Which is Bigger - Words Ever Spoken or Stars in the Universe?
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- Опубліковано 21 вер 2024
- There are some truly large quantities out there! And it takes a lot of work to guessimate their value. Here we explore how math and data can be used to estimate the numbers of words ever spoken in human history and the number of stars in the universe and compare them to how large a googol is. Think we'll get close? Let's find out!
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From my calculations the observable universe filled with a googol atoms would have a density of 4,65 E−8 kg/m³ and the density of hydrogen gas is 0.08375 kg/m³, so out universe would way less packed than a cloud of hydrogen gas, easily being able to hold this amount of molecules
how many hydrogen atoms could the observable universe hold in theory?
@@ianweckhorst3200make it as dense as a black hole i guess(volume being schwartzchild radius sphere), black hole density: 4x10^14g/cm^3, so about 1.86*10^122 atoms make the entire observable universe a big black hole
@@lih3391 How did you get that density? The volumes of blackholes are proportional to the cube of the mass (assuming the volume is the event horizon, of course, since that's the only meaningful volume we can measure.) The smaller the blackhole, the denser it is. The larger a black hole, the less dense it is. In fact, a blackhole with a diameter of Neptune's orbit is about as dense as cotton candy.
@@GoofyAhOklahoma I didn't account for that, feel free to correct me
@@lih3391 No problem. I just wanted to know how you got that number.
Just incase you're going to be one of his future students: the volume of the observable universe in cubic Planck lengths > 1 googol
Galaxies are not uniformly distributed in the universe, so you have to be careful what part of the sky you choose for your estimate. Since this is a rough estimate for comparison purposes, it isn't that critical.
Galaxies are assumed to be uniformly distributed in the universe. This is the cosmological principle, which in mathy language states that the universe is homogenous (same everywhere) and isotropic (same in every direction) at large enough scales. That said, the galaxies in that Hubble image are definitely not a representative sample of all galaxies so the math is still iffy
4:57 Mathe guy, the number shown is 75 followed by 17 zeros which 7.5 x 10^18 not 10^17.
My guess is smallest to largest 1. Grains of sand 2. Words uttered 3. Molecules in cup of water 4. Stars in the universe 5. Atoms in the universe 6. The googol
This is a pure guess with no reasoning what so ever and I'm only commenting it because I've already lost it twice and I wanted to write it down somewhere but I'm comfy in my bed and pen and paper are out of reach
1. Atoms in the universe
2. Molecules in a cup of water
3. Grains of sand
4. Stars in the universe
5. Words uttered
These ways of estimating and approximating quantities that seem unobtainable - remind me of the book "How to Measure Anything" by Douglas W. Hunbard and "Street Fighting Mathematics" by Sanjoy Mahajan.
It is easy to come up with something larger than 1 googol. Just the number of ways to arrange 2 unique decks of regular playing cards, this is 104!, which will definitely clear it. This is a product of 104 numbers, 95 of them are greater than or equal to 10. So we are easily >10^95, 5 of those are greater than 100, so that is 5 more powers of 10. We are now are >10^100 and this is a very conservative estimate.
Looking it up, it seems like 104! ~= 10^166. Like I said, a very conservative estimate. That is the power of using products instead of sums.
Those are possibilities, not actual things existing.
@@Irol. I don't think words spoken are actual things existing either
@@skyland1a218and I would also consider that answer incorrect
@@Irol.The original question posed in the video was to come up with “something that has a quantity” (larger than googol). The part about it having to be a physical object was just a rule you made up.
When I think of big numbers I always think of combinations. They always end up being super large number.
The first thing that popped into my head was the total number of possible images my tv can display.
My tv is a HDR (10 bit) 4k screen. (ignoring the w in the OLED) that would be 2^10=1024 different positions for each sub pixel. So 1024^3 (~10^9) different colors for each pixel.
4k resolutions is 3840 × 2160 = 8294400 pixels.(~8.3*10^6)
Each pixel with each color (10^9)^(8.3*10^6) = ?
I tried "Big Number Calculator" but the number is too big. But i guess it is larger than a googol
I actually think a 8 bit 1080p screen also would result in a number larger than a googol.
I think you only need 14 pixels with 3 8bit sub pixels to pass a googol. (16e6^14~googol I think)
Combinations are crazy.🤯
I tries calculating it in python. My best estimate for 8bit 1080p is ~10e14'981'180
So 14 million vs 100. It is much much larger than a googol. 🙂
((2**8)**3)**(1920*1080)
1:12 Before I watch any further
1 3 4 2 5
From least to largest
You should do a video on fermi estimation!
Do more calculus videos. I loved the one with the Arby's sauce. Do more with maximizing or minimizing values with some weird way (solid of revolution was just genius)
Off the cuff
Words ever uttered
Grains of sand
Molecules in cup of water
Stare in universe
Atoms in universe
Not super sure about the cup and stars
Not a single one over google, since IIRC the atoms in the universe is something like 10^86
One thing I know is bigger than google is 10↑↑10
"What is larger than a googol?"
2 googols
The density of matter in a star may be orders of magnitude larger than that in "a glass of water" so the multiplication at 9:59 may be a bit off. You could argue, of course, that collapsed atomic nuclei in a neutron-star no longer count as "atoms", and you'd be technically correct, the best kind of correct, but still..
Order guesstimation:
Words ever uttered
Grains of Sand
Molecules in cup of water
Stars in universe
Googol
Atoms in universe
Happy with that
How about neutrinos? Or all fermions? All elementary particles?
The observable universe can be approximated by a sphere of radius ~46.5B ly ... a cube inscribed inside this sphere would be of edge length 53.7B ly or 5.08 E 26 m ... then taking the cube root of a google yields ~2.154 E 33 ...... and the length of an atom is 1.0 E -9 m ......... so you would need 2.154 E 24 m and we have 200x that.... granted this is not accounting for ANY empty space sooooooooo.... but the short answer is yes you can
Number of universes in the unobservable universe.
The quantity of real numbers between the interval (0,1)
This is wild.
Knowing the critical density is ~10^-26kg/m³, the observable universe would be able to hold probably around 10^81 atoms (also depends on the definition of "observable" here), so not even close to a googol.
In terms of rough volume, it would be able to hold it. But it would collapse under gravity. :D
And most importantly, cease to be atoms. In fact, given that neutron stars aren't really made up of atoms anymore, the critical density may be far lower.
3:21 Actually you are one order of magnitude off, which is not really in the neighborhood.
I mean, given the level of simplification and eyeballing, it's a really good result. Often in physics you try to estimate something and are really happy if you are within one order of magnitude from the true value.
This is a kind of estimation often called Fermi estimation. The order of magnitude (ie power of ten) is all you really care about, smaller differences really don't matter when your comparing to a googol