r/theydidthemath 1d ago

[Request] Is this vaguely true?

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1.3k

u/HAL9001-96 1d ago

not quite

now they do probably mean logarithmically speaking

and specks of dust come in very differnet sizes

and hte size of an atom is ab it tricky to define

but we're talking something like 10^-11 to 10^-9 meters and about 10^7m so the middle is about 10^-2 to 10^-1 meters so about 1-10 cm

now an atoms core would only be abut 10^-15 to 10^-14 meters putting the middle to about 10^-4m or 0.1mm which is a relatively large dust particle but in the right range

but while that depiction of an atom is a bit of an inaccurate simplification anyways it clearly shows a whole atom, not a nucleus

also, of course, linearly rather htan logairthmically speaking the middle between an atom and hte earth in diameter would be a planet half hte size of the earth so roughly mars

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u/Futuressobright 1d ago

So would it be right to say if an atom were the size of a speck of dust a speck of dust would be the size of the earth?

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u/HAL9001-96 1d ago

no

going form an atom to a large speck of dust would be going from about 10^-10 to about 10^-4 so about a factor 1 million

go another factor one million and oyu are at 10^2, only 100 meters

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u/Bright-Historian-216 1d ago

yeah, if i understand it correctly you would need to increase each 10 billion times their size.

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u/HAL9001-96 1d ago

no, one is a factor 1 million the nex tstep would be afactor 100 billion

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u/KosmosKlaus 1d ago

Or maybe a golf ball is roughly in the middle of an atom and the earth

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u/NetworkSingularity 1d ago

On a logarithmic scale, specifically. On a regular old linear scale it’s Mars, as someone else said

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u/chroniclerofblarney 1d ago

You should just switch the H and T keys on your keyboard at this point.

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u/488302020 1d ago

noh quihe

now htey do probably mean logarihtmically speaking

and specks of dush come in very differnet sizes

and the size of an ahom is ab ih hricky ho define

but we’re halking somehting like 10-11 to 10-9 mehers and abouh 107m so hte middle is abouh 10-2 to 10-1 mehers so abouh 1-10 cm

now an ahoms core would only be abuh 10-15 ho 10-14 mehers puhhing hte middle ho abouh 10-4m or 0.1mm wtict is a relahively large dush parhicle buh in hte rigth range

buh wtile htah depichion of an ahom is a bih of an inaccurahe simplificahion anyways ih clearly stows a wtole ahom, noh a nucleus

also, of course, linearly rahter than logairhtmically speaking hte middle behween an ahom and the earht in diameher would be a planeh talf the size of hte earht so rougtly mars

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u/Mr_Minecrafter88 1d ago

+100 Science

-100 English

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u/HAL9001-96 1d ago

better than the other way round lol

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u/borsalamino 1d ago

goddamn rigth

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u/FuckingStickers 1d ago

What hte fuck?

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u/Mcipark 1d ago

Yeah haha, a 1/2 slice of the earth is halfway between an atom and the earth, a speck of dust is not.

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u/HAL9001-96 1d ago

well log scale it.. almost is sortof

or linearly you ight call it "rootway between"

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u/YeetToElite 1d ago

On that note, this is an incredibly good way to think of logarithms thank you.

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u/tico600 1d ago

Missed an occasion to compare to a grain of sand then, because 0.1mm would totally be the right size

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u/HAL9001-96 1d ago

also varies in size, similar ot a grain of dust which means the picture would be equally wrong for both

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u/tico600 1d ago

Of course it varies, but wouldn't a 0.1mm grain of sand make much more sense than a speck of dust ?

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u/HAL9001-96 1d ago

I already used the upper end of dust at 0.1mm as well

go any lower tha nthat which both dust and sand do at times and it gets even worse

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u/CakeHead-Gaming 1d ago

Are you HAL 9097, The 96th HAL 9001, or HAL 8905?

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u/Ok_Zebra_1500 1d ago

There was a public radio episode that also estimated 10^-2 or so. Large single celled organism IIRC.

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u/HAL9001-96 1d ago

10^-2 m is 1cm, thats very much visible everyday scale

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u/Ok_Zebra_1500 1d ago

I did not say you couldn't see it just the size of a large single celled organism. Large bubble algae or small plasmodial slime mold.

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u/HAL9001-96 1d ago

technically yeah but thats just becuase some single celled organisms can be surprisingly big, its certianly not hte first comparison I'd go for for something the isze of a fingernail

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u/piskle_kvicaly 1d ago

Or a sparrow egg.

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u/oklutz 14h ago

So, just change “speck of dust” to “dust bunny” and this would be more or less accurate?

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u/HAL9001-96 14h ago

yep or atom to nucleus

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u/jonquillejaune 3h ago

Lmaoooooo that last paragraph

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u/Centaurus3850 1d ago

interesting… i don’t understand this at all…

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u/HAL9001-96 18h ago

its literally logairthms and averages

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u/Centaurus3850 11h ago

and i’m an idiot 😔

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u/Ingraved 1d ago

Not accurate.
Earth (E) ~1.2 x 10 ^(7) m
Dust (D) ~ 2.5 x 10 ^(-6) m
Atom (A) ~ 1 x 10 ^(-10) m

E-------------D----A
A crude scale.

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u/Ingraved 1d ago

A speck of dust is closer to being halfway between a human's size and an atom.

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u/realberkeser 20h ago

And more closer between a penis size and an atom

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u/ebolaRETURNS 1d ago

E-------------D----A

Trust the dirty ASCII art...

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u/DeltaAlphaGulf 1d ago

Whats halfway between an electron and the galaxy or the observable universe?

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u/zrice03 1d ago

Well, we don't know the radius of an electron, assuming it's not an actual point particle. Though we do know it's less than 10^-22 m, so we'll just use that. Our galaxy is 100,000 LY across, or 9.46 x 10^20 m. The observable universe has a radius of about 46.5 billion LY, or 4.4 x 10^26 m.

Halfway between an electron and the galaxy would be 0.307 meters, or about just about 1 foot. Halfway between an electron and the observable universe would be 200 meters.

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u/shaonafle21 1d ago

A human egg is halfway between the plank length and observable universe.

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u/gorka_la_pork 1d ago

I'd heard it was a brain cell, but either way that means we're bigger than average :D

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u/DeltaAlphaGulf 1d ago

Even better.

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u/sOrdinary917 1d ago

Linearly speaking, = half a galaxy plus half an electon. Approx = half a galaxy

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u/Tryingtoknowmore 1d ago

Could I get this scale for where Humans are between the Planck length and the observable universe? I've heard we too are about halfway between them.

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u/Ingraved 1d ago

Observable Universe (O)    8.8 x 10 ^( 26) m  
Human Adult Height (H)     1.7 x 10 ^( 0 ) m  
Planck Length (P)          1.6 x 10 ^(-35) m  
Center Line (|)

O----------------------------H--|-------------------------------P  
Crude Scale

Close, only off by a kilometer... You could only fit like 1 billion people in a kilometere sized sphere...

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u/Tryingtoknowmore 1d ago

Thank you for the calculation and the hamster ball of death reference. Learning is never disappointing.

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u/FatMax1492 1d ago

what would be a more accurate centerpoint?

0

u/DatGuy2007 1d ago

Probably the moon

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u/IronPotato3000 1d ago

As a moron who basically only knows 5th grade math, I love this scale lol

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u/Sunfried 1d ago

So I get halfway as 3.5 x 10-2 m, or 3.5cm. So the middle object could be a chicken nugget.

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u/qrpc 2✓ 1d ago

That is a picture of a lithium atom with an atomic radius of about 0.000000000105 meters. The radius of the earth is 6,378,137 meters. The midpoint between nearly zero and 6.4 million is around 3.2 million meters.

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u/PESSSSTILENCE 1d ago

this is the correct answer, they tried to mean logarithmically but like.. its a linear question as far as i can tell

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u/qrpc 2✓ 1d ago

I guess saying the log of the geometric mean of the size of the two is like a speck of dust isn't that impressive.

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u/MonitorPowerful5461 1d ago

They mean logarithmically

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u/UniqueUsername014 1d ago

maybe they think that, but what they said has a very different meaning

the object halfway between the size of the earth and an atom definitely has the size of half an earth

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u/vwibrasivat 1d ago

It's wrong in every possible way, including "They mean logarithmically".

(reporting diameters)

Smallest salt grain is 0.2 millimeters. = 2.0x10-4 m

Lithium atom (shown) is 304 picometers = 3.04 x 10-10

The ratio is 6 orders of magnitude. 106

Earth diameter is 1.2742018 × 107 meters

Ratio of (earth):(salt grain) is 11 orders of magnitude 1011

log_base_10 would report that 6 not equal 11.

22

u/Apart_Astronomer9944 1d ago

Not sure about this but.. Size of earth is about 106 m Size of an atom is 10-10 Size of dust is according to google 10-6 So no about a third of the way

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u/nwbrown 1d ago

Yeah, that's not how exponents work.

A spec of dust is, using your numbers, 104 times bigger.

Earth is 1012 times bigger than a spec of dust.

So the spec of dust is 1/108th, or 1/100,000,000 of the way there.

100,000,000 is a little bigger than 3.

10

u/zrice03 1d ago

No:

Earth ~ 10^7 meters,

Atom ~10^-10 meters.

Seventeen orders of magnitude different, so 8.5 orders of magnitude to get halfway. That's at 10^-1.5 meters, or about 3 cm.

About the width of the human testicle.

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u/creiij 1d ago

We should use multitudes of human testicles as a standard form of measurement.

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u/soyalguien335 1d ago

An atom has a size of around 0.1nm Earth has a diameter or more than 10000km In meters that means 10-10 and 107 The geometric average of both is roughly 10-1.5 meters or 3 centimeters, which is more than the diameter of a ping pong bal, much much bigger than a speck of dust of 0.2 milimeter.

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u/Striking_Credit5088 1d ago

That'd have to be one hell of a speck of dust.

A lithium atom (likely what's depicted) is about 2 · 10-10 m
Earth is 1.3 · 107 m

Something halfway between would be about 6,371 kilometers wide, the approximate size of Russia

----

Another way to look at it is that a speck of dust is about 50,000 times the size of an atom, while earth is more than a trillion times the size of a speck of dust.

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u/MonitorPowerful5461 1d ago

They mean logarithmic, not linear, scale

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u/Striking_Credit5088 1d ago

Oh well if you take the geometric mean of ( 2 · 10-10 m · 1.3 · 107 m)1/2 = 5.1cm or about the size of an apple.

Still one hell of a speck of dust.

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u/TheNorthComesWithMe 1d ago

If they meant that they could have said that

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u/Icy_Sector3183 1d ago

No.

An atom is about 1e-10 m in diameter, a speck of dust is about 1e-5 m, and the earth is about 1,2e7 m in diameter.

If you just look at the degrees of magnitude atom -> dust is x 10 000, and dust -> earth is x 1 000 000 000 000.

You'll need to put in some more work to explain how the speck of dust is halfway between an atom and the earth.

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u/Instructor_Alan 1d ago

Atom is roughly 10-10 m (1 Ångstrom), a speck of dust is 10-4 m (100 μm), and Earth's diameter is roughly 1.2*107 m (12000 km). So not exactly halfway but close.

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u/Busalonium 1d ago

I'm not sure how you'd define halfway between to get that answer. I think a conventional understanding of halfway between an atom and the earth would give you something that is half the size of earth.

My first thought was maybe it's about orders of magnitude. But just looking at the order of magnitude in metres;

Atoms: 10-10 Earth: 106

So anything halfway between there would be 10-2 metres.

According to this site

https://www.engineeringtoolbox.com/particle-sizes-d_934.html

Dust is smaller than that and the only thing on that list that big is gravel.

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u/bartekltg 1d ago

If 'halfway' is on the logarithmic scale (cant be on linear, it would be just half of the earth;) ) it rather a small pebel. ~4cm (taking the diameter of the carbon atom)
https://www.wolframalpha.com/input?i=sqrt%28diameter+of+earth+*+diameter+of+carbon+atom%29

If we take diameter of only the nucleus, we are closer, 0.24mm
https://www.wolframalpha.com/input?i=sqrt%28diameter+of+earth+*+diameter+of+carbon+atom+nucleus%29

This already can be qualified as dust, on the bigger part of the scale. But the picture is wrong, we have to take the size of only the nucleus, not the whole atom.

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u/vwibrasivat 1d ago

It's wrong in every possible way, including "he means logarithmically".

(reporting diameters)

Smallest salt grain is 0.2 millimeters. = 2.0x10-4 m

Lithium atom (shown) is 304 picometers = 3.04 x 10-10

The ratio is 6 orders of magnitude. 106

Earth diameter is 1.2742018 × 107 meters

Ratio of (earth):(salt grain) is 11 orders of magnitude 1011

1

u/FIicker7 1d ago

What object would be halfway between the two?

A golf ball or baseball or a bowling ball?

Just curious

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u/transguy357 1d ago

I mean it depends what kind of halfway you’re talking about. The arithmetic mean of the masses of a Lithium atom and the Earth is 2.986x1027g.

(A Lithium atom’s mass is 1.153x10-23g according to google. The Earth’s is 5.972x1027kg.)

The geometric mean is a more likely calculation which is basically half way between them in terms of orders of magnitude. My calculator gives this at 262g, which is closer but certainly not the mass of a speck of dust.

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u/mneri7 1d ago

Technically speaking the middle point between the size of the Earth and 0 is half the size of the Earth.

So I'd say the middle point between the size of an atom and the size of the Earth is approximately half the size of the Earth.

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u/nwbrown 1d ago

If you specifically construct a scale designed to prove this true, sure.

If you use a linear scale a speck of dust is about halfway between an atom and two specs of dust.

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u/KosmosKlaus 1d ago

Are you saying that Mars is in the middle between an atom and earth in size?
That seems like nonsense 🤷🏻‍♂️ Mars is half the size of Earth, but way more than double the size of an atom

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u/CybershotBs 1d ago

Linearly speaking definitely not, even if an atom had size 0 the middle between 0 and the earth would be half the earth

Logarithmically speaking, other comments have answered

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u/Aeon1508 1d ago

I remember hearing at some point that The size of the smallest known particle relative to humans is the same as the size of human relatives to the observable universe. Or something like that

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u/TeririHerscherOfCute 1d ago

by volume, absolutely no, by scale, sure, but scale means nothing in a universe where the entire planet we live on makes up less than 0.00000000000000001% of it's total mass

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u/ADMINISTATOR_CYRUS 1d ago

In terms of logarithms, maybe that's what they meant but it's a bit off I think.

Size of the earth is around 106 m.

Size of dust is 10-6

Size of an atom is 10-10

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u/Laffenor 20h ago

All of these comments with massive numbers discussing whether it is 1/3 or 1/4 the way between the earth and an atom.

The formula to find what is half way between the size of an atom and earth (let's call it X) should be this (A = size of atom E = size of earth)

X = (E - A)/2 + A.

So if we say that the diameter of earth is 12 756km and the diameter of an atom is 0km, the spec of dust in question has a diameter of 6 378km. That's larger than even the biggest dust bunny in the farthest corner under the basement sofa of most homes.

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u/Specialist-Two383 20h ago

I like this sort of comparison. It's like how the breadth of a hair is as small compared to the Hubble scale as the Planck scale is to the breadth of a hair. So it's sort of the middle scale of the universe.

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u/Yzaamb 10h ago

It’s an interesting fact that the human scale is about the middle of the range of log sizes from the universe to the effective diameter of a neutrino.