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fractalman comments on Rationality Quotes July 2013 - Less Wrong
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Our PLANET is mind-numbingly big. If you don’t believe me go to the grand canyon and look down. Did I say go to the grand canyon? Make that HIKE to the grand canyon from yellowstone national park. Still not convinced? ROW across the ocean to china. Bonus points if you can hit Japan without a gps.
So in a twisted sort of sense, the milky-way galaxy is less mind-bogglingly big, because our [or at least my] built-in distance-comprehension hardware shorts out so quickly when attempting to deal with the milky way galaxy we don't really even notice it and so we switch to rigorous numbers which do not have this short-circuiting problem.
I think that shorting out effect is what is meant by "mind-bogglingly".
People have walked from yellowstone to the grand canyon. I couldn't do it myself, but I can read their accounts and understand them.
Earth is big, but our minds are amazed, not boggled. It's with the galaxy that we just start thinking "system error".
An easy way to bridge such distances is to construct a lot of intermediate steps. Take the Milky Way, containing 100 to 400 billion stars (let's take 250 billion). The problem of grasping 250 billion stars going off from just our sun is not too dissimilar from imagining someone with 250 billion dollars, going off from just 1. Lots of intermediate steps: So and so many dollars for a current generation smart phone, so and so many smart phones for, say, a villa, so and so many villas to buy, say, Microsoft. Of course different examples work differently well, but you get the picture, I suppose.
Incidentally, the number of US citizens is higher than the number of stars in the Milky Way in thousands, so if you find yourself a good way of visualizing the former, you can transfer that understanding to the latter, then just unpack the "thousand".
Nothing interesting, not even the size of our Hubble volume, is more than a couple dozen orders of magnitude away, which makes it -- in my opinion -- quite accessible even to our widdle bwains.
So, there are more than 100 billion US citizens?
Thanks for noting, corrected.
You're welcome.
To clarify:
The point is that a few orders of magnitude can be visualized / grasped just by adding another step to the ladder, chopping off only as large a step as you can take at a time.
Then even a whole lotta orders of magnitude just become a short sequence of steps, going off of concepts you find more familiar.
I often start with 10^3 as "number of students in my high school", I have a distinct image of some school photo in the school yard where everyone was on there. After that e.g. the number of images (each showing one yard-full of students) in a photo album. Number of photo albums that could fit in an Ikea shelf. Number of Ikea shelves in a library. Etcetera, though that alone should get you to 10^10 or so.
Suddenly the steep mountain slope has a stairway, and doesn't seem quite so daunting anymore.
Imagining grains of sand can get you to bigger numbers faster.
A couple dozen orders of magnitude of nearly anything will tend to stretch beyond human borders of intuitive comprehension in either direction.
A couple dozen orders of magnitude = 1 mole (roughly). The relationship between a single molecule and a handful of the macroscopic substance.
Yes, I can handle numbers in terms of orders of magnitude. But I challenge you to picture yourself the size of a molecule, sitting "on the floor", looking towards your real body, and visualize what you would see without doing any calculations.
I'm not sure what the thought experiment is. For me to be shrunk to the size of a molecule, all of the molecules I am made of would have to be shrunk, as would the light waves I see by, leaving my perception of my body unchanged. I don't think this is the scenario you mean, but I don't know in what way to change this to make it the one you mean.
I just meant in a semi-magical, non-physical way, only for visualising scale. Like a computer simulation of the world that scales up everything other than you twenty orders of magnitude, then uses some hacked-in rendering convention that lets you “see” without trouble from stuff like wavelengths.
Or if you want something more physical-like, imagine looking from “floor level” at a human statue 10 million light-years (relative to our c) in size, of correct proportions and colors (but no universe-crushing gravity), in a non-relativistic universe (to get around light-speed issues). Do you think you could tell the difference between that and a 10000 light-years one without seeing them side by side nor using instruments?
Then I'd see something like the ball-and-stick models that chemists build. We already know the shapes of molecules, and the photographs made of them in the last few years look just like that.
OK, sorry. It appears I’ve rolled a critical failure in communication :-)
I wasn’t referring to the small scale structure, just the ability to comprehend scale. Something like the way that when you’re at the foot of the mountain, the brain doesn’t really capture the difference between a 1km-tall and a 8-km tall one. Or how the distinction between a 10-story building and a 100-story one isn’t really manifest in the mind unless they’re side by side. Now take that and multiply both scales by enough orders of magnitude to span molecule-to-human scales.
Let me try a better example. Take this image. Without using symbolic math (i.e. actually figuring orders of magnitude and doing arithmetic with them), what can your brain do that simultaneously includes numbers of the scales “the width of one of the galaxy’s arms”, “the diameter of one of the stars” and “the height of a person on one of the planets”?
I mean, I don’t have to resort to math to know that ten people in a normal car would be crowded, or that a bucket of nails are hard to fit in a typical person’s pockets. I can have an intuitive comprehension (albeit inaccurate) of how much work might be needed to dig a small ditch. But I have no intuitive feel for similar problems posed at astronomical scales other than “intuition overflow, use math”. E.g., I’ve no chance of estimating the number of people needed to crowd just the solar system, let alone the galaxy, within a couple of orders of magnitude, unless I actually do at least a few back-of-the-envelope calculations.
Of course, a molecule is rather notoriously outside the scale of our ability to visualize; it's small enough that our hardwired understanding of how materials are supposed to behave simply cease to apply.
Would a photograph of one help?
It seems comprehensibly big. It would take between three and four years to walk around the Earth, walking for a sustainable number of hours at a reasonable pace every day, if you could walk around it in a straight line.
Walk on the surface of a sphere, in a straight line?
A straight line in elliptic geometry, presumably.
That's called a "geodesic". I'm not sure why they don't just call it a "line", but they don't.
[joke mode] congratulations, you just walked into the ocean. [/joke mode]
Now, about looking down at the grand canyon floor from the glass platform to engage your visual cortex?