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A Question for My Fellow Ricochetti
I’ve got a question I’m trying to answer, and it occurs to me that someone here might be able to help me. One of the things I like most about Ricochet is the thoughtfulness and intelligence of the members. Another thing that impresses me is the diversity of this crowd. So I’m going to toss this out there and see if anyone has any thoughts to offer.
I wrote a post not too long ago about the need for a civil dialog across the political divide. A fellow in New York City, one of these young, hyper-educated computer entrepreneur types, read it and invited me to participate in a new podcast he’s launching soon. He wants his first episode to feature someone from the left and someone from the right holding a civil discussion on matters about which they disagree.
The person on the left is another hyper-educated individual — Ph.D. from MIT in machine learning, something like that — who recently left Google to found a climate change advocacy organization in D.C. I’m the person on the right. We’re going to have a civil conversation, which I am going to assume will be centered around climate change, though that hasn’t actually been stated. The conference call will take place this Wednesday afternoon.
This isn’t intended to be a debate, but rather a conversation, a discussion, a meeting of minds. That’s the hope, anyway: ideally, we’ll each come away understanding the other’s perspective a little better. I’m an old dog, and I can’t honestly say that I want or expect my own views to change. (I think that’s probably true of most people, old dogs or not.) But I intend to do my best to listen, and to take a pleasant, non-confrontational tone.
I’ll get to my question for you in a moment.
My general thinking on climate change is pretty simple, and goes as follows:
- I’m agnostic about anthropogenic climate change. It wouldn’t surprise me at all if we’re warming the planet; might surprise me a little if we aren’t.
- I’m skeptical that we can project with any significant confidence the state of the climate 80 years from now, but I’m willing to entertain the possibility that we’re getting very good at modeling the complex dynamic system we call climate.
- I am more than skeptical that we can effectively model the several other complex dynamic systems involved in making cost/benefit analyses of various climate change mitigation strategies over a similar time scale. These include patterns of land use, agricultural production, technological evolution, urbanization, global distribution of poverty, etc. Eighty years is a very long time in terms of technological and economic development. (Step back to 1940 and imagine what futurists thought 2020 would be like; how much do you think they got right?)
- Given that I believe we can’t realistically evaluate the economic consequences of climate change 80 years from now, perhaps not even the sign of those consequences, I can not begin to justify imposing large-scale controls on current energy policy. While it’s difficult to model complex systems, history is full of examples of what happens when you create concentrated authoritarian control structures — and that’s what would be required to transform our energy economy as the climate change alarmists seem to desire.
I am ignoring two things, both of which are important in the discussion but neither of which is central to my argument. One is the impracticality of actually changing the future climate in a predictable way — at least, of doing so without crippling the global economy. The other is nuclear power, which I believe all climate change alarmists should eagerly embrace — believe so strongly that I distrust the motives or the intelligence (or both) of any climate change alarmist who doesn’t support nuclear power.
So my argument revolves around the assertion that we are not capable of making reliable long-term predictions about complex systems, and that climate mitigation strategies require us to make such predictions about several independent but linked complex dynamic systems. My question is this:
What examples do we have of anyone making successful predictions of the long-term behavior of complex systems?
Say that long-term is on the order of 50 years, give or take. Complex systems are “complex” in a relatively formal way, involving multiple interacting factors that are difficult to measure, the interactions of which may be poorly understood, chaotic, and involve feedback mechanisms.
Economies, political and social movements, markets, and technology-driven change all exhibit the behavior of complex systems. They are difficult to predict because they involve a lot of independent elements (often, people) making individual contributions based on an evolving range of factors. They are difficult to precisely describe, precisely measure, and accurately predict over any but the shortest time frames. They may exhibit sudden and chaotic changes in response to relatively small inputs (the shooting of an Archduke, for example).
In contrast, sending a rocket to the moon, designing a super-computer, making the next breakthrough in material science or battery technology or solar power or advanced medical imaging — all of these things may be complicated, but they are not complex. They are achieved by solving a large number of well-defined problems, with each solution contributing to the final goal. These systems are not characterized by chaotic behavior, subtle feedback loops, or factors that are difficult to define or measure.
We are very good at making predictions about non-complex systems, even fairly complicated ones, over pretty much any time frame. But I can think of no truly complex system about which we’ve ever successfully made an accurate long-term prediction. Hence my question.
Any thoughts?
Published in General
[ KE, I love this topic, so I probably won’t stop until you do. ]
2 / 2 is a pair of integers that have a ratio of .999999999999… .
32768/32768 is another. I can name more. ;)
Naw, those are just “word games” again. “2/2 = .9999…” is just another “arm-waving proof.” Our limited language ability to express things, is not binding on math, or numbers.
Dude, that’s like the definition of “begging the question”.
KE, I understand what you’re saying, but you’re mistaken. It isn’t sophistry, it’s just plain math. No gimmick here.
The math is correct; the mistake is in our misinterpretation of what that ellipsis represents.
No the problem there is you’re starting with the “conclusion” in advance that .999999… = 1 and then claiming that other things which also reduce to 1 are also = .9999999……… as if that somehow proves your original assumption. But as Bertrand Russell wrote, “The finding of arguments for a conclusion given in advance is not philosophy, but special pleading.” And if you ever had a math test asking, say, what is 4/2? and you answer 1.99999999999999… the teacher should either mark it wrong or lose their job.
P.S. Zeno’s Paradox is bunk too.
I think the problem is that you’re misinterpreting what the ellipsis actually represents because you’re seeing it in human terms, something like “close enough.”
Also, the issue of “an infinite number of rational numbers between any two other rational numbers” is a human construct, but which also needs to take into account irrational numbers.
Zeno’s paradox is bunk. It’s nonsense.
It’s nonsense because what Zeno described was an infinite series. It goes like this:
1 – ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + … )
That infinite series looks like it must evaluate to … something just a little bit more than zero. Right?
Because we’re subtracting 1/2 from one, giving us 1/2.
Then we’re subtracting half of what’s left — 1/4 — so we’re now at 1/4.
Then we’re subtracting half of what’s left — 1/8 — so we’re now at 1/8.
Etc.
Zeno was counting on people seeing that series and saying to themselves “well, that’s going to get awfully small, but it will never get to zero.”
But we know that the arrow does eventually hit the target — or miss it and fly past it.
That’s because it’s an infinite series, and it’s one that converges on an integer. In this case, it converges on zero: it equals zero.
It’s exactly the same idea as the other infinite series we’ve been talking about. You’ve just demonstrated that the math is real.
I’m pretty sure that’s the conclusion and is not a premise in HR. It is in my way of thinking. The equality of .99999… and 1 follows from two premises:
1. If they were not equal, then there would be some quantitative difference between them.
2. The only conceivable quantitative difference between them is infinitely small.
The rest is just logic: The difference would have to be an infinitely small quantity, and that is nonsense, and so they are equal after all.
No it’s bunk because you happen to pass through those points while covering the distance but that’s not HOW you cover the distance.
If you’re, say, two steps from something, nobody takes one step, and then half a step…
But that’s the made-in-advance definition of rational numbers that does not take into account irrational numbers such as pi, the square root of 2, or .99999999….. among others.
No, it’s just the facts about numbers.
Or if it’s not, then I have no idea at all what you are talking about.
So do you think a difference between two numbers is not necessarily some quantity?
Well, maybe it’s not the best example but in terms of the limitation of human language – and maybe even human thought – the idea that we can’t think of a number between .999999… and 1 is no more relevant than there being no integer between 1 and 2.
But I would like to emphasize again that while all rational numbers are real numbers, not all real numbers are rational numbers. It seems pretty clear that it’s impossible to… “approach?”… any irrational number – from EITHER “direction” – because it has no definite boundary. But that doesn’t mean an irrational number has no specific value of its own. And .9999999… is just a particular case of that.
Why not answer my question?
You actually can approach an irrational number with a series that converges on that number. And when an infinite series converges on a value, that value is the sum of the series — the value of the series. That’s what the series equals.
Here is a series that converges to — that actually equals — pi:
pi = 4 ( 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + … )
And pi, of course, is irrational (but very real).
And sometimes quite delicious.
but if you’re dealing with irrational numbers vs irrational numbers, that’s different too.
But is it not possible that the word games came first and then the numbers followed? For instance, I imagine that imaginary numbers had to have been thought about in words first, perhaps. After all, while the concept was being thought up, such that someone created the imaginary unit i, defined as it is by its property i² = −1, words would have to be used while the person who was the first person to deal with it figured it out.
Of course this concept falls outside of the rules as described in the comment above.
Where there is a trick to this is if you are a programmer working for some huge bank, like Bank of America, and you had programmed the bank’s computer to put the sum of 0.000000000001 % that would get lost by an assortment of other programing tricks to fall into the account that you had your spouse establish at that bank.
On its own, in a single occurrence, the amount is irrelevant. But since it might be re-occurring trillions of times over the life of that program, it would make a huge difference in the difference between 0.000000000099 cents and one cent.
Henry, Here are some off the beaten path type websites, which might be up your alley:
A relevant quote:
“MUCH that passes as idealism is disguised
hatred or disguised love of power.”
– Bertrand Russell
Then the following website, which has a decent take on the debate:
https://thebestschools.org/features/top-climate-change-scientists/
From the above:
“Simply stated, we maintain that appeals to authority and scurrilous ad hominem attacks are no substitute for rational argument. We also hold that what is sauce for the goose is sauce for the gander. This means, among other things, that mainstream climate scientists who roundly condemn climate skeptics for seeking support from private industry ought to be a bit more circumspect, seeing that they themselves receive millions in financial backing from government agencies. The tacit assumption behind their indignation — that only private actors have material interests, while public actors are by definition impartial seekers after truth — simply won’t wash. We strongly suspect that in, say, 100 years’ time, when (we hope!) scholars will be in a position to investigate this whole disgraceful episode in the history of science more objectively, they will find plenty of blame to go around.”
###############################
Finally: The editors at this site list their choices for the top ten pro-global climate crisis scientists as well as five scientists who are skeptics:
https://climatism.blog/2019/01/09/the-catastrophic-anthropogenic-global-warming-scam/
The following names are the five scientists they went and chose for the skeptics side:
Lennart O Bengtsson
John R Christy
Dr Judith Curry
Richard S Lindzen
Nir J Shaviv
##############
And then there is this, behind a subscription based paywall. (Though you do get a 30 day free trial) The service is called Scribd, so you might already be signed up:
https://www.scribd.com/doc/294684898/12-04-15-Why-Scientists-Disagree
Can I just say that I really hope this isn’t the conversation you end up having with your left-leaning friend? Not because it wouldn’t be important and fascinating, and even fruitful, but because I want to hear about this conversation, and…I’d like it to be understandable. By me.
I agree with you, CarolJoy.
Scattered responses:
Human beings are not good at risk assessment, not good at weighing relative risks and definitely not good at prioritizing (or even recognizing) someone else’s actual suffering over our own potential suffering.
This isn’t necessarily because we’re selfish and, as a species, afflicted with ADHD (though we are). Often it’s because we—each of us, all of us—focus on the problem we find interesting or compelling (yes, and/or remunerative). Lots of these are genuine problems, and solving them would result in genuine relief for real people.
Seeking a cure for a rare childhood cancer, for instance. The problem is undoubtedly fascinating, involving as it does all the mysteries of how the body is created, sustained and broken down… before you even get to the genuine, motivating desire to relieve pain and extend human life. Someone who studies a rare cancer is undoubtedly asked why fixing this one problem, that affects a relatively small group of people, shouldn’t be postponed while “we” address, say, the obesity epidemic that kills far more and may even predispose some to getting that very cancer or complicate its treatment?
On the other hand, if it’s your kid who has the rare childhood cancer…
But that’s about real problems and people who are really looking for solutions.
As I think about this, I am more persuaded that there are persons who solve problems…and persons who don’t actually want problems to be solved.
I remember, here, the reactions of left-y friends when I told them about a process recently discovered for removing CO2 from the atmosphere (apparently, this doesn’t really exist, but it made for an interesting thought experiment). “So we can go right on driving SUVs and polluting?” I was asked, but not happily. Angrily. How dare we solve this problem other than by punishing ourselves, in perpetuity, for our sins? I should say that these were not friends who had a pecuniary interest in maintaining climate change alarmism. Just an emotional one.
Robin diAngelo, to name an obvious example, does not want white people to stop being racist. She comes right out and tells her deep-pocketed customers that their sin can’t be fixed. This isn’t just because she’s made a tidy livelihood out of guilt-tripping other white people. It’s also, I think, because her ego is fed by the idea that her discontent isn’t just ordinary human discontent but is actually the existential anguish of the prophet who sees that all is lost. She gets to see herself as a tragic figure, a secular Christ, standing before doomed Jerusalem, seeing clearly what others do not even glimpse, and shedding her holy, and immensely gratifying, tears. It is this fantasy—somehow appealing to so many—that people pay for the privilege of sharing, if only for the duration of the workshop. “Isn’t it so, so tragic?” they ask one another. “I’m literally shaking.” Before scheduling a mani-pedi.
In an intellectually healthy capitalist culture, ideas, projects and priorities are in competition with one another. Lots of these find backing —financial, intellectual, social—but even the eccentric passionately attempting to revive community theater, or prep for the Rapture can set her own priorities that the rest of us need have little or no opinion about. Occasionally the eccentric produces something really wonderful, that benefits and delights us all. Eventually, presumably, the apocalyptic (of whatever tilt) will be proven right—everyone dies and everything ends, after all.
What is peculiarly destructive about climate change alarmism, like the COVID alarmism, is that it is a.) gummint and b.) totalizing—“We’re All Going To Die” being a pretty much unanswerable argument to just about any other proposed, but unfavored, project. Or rather, when the correct, inevitable answer is “no, we’re not all going to die” the climate change alarmist —as opposed to the problem-solver—says “Shut up.”
SA, you’ve brought up the question if infinitely small quantities a few times, and I made the mistake of using the word infinitesimal myself in an earlier comment.
In fact, there are no numbers among the real numbers that are infinitely-close-but-not-equal to some other real number. That would require that the two numbers have no “space” between them into which could be inserted other real numbers (an infinite number of them, in fact), and that’s a no-no by the definition of real numbers.
However, there are other kinds of mathematics — strange, unwholesome, vaguely disreputable varieties — in which it’s possible to find such infinitesimal numbers. It’s possible, if we allow these ugly little beasts to creep into our well-ordered universe of numbers, to find a value so peculiarly small that it fits in the tiny little non-space between 0.99999… and 1 — even though no real number would fit there. These are referred to as surreal numbers, and for good reason: they aren’t “real numbers,” though they may really be numbers.
We can thank Georg Cantor for inventing and/or revealing these beasts, and the whole monstrous world of set theory from which they spring. But we can safely pretend that they don’t exist, because they have absolutely no place in the lives of decent G-d fearing Americans.
Wow, leave a topic for a day and it explodes into über-mathematical geekery. At first I thought it was @kedavis trolling @henryracette, but apparently not.
I do hope you’ve conceeded, @kedavis, because you’re wrong. 9.9999…. and 10.0 really are the very same real, non-irrational number. I do hope you aren’t building bridges or skyscrapers or other things where people’s lives depend on your fundamental understanding of real numbers.
In fairness, Phil, it’s a wildly non-intuitive truth, and one that almost no one is comfortable with at first. Anyone who isn’t at least a bit of a math geek is going to find it vaguely offensive.
Maybe. But not being able to follow your (excellent) explanations should spark at least a bit of doubt about one’s position and spur an inquiry. Not drive one into mindless repetition of one’s error. Not liking you (or me) as an authority doesn’t mean one can’t look up other authorities. None of which will show that infinite series as anything but equals.
@henryracette himself mentioned the “surreal numbers” issue, and I also point out – or just argue – that… conflating, for lack of a better term… irrational numbers (such as .9999…) and rational numbers or in this case a whole number – 1 – would be an error. Or, to use other words, a rookie mistake. To me it’s akin to the “arm-waving proofs” I’ve mentioned elsewhere that go something like “6 is an even number, but 6 is an odd number of legs for a horse..” and go downhill from there. But the main thing is, if you start out with an error – in this case, conflating irrational and rational or even whole numbers – nothing that comes from it will be correct. Even if “the math works out.”
https://www.youtube.com/watch?v=wlrOKpQ6UBI
It is useful to have an appropriate perspective when considering the matter of
global warmingclimate change. Firstly, it is normal for climate to change. In fact the evidence to date suggests that any planet that can support life must have periodic changes in its climate. The factors that allow a planet to be habitable are the same ones that allow a climate to exist and drive changes in the climate. As to the issue at hand, I think the best answer as to whether there is anthropogenic climate change on Earth (ne “global warming”) is to look at the scientific record. The answer is best summed up in the following graph (from Wikipedia)The right-most side is now. The left most side is 542 million years ago. The natural cycles and trends are obvious. Note the high averages before us. We are currently living in the 2nd coldest period of global temperatures. Note the much warmer averages during the Triassic and Jurassic (when dinosaurs ruled the earth and didn’t drive SUVs or burn oil/coal).
The rational conclusion to draw from the known scientific facts is that any anthropogenic effects on climate change are — at most — localized and on the margins. The sun’s cycles, periodic interstellar radiation baths, the earth’s magnetic pole reversals (which may be starting), the ocean shape/size changes from the shifting of the tectonic plates, and other natural causes are the overwhelming drivers for climate change.
The Church of Climate Change is a major sect in the Godless religion of the Left, along with the Church of BLM, etc. “New Normal”, “make do with less”, are some of its central tenets. The religious fanatics of the Left pushing their Climate Change doctrine want us to sacrifice our valuable possessions (the economy and 1st world way of life) to their angry, vengeful god of climate. It’s no different than throwing young virgins into a volcano to end a famine, and it appeals to the same motive.
And it has the same result!
Dude, the infinitely repeating 0.999999…. is a rational number. In exactly the same way that ⅓ => 0.333333…. is a rational number. And ⅔ => 0.666666… is a rational number.
0.999… is also a whole number, as it happens.
This stuff really is counter-intuitive.