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Fantastic! A rigorous explanation (thank you). So you are saying that the mixtures of weather distributions are stable but the individual distributions can shif

Fantastic! A rigorous explanation (thank you). So you are saying that the mixtures of weather distributions are stable but the individual distributions can shift. I gotta think about that and dont know enough about weather distributions or probability to understand why climate (the mixtures) can be stable but individually weather cannot.

jfengel 6y ago
Weather is unstable because you need to know many factors (temperature, humidity, cloud cover, etc) over every single piece of land and water (over many different terrains). And those are unstable minute by minute. To report the weather, you need a moving weather map. By contrast climate is "simple" in that it can have fewer variables. The most basic climate model is literally zero-dimensional: it treats the earth as a homogeneous gas mixture and that's it. It can be reported in a single variable, the temperature. The zero-dimensional model won't tell you all of the things that happen: some places get more rain, some less, some even get cooler. There are more complicated models that do that, and to make specific policy recommendations you need those. But there is a crucial discussion that comes from that single number: yes, the world is getting warmer, because of humans turning carbon in the ground into CO2 in the atmosphere, and it's bad enough that action needs to be taken. The model is still unstable, but much more tightly constrained, to within a fraction of a degree C per year. That's because the atmosphere is so large, and the sheer mass of it means it has to change slowly, but predictably. Over very long scales (tens of thousands of years) additional factors create more instability, but they're not pressing problems the way highly predictable century-scale changes are.
6gvONxR4sf7o 6y ago
Consider the distribution of places you spend your time during peak shelter in place. It was probably mostly at home. Your bedroom, the kitchen, the bathroom, and occasionally going out to the store. Take the math out of it for a second. I’m not nearly smart enough to predict which room you’ll be in during a specific minute of a specific day. Predicting that you’re going to be hungry at exactly 12:42 and you’ll go to the store this Sunday at 9:21 is well beyond me. But I could be much more accurate if I abstract it a bit to a few important properties. During shelter in place, you probably spend 25-35% of the time asleep, maybe 0.1-0.5% at the store (once every 1-3 weeks maybe), etc. I can even confidently predict that as shelter in place relaxes, you’ll likely go out more often, but probably still very rarely to the grocery store more than twice per week. Your precise movements are impossible to accurately predict more than a few moments out, but their distribution from one day to the next during shelter in place is pretty stable. On a longer timescale, that distribution will shift once shelter in place lifts, and it’s even reasonable to predict how it’ll change. Another timely analogy might be modeling specifically who has COVID-19 at a point in time versus modeling the distribution. The percent of people in a place who have it is the distribution in question here: the probability that any given person there has it is a simple distribution over true or false. There’s no question of stability over time here because it’s a distribution over people instead of time. You can model how that spreads over time and location so much more easily than predicting the specific individuals who will get it and transmit it.

jfengel 6y ago

Weather is unstable because you need to know many factors (temperature, humidity, cloud cover, etc) over every single piece of land and water (over many different terrains). And those are unstable minute by minute. To report the weather, you need a moving weather map. By contrast climate is "simple" in that it can have fewer variables. The most basic climate model is literally zero-dimensional: it treats the earth as a homogeneous gas mixture and that's it. It can be reported in a single variable, the temperature. The zero-dimensional model won't tell you all of the things that happen: some places get more rain, some less, some even get cooler. There are more complicated models that do that, and to make specific policy recommendations you need those. But there is a crucial discussion that comes from that single number: yes, the world is getting warmer, because of humans turning carbon in the ground into CO2 in the atmosphere, and it's bad enough that action needs to be taken. The model is still unstable, but much more tightly constrained, to within a fraction of a degree C per year. That's because the atmosphere is so large, and the sheer mass of it means it has to change slowly, but predictably. Over very long scales (tens of thousands of years) additional factors create more instability, but they're not pressing problems the way highly predictable century-scale changes are.

6gvONxR4sf7o 6y ago

Consider the distribution of places you spend your time during peak shelter in place. It was probably mostly at home. Your bedroom, the kitchen, the bathroom, and occasionally going out to the store. Take the math out of it for a second. I’m not nearly smart enough to predict which room you’ll be in during a specific minute of a specific day. Predicting that you’re going to be hungry at exactly 12:42 and you’ll go to the store this Sunday at 9:21 is well beyond me. But I could be much more accurate if I abstract it a bit to a few important properties. During shelter in place, you probably spend 25-35% of the time asleep, maybe 0.1-0.5% at the store (once every 1-3 weeks maybe), etc. I can even confidently predict that as shelter in place relaxes, you’ll likely go out more often, but probably still very rarely to the grocery store more than twice per week. Your precise movements are impossible to accurately predict more than a few moments out, but their distribution from one day to the next during shelter in place is pretty stable. On a longer timescale, that distribution will shift once shelter in place lifts, and it’s even reasonable to predict how it’ll change. Another timely analogy might be modeling specifically who has COVID-19 at a point in time versus modeling the distribution. The percent of people in a place who have it is the distribution in question here: the probability that any given person there has it is a simple distribution over true or false. There’s no question of stability over time here because it’s a distribution over people instead of time. You can model how that spreads over time and location so much more easily than predicting the specific individuals who will get it and transmit it.