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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
An irrational number is one that cannot be made as the ratio of two integers. .99999… qualifies. Saying that it’s a rational number because 2/2 = .9999…. is assuming in advance that .99999…. = 1, which is the issue at hand, not the ANSWER to the issue at hand. Anything else is verbal flim-flammery, as pointed out earlier.
The single biggest mistake mathematicians – especially hardcore mathematicians – make is believing that math/numbers actually IS/ARE the universe. That’s some kind of philosophical claptrap, but I don’t remember what kind. Math/numbers is/are sort of a language useful for DESCRIBING the universe, but they are NOT The Universe. No more than the words “Henry Racette” actually ARE Henry Racette.
This is heavy stuff — at least for this nuts and bolts engineer sort. I don’t do philosophy much, mostly because I’m not up to the challenge.
I’ll just say it this way:
0.999… = 1 is true in the same sense that 2 + 2 = 4 is true; just as true, and for the same kinds of reasons. They’re both true statements with the same universe of mathematics. Whatever you think of the more prosaic statement of addition applies as well to the less obvious statement of simple equality.
There. Hopefully that avoids all the highbrow stuff I’m not equipped to argue.
Yes, for nuts and bolts engineering, they are equivalent. Although that’s really not the same as “true.” Probably not even for engineering, really. But in nuts and bolts engineering, something like .9999999 even without the … is the same as 1. You really couldn’t measure or make something to precisely .9999999 length or width or something, no matter how hard you tried. You would end up with .99999990000001 or ..99999989999 or something.
Which is also something I pointed out earlier. You couldn’t measure or make something exactly 1″ wide no matter how hard you tried. You would actually get .9999999897874 or 1.0000001192982 or something. Which is part – perhaps the main part – of why numbers/math are a descriptive language, not Reality.
But it is. Do you accept that ⅓ is represented as the infinitely repeating 0.333333…. ? (From grade school, for most Americans.) Let me boil the rest down to grade school level:
Take both sides and multiply by 2, yielding ⅔ and 0.666666…. All those repeating ‘3’s become ‘6’s, right?
Now multiply instead by 3, yielding 3/3 and 0.999999…. All those repeating ‘3’s become ‘9’s. See? Basic multiplication still. And we also know that 3 divided by 3 is 1. Meaning 0.999999… really–really and truly–equals 1.
You can also do the same exercise with ⅑ times 2, 3, 4,… , 9, where that 9/9 again equals 1.
The issue here is that decimals can only represent fractions having denominators factoring into 2 and/or 5 to have a terminating decimal representation. All other fractional denominators will repeat infinitely. Grade school, still. You can multiply such repeating decimals by the denominator involved and you get a whole number, even if you are still showing it as a repeating ‘9’s. It is a visual quirk that (obviously) troubles some people, but has no bearing on the reality of the numbers involved.
KE, I’m just going to pause to point out that you are digging a hole, albeit digging with grace and a charming enthusiasm. This isn’t some fringe or cutting edge bit of math theory, just an odd little detail of mathematical reality. It isn’t a situation in which saying “that doesn’t make sense, so it shouldn’t be that way” is a winning strategy.
I remember getting into an argument with my college roommate my freshman (i.e., only) year of school. I was tutoring him on calculus, since I’d had it and he hadn’t — and he was a physics major who needed to know the math. We got onto the subject of torque, and I remember us arguing vehemently and long into the night about it, with me taking the (mistaken) view that the universe couldn’t possibly care about left versus right, that it must be symmetric, and him patiently (though probably with dwindling patience as the wee hours waned) pointing out that, whatever I thought about it, the universe appeared to “care” quite a lot.
He went on to get his Ph.D. in atmospheric physics and work for NASA before becoming something vague and spooky in the defense contracting business. (His briefcase doesn’t have to go through the TSA scanner, for some reason.) I went on to raise kids and write software, and wonder why I ever thought I should try to disprove established physical principles late one night in my first (and, again, only) year of college.
Anyway. the math is right on this one.
I’m quite familiar with that kind of stuff. I mentioned early on that I can “prove” both that 2/3 + 1/3 does, or does not, equal 1. The point being, as I’ve also covered more than once, that numbers/math are just a language for describing reality/the universe, but math/numbers are NOT The Universe itself. And like other languages, it has definitions, and flaws… This is one of them.
The math is just a language to describe the universe, it is NOT The Universe itself. It has flaws like any other language. This is one of them.
No, you are moving the goalposts. You very clearly asserted, multiple times, that 0.999999… was not mathematically equal to 1. And compounded the error by mixing up real, rational, and irrational numbers. Philosophical considerations of the universe were not in play. You are arguing in bad faith when shown to be wrong in a fundamental way. I think you owe Henry an apology for switching the argument to a strawman.
No, no apologies needed. This is a fun exercise in argumentation.
But you’re right about moving the goalposts. And KE, you don’t really have a proof that 2/3 = 1/3 doesn’t equal 1. ;)
The problem is, due to the vagaries that come with any human construct, you can use the “cracks” in math to make it LOOK LIKE .999999… is the same as 1. In a way it’s the same order, but only a different degree, of “6 is an even number, but 6 is an odd number of legs for a horse.”
Years ago – decades now, really – when I lived in Oregon, I was in a group of friends who would play board games, go to book stores, etc. One of us was a math Ph.D. Every now and then – maybe it was right after he’d made some great “discovery,” I don’t know – he would start “waxing poetic” about how perfect math was, math is the universal language, etc etc. Finally one of us – I don’t remember if it was me, or one of the others – said “Okay, Gary. Great. Math is the universal language. You see that girl over there with the pretty eyes? Go tell her she has pretty eyes. Tell her she has pretty eyes using MATH, Gary.”
Ok, then. I’ll take your approach to being wrong into account in the future.
My favorite bit of math misdirection is the statement that “all prime numbers are odd.”
(Unfortunately, most people don’t bother to try to correct it.)
That bit might have been included in the 6 legs for a horse bit, I don’t remember exactly how it went. (There is no need to remember it exactly.)
Oh, but I’ll tell you!
A: “All prime numbers are odd.”
B: “Wait. What about two? Two is prime, and it’s even.”
A: “That makes it the oddest prime of all.”
Ba dum.
Sounds familiar… :-)
Also this:
https://www.youtube.com/watch?v=iuumnjJWFO4&t=127
Henry, Here is my argument against AGW.
https://ricochet.com/215897/archives/better-way-forward-climate-change/#comment-2576008
Humor + math geeks = tragedy.
In other words, an infinitely small quantity is no quantity at all, but people who know more math than I do will say that a number is not necessarily a quantity? One premise of my argument is false according to them? (And you don’t like them very much.)
Mathematical realism? Numbers are not the universe, but they do exist. It’s a very respectable metaphysics. I explain why in “I Think Numbers Exist.” Link on my profile page.
No, that’s why our perception of numbers is not the same thing as physical reality. But perception isn’t reality, and not all reality is physical.
So, maybe all quantities are – or at least, as my argument might be, CAN BE REPRESENTED BY – numbers, but not all numbers are quantities. That kind of thing happens in a lot of places, shouldn’t be a surprise that it crops up here too.
Well, you might have an argument for it, but I wouldn’t buy it. Numbers are something humans basically created to help describe “Life, The Universe, And Everything” but I think it’s some kind of ecclesiastic sophistry or something, to claim that numbers exist independently.
And if the only alternative is to define math and geometry as branches of psychology, you’re ok with that?
Well, if your view is that not all numbers are quantities, you should have just said so. I’ve been spelling out the argument for you and asking what your view is for awhile now. All you had to do was read and answer: You disagree with the first premise of my argument in # 188.
What did we create? What do you think numbers are?
A way to measure quantity and to measure comparisons.
Like if you wanna give me 9.999999…% of something and I want the full 10.
So on this theory of yours the quantities themselves exist independently of our perceptions?
And the number 10 does exist? But it’s only a thing we invented–the number 10 itself has less to do with those mind-independent quantities than with, say, a yardstick, or for that matter with the English word “ten”?
Philosophically speaking, the number “ten” is a mere concept.
Right now, my dog is having another false pregnancy. The nest under the picnic table is filled up with leaves and a blanket she has dragged up there, as she puts together the birth center to be with great determination.
I have no idea if she expects one puppy in that imaginary litter, or ten.
But if during some time period in the future, she has a fence-scaling coyote lover sneak in to the yard and bring her empty womb to fruition, ten puppies would be all too real for me. (And possibly for her too.)
So why not answer my questions? Do the quantities of things like puppies exist independently of our minds? And are numbers things more like words or yardsticks than like those quantities?
Well, that exception is the only case where X * X = X + X ≠ X – X. After all, a prime is divisible only by itself and one, and odd numbers are not divisible by two.
The real interesting question is whether 1 is prime, because it is certainly not composite.
Obviously, quantity exists. More than or less than is something which does not need to be taught. It is instinctual to be able to detect 3 items are “more” than 1 item and less than 10 items. There are certain effects that will only occur when a quantity is more than some value.
Now, all quantities are determined by comparison with a singular exception: absence. Nothing / 0 is something that clearly is describable. If you have absence or 0, you can define a number line and arithmetic.