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naraburns  nihil supernum  2yr ago (text post)   30744 thread views

Culture War Roundup for the week of November 21, 2022

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Just to pick up on one aspect of this, I completely agree about the importance of having decent Fermi estimation skills, and it’s something you can definitely train. I’m continually amazed at how many people don’t have basic frames of reference for things like populations, money, timescales, distances, etc..

I remember hearing a prominent philosophy academic once say in a talk that “octopuses evolved 500 billion years ago”. I assumed it was a slip of the tongue, but then she gave the same talk a month later and made exactly the same mistake. I assume she read “500 million” somewhere and it got transmuted to “500 billion” in her head, but jeez, you should be instinctively sanity-checking and filtering that stuff in your head (“are octopuses an order of magnitude more ancient than the universe itself?”).

In the interests of fun, here’s one of my favourite (paired sets of) Fermi questions for the sub.

(1) Imagine our sun as the size of a baseball located in New York. Mutatis mutandis, how far away would the nearest star (Proxima Centauri) be?

Answer: about 2000km (approximately the distance from NYC to Oklahoma City).

Reasoning: Proxima Centauri is 40,208,000,000,000 km away. Our sun is 1,392,700 km in diameter, so it would take approximately 28 million suns in a line to reach to Proxima Centauri. A baseball is approximately 7cm in diameter, and 28 million baseballs would stretch approximately 2000 km.

(2) Imagine our galaxy as the size of a dinner plate (again let’s say in NYC). Again mutatis mutandis, how far away would the nearest galaxy (Andromeda) be?

Answer: about 7.5 metres away!

**Reasoning: the Milky Way is approximately 100,000 light years in diameter. Andromeda is approximately 2.5 million light years away, so it would take 25 Milky Ways stacked end to end to reach it. A large dinner plate is approximately 30cm in diameter, so 25 of them stacked end to end would extend 7.5m.

My surprised upshot: compared to interstellar distances, galaxies are unbelievably close to each other!

octopuses evolved 500 billion years ago

According to the 15 seconds I spent on Wikipedia, octopuses evolved 155 million years ago, so you can't even fix it by flipping a bit

My Fermi estimate of (1) before looking at the answer:

  • Proxima Centauri is 4 light years away

  • Speed of light is 300 million meters

  • There are 365 * 24 * 60 * 60 seconds in a year

  • The Earth is roughly 20,000 km thick. idk how big the sun is but maybe 100x bigger (by length) so let's say 1 million km

  • A baseball is roughly 0.1 m

Therefore the scaled-down Proxima Centauri would be a distance away equal to

4 light years * # seconds per year / size of sun * size of baseball / meters per km


= 4 * 365 * 24 * 60 * 60 * 3e8 / 1e9 * 0.1 / 1000

= 3784 kilometers

I didn't do (2) because I didn't see it until after I looked at the answer for (1).

(1)

Earth circumference c. 40,000 km (from original definition of meter).

Sun c. 100x size of Earth -> 4,000,000 km -> 4e9 m.

Guess size of baseball c. 1 foot circumference? 40 cm? 4e-1 m.

Ratio c. 10 orders of magnitude.

Proxima Centauri distance = 4.3 ly.

c. 500,000 minutes per year -> 2e6 light-minutes -> 120e6 or 1.2e8 light seconds.

c c. 300,000 km/s -> 300,000,000 m/s -> 3.6e16 m

Apply ratio -> 3.6e6 m -> 3.6e3 km -> 3600 km -> continent scale

Los Angeles?

(2)

Milky Way diameter c. 100,000 ly

Andromeda distance c. 2,000,000 ly

Ratio c. 20:1

Still in New York.

I'm going to type out my unfiltered thoughtprocess. And not use a calculator or spend more than 30 seconds per problem because that would be against the Spirit of Fermi estimation.

(1) Imagine our sun as the size of a baseball located in New York. Mutatis mutandis, how far away would the nearest star (Proxima Centauri) be?

  • I know that the sun is 150*10^6 km away and the nearest start is 4 lightyears away. So it would be cheating.

  • But fuck that, I know it takes light 8 minutes to reach The Sun and 4 years to reach the nearest star.

  • So 8 minutes to 4 years is one ratio, and baseball and the sun is the other ratio.

  • Wild out of my ass guess would be the ball is outside the atmosphere of earth.

Revelation: Annnddd I was wayyy off. By an order of magnitude.

(2) Imagine our galaxy as the size of a dinner plate (again let’s say in NYC). Again mutatis mutandis, how far away would the nearest galaxy (Andromeda) be?

  • I know Andromeda is 2*10^6 light years away.

  • Repeat the same process as before.

Revelation: Wild overestimate again. Off by many orders of magnitude.

I need to get better at intuiting ratios.

Also, a persons Fermi estimating abilities are a very good indicator of how much they read as a child. Serious.

Many of the intuitions such as astronomic distances, evolutionary timelines, depth of natural features like the oceans are things I learned straight out of my middle school textbooks or Children's encyclopedias.

I know it takes light 8 minutes to reach The Sun and 4 years to reach the nearest star.

Sounds like you are treating the baseball as the size of the earth's orbit around the sun, rather than the size of the sun itself. But that would give you an answer that's too small rather than too big so idk how you got your answer.

So 8 minutes to 4 years is one ratio, and baseball and the sun is the other ratio.

I am confused about your reasoning here...are you calculating (4 years / 8 minutes) * (radius of baseball / radius of sun)? That would give you a unitless value, not a distance. I think you were using the wrong values in your calculation but I can't tell what you were using.

You are right, I goofed by taking the distance from earth to the sun instead of the size of the sun. The answers being even remotely a few orders of magnitude away is a coincidence.

I feel like the magnitudes involved in interstellar and intergalactic distances are so vast that it's not really a mark against your intuition that you find it difficult to wrap your head around. For everyone that isn't an astronomer it's really just trivia anyway.

Whereas people work with and talk about money all the time, so I think people should be expected to have better intuition in that regard.

I didn't realize either how close galaxies are to each other compared to stars within galaxies to each other. I overestimated both, with "Los Angeles" for 1 and "Boston" for 2, but 1 was only off by about a factor of 2, while 2 was off by a factor of at least 10, probably at least 50.

“are octopuses an order of magnitude more ancient than the universe itself?”

Iä! Iä!

“are octopuses an order of magnitude more ancient than the universe itself?”

"Yes. I refuse to elaborate."

The drama of creation, according to the Hawaiian account, is divided into a series of stages, and in the very first of these life springs from the shadowy abyss and dark night... At first the lowly zoophytes and corals come into being, and these are followed by worms and shellfish, each type being declared to conquer and destroy its predecessor, a struggle for existence in which the strongest survive. Parallel with this evolution of animal forms, plant life begins on land and in the sea--at first with the algae, followed by seaweeds and rushes. As type follows type, the accumulating slime of their decay raises the land above the waters, in which, as spectator of all, swims the octopus, the lone survivor from an earlier world.

-- Roland Dixon, Oceanic Mythology, 1916

Turns out, it isn't turtles all the way down, it's octopuses.

I'd say "if you wish to know more, I would refer you to the works of my colleague Abdul Alhazred".

My surprised upshot: compared to interstellar distances, galaxies are unbelievably close to each other!

Is that generalizable, or does it only apply to Andromeda and the Milky Way? Because the latter does not surprise me - anyone remotely interested in astronomy will have heard of the impending collision - but the former does!

It can’t be inferred from the calculation I provided, of course, but apparently the average distance between galaxies is just 1 million light years, making the distance between the Milky Way and Andromeda greater than average! (although we also have the Magellanic Clouds for company, and they are MUCH closer to us)

I was also surprised by your Andromeda galaxy example and had to recheck. Turns out it actually is this big in the sky, I just need to move to a darker location. I then checked if it's only the local cluster (Milky Way, Andromeda and smaller friends) that is so close-packed, but even the next cluster over, M81, is "just" 12 megaly away, much closer to our galaxy than Proxima Centauri is to Sol.

Three hundred megabytes!

Yeah, I realise numbers are often used like that, but it still makes me wince at the sheer magnitude of the error. It’s not a mistake that an even vaguely numerate and scientifically informed person should make. It’s like saying “billions of people died in the Second World War”, or thinking a banana would cost $10.

Shakespeare lived around 1200 or something? Maybe 1930? 1600 BC?

Related to this, I'd often heard the fact that the time between Cleopatra and today is shorter than the time between Cleopatra and the building of the pyramids. I found that surprising at first, but then more recently I learned that Cleopatra was a contemporary of Caesar (i.e., she lived around 0 AD). At which point the fact became obvious to me—the pyramids are 5000 years old, Cleopatra lived 2000 years ago, of course 5000 - 2000 > 2000. My confusion came from "ancient Egypt = 5000 years ago, Cleopatra is ancient Egypt, therefore Cleopatra = 5000 years ago". Not sure if this makes me dumber or less dumb.

There's a status danger of looking like a trivia nerd. Instead, people want to be the visionary, big picture person.

I think there are a few competing memes that result in this.

  1. The superficial status risk to looking like a nerd.

  2. Implicit in the above is that, it's all book smarts with no actual smarts to back it up. Ignorant to the process that one has to be book smart first let that be through reading books or experience before one can actually be smart.

  3. The belief that the "big picture" is a thing of its own and not a collage of various smaller pictures.

I would classify all of the above as infohazards. I can only shudder at the amount of things people didn't learn because they fell for any of the above, and the collective loss as a result of that.

The older I get the more wisdom I see in the old Egyptian character for a large number sometimes presented as one million, it was a guy throwing his hands up as if exclaiming how could there even be this many things. That seems to be about where most non math people just stop worrying about numbers.

Same with the Mandarin word for "a big number" being translated as 10,000 (IIRC it literally means 10,000 in Mandarin).

I guess this is what leads to people thinking $500 million dollars is enough to make every American a millionaire.

Or my favorite recently, that charging every American a $1 per Capita head tax would in any way be a revenue raiser instead of a symbolic gesture.

The look on his face as I sketched out how little and narrow a wealth tax on fortunes above $1bn would be necessary to raise that same amount.

What you are doing is not estimation it is calculation. If you know the facts you need not estimate. The tricky part is if you don't know all of them.

If I ask you: The closest star to the sun is 4 light years away, the whole of milky way is 100000 light years wide, It has 100 billion stars, galaxies tend to cluster in the grand scale of things. Estimate how far Andromeda is. What will be your answer and why?

Of course, the answers I provide here are calculations, and anyone can do that; the challenge I’m posing is for readers to come up with mental estimates which they can check against the calculations to see if they got within an OoM.

No one has any normal references for galaxies and how far/close they are to each other which makes this just a calculation.

I can make references on things associated with daily life or general knowledge. These things don’t fit those areas.

Like most who commented I was very surprised about galaxies being that close. Thanks for the info. But I have no idea how that was supposed to test my estimation skills tbh. It's clearly not common knowledge.

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