A useful skill not often taught is doing back of the envelope calculations, so called because they can be, sometimes are, done on the back of an envelope destined for the waste basket. The idea is to use approximate data and approximate models to try to get the right answer to a question to within about a factor of ten in either direction.
This is a good skill. But it's easy to pick the wrong numbers.
Let's take your computation about housing vs farmland. Your calculation has some implicit assumptions.
1) All land is created equal. In fact some land is good for farming; some is meh; some is useless. It's common to claim that housing is being preferentially sited on good farmland, not on barren areas. Should the denominator be the amount of potential good farmland in the US, not the total land area?
2) My house is about 1200 square feet, but it comes complete with a decent sized lot, which in typical modern fashion contains lawn, flowers, etc. It also comes complete with road access. So my two person household (in what was once prime farming country) consumes notably more than 600 square feet of potential farm land per person. This is not at all uncommon, though balanced somewhat by those living in multi-story buildings. I'd say this might substantially increase your numerator.
Note that I'm not saying "OMG, we're running out of farmland" - just that your estimates is way too low.
I'd be unsurprised if it were off by more than a factor of ten. But on the other hand, I'd also be unsurprised if it were off by somewhat less.
I was explicitly calculating only land occupied by housing, not including the rest of uses in residential communities.
I am not sure whether you are correct that land for housing is preferentially located on good farming land — I wouldn't want to farm in San Francisco — but if it is that is evidence that farming land is not sufficiently scarce to discourage its use for other purposes.
Population of New York City is 8,550,405 over a land area of about 782 square km. If the world's 7,400,000,000 people lived in one area with the same population density, it would have an area of about 676,819 square km, slightly larger than the country of Myanmar. The world's total land area is 148,900,000 square km, so this megacity would represent about 0.45% of the total land area. (Note that this total area includes Antarctica, which is largely uninhabited.)
May we re-visit the risks for an asteroid strike, in comparison to and informed by discussions of "global warming" ? I agree with the Siberian strike as the "pure physics" case, but as with notions of AGW it seems to me the model may usefully consider secondary consequences.
So what are the chances and magnitude of "feedbacks" after a strike? Does a strike near a fault line trigger earthquakes, for instance? Does an ocean strike create tsunami waves? Does a previously undetected asteroid, passing over a continent, resemble an ICBM, and does a strike resemble an nuclear attack? What are the costs to the civilizational "grid" of powerlines, pipelines, railroads and river routes if a big crater is imposed into the middle of the map?
Create a global model of "grid cells" as is done for climate. Some cells are, like the Siberian Arctic, able to absorb a strike with minimal consequences. Is most of Earth's surface "Siberian"? (Which seems to be the underlying assumption on the back of your envelope...) Other parts of the globe -- like a cell centered on the German Rhine river -- might have maximal consequences. How many are such? Does it shut down the entire EU (China, US...), or just degrade the continental economy by some fraction? What percent of the cells are logistic-critical? Strikes in the ocean are more probable than those on land, but strikes on the fault lines of the so-called Pacific "Ring of Fire" arguably are the most likely to trigger follow on catastrophes of quake and waves. What percentage of ocean "cells" are most at risk?
Actually, I'm not asking you to do this calculation, and certainly not on the back of an envelope. I know I can't, certainly not even fully empowered with Google Maps and Microsoft Excel. But it irks the hell out of me that physicists so vocal about Global Warming have never, to my knowledge, talked to mass media and political figures about the chances and costs of an asteroid impact versus the costs of a space program to detect and deflect such potential rocks.
On the food comment, I've had a really really hard time personally making meal plans that actually end up with the correct macros and micros on reasonable budgets
Basically my challenge to you and any reader (I'll put up money probably ~100, I'll pay you in cash if you think that's better ) is to come up with the cheapest meal plan you can that statisfie's the following conditions
1. Contains 2200-2300 calories
2. Meets the recommended daily amounts of vitamins/minerals/omega3/omega 6s/fiber (determined by chronometer for a 155 pound man)
3. Has at least 130 grams of protein
I should mention 3 asterisks
1. because many multivitamins are scams with bad bioavailability and checking them manually is too hard I ban multivitamins even though I wish I could accept them.
2. if you come out under on the calorie total I can just add fried dough in soybean oil if you need more calories. Focus on the micros/protein.
...One reason people overestimate population density is that they form their opinion based on what they see around them...
This holds for lots of topics. Environmentalists are mainly big-city people, who may view the world as tiny areas of green surrounded by concrete. Or Black nationalists, who imagine they have enough power to carve themselves out their own country somewhere in the USA. After all, where they live, it's mostly black people, so they might grossly overestimate their numbers. It's hard to overcome mental blinders. I try to imagine my own.
On the contrary, it is a way of using arithmetic to check your intuitions, in particular to see if they are wildly wrong.
For a simple example, what is your intuition for the average population density of the US? My guess is that, for many people, it is wildly high. For per capita water consumption (all uses)? My guess is, for many people, the estimate would be wildly low.
It's bad enough when people take real statistics and mess them up. Fermi estimating seems to be mostly used by smart people to "prove" that they're probably right.
Let's Fermi estimate the amount of time the average person spends with their kids over the course of a year.
You can look up some sort of statistics, like free time total of workers, then substract from reported parents time.
Or, you could Fermi estimate the opposite way. Ask the people around you how much time they spend with their kids, and extrapolate from there. You'd probably get two very different answers, and neither of them would be particularly interesting or true.
Except perhaps for anonymization purposes on the internet. That's the one thing I use it for
This is a good skill. But it's easy to pick the wrong numbers.
Let's take your computation about housing vs farmland. Your calculation has some implicit assumptions.
1) All land is created equal. In fact some land is good for farming; some is meh; some is useless. It's common to claim that housing is being preferentially sited on good farmland, not on barren areas. Should the denominator be the amount of potential good farmland in the US, not the total land area?
2) My house is about 1200 square feet, but it comes complete with a decent sized lot, which in typical modern fashion contains lawn, flowers, etc. It also comes complete with road access. So my two person household (in what was once prime farming country) consumes notably more than 600 square feet of potential farm land per person. This is not at all uncommon, though balanced somewhat by those living in multi-story buildings. I'd say this might substantially increase your numerator.
Note that I'm not saying "OMG, we're running out of farmland" - just that your estimates is way too low.
I'd be unsurprised if it were off by more than a factor of ten. But on the other hand, I'd also be unsurprised if it were off by somewhat less.
I was explicitly calculating only land occupied by housing, not including the rest of uses in residential communities.
I am not sure whether you are correct that land for housing is preferentially located on good farming land — I wouldn't want to farm in San Francisco — but if it is that is evidence that farming land is not sufficiently scarce to discourage its use for other purposes.
Population of New York City is 8,550,405 over a land area of about 782 square km. If the world's 7,400,000,000 people lived in one area with the same population density, it would have an area of about 676,819 square km, slightly larger than the country of Myanmar. The world's total land area is 148,900,000 square km, so this megacity would represent about 0.45% of the total land area. (Note that this total area includes Antarctica, which is largely uninhabited.)
May we re-visit the risks for an asteroid strike, in comparison to and informed by discussions of "global warming" ? I agree with the Siberian strike as the "pure physics" case, but as with notions of AGW it seems to me the model may usefully consider secondary consequences.
So what are the chances and magnitude of "feedbacks" after a strike? Does a strike near a fault line trigger earthquakes, for instance? Does an ocean strike create tsunami waves? Does a previously undetected asteroid, passing over a continent, resemble an ICBM, and does a strike resemble an nuclear attack? What are the costs to the civilizational "grid" of powerlines, pipelines, railroads and river routes if a big crater is imposed into the middle of the map?
Create a global model of "grid cells" as is done for climate. Some cells are, like the Siberian Arctic, able to absorb a strike with minimal consequences. Is most of Earth's surface "Siberian"? (Which seems to be the underlying assumption on the back of your envelope...) Other parts of the globe -- like a cell centered on the German Rhine river -- might have maximal consequences. How many are such? Does it shut down the entire EU (China, US...), or just degrade the continental economy by some fraction? What percent of the cells are logistic-critical? Strikes in the ocean are more probable than those on land, but strikes on the fault lines of the so-called Pacific "Ring of Fire" arguably are the most likely to trigger follow on catastrophes of quake and waves. What percentage of ocean "cells" are most at risk?
Actually, I'm not asking you to do this calculation, and certainly not on the back of an envelope. I know I can't, certainly not even fully empowered with Google Maps and Microsoft Excel. But it irks the hell out of me that physicists so vocal about Global Warming have never, to my knowledge, talked to mass media and political figures about the chances and costs of an asteroid impact versus the costs of a space program to detect and deflect such potential rocks.
On the food comment, I've had a really really hard time personally making meal plans that actually end up with the correct macros and micros on reasonable budgets
Basically my challenge to you and any reader (I'll put up money probably ~100, I'll pay you in cash if you think that's better ) is to come up with the cheapest meal plan you can that statisfie's the following conditions
1. Contains 2200-2300 calories
2. Meets the recommended daily amounts of vitamins/minerals/omega3/omega 6s/fiber (determined by chronometer for a 155 pound man)
3. Has at least 130 grams of protein
I should mention 3 asterisks
1. because many multivitamins are scams with bad bioavailability and checking them manually is too hard I ban multivitamins even though I wish I could accept them.
2. if you come out under on the calorie total I can just add fried dough in soybean oil if you need more calories. Focus on the micros/protein.
3. please also don't have red bars on cronometer
...One reason people overestimate population density is that they form their opinion based on what they see around them...
This holds for lots of topics. Environmentalists are mainly big-city people, who may view the world as tiny areas of green surrounded by concrete. Or Black nationalists, who imagine they have enough power to carve themselves out their own country somewhere in the USA. After all, where they live, it's mostly black people, so they might grossly overestimate their numbers. It's hard to overcome mental blinders. I try to imagine my own.
I've seen the term Fermi calculations.
I'll be honest - it seems to me a way of dressing up your intuitions with mathematics.
On the contrary, it is a way of using arithmetic to check your intuitions, in particular to see if they are wildly wrong.
For a simple example, what is your intuition for the average population density of the US? My guess is that, for many people, it is wildly high. For per capita water consumption (all uses)? My guess is, for many people, the estimate would be wildly low.
I'd rather say that I don't know.
It's bad enough when people take real statistics and mess them up. Fermi estimating seems to be mostly used by smart people to "prove" that they're probably right.
Let's Fermi estimate the amount of time the average person spends with their kids over the course of a year.
You can look up some sort of statistics, like free time total of workers, then substract from reported parents time.
Or, you could Fermi estimate the opposite way. Ask the people around you how much time they spend with their kids, and extrapolate from there. You'd probably get two very different answers, and neither of them would be particularly interesting or true.
Except perhaps for anonymization purposes on the internet. That's the one thing I use it for