Comment by sebmellen
7 days ago
The scale here is absolutely nuts to me. 86 billion nuclei represent only 29 picograms. One gram is 10^12 picograms.
1,000 billion billion gold nuclei per gram of gold.
7 days ago
The scale here is absolutely nuts to me. 86 billion nuclei represent only 29 picograms. One gram is 10^12 picograms.
1,000 billion billion gold nuclei per gram of gold.
The analogy I heard was that if you take a golf ball and enlarge it to the size of the Earth, the atoms in the enlarged golf ball would be about the size of the original golf ball.
It took me a while to understand this comment, because I imagined that scaling up a golf ball would involve creating new atoms, but what you said only makes sense if you are scaling up the individual atoms.
What you're saying is that the ratio of the size of an atom to the size of a golf ball is approximately the same as the ratio of the size of a golf ball to the size of the earth.
I'm surprised atoms are so big, I would have guessed much smaller.
The analog is no good because it assumes people have an intuitive understanding of the volume of the Earth, which basically 0 people do because it's stupidly absurdly counter-intuitive (like volume in general). So let's go for something way smaller. Imagine we take just one little 'cube' of Earth that's just 1 mile on each side. And let's start placing boxes in it that are 1 cubic foot in size, so about the size of a micro microwave. How many of these boxes would it take to fill our little cube? The math is simple, but the answer is no less stupefying or counter-intuitive. It's more than 147 billion!!
Ok. Imagine we take those cubes that filled our 'little' cube of earth and taped them in one giant stack. That stack would not only reach to the Moon, but reach to the Moon 116 times over! In fact you'd be nearly able to reach Mars at its closest approach (34.8 million miles, vs 27.8 million miles for our box stack). And that's in 1 cubic mile of volume. The volume of Earth is about 260 billion cubic miles. To wrap up by getting back to golf balls - you can fit about 700 golf balls in 1 cubic ft.
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Actually a somewhat macabre example came to mind. How many humans could we fit in our little cubic mile? And the answer is literally all of us, many times over in fact! And that's in just one cubic mile of the 260 billion total on Earth.
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> I'm surprised atoms are so big, I would have guessed much smaller.
Me too. Perhaps what we should realise is not how big atoms are, but how small we are. I wonder if life can be sustained at larger scales. Could we have galaxy-sized lifeforms that make us look like bacteria?
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But that comment is about atoms, while ALICE is talking about nuclei, which are way smaller than atoms. Not sure what would be the analogy there.
Atoms are large enough to have noticeable Brownian motion visible with an optical microscope.
They're small but not impossibly so.
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Now consider that most of that volume is empty space. Scaling up an atom such that a nucleus is the size of the Sun, you'd end up with an electron cloud about the size of the planetary solar system.
Atoms are relatively large and relatively dense in solids, atomic nuclei are small.
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This makes more sense to me shrinking down instead of sizing up: "Hold a golf ball. Imagine you're looking at the Earth with its own golf balls. Those smaller golf balls are the same size as atoms in the original golf ball you're holding."
Speaking of scale, this is a fun video at the other end of the spectrum:
https://www.youtube.com/watch?v=7J_Ugp8ZB4E
That's actually how they chose the size of a golf ball.
Yeah. I think most ppl (incl me) lack strong intuition about things at scales outside our human day-to-day. Reminds me of a conversation about wealth, someone said "The difference between a million and a billion is... about a billion."
A tenth of a percent is often a rounding error. So the difference between a million and a billion truly is about a billion.
When the above isn’t enough to light a bulb, I like introduce that as analogous to pennies.
1 penny is $0.01 10 pennies is $0.1 100 pennies is $1 1,000 pennies is $10 10,000 pennies is $100 100,000 pennies is $1,000 1,000,000 pennies is $10,000 10,000,000 pennies is $100,000 100,000,000 pennies is $1,000,000 1,000,000,000 pennies is $10,000,000
Most people understand that ten million dollars is not just a different amount but a distinct kind of amount from ten thousand dollars. The powers of ten seem to become clearer with a smaller starting amount. Once they grasp the above, point out that the relationship is the same if everything starts 100 times as large.
There’s also a great one out there comparing 1,000 to 1 million to 1 billion seconds, converted to years plus days.
Avogadro's number has a 10^23 in it to account for this atom-->physical matter sort of "scale up" conversion. Atoms are really small...
Sometimes I have a hard time wrapping my head around reconciling that with the estimated number of protons in the observable universe which is "only" ~10^80 (https://en.m.wikipedia.org/wiki/Eddington_number). Seems like it "should" be much higher, but orders of magnitude are sometimes deceptive to our intuition.
Unrelated, but I moved to a more rural area a while back and I’m surrounded by orchards and fields a fair amount of time, and my mind just can’t wrap itself around the scale of agriculture.
One avocado tree can produce around 200 avocados per year, and the orchards around here are probably around 150 trees/acre, so 30k avocados/acre/year.
Each avocado has about 250 calories (and that is just the parts that we eat, the tree has to put energy and mass into the pit and skin etc). These are food calories / kcal, so that’s 250k calories per avocado, or ~7.5 billion calories per year per acre.
7.5B calories/year is just about exactly 1kW, so that orchard is converting sunlight (and water, air, and trace minerals) to avocado calories at a continuous rate of 1kW. It’s incredible. The USDA says that as of 2022 there were about 880M acres of farmland in the United States alone.
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It takes a bit to accept your (10^0 m) place in the universe on the length scale between the Planck length (10^-35 m), the width of a proton (10^-15 m) and the diameter of the observable universe (10^27 m).
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My brain says that's only 4 times as many.
Avogadro was a weird looking guy https://en.wikipedia.org/wiki/File:Amadeo_Avogadro.png
Aren't we all a bit weird looking? I'm more entertained that URL was already in my browser history
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It looks like his MIND=BLOWN, then popped and re-inflated in Theme Hospital. It just goes to show how dangerous it is to think about such big numbers.
https://www.youtube.com/watch?v=Le_znuXcP2M
He was obviously an alien.
Ah, the source of "hey girls, take my number" meme.
> The scale here is absolutely nuts to me.
Being able to detect these tiny amounts is nuts to me.