some then on others. Protecting the environment for future generations wasn’t one of their proudest accomplishments.
harrywr2, good point.
KAP, you could check out Donora or London smogs too.
http://en.wikipedia.org/wiki/1948_Donora_smog
http://history1900s.about.com/od/1950s/qt/greatsmog.htm
Bruce (Comment #83783)
> KAP, satellite sea level is going down.
Temporarily, because of unusually large continental sequestration. It’s not due to refreezing. As I’m sure you know but choose to ignore.
> When you try to accuse me of committing genocidal sea level rise …
Oh “genocidal” now? And where did I use that word? Are you lying outright, or are you just trying to build a strawman?
> wait until it is actually rising at a level that is even remotely close to the chicken little claims. Otherwise you look kind of dumb.
You continue to miss the point of my initial post: if we wait as long as you want, the tipping point will have already passed, and it will be too late to stop loss of the icecaps.
>And KAP, assuming people are standing in place long enough for 2mm a year to drown them … they would need to be really, really short.
How much non-mobile infrastructure is there worldwide at or below 7 meters above current sea level? How much will it cost to replace all of that? And where will those refugees whose homes have been lost go? And who will bear the cost of their relocation? Please be specific with dollar amounts. Because only then can we rationally discuss whether mitigation is worth the cost.
Re: KAP (Oct 14 21:01),
If 450 ppm is indeed the ‘tipping point’ for retention of the Greenland and Antarctic ice caps, it’s already too late. There is simply no way that CO2 emissions will be cut on a time scale that will keep atmospheric CO2 below 450 ppm. In fact, they aren’t going to be cut at all, and will continue to increase for several decades at least.
KAP:
“Bruce (Comment #83783)
> KAP, satellite sea level is going down.
Temporarily, because of Bruce (Comment #83783)
> KAP, satellite sea level is going down.
Temporarily, because of unusually large continental sequestration. It’s not due to refreezing. As I’m sure you know but choose to ignore.”
–
How do Bruce and you _know_ that, KAP? If sea level is in fact going down I will bet it is an effect of cooling oceans.
“Unusually large continental sequestration”, that sounds to me like an unverifiable ad hoc explanation for adverse data.
KAP: “How much non-mobile infrastructure is there worldwide at or below 7 meters above current sea level?”
Don’t know. But sea level rises around 2mm a year normally anyway, so 3500 years from now it will be under water no matter what we do. If we trust predictions out 3500 years.
KAP, think of Venice. People adapt.
Besides, the good news is that if sea level is a proxy for rising temperatures, it isn’t actually getting any warmer. Tide Gauges have never shown evidence of catastrophic sea level rise.
Places where money would be better spent than on trying to study the effects of or avert “climate change”
1. The Druid wave dance ritual to stop ocean waves from advancing
2. The Buddhist wheel rotational chant – “Thus far and no further”
3. Scuba diving kits for the Maldive and Tuvalu residents
….
999,998. Missile defence shield against asteroids
999,999. Research on Science and Medicine
1,000,000. Education
Meanwhile, on planet Earth . . .
http://i.imgur.com/LvNDG.gif
Bruce (Comment #83806): “But sea level rises around 2mm a year normally anyway,”
No. Historically it *has not* risen around “2mm a year normally”. That is only what it has done for about the last century. For about 2000 years before that it rose less than 0.1 mm per year on average.
http://www.cmar.csiro.au/sealevel/sl_hist_intro.html
“As the climate has warmed following the end of a recent cold period known as the “Little Ice Age†in the 19th century, sea level has been rising about 1 to 2 millimeters per year due to the reduction in volume of ice caps, ice fields, and mountain glaciers in addition to the thermal expansion of ocean water.”
http://pubs.usgs.gov/fs/fs2-00/
There is some evidence sea level actually dropped by 1 meter at the end of the MWP.
http://onlinelibrary.wiley.com/doi/10.1002/1520-6548(200010)15:7%3C715::AID-GEA4%3E3.0.CO;2-L/abstract
There are those who might try and draw a flat line from Roman times to the end of the LIA … but they would be the type of people who deny the existence of the MWP and LIA.
Benjamin Franz (Comment #83849)
“Historically it *has not* risen around “2mm a year normallyâ€. That is only what it has done for about the last century. For about 2000 years before that it rose less than 0.1 mm per year on average.”
http://www.cmar.csiro.au/seale…..intro.html
That graph that you have linked to shows a rise of about 0.4 m from -1,000 to 1,000 ie 2,000 years which comes to 0.2 mm per year approx.
Also the line is red is shown without any error bars. Have they made the classic mistake of appending actual readings onto reconstructions?
Benjamin:
Yeah, especially if you fold in the Little Ice Age.
Also keep in mind that according to the IPCC it wasn’t until about 1970 that CO2 forcing exceeding cooling from sulfate emissions… so according to them the warming prior to 1970 (chiefly from 1905-1950 since 1950-1970 was a period of more-or-less constant temperature) was entirely natural.
It’s interesting that we have the rapid increase in sea level in your figure that precedes significant anthropogenic forcing.
Also, based on the number of underwater structures from the Roman era, I’m guessing that their estimates of the amount of sea level rise between now and then is a bit understated. Almost as if somebody had a political agenda.
Benjamin, Don’t forget about the transgressions.
“The Older Peron was a “transgression” in the sense of marine transgression, a period of advancing global sea level. Warm temperatures forced a retreat in the glaciers and ice sheets of the global cryosphere; throughout the period, global sea levels were 2.5 to 4 meters (8 to 13 feet) higher than the twentieth-century average. The higher sea level lasted for several centuries and eroded coastlines. Several locations around the world have “Older Peron terraces” along their coasts as a result
The Older Peron transgression was one of a series of gradually diminishing marine transgressions during the middle Holocene. It was followed by the Younger Peron, Abrolhos, and Rottnest transgressions. During the Younger Peron transgression (c. 4000–3400 BCE), sea level peaked at 3 meters above the twentieth-century level; during the Abrolhos (c. 2600–2100 BCE), 1.5 meters; and during the Rottnest (c. 1600–1000 BCE), 1 meter.”
http://en.wikipedia.org/wiki/Older_Peron
It’s interesting that we have the rapid increase in sea level in your figure that precedes significant anthropogenic forcing.
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It’s a quadratic fit.
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Also, based on the number of underwater structures from the Roman era, I’m guessing that their estimates of the amount of sea level rise between now and then is a bit understated. Almost as if somebody had a political agenda.
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Or almost if the Napoli area was not very stable. That site is located 15 miles away from Mount Vesuvius.
toto:
Got it. It’s not even data, which is why it looked so strange.
Possibly, but we’re seeming to find a lot of ruins under water (I said “Roman era” even admittedly the link was to that site), such as Cleopatra’s palace in Alexandria or the ruins of Mahabalipuram.
I dunna, it could just be that historical sites are built in “interesting places” that happen to be geologically active too. It just starts to look a bit coincidental after awhile.
I realize that the situation is messy–isostatic rebound as well as geologically active regions. Not a problem I would lightly dabble in.
Should have gone to wikipedia… more reliable site, go figure.
The actual data is much messier The Loess curve they show looks overfit. If I were to try and smooth the original data, I’d probably trying to use the AIC criterion to pick the optimal fit curve.
My suspicion is political bias is playing a role in trying to force the data to a fit a particular narrative, and no climate science is not immune to that proclivity.
(The data themselves suggest that the sea level may have been 2-m higher than current during the holocene climate optimum… a period where the temperatures are thought to have been warmer too of course. Usual caveats about paleo data apply.)
“The idea of irregular sea level rise, introduced my Fairbridge (1961), and subsequently dismissed by uniformitarian interpretations, has recently been reinforced by analysis of Australian coral reefs(4).
Fairbridge’s sea level curves are discussed in the Encyclopedia Brittanica. They had been suppressed in favor of the more uniform curve of Shepard, thougt the irregular model is now coming back into vogue with the return to respectability of more catastrophic ways of looking at the data. ”
http://www.stanford.edu/~meehan/donnellyr/sealevel.html
The light blue line is labeled Fairbridge.
http://geology.uprm.edu/Morelock/3_image/holcrv.gif
E[f(X)] does not equal f(E[X]) right?
where X = number on dice
and f = amount paid; f(x) = 2^X
-> Then the amount you should pay is E[f(X)] =
SUM from X = 1 to 12 [ Prob(X) * f(X) ] = 441
( not 2^( E[X] ) = 256 )
SUT
That’s the general rule. It can be equal for the special case where f(x) is linear. But of course in this game f(x) is not linear.
This is why everyone ways the ‘point’ Michael calls essential is obvious. I think it’s obvious to people who know math and it’s equally obvious to people who don’t know math.
Can you attend Kevin Trenberth’s discussion at NCAR with Anthony Watts?
http://appsumo.com/~bGNt
“Michael Tobis suggests a betting game that (I guess) is supposed to reveal something about how we should react to climate uncertainty.”
“He uses statistics as a drunken man uses lamp-posts… for support
rather than illumination.”
This is why everyone ways the ‘point’ Michael calls essential is obvious. I think it’s obvious to people who know math and it’s equally obvious to people who don’t know math.
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I am not so sure about the second statement.
While it is strikingly obvious why it is trivial when one translates the “game” in one line of maths, I suspect that the author thinks that people who can’t write this line (perhaps even himself included) will get some deep non trivial insight in the mysterious nature of distribution tails..
And I could imagine that he is not so wrong because when one reads the “game”, one feels some kind of tautology but may be sufficiently confused to not be able to put the finger on it.
So it is surely more confusing than stupid because his target is arguably to convince people that we should spend much money now and that this “game” is the icontrovertible proof why this is the reasonable thing to do.
bouldersolar (Comment #83905)
If I understand corretly, R.Gates was the one who initiated this. I think it’s nice of Trenberth to be willing to comply, and wonderful that Anthony has the time and travel money. I encourage anyone who lives near NCAR and who has the time to spare to go.
However, I will not be attending. There is no way I can justify the time or expense of traveling to Colorado to spend a 1/2 day watching presentations. This is what I told Anthony when he brought up the subject a while back.
The f(x) would in fact increase slowly after a point. This is because of the cost structure of typical adaptation works dealing with the effect of climate change.
Consider, for example, building a dyke to deal with sea level rise. Once you have commited to the cost of a dyke, the additional cost of building a dyke 1 metre taller is not that much greater.