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luzulaAt the moment I am really annoyed with people who base their argument on the exponential function without actually understanding it. I bring you these examples, which are based on opposite misunderstandings:
1) I am currently writing a response to a government report, which touts "sustainable growth" as something they tacitly assume is possible. By this they mean an economy which grows by a few percent a year (i e exponentially), while the ecosystems of which we are a part remain diverse and functional. They do not make an argument for why they think this is possible. An economy is based on physical resource use, among others the use of ecosystem production, which cannot grow exponentially. Some make the argument that you can decouple economic growth from physical resource use, which, sure, that is probably possible to some extent. But the point of the exponential function is that it is not enough to reduce physical resource use per economic unit to 50%, or 30%, or whatever. That would only delay the exponentially growing resource use, not stabilize it on a constant level. To do that you would need to exponentially decouple economy from resource use, i e physical resource use per economic unit would need to asymptotically approach zero. They do not make the argument that this is possible, which to me says that they do not understand the exponential function. Or they do and they're ignoring it because that's more comfortable.
2) My second example is one of those people who say that the Singularity (i e an intelligence explosion of AI) is coming. He said that so far, processor speeds have doubled about every two years (Moore's law). This is an exponential growth. Then he drew a graph which had a vertical asymptote at some time T in the future (that is, the value of the function approached infinity as t approached T), and said that was when the Singularity would come. No!! Exponential functions do not have vertical asymptotes! His misunderstanding is the opposite of the first one--in the example above, it would be the equivalent of saying that if the economy grows by a certain percentage every year then there will be an infinite amount of money in 2100 (or whenever).
(I do not actually have an opinion on whether the Singularity will come--actual serious arguments for that do not rely on his misunderstanding. I mean, it could be that it's enough to reach a certain [fast] processing speed, and that combined with self-improving code could quickly make AI more intelligent than humans.)
1) I am currently writing a response to a government report, which touts "sustainable growth" as something they tacitly assume is possible. By this they mean an economy which grows by a few percent a year (i e exponentially), while the ecosystems of which we are a part remain diverse and functional. They do not make an argument for why they think this is possible. An economy is based on physical resource use, among others the use of ecosystem production, which cannot grow exponentially. Some make the argument that you can decouple economic growth from physical resource use, which, sure, that is probably possible to some extent. But the point of the exponential function is that it is not enough to reduce physical resource use per economic unit to 50%, or 30%, or whatever. That would only delay the exponentially growing resource use, not stabilize it on a constant level. To do that you would need to exponentially decouple economy from resource use, i e physical resource use per economic unit would need to asymptotically approach zero. They do not make the argument that this is possible, which to me says that they do not understand the exponential function. Or they do and they're ignoring it because that's more comfortable.
2) My second example is one of those people who say that the Singularity (i e an intelligence explosion of AI) is coming. He said that so far, processor speeds have doubled about every two years (Moore's law). This is an exponential growth. Then he drew a graph which had a vertical asymptote at some time T in the future (that is, the value of the function approached infinity as t approached T), and said that was when the Singularity would come. No!! Exponential functions do not have vertical asymptotes! His misunderstanding is the opposite of the first one--in the example above, it would be the equivalent of saying that if the economy grows by a certain percentage every year then there will be an infinite amount of money in 2100 (or whenever).
(I do not actually have an opinion on whether the Singularity will come--actual serious arguments for that do not rely on his misunderstanding. I mean, it could be that it's enough to reach a certain [fast] processing speed, and that combined with self-improving code could quickly make AI more intelligent than humans.)
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Date: 2016-10-28 01:47 pm (UTC)Even more amusingly, Moore's Law actually talks about transistor density, but it used to be that "transistor density" and "clock rate you can run" were very closely correlated. But it has, from what I understand, started slowing down. We're approaching a point where, if you want more computational power, you have to provide more computational substrate (basically, "more cores"). Barring, of course, new advances in chip manufacturing.
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Date: 2016-10-28 02:47 pm (UTC)I didn't even talk about his assumption that Moore's Law would continue to be true in the future, but yeah, his argument also rests on that, of course. I don't know enough about computer hardware to be able to judge how long it can continue to be true. Interesting that it seems to be slowing down.
(no subject)
Date: 2016-10-28 02:55 pm (UTC)(no subject)
Date: 2016-10-28 07:58 pm (UTC)(no subject)
Date: 2016-10-28 10:08 pm (UTC)(no subject)
Date: 2016-10-28 09:25 pm (UTC)Apparently a lot of people find math extremely tiring.
(That is not an excuse.)
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Date: 2016-10-28 10:12 pm (UTC)I don't mind if random people on the street don't understand the exponential function--it's just people who are basing an argument on it and portraying themselves as experts.
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Date: 2016-10-28 09:48 pm (UTC)(no subject)
Date: 2016-10-28 10:13 pm (UTC)