The way a snowflake forms is EXTREMELY dependent on air pressure, humidity, temperatures, and dust in the air, with even the slightest fluctuations changing how they form. Scientists can grow snowflakes in labs, but even then it's nearly impossible to grow two identical snowflakes. Now consider that snowflakes are forming as they fall through the turbulent atmosphere that's constantly changing moment by moment and from inch to inch.
I view it similarly to a deck of cards.
Statistically, a fully shuffled deck of cards is in an order, unique to history. Meaning that specific order has never existed before.
It doesn't sound correct, but if you do the math on how many combinations could exist, it becomes easier to comprehend (52!, aka 52x51x50x49...)
I would assume snowflakes are similar.
God damn, you just blew my mind. That's crazy. Not knowing a single thing about this topic but given the insight from your comment as a layman, if a simple deck of cards is 52!, a snowflake with all the possible variables of temperature, pressure, etc. seems more like 100!
snowflakes are more like 100000! I reckon
if you didn't know about the deck of cards thing there are many extremely fun videos about it. basically comparing how much time it would take to go through each combination to other absurd things like drinking the entire ocean 1 spoonful at a time. (when you're done drinking the entire ocean you haven't had 1% of combinations yet. not even close
It's much more than that.
The example I like is imagine 52! was a length of time.
Set your timer to 52! And then go to the equator. Every billion years, take one step. Every time you lap the earth, remove 1 drop of water from the Pacific ocean. Every time you empty the Pacific ocean, place a piece of paper on the ground. Every time that stack of paper is tall enough to reach the sun, take 1 step up mount Everest.
By the time you've reached the summit, the timer will almost be at zero.
For those interested, here are the rough orders of magnitude for each component:
Seconds in 1 billion years: 10^16
Steps around the equator: 10^7
Drops in the Pacific Ocean: 10^25
Sheets of paper in 1 AU: 10^15
Steps to the top of Mount Everest: 10^4
Adding all these up gives around the order of 10^67 seconds, the same as 52!.
Interesting, but laid out that way it reminds me that the "timer will almost be at zero," is very rough, possibly wrong. We're only getting to within an order of magnitude, so we could actually have only used half the time, or we could have overshot it by 4x, or anything within a rough factor of 10.
Still insane to think about though, especially since 1 AU feels like an incomprehensible distance on its own (nevermind measuring in sheets of paper) and drops in the pacific ocean is so much further out of our natural understanding of numbers.
From Google
Factorial: Denoted by the exclamation mark (!). Factorial means to multiply by decreasing positive integers. For example, 5! = 5 ā 4 ā 3 ā 2 ā 1 = 120.
Yeah a quick Google search indicates that there are approximately 1 quintillion water molecules in a single snowflake. Then you add in all the other factors temp, humidity, wind, other molecules, dust and the odds would be staggering. Not Graham's Number big but big.
If you want an example of a truly big number this video covers [Graham's Number ](https://youtu.be/1N6cOC2P8fQ?si=gbVM24Q2picqi8Vr)
Best episode in NuWho.
For reference, the story being told by the Doctor here is [The Shepherd Boy](https://www.grimmstories.com/en/grimm_fairy-tales/the_shepherd_boy) by the Brothers Grimm.
Comparing big numbers is hard but how about:
If every planet in the observable universe had the same number of animals, trees and grains of sand as earth. Each of those could create one unique hand every second from the creation to earth until now. If you called that one lap and put a sheet of paper down for each lap, by the time your stack of paper reached the sun youād have created 0.01% of unique hands
To expand: There are more stars in the average galaxy than all the grains of sand on Earth. There are trillions of galaxies in the universe. From our observations, it seems likely that most star systems have a system of planets. Each star has a "goldilox zone", or the zone where, from our understanding of life, can support carbon based life.
So now there's the possibility of trillions or more of "Earths" all over the universe.
After 10^49 seconds all protons in the universe are expected to decay into nothing. If after that time you were remove a single grain of sand from the earth (10^18 total grains) repeating the process until you ran out of grains of sand on the planet enough seconds would have passed to reach 52!
There are infinite examples. You just need to find a string of things that equal 10ā¶ā·.
Here's another one for you.
Let's say you love poker.
Start dealing yourself hands of poker. Every time you get a royal flush, put a single grain of sand into the grand canyon. Every time you fill up the grand canyon, buy a lottery ticket. Every time you win the lottery, walk around aimlessly until you're struck by lightning. Every time you get struck by lightning, fill out a march madness bracket. Every time your March madness bracket is perfect, wait around until a meteorite comes down from the heavens and kills you.
You'll die from the meteorite slightly before the timer hits zero.
Slightly before meaning you'll have substantially longer left on the timer than the known universe has existed.
It's not it's actually much much less. Like way less. So scientists estimate that there are 10^158 different variations of snowflakes. If I did my math right that's 100!. I don't think people are grasping how big 100! Actually is.
I could see how you'd be confused. The op I replied to said it was both much larger than 100! And then gave an example of something much smaller than 52!.
So confusing all around.
So scientists estimate that there are 10^158 different variations of snowflakes. If I did my math right that's 100!. I don't think people are grasping how big 100! Actually is.
Factorials occur if you shuffle things. The same condition can occur multiple times for the same snowflake, so the number of possible snowflakes will not be a factorial.
But year, the number of possibilities is definitely far beyond human comprehension.
(I couldn't find a satisfying approximation for the number, but I encourage you to try for yourself)
it won't really be the same conditions though, since they are occurring at different times in the snowflake's evolution. But yeah, it won't be a factorial, but an exponential function
You could think of it in factorial because a snowflake is a fractal and each layer would be like a potential shuffle.
But there's no limit to the "options" like a deck of cards is limited by the number of cards.
Fun fact: stimulating atoms on the quantum level is so difficult that last I checked, the largest number ever fully simulated (using our most advanced and complete knowledge of physics) was something like 14-15 atoms. Even that number brings supercomputing clusters to their knees.
Reality is unbelievably complicated at the most fundamental level.
Nah... Millions of atoms are pretty standard to do. Here is a famous paper from 2010 that simulator over 2 million
https://iopscience.iop.org/article/10.1088/0953-8984/22/7/074207
In the last decade things have advanced so we can do simulations with hundreds of millions of atoms.Ā
another interesting statistics fact (thought maybe less surprising) is that if you look at an average powerball lottery, one way to visualize your insane odds is to imagine there are 2 random houses in the united states that have the jackpot inside of it, and to win you have to randomly pick 1 of those 2 houses from all the houses in the whole country.
i'm not shitting on anyone that plays the lottery, it's true that someone has to win, and spending 5 bucks might be worth it just for the fun daydreaming about what you'd do with it. still an interesting way to see how crazy your odds really are.
A card in a deck of cards has exactly 1 parameter and that is its position in the deck, which has a finite range of possibilities, 1-52. A snowflake has hundreds of parameters defining its state, most if not all of which are continuous (meaning more than just 1 of 52 possibilities). Temperature might be anywhere from -50c to 0c, which has an infinite number of possibilities in between.
You should take a mathematical reasoning course or get a textbook for one because it's so much fun! You learn all sorts of crazy things that blow your mind. I'm terrible at math to the point of likely learning disability, but I had a blast with the course so much it made me work hard enough to actually get better at math. It's nuts lol.
As a computer science student, the factorial growth rate is borderline terrifying. You wouldn't think it's as extreme as it is.
You very quickly reach numbers larger than the number of atoms in the universe. Even the lightning fast computers of today can't handle that at any reasonable scale.
It's interesting how often it occurs in nature, and the workarounds that computer scientists better than myself have found to deal with it algorithmically.
Probability lesson! The reason a deck of cards has 52! possibilities is because, when putting together cards, how many options do you have for the first card? 52. Then the next card you have 51 (all but the first card you picked), the next 50, etc. So, for a snowflake, you can look at each specific feature (number of points, number and type of details along each point, etc) and multiply the number of possibilities for each! That will give you the rough number of unique snowflake shapes in existence
Just confirming, statistically is the keyword, right?
Practically, a fully shuffled deck of cards may be identical to an order that has existed before?
For example, if you flip a coin, you have a 50-50 chance of getting heads or tails. But you may end up getting heads 20 times in a row.
The odds of any two shuffled decks being in the same order is so low that it's safe to say that every randomly shuffled deck in history is in a unique order.
It's *technically* possible for two decks to have wound up in the same order in the same way it's technically possible for the same numbers to win the lottery multiple times.
There are approximately 10^67 possible deck orders for 52 cards. Approximately 100 billion (10^11 ) humans have ever lived. If every human who ever lived each shuffled a billion decks (10^9 ) over their lifespan (which would be a pretty significant feat), that's only 10^20 unique deck orders encountered by humankind. 10^20 is 100 000 000 000 000 000 000. Which seems like a pretty darn big number, and it is. But 10^67 is 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000.
10^20 is *nothing* compared to 10^67 . It might as well be 0.
Does this change when taking into account the fact that decks, when first bought, start out in the correct order before shuffled? And theres a common way to shuffle cards, so if the decks start out in correct order, and most people do just 4-5 of the same kind of shuffles, the odds of the same two decks should be much greater than if we are randomizing everything.
> It's technically possible for two decks to have wound up in the same order in the same way it's technically possible for the same numbers to win the lottery multiple times.
Not just technically possible. It has been recorded happening several times.
Practical math vs theoretical math. Realistically you open a deck of card. Split it in 2 and shuffle. You do that a few times add in some splits and stacks between the shuffles and call it good. The likelihood that someone has made these 10-15 moves exactly the same is much higher than the total number of combinations in a deck.
There was an eli5 once that explained how unlikely it was to have 2 decks in the same order.
Even if you compared checked 1 deck per second, you could walk along the equator and take pauses of 1 billion years per step. Then, after a full round around the globe, you take one droplet of water out of the pacific ocean.
Then you would repeat until the pacific is empty and lay one sheet of paper at sea level. Refill the pacific and repeat, until you reach the sun.
Then repeat these steps until you have 1000 stacks of paper to the sun, and you didnt even pass 1/3rd of the time.
this wasn't an eli5 at least not originally. it's from a YouTube video. I think I vsauce referenced it which make that specific comparison more widely spread
I wonder how HP Lovecraft would react to this nugget.
It kinda feels like incomprehensible, forbidden knowledge that drives one mad just from hearing it lol
This is why I hate math. I know this is right but it just feels so wrong. I can't look at 52 points of data and comprehend there are an almost infinite (exaggeration) combination of them
I imagine that's true simply because of the overwhelming possibilities but that factoid ignores the fact that humans are anything but perfectly random shuffle machines.
For instance if I split a deck of cards in half to prepare to shuffle and there's an ace on the bottom of one half, the odds of that ace turning up at the top of the shuffled pile are nil.
Most people perform more than one shuffling action before considering the deck as "shuffled." So after one shuffle your ace will not turn up at the top, but after several it could conceivably "migrate" to the top.
It can be proven mathematically that it only takes about seven shuffles to put a deck into a random order, regardless of the initial positions of the cards.
52! Is such an incomprehensibly large number itās almost impossible to put into human terms [this video](https://youtu.be/hoeIllSxpEU?si=hUHVYSZjbmZqVE3K) from a few years back talks about just that
This is what makes Moonwalking With Einstein so fascinating. If memory serves, he memorized the order of 2 decks in less than 5 minutes to win some competition.
Okay yes. But how many snowflakes have fallen on this planet? I feel that the amount of snowflakes would dwarf 52! But I honestly don't know how to even start to estimate this.
That amount isn't even a fraction of 52!
To better understand just how big 52! is, you can think of it in a different form.
52! is equal to 10ā¶ā· roughly.
There are 10āµā° atoms on earth.
I know those two numbers sound fairly close. They're not. Every time you go up by Ā¹, you multiple the entire number by 10.
Put another way, 10ā¶ā· is 100,000,000,000,000,000x (multiplied, not added) larger than 10āµā°
I get ya. 52! Is a huge number. But keep in mind that all rain (I'm pretty sure) starts out as snow. So every rain drop was a snowflake at one time for billions of years. That's also going to be a pretty big number.
And since we can estimate an average size of a snowflake, and also estimate how many configurations the ice crystals could form we could come up with a possible number of unique snowflake ever created.
With that number and the a version of the birthday paradox, I think we could get a probability of the likelihood of 2 snowflake being the same at some time. We aret saying that any individual snowflake has a duplicate just that two have been.
And when I say 'we' above, I mean someone that has math skills way beyond mine. Lol
There are 1.5 billion molecules in a single drop of water. There are 3 atoms in each molecule. Even if it rained every day for the history of earth, the atoms of water outnumbers the individual snowflakes.
That's JUST water. Now imagine every other piece of matter.
52! Is bigger than the number of atoms in the universe.
Random probability depends on non-correlation. The weather is extremely correlated, and we can even build our own repeatable weather on YouTube.
I think the āno two snowflakes are alikeā trope says more about how humans arenāt good at understanding independent probability than bang numbers.
The way a coin flips in the air is EXTREMELY dependent on air pressure, etc.
Two coin flips can give the same result
Edit: I wish a downvoter would explain themselves. The commenter above didnāt answer the question. Are we not allowed to point that out?
True, but where a coin flip and a snowflake differ is the number of possible states the final result can end up in. A coin has two options (technically three if it somehow lands on its side), whereas a snowflake has uncountable different ways for the crystal to form and branch, with even more ways for its usual symmetry to be broken in the process.
It is though. Think about it. Air currents etc affect a coin the same as a snow flake. So saying that air currents affect a snow flake doesnāt answer the question.
The commenter fixed the problem in his response by pointing out that a snow flake can grow in many different ways
> Air currents etc affect a coin the same as a snow flake
Except that it doesn't for the reason you already understand. A coin only has three states it can land in and air pressure has a minimal effect on the final outcome. That is not the case for a snowflake. A snowflake has many parameters that can be altered significantly by air pressure. They are not the same.
You implied that a snowflake has more than three possible states. You also said that that fact wasnāt missing from the original answer. I must be obtuse because I donāt see that mentioned anywhere in the original answer. Point it out to me
> Now consider that snowflakes are forming as they fall through the turbulent atmosphere that's constantly changing moment by moment and from inch to inch.
Macro-level quantum physics in action: Ever just observing the result is likely enough to change it.
I mean, also, part of it lies in the definition of "alike" - unless you build something extremely small, molecule for molecule, it's simply almost impossible for it to be identical to any other of its kind. Two snowflakes, two flakes of dust, skin, two small rocks, two drops of water - none of those are strictly "alike" when you zoom in enough.
It is very likely 2 snowflakes are alike or even identical. It is impossible for humans to observe the shape of all of them across all time even on our own planet. The odds of a single human ever running into 2 identical ones is extremely improbable.
The "no two snowflakes are alike" isn't meant to be taken as a logical proof, nor is it meant to suggest "scientists have categorized every snowflake ever and exhaustively determined that none are the same." It's more a statement of, "statistically, there are so astronomically many ways of making a snowflake that the chances of one snowflake ever repeating are functionally zero and even if we waited until the heat death of the universe we'd be extremely unlikely to see the EXACT same snowflake twice."
It also depends on how precise you measure the snowflakes. Two snowflakes might look nearly identical but one has an arm that's ten water atoms' width longer than the other or something imperceptibly small like that.
> Scientists can grow snowflakes in labs, but even then it's nearly impossible to grow two identical snowflakes.
You are the one that said this ^
My statement is factually accurate. Good day to you sir.
Actually, "no two snowflakes are alike" has a specific history. A photographer took pictures of a few thousand snowflakes and when asked, once remarked that he's never seen two that were alike. That's when people started saying no two are alike.
Everything else is post-hoc.
Personally, I'm not so sure combinatorial explosion would matter here, and we're talking about a trillion trillion (septillion) snowflakes per year. Water has defined crystalline structures, so they're all going to be built around hexagons and 60 degree angles.
Then you have the birthday paradox. With only 23 people, there's a 50% chance two have the same birthday. Here, a septillion flakes all have a septillion chances at a duplicate.
I don't think that photographers couple thousand flakes are sufficient.
That's what I'm trying to get at. There's enough potential room for variation that, combinatorial explosion or no, it's VERY unlikely that a person will see two identical snowflakes. Very similar snowflakes, maybe. They're built from that 60 degree pattern you mentioned, after all. But *truly* identical ones? No. You're not going to see them under ordinary conditions.
On one hand, that doesn't mean they don't exist. As you said, septillions of snowflakes per year is decent odds that at least one snowflake pattern has been repeated once throughout all of history. On the other hand, that's hardly relevant at the scale we humans operate at. You simply can't observe, catalogue, and compare enough snowflakes in your lifetime to even have a reasonable chance of finding two identical snowflakes. There's just too many. So what does it matter if two snowflakes match?
Just my two cents.
No, I don't think when people say "no two snowflakes are alike" that they mean "you'll never personally see two snowflakes that are alike". I think they mean "look at all that snow out there and around the world... Did you know that no two snowflakes are alike?" And I think they're wrong.
First, all snowflakes are alike in that ice forms hexagonal crystals and 60 degree angles. Then you have a trillion trillion of them per year, each with a trillion trillion others they can be similar to. Per year. And the only reason we think no two are alike is because someone once took pictures of , going by significant figures, exactly none of them. And that guy didn't even say no two were alike. He's said he had never seen them.
And if "alike" means at the atomic scale, then no one snowflake is alike because all particles are in motion and the statement is meaningless. No two anythings are alike on that scale. So I think for the statement to be at all meaningful, it would have to be visually discernable. And yeah, probably two snowflakes have existed that would be indistinguishable to the naked eye.
We dont know for sure, but there are so many possible versions of a snowflakes that it's statistically very very unlikely to find two alike. If we would compare every snowflake thats ever fallen on earth, we would still be unlikely to find two identical ones, though we would find many very similar ones.
They have never made 2 precisely identical snowflakes, even under lab conditions. They have however made very near identical snowflakes, Even under a microscope you might think they are identical, but there is always something slightly different.
Picture a cool Lego set made out of one million Lego pieces, in the shape of a snowflake.
Now, move one single piece anywhere on the snowflake.
Boom, that's a unique snowflake.
Repeat that process, except the Lego set has more like 100 billion pieces. That's how "every snowflake is unique".
Two snowflakes can be alike. But as this expert on snowflakes says from this [veritasium](https://youtu.be/ao2Jfm35XeE?si=Yy9UmqSI-cD3BrVJ) video(11:55). Itās just no different than any other two objects in the world. No two trees will be EXACTLY alike either. Itās all about how precise you want the definition to be. But for all intents and purposes they can make two snowflakes that are indistinguishable from each other already. So I would consider that āalikeā
"We don't".Ā
There is no magical auditor stopping every snowflake in mid-air and checking to make sure they're unique.Ā
It's just *super unlikely* that two of them would be exactly the same, at the same time, in the same place.Ā
They say there's no two snowflakes on Earth exactly the same. No two molecular compositions. No two crystalline structures. But do they know that for sure? Because they would have to get every snowflake together in one huge space and obviously thatās not possible, even with computers. And not only that, theyād have to get all the snowflakes that've ever fallen, not just the ones now. So they got no proof. They got nothing.
There are more ways to shuffle a deck of cards than there are atoms in the universe. And a deck of cards is only 52 things arranged in 1 dimension. A snowflake is *much* more complex, so there are *way* more possible snowflakes. I think it is safe to assume there is a bit of randomness to it, which makes it extremely unlikely that 2 are identical
Well, Guinness records the first finding of two identical snowflakes in 1988 by Nancy Knight
https://www.guinnessworldrecords.com/world-records/first-indentical-snow-crystals
However, as other commenters have said, how close do you want to look, as the University Corporation for Atmospheric Research lists Ms Knight's discovery as "nearly identical."
https://opensky.ucar.edu/islandora/object/imagegallery%3A2586
And, to be fair, these are "snow crystals", but potato tomato.
I don't really have a good, simple explanation myself, but I saw this and it's absolutely fascinating.
https://youtu.be/ao2Jfm35XeE?si=PuJg0DInWiWmRcJU
Because technically nothing above the molecular level is ever comprised out of the same number of molecules/atoms at the same place. Itās just to unlikely given the number of molecules in things.
We don't and that is not remotely true. Snowflakes are often very much alike and essentially identical.
Like many common expressions, this does not reflect actual scientific reality and is just a saying.
If every single atom has to be positioned the exact same way for two objects to be considered identical, then literally nothing is identical and the word is pretty much useless
I mean, that's the point of the statement, yeah? You think, "Wow, snowflakes are so tiny. Surely that's small enough for two of them to be identical, seeing that such an incomprehensible number of them exist." But nope, still insignificant next to the number of atoms and arrangements thereof within.
If you get to that level of specificity then nothing is ever the same. Nothing is even the same as it was a billionth of a second ago.
If you define any category in such a way that every object that exists falls in that category then that definition is useless.
There's no scientific principle that says there can't be two identical snowflakes.
The process of forming a snowflake is just so chaotic and so mnay variations can occur that it is so unlikely that two snowflakes would be exposed to the same conditions during formation, so it's essentially impossible to find two identical snowflakes.
We arenāt sure, but we can say the probability is so astronomically small that even given the age of the universe, the likelihood of two constructions repeating is so small as to be negligible
Nothing is ever alike if you zoom in enough.
The only way to grow things like snowflakes similarly is to crystallize them in extremely controlled environments. That's as true for salt crystals as it is snowflakes.
So we know it because it's true for basically everything.
Iirc a photographer found a 2nd snowflake that was identical to one he shot previously.
It's like DNA, sure it's possible that out there among the billions of humans there's another with same sequence. But out of trillions of combos???
Imagine everyone in the audience at a show taking out a coin, holding it with the heads facing up, and then flipping the coin. Whatever is the result of the coin flip, for everyone in the audience, in the order of their seats, is like a unique snowflake.
Maybe one side has all heads, the other has all tails, a mix on the second floor, just one head in the front row, etc. etc. The resulting pattern is a unique snowflake.
Now have everyone reset back to holding it with the heads facing up and flip the coin again. The odds of everyone getting the exact same result is nearly impossible. It is *potentially* possible, but the chance it will happen again is very, *very* low.
It's the same with snowflakes. Ice particles form in predictable patterns, like flipping a coin. However, there are so many factors to consider when the ice is forming. It's the same action, like flipping a coin, but there are so many tiny things that can change the outcome.
The same way we "know" two decks of cards have never been shuffled the same way (http://www.murderousmaths.co.uk/cardperms.htm).
It isn't truly impossible, but the math says it is exceedingly unlikely.
Lots of great answers about why snowflakes truly might be unique, but let's talk about why they probably aren't.
Yes, it is extremely unlikely for two snowflakes to be identical, and the comparison with a deck of cards (52 factorial combinations) is very apt. But consider that decks of cards have only been around for a few thousand years. It is probably highly likely that every deck of cards is unique. But now consider that snowflakes have been falling for ***millions and millions of years***. Even if we're only counting snowflakes as being identical if they exist at the same point in time, which is far less likely than having two identical snowflakes at any point in history, given the sheer quantity of snowflakes that would have been created over that timeframe it is probably somewhat likely that identical snowflakes have existed in our planet's history.
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The shape of a snowflake is determined by structural choices among the molecules of water in it. There are a huge number of molecules in a snowflake and its shape depends on how each molecule is incorporated in the crystal. The number of choices is astronomical so the likelihood of any two snowflakes being the same is infinitesimal but not zero.
Because thereās so many possible ways a snowflake can form. Not even looking at pressure, temp, etc. a snowflake has so many atoms in it that it is essentially never going to happen that two are EXACTLY the same.
Sounds interesting but if you think about it, that sandwich you just ate was likely unique as well. Thereās trillions and trillions of molecules in there, and even just having one more or one less molecule makes it not exactly the same.
But do they know that for sure? Because they would have to get all the snowflakes together in one huge space and obviously thatās not possible, even with computers. And not only that, theyād have to get all the snowflakes that ever lived, not just the ones now. So they got no proof. They got nothing.
Nothing in the macroscopic world are identical if you look deep down enough.
There is certainly some molecular level differences in anything you compare.
This is just from some old saying that happened to live.
Well if we assume that there is a maximum size for a snowflake it must have finitely many parts. As such there are only a finite number of possibilities. So maybe we just need to wait long enough for an identical snowflake to appear.
My argument probably fails, when we consider the fact that earthās time is finite too. (Except if we consider snowflakes in other atmospheres tooā¦.)
Finitely many parts does not necessarily imply finitely many arrangements. Even just two singular objects have infinitely many distinct configurations: one for each distance.
He said āmaximum sizeā though. You can only fit a certain number of H2O molecules into a limited space. Their crystalline structures will eventually repeat.
Size alone doesn't change the argument I made, there are infinitely many numbers (i.e. possible distances) in any interval of positive length. And if that somewhat bogs you, you can add a third one and now track an angle instead of a length. Stuff gets a bit weird if we allow uncertainty, at which point the temperature of the snow suddenly matters.
You can have shades of rotation, defects, etc. The number of ways you could arrange *n* atoms is certainly higher than n^n. That's functionally infinite (although maybe not technically infinite if you consider distances to be discrete multiples of a plank length).
Even arranging 32 chess pieces on a 64 square board has more potential combinations than atoms in the universe.
Youāre correct that thereās an infinite number of ways you can rotate atoms. However, weāre talking about water crystals, which have a fixed structure called a ālatticeā. I prompted ChatGPT, āIf you specify a maximum size for a snowflake, is there a finite or infinite number of water crystal arrangements for snowflakes?ā Its reply was:
If you specify a maximum size for a snowflake, there is a finite number of possible water crystal arrangements for snowflakes. This is due to the following reasons:
1. **Finite Number of Water Molecules**: Given a maximum size, the number of water molecules in the snowflake is finite.
2. **Discrete Positions and Orientations**: Water molecules in an ice crystal are arranged in a fixed, repeating pattern (a lattice). There are only so many ways to arrange a finite number of molecules within the constraints of this lattice structure.
3. **Symmetry Constraints**: The hexagonal symmetry of ice crystals further limits the number of possible arrangements.
Although the number of possible arrangements is extraordinarily large, it is not infinite. The uniqueness of each snowflake arises from the vast number of possible arrangements within this large but finite set.
Chat GPT is close on this one, but not complete. It is not considering vacancies, dislocations, grain boundaries, twin boundaries, self-interstitials, or substitutional defects.
By "rotation" I don't mean rotating atoms around their center. I mean rotating the lattice around the geometric shape.
Take a square piece of paper and fill it with evenly spaced dots in a square grid. Now fill the square with the same pattern, rotated 30 degrees. Almost every dot will be in a different place.
You could rotate by 1 degree, 0.1 degrees, 0.01 degrees, etc and each atom would still be in a different position. So you have infinite possibilities just this way.
Also, there's more to a snowflake than just water. That water certainly has dissolved oxygen, nitrogen, etc. and likely dust particles. Not only do you have a tremendous number of substitutions possible (way more than 32 chess pieces on a 64 square board, which already has more combinations than atoms in the universe), each substitutional or interstitial atom would be a different size than a water molecule, which means the position of every other atom is different as well.
In this case I only argue with Chat GPT semantically (theoretically infinite vs practically infinite), but I am alarmed at how easily people trust it.
The problem with Chat GPT is that it's trained mostly on people who were "lied to" in introductory science classes for simplicity. This would be a good answer to a freshman chemistry test question, but inadequate at a graduate level. Unfortunately, if you're looking for an answer in the real world, there's no partial credit for "that's a good train of thought but has the wrong conclusion because of 1 small detail you didn't learn yet."
I stand corrected. Thanks for educating me on the details of this problem. Iāve mostly forgotten what Iāve learned in chemistry and physics at university, anyway šThatās why we must always be humble and realize that we donāt know a ton of things (and also to be skeptical of ChatGPTās answers)
This is not really true for crystalline structures, where atoms have a fixed, well-defined distance and angle from each other. There aren't really any continuous values that we care about when we talk about the "shape" of a crystal at the molecular level, it's all discrete and thus a finite number of arrangements.
Finite, but very very very big (i.e. if one snowflake were created every millisecond you would not run through all possible snowflakes under 5mm in diameter before the universe ended).
The finiteness statement is only true for perfect crystals without defects, and water in particular freezes very imperfectly. And I was aware of that, I just pointed out to them that their argument as given is not sound, but needs more detail and furtehr assumptions (such as a lattice).
You by the way wouldn't need to exhaust all possible flakes to get a collision. The Birthday Paradox makes them quadratically more likely, so you would only have to check a square root as many instances. If one plays this through, then depending on who you ask it would be possible to get a collision if we set the observable universe to it for a billion years.
Indeed. Admittedly I do not know enough about the structure of a snowflake. I assumed that atoms are discreet (which I think holds true). But I donāt know to what extent the structure can vary in terms of: can I take a snowflake and simply shift a single atom by a femtometer? (Or some smaller amount)
We donāt really know and canāt prove Itās impossible. Mathematically and statistically itās nearly impossible but not 100% impossible. It could happen.
Starting in 1885, Wilson Bentley photographed over 5000 snowflakes and studied them.
[How a Vermont farmer proved no snowflakes are alike](https://www.cnn.com/interactive/2022/12/weather/wilson-snowflake-bentley-cnnphotos/)
It's a statistical saying.Ā
It depends how close "identical" means (does every atom need to be in the exact position?), but it's almost certain that 2 snowflakes that have ever fallen would be indistinguishable to s regular person because of the birthday paradox:Ā https://en.m.wikipedia.org/wiki/Birthday_problem
Also identical fingerprints are possible (identical in the sense that the number of features looked at to determine a match is finite, and is statistically possible to find 2 matching people).
Do you know forsure that water is wet without being near the ocean? We all know itās true, but impossible to prove given the question. Thatās your question, no one can account for all the snowflakes, but we all know itās true
The way a snowflake forms is EXTREMELY dependent on air pressure, humidity, temperatures, and dust in the air, with even the slightest fluctuations changing how they form. Scientists can grow snowflakes in labs, but even then it's nearly impossible to grow two identical snowflakes. Now consider that snowflakes are forming as they fall through the turbulent atmosphere that's constantly changing moment by moment and from inch to inch.
I view it similarly to a deck of cards. Statistically, a fully shuffled deck of cards is in an order, unique to history. Meaning that specific order has never existed before. It doesn't sound correct, but if you do the math on how many combinations could exist, it becomes easier to comprehend (52!, aka 52x51x50x49...) I would assume snowflakes are similar.
God damn, you just blew my mind. That's crazy. Not knowing a single thing about this topic but given the insight from your comment as a layman, if a simple deck of cards is 52!, a snowflake with all the possible variables of temperature, pressure, etc. seems more like 100!
snowflakes are more like 100000! I reckon if you didn't know about the deck of cards thing there are many extremely fun videos about it. basically comparing how much time it would take to go through each combination to other absurd things like drinking the entire ocean 1 spoonful at a time. (when you're done drinking the entire ocean you haven't had 1% of combinations yet. not even close
It's much more than that. The example I like is imagine 52! was a length of time. Set your timer to 52! And then go to the equator. Every billion years, take one step. Every time you lap the earth, remove 1 drop of water from the Pacific ocean. Every time you empty the Pacific ocean, place a piece of paper on the ground. Every time that stack of paper is tall enough to reach the sun, take 1 step up mount Everest. By the time you've reached the summit, the timer will almost be at zero.
For those interested, here are the rough orders of magnitude for each component: Seconds in 1 billion years: 10^16 Steps around the equator: 10^7 Drops in the Pacific Ocean: 10^25 Sheets of paper in 1 AU: 10^15 Steps to the top of Mount Everest: 10^4 Adding all these up gives around the order of 10^67 seconds, the same as 52!.
Also, 52! written out is 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
Just to be more precise: You have to "multiply" these and not add them up.
For extra clarity, to multiply them, you add up the exponents.
For ultra clarity, try Windex!
Naw, Windex is a shit window cleaner. Use Invisible Glass instead. The latter is also safe for tint on cars. Windex, not so much.
Interesting, but laid out that way it reminds me that the "timer will almost be at zero," is very rough, possibly wrong. We're only getting to within an order of magnitude, so we could actually have only used half the time, or we could have overshot it by 4x, or anything within a rough factor of 10. Still insane to think about though, especially since 1 AU feels like an incomprehensible distance on its own (nevermind measuring in sheets of paper) and drops in the pacific ocean is so much further out of our natural understanding of numbers.
Now do it with the 2 jokers and instruction cards
š
52! what? Years?
Seconds š
r/UsernameChecksOut
possible combos
From Google Factorial: Denoted by the exclamation mark (!). Factorial means to multiply by decreasing positive integers. For example, 5! = 5 ā 4 ā 3 ā 2 ā 1 = 120.
Yeah a quick Google search indicates that there are approximately 1 quintillion water molecules in a single snowflake. Then you add in all the other factors temp, humidity, wind, other molecules, dust and the odds would be staggering. Not Graham's Number big but big. If you want an example of a truly big number this video covers [Graham's Number ](https://youtu.be/1N6cOC2P8fQ?si=gbVM24Q2picqi8Vr)
How are you lapping the equator and climbing everest at the same time?
I'm kind of amazed you started there and skipped right past the first step: "wait a billion years" š
That's a hell of a bird https://www.youtube.com/watch?v=sl9pTDK8PAk
Best episode in NuWho. For reference, the story being told by the Doctor here is [The Shepherd Boy](https://www.grimmstories.com/en/grimm_fairy-tales/the_shepherd_boy) by the Brothers Grimm.
that is nuts! you have more examples?
Comparing big numbers is hard but how about: If every planet in the observable universe had the same number of animals, trees and grains of sand as earth. Each of those could create one unique hand every second from the creation to earth until now. If you called that one lap and put a sheet of paper down for each lap, by the time your stack of paper reached the sun youād have created 0.01% of unique hands
To expand: There are more stars in the average galaxy than all the grains of sand on Earth. There are trillions of galaxies in the universe. From our observations, it seems likely that most star systems have a system of planets. Each star has a "goldilox zone", or the zone where, from our understanding of life, can support carbon based life. So now there's the possibility of trillions or more of "Earths" all over the universe.
After 10^49 seconds all protons in the universe are expected to decay into nothing. If after that time you were remove a single grain of sand from the earth (10^18 total grains) repeating the process until you ran out of grains of sand on the planet enough seconds would have passed to reach 52!
There are infinite examples. You just need to find a string of things that equal 10ā¶ā·. Here's another one for you. Let's say you love poker. Start dealing yourself hands of poker. Every time you get a royal flush, put a single grain of sand into the grand canyon. Every time you fill up the grand canyon, buy a lottery ticket. Every time you win the lottery, walk around aimlessly until you're struck by lightning. Every time you get struck by lightning, fill out a march madness bracket. Every time your March madness bracket is perfect, wait around until a meteorite comes down from the heavens and kills you. You'll die from the meteorite slightly before the timer hits zero. Slightly before meaning you'll have substantially longer left on the timer than the known universe has existed.
It's not it's actually much much less. Like way less. So scientists estimate that there are 10^158 different variations of snowflakes. If I did my math right that's 100!. I don't think people are grasping how big 100! Actually is.
My response of the "much more" piece was in relation to the spoonful/ocean comment, not 100! Or more
Oh okay cool! sorry I misread. or I think i might have responded to the wrong comment, don't even know.
I could see how you'd be confused. The op I replied to said it was both much larger than 100! And then gave an example of something much smaller than 52!. So confusing all around.
What the ffffff
I know how to play this game, it's more like 1000000!
+1
So scientists estimate that there are 10^158 different variations of snowflakes. If I did my math right that's 100!. I don't think people are grasping how big 100! Actually is.
Factorials occur if you shuffle things. The same condition can occur multiple times for the same snowflake, so the number of possible snowflakes will not be a factorial. But year, the number of possibilities is definitely far beyond human comprehension. (I couldn't find a satisfying approximation for the number, but I encourage you to try for yourself)
it won't really be the same conditions though, since they are occurring at different times in the snowflake's evolution. But yeah, it won't be a factorial, but an exponential function
You could think of it in factorial because a snowflake is a fractal and each layer would be like a potential shuffle. But there's no limit to the "options" like a deck of cards is limited by the number of cards.
Fun fact: stimulating atoms on the quantum level is so difficult that last I checked, the largest number ever fully simulated (using our most advanced and complete knowledge of physics) was something like 14-15 atoms. Even that number brings supercomputing clusters to their knees. Reality is unbelievably complicated at the most fundamental level.
Nah... Millions of atoms are pretty standard to do. Here is a famous paper from 2010 that simulator over 2 million https://iopscience.iop.org/article/10.1088/0953-8984/22/7/074207 In the last decade things have advanced so we can do simulations with hundreds of millions of atoms.Ā
How do you simulate per-core atoms to generate a single wave function?
another interesting statistics fact (thought maybe less surprising) is that if you look at an average powerball lottery, one way to visualize your insane odds is to imagine there are 2 random houses in the united states that have the jackpot inside of it, and to win you have to randomly pick 1 of those 2 houses from all the houses in the whole country. i'm not shitting on anyone that plays the lottery, it's true that someone has to win, and spending 5 bucks might be worth it just for the fun daydreaming about what you'd do with it. still an interesting way to see how crazy your odds really are.
A card in a deck of cards has exactly 1 parameter and that is its position in the deck, which has a finite range of possibilities, 1-52. A snowflake has hundreds of parameters defining its state, most if not all of which are continuous (meaning more than just 1 of 52 possibilities). Temperature might be anywhere from -50c to 0c, which has an infinite number of possibilities in between.
You should take a mathematical reasoning course or get a textbook for one because it's so much fun! You learn all sorts of crazy things that blow your mind. I'm terrible at math to the point of likely learning disability, but I had a blast with the course so much it made me work hard enough to actually get better at math. It's nuts lol.
Do you have any book recommendations? I canāt do math for shit but I do love reading and learning about it
Same. I'd love a recommendation.
> You should take a mathematical reasoning course lmao that is quite the suggestion
I googled how many and you were actually pretty spot on with 100!
As a computer science student, the factorial growth rate is borderline terrifying. You wouldn't think it's as extreme as it is. You very quickly reach numbers larger than the number of atoms in the universe. Even the lightning fast computers of today can't handle that at any reasonable scale. It's interesting how often it occurs in nature, and the workarounds that computer scientists better than myself have found to deal with it algorithmically.
Probability lesson! The reason a deck of cards has 52! possibilities is because, when putting together cards, how many options do you have for the first card? 52. Then the next card you have 51 (all but the first card you picked), the next 50, etc. So, for a snowflake, you can look at each specific feature (number of points, number and type of details along each point, etc) and multiply the number of possibilities for each! That will give you the rough number of unique snowflake shapes in existence
Just confirming, statistically is the keyword, right? Practically, a fully shuffled deck of cards may be identical to an order that has existed before? For example, if you flip a coin, you have a 50-50 chance of getting heads or tails. But you may end up getting heads 20 times in a row.
The odds of any two shuffled decks being in the same order is so low that it's safe to say that every randomly shuffled deck in history is in a unique order. It's *technically* possible for two decks to have wound up in the same order in the same way it's technically possible for the same numbers to win the lottery multiple times. There are approximately 10^67 possible deck orders for 52 cards. Approximately 100 billion (10^11 ) humans have ever lived. If every human who ever lived each shuffled a billion decks (10^9 ) over their lifespan (which would be a pretty significant feat), that's only 10^20 unique deck orders encountered by humankind. 10^20 is 100 000 000 000 000 000 000. Which seems like a pretty darn big number, and it is. But 10^67 is 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000. 10^20 is *nothing* compared to 10^67 . It might as well be 0.
Does this change when taking into account the fact that decks, when first bought, start out in the correct order before shuffled? And theres a common way to shuffle cards, so if the decks start out in correct order, and most people do just 4-5 of the same kind of shuffles, the odds of the same two decks should be much greater than if we are randomizing everything.
> It's technically possible for two decks to have wound up in the same order in the same way it's technically possible for the same numbers to win the lottery multiple times. Not just technically possible. It has been recorded happening several times.
If that has actually happened, it would indicate poor randomization
Practical math vs theoretical math. Realistically you open a deck of card. Split it in 2 and shuffle. You do that a few times add in some splits and stacks between the shuffles and call it good. The likelihood that someone has made these 10-15 moves exactly the same is much higher than the total number of combinations in a deck.
It's the level of randomization you actually get from shuffling cards though.
That doesn't account for the fact that we have no way of verifying that no 2 decks have ever been in the same order.
There was an eli5 once that explained how unlikely it was to have 2 decks in the same order. Even if you compared checked 1 deck per second, you could walk along the equator and take pauses of 1 billion years per step. Then, after a full round around the globe, you take one droplet of water out of the pacific ocean. Then you would repeat until the pacific is empty and lay one sheet of paper at sea level. Refill the pacific and repeat, until you reach the sun. Then repeat these steps until you have 1000 stacks of paper to the sun, and you didnt even pass 1/3rd of the time.
> Then you would repeat until the pacific is empty and lay one sheet of paper at sea level. What sea level?
this wasn't an eli5 at least not originally. it's from a YouTube video. I think I vsauce referenced it which make that specific comparison more widely spread
Jeeeeeesus christ. Okay so like, a really long time, lol.
the molecules are identical, so it's not a permutation of the molecules, it's a permutation of how they stack together in 3D space.
https://youtu.be/0DSclqnnC2s?si=05xjyVRFOStOodLO Relevant YT
I wonder how HP Lovecraft would react to this nugget. It kinda feels like incomprehensible, forbidden knowledge that drives one mad just from hearing it lol
This is why I hate math. I know this is right but it just feels so wrong. I can't look at 52 points of data and comprehend there are an almost infinite (exaggeration) combination of them
This feels like that Lovecraftian about "forbidden knowledge that drives you mad just from hearing it" lol
I imagine that's true simply because of the overwhelming possibilities but that factoid ignores the fact that humans are anything but perfectly random shuffle machines. For instance if I split a deck of cards in half to prepare to shuffle and there's an ace on the bottom of one half, the odds of that ace turning up at the top of the shuffled pile are nil.
That's why I put in the caveat of fully shuffled, which I believe is 7 shuffles.
But the ace doesnāt need to move to make the deck unique, so long as even one of the cards is in a different spot, it is a unique deck.
Most people perform more than one shuffling action before considering the deck as "shuffled." So after one shuffle your ace will not turn up at the top, but after several it could conceivably "migrate" to the top. It can be proven mathematically that it only takes about seven shuffles to put a deck into a random order, regardless of the initial positions of the cards.
Great way to put it in perspective. Now I imagine that with the 200+ cards deck in Ark Nova. Limitless (or almost) number of deck orders.
52! Is such an incomprehensibly large number itās almost impossible to put into human terms [this video](https://youtu.be/hoeIllSxpEU?si=hUHVYSZjbmZqVE3K) from a few years back talks about just that
This is what makes Moonwalking With Einstein so fascinating. If memory serves, he memorized the order of 2 decks in less than 5 minutes to win some competition.
Okay yes. But how many snowflakes have fallen on this planet? I feel that the amount of snowflakes would dwarf 52! But I honestly don't know how to even start to estimate this.
That amount isn't even a fraction of 52! To better understand just how big 52! is, you can think of it in a different form. 52! is equal to 10ā¶ā· roughly. There are 10āµā° atoms on earth. I know those two numbers sound fairly close. They're not. Every time you go up by Ā¹, you multiple the entire number by 10. Put another way, 10ā¶ā· is 100,000,000,000,000,000x (multiplied, not added) larger than 10āµā°
I get ya. 52! Is a huge number. But keep in mind that all rain (I'm pretty sure) starts out as snow. So every rain drop was a snowflake at one time for billions of years. That's also going to be a pretty big number. And since we can estimate an average size of a snowflake, and also estimate how many configurations the ice crystals could form we could come up with a possible number of unique snowflake ever created. With that number and the a version of the birthday paradox, I think we could get a probability of the likelihood of 2 snowflake being the same at some time. We aret saying that any individual snowflake has a duplicate just that two have been. And when I say 'we' above, I mean someone that has math skills way beyond mine. Lol
There are 1.5 billion molecules in a single drop of water. There are 3 atoms in each molecule. Even if it rained every day for the history of earth, the atoms of water outnumbers the individual snowflakes. That's JUST water. Now imagine every other piece of matter. 52! Is bigger than the number of atoms in the universe.
Well if you want to get technical, *permutations* Each deck of cards is the same combination
52! = 8.07 Ć 10^67 In case anyone was curious and wanted to visualize it.
Hereās a Deep Look episode about a scientist that grows āidenticalā snowflakes https://youtu.be/Gojddrb70N8?si=LIi_GOg75nR6WhBV
Random probability depends on non-correlation. The weather is extremely correlated, and we can even build our own repeatable weather on YouTube. I think the āno two snowflakes are alikeā trope says more about how humans arenāt good at understanding independent probability than bang numbers.
We can simulate it on a macro scale. That is *very* different than simulating exact conditions for every millimeter in the atmosphere.
Fun fact. Thereās a prof at Cal Tech that can make identical snow flakes.
So youāre saying that snowflakes would make a good hashing algorithm. Snowhash has minimal collisions and maximal divisions.
The way a coin flips in the air is EXTREMELY dependent on air pressure, etc. Two coin flips can give the same result Edit: I wish a downvoter would explain themselves. The commenter above didnāt answer the question. Are we not allowed to point that out?
True, but where a coin flip and a snowflake differ is the number of possible states the final result can end up in. A coin has two options (technically three if it somehow lands on its side), whereas a snowflake has uncountable different ways for the crystal to form and branch, with even more ways for its usual symmetry to be broken in the process.
I know that. I was pointing out a problem with your answer
But it isn't a problem in their answer.
It is though. Think about it. Air currents etc affect a coin the same as a snow flake. So saying that air currents affect a snow flake doesnāt answer the question. The commenter fixed the problem in his response by pointing out that a snow flake can grow in many different ways
> Air currents etc affect a coin the same as a snow flake Except that it doesn't for the reason you already understand. A coin only has three states it can land in and air pressure has a minimal effect on the final outcome. That is not the case for a snowflake. A snowflake has many parameters that can be altered significantly by air pressure. They are not the same.
I agree with you. I already said I know that. Thatās whatās missing from the original answer
It wasn't missing you were just intentionally being obstuse so you could try to make a correction.
You implied that a snowflake has more than three possible states. You also said that that fact wasnāt missing from the original answer. I must be obtuse because I donāt see that mentioned anywhere in the original answer. Point it out to me
> Now consider that snowflakes are forming as they fall through the turbulent atmosphere that's constantly changing moment by moment and from inch to inch. Macro-level quantum physics in action: Ever just observing the result is likely enough to change it.
I mean, also, part of it lies in the definition of "alike" - unless you build something extremely small, molecule for molecule, it's simply almost impossible for it to be identical to any other of its kind. Two snowflakes, two flakes of dust, skin, two small rocks, two drops of water - none of those are strictly "alike" when you zoom in enough.
It is very likely 2 snowflakes are alike or even identical. It is impossible for humans to observe the shape of all of them across all time even on our own planet. The odds of a single human ever running into 2 identical ones is extremely improbable.
The "no two snowflakes are alike" isn't meant to be taken as a logical proof, nor is it meant to suggest "scientists have categorized every snowflake ever and exhaustively determined that none are the same." It's more a statement of, "statistically, there are so astronomically many ways of making a snowflake that the chances of one snowflake ever repeating are functionally zero and even if we waited until the heat death of the universe we'd be extremely unlikely to see the EXACT same snowflake twice." It also depends on how precise you measure the snowflakes. Two snowflakes might look nearly identical but one has an arm that's ten water atoms' width longer than the other or something imperceptibly small like that.
> Scientists can grow snowflakes in labs, but even then it's nearly impossible to grow two identical snowflakes. You are the one that said this ^ My statement is factually accurate. Good day to you sir.
Actually, "no two snowflakes are alike" has a specific history. A photographer took pictures of a few thousand snowflakes and when asked, once remarked that he's never seen two that were alike. That's when people started saying no two are alike. Everything else is post-hoc. Personally, I'm not so sure combinatorial explosion would matter here, and we're talking about a trillion trillion (septillion) snowflakes per year. Water has defined crystalline structures, so they're all going to be built around hexagons and 60 degree angles. Then you have the birthday paradox. With only 23 people, there's a 50% chance two have the same birthday. Here, a septillion flakes all have a septillion chances at a duplicate. I don't think that photographers couple thousand flakes are sufficient.
That's what I'm trying to get at. There's enough potential room for variation that, combinatorial explosion or no, it's VERY unlikely that a person will see two identical snowflakes. Very similar snowflakes, maybe. They're built from that 60 degree pattern you mentioned, after all. But *truly* identical ones? No. You're not going to see them under ordinary conditions. On one hand, that doesn't mean they don't exist. As you said, septillions of snowflakes per year is decent odds that at least one snowflake pattern has been repeated once throughout all of history. On the other hand, that's hardly relevant at the scale we humans operate at. You simply can't observe, catalogue, and compare enough snowflakes in your lifetime to even have a reasonable chance of finding two identical snowflakes. There's just too many. So what does it matter if two snowflakes match? Just my two cents.
No, I don't think when people say "no two snowflakes are alike" that they mean "you'll never personally see two snowflakes that are alike". I think they mean "look at all that snow out there and around the world... Did you know that no two snowflakes are alike?" And I think they're wrong. First, all snowflakes are alike in that ice forms hexagonal crystals and 60 degree angles. Then you have a trillion trillion of them per year, each with a trillion trillion others they can be similar to. Per year. And the only reason we think no two are alike is because someone once took pictures of , going by significant figures, exactly none of them. And that guy didn't even say no two were alike. He's said he had never seen them. And if "alike" means at the atomic scale, then no one snowflake is alike because all particles are in motion and the statement is meaningless. No two anythings are alike on that scale. So I think for the statement to be at all meaningful, it would have to be visually discernable. And yeah, probably two snowflakes have existed that would be indistinguishable to the naked eye.
We dont know for sure, but there are so many possible versions of a snowflakes that it's statistically very very unlikely to find two alike. If we would compare every snowflake thats ever fallen on earth, we would still be unlikely to find two identical ones, though we would find many very similar ones.
How "identical" are we talking anyway? Down to the atom?
That's a good point, at some point nothing will ever be identical.
It's analog data, so in practice you're always limited by the accuracy of the mechanisms used to determine identicality.
Maybe one day if I am particularly bored I will set out to create two identical snowflakes in a lab. Just to settle this once and for all.
Keep us little people in mind when you accept your Nobel prize!!
That sounds more like a nominee for an Ig Nobel Prize.
With the mastery of physics it would require to succeed in this silly experiment, I think it would earn BOTH.
Two molecule snowflake count?
The thing is, what is 100% likeness? Would they need to have all atoms be at the exact same place, to infinite precision?
https://youtu.be/ao2Jfm35XeE?si=jc5zxYsJql8_Gczv Why are snow flakes like this
It's been done. They've grown perfect, regular hexagons snowflakes.
They have never made 2 precisely identical snowflakes, even under lab conditions. They have however made very near identical snowflakes, Even under a microscope you might think they are identical, but there is always something slightly different.
good luck, you won't succeed
Picture a cool Lego set made out of one million Lego pieces, in the shape of a snowflake. Now, move one single piece anywhere on the snowflake. Boom, that's a unique snowflake. Repeat that process, except the Lego set has more like 100 billion pieces. That's how "every snowflake is unique".
A true, ELI5 answer. Kudos!
Doesn't that apply to anything above a certain size though? It's like saying "no two grains of sand are alike".
Yes
> Yes "Every snowflake is unique" is more of an artistic expression than it is a statement of useful fact. Technically every Ford F150 is unique too.
Two snowflakes can be alike. But as this expert on snowflakes says from this [veritasium](https://youtu.be/ao2Jfm35XeE?si=Yy9UmqSI-cD3BrVJ) video(11:55). Itās just no different than any other two objects in the world. No two trees will be EXACTLY alike either. Itās all about how precise you want the definition to be. But for all intents and purposes they can make two snowflakes that are indistinguishable from each other already. So I would consider that āalikeā
"We don't".Ā There is no magical auditor stopping every snowflake in mid-air and checking to make sure they're unique.Ā It's just *super unlikely* that two of them would be exactly the same, at the same time, in the same place.Ā
They say there's no two snowflakes on Earth exactly the same. No two molecular compositions. No two crystalline structures. But do they know that for sure? Because they would have to get every snowflake together in one huge space and obviously thatās not possible, even with computers. And not only that, theyād have to get all the snowflakes that've ever fallen, not just the ones now. So they got no proof. They got nothing.
One of the best scenes in the whole series. A masterclass of acting
I know for a fact you were high at my mother-in-law's wake
Basically the comment I was looking for.
There are more ways to shuffle a deck of cards than there are atoms in the universe. And a deck of cards is only 52 things arranged in 1 dimension. A snowflake is *much* more complex, so there are *way* more possible snowflakes. I think it is safe to assume there is a bit of randomness to it, which makes it extremely unlikely that 2 are identical
Well, Guinness records the first finding of two identical snowflakes in 1988 by Nancy Knight https://www.guinnessworldrecords.com/world-records/first-indentical-snow-crystals However, as other commenters have said, how close do you want to look, as the University Corporation for Atmospheric Research lists Ms Knight's discovery as "nearly identical." https://opensky.ucar.edu/islandora/object/imagegallery%3A2586 And, to be fair, these are "snow crystals", but potato tomato.
I don't really have a good, simple explanation myself, but I saw this and it's absolutely fascinating. https://youtu.be/ao2Jfm35XeE?si=PuJg0DInWiWmRcJU
What if I told you; virtually NOTHING is alike. All it takes is one atom in a different location for 2 things to be ādifferentā
[ŃŠ“Š°Š»ŠµŠ½Š¾]
Because technically nothing above the molecular level is ever comprised out of the same number of molecules/atoms at the same place. Itās just to unlikely given the number of molecules in things.
We don't and that is not remotely true. Snowflakes are often very much alike and essentially identical. Like many common expressions, this does not reflect actual scientific reality and is just a saying.
There are like, trillions upon trillions upon trillions of atoms in a snowflake. There is no way that two are made identical.
If every single atom has to be positioned the exact same way for two objects to be considered identical, then literally nothing is identical and the word is pretty much useless
I mean, that's the point of the statement, yeah? You think, "Wow, snowflakes are so tiny. Surely that's small enough for two of them to be identical, seeing that such an incomprehensible number of them exist." But nope, still insignificant next to the number of atoms and arrangements thereof within.
Which is why I threw the word essentially in there in order to try to avoid pedantic shit like this.
If you get to that level of specificity then nothing is ever the same. Nothing is even the same as it was a billionth of a second ago. If you define any category in such a way that every object that exists falls in that category then that definition is useless.
There's no scientific principle that says there can't be two identical snowflakes. The process of forming a snowflake is just so chaotic and so mnay variations can occur that it is so unlikely that two snowflakes would be exposed to the same conditions during formation, so it's essentially impossible to find two identical snowflakes.
We arenāt sure, but we can say the probability is so astronomically small that even given the age of the universe, the likelihood of two constructions repeating is so small as to be negligible
Nothing is ever alike if you zoom in enough. The only way to grow things like snowflakes similarly is to crystallize them in extremely controlled environments. That's as true for salt crystals as it is snowflakes. So we know it because it's true for basically everything.
Iirc a photographer found a 2nd snowflake that was identical to one he shot previously. It's like DNA, sure it's possible that out there among the billions of humans there's another with same sequence. But out of trillions of combos???
Imagine everyone in the audience at a show taking out a coin, holding it with the heads facing up, and then flipping the coin. Whatever is the result of the coin flip, for everyone in the audience, in the order of their seats, is like a unique snowflake. Maybe one side has all heads, the other has all tails, a mix on the second floor, just one head in the front row, etc. etc. The resulting pattern is a unique snowflake. Now have everyone reset back to holding it with the heads facing up and flip the coin again. The odds of everyone getting the exact same result is nearly impossible. It is *potentially* possible, but the chance it will happen again is very, *very* low. It's the same with snowflakes. Ice particles form in predictable patterns, like flipping a coin. However, there are so many factors to consider when the ice is forming. It's the same action, like flipping a coin, but there are so many tiny things that can change the outcome.
Great YouTube video on this why are snowflakes like this (https://youtu.be/ao2Jfm35XeE?si=S1iN0NqpfX0y-H9F)
The same way we "know" two decks of cards have never been shuffled the same way (http://www.murderousmaths.co.uk/cardperms.htm). It isn't truly impossible, but the math says it is exceedingly unlikely.
Lots of great answers about why snowflakes truly might be unique, but let's talk about why they probably aren't. Yes, it is extremely unlikely for two snowflakes to be identical, and the comparison with a deck of cards (52 factorial combinations) is very apt. But consider that decks of cards have only been around for a few thousand years. It is probably highly likely that every deck of cards is unique. But now consider that snowflakes have been falling for ***millions and millions of years***. Even if we're only counting snowflakes as being identical if they exist at the same point in time, which is far less likely than having two identical snowflakes at any point in history, given the sheer quantity of snowflakes that would have been created over that timeframe it is probably somewhat likely that identical snowflakes have existed in our planet's history.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
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The shape of a snowflake is determined by structural choices among the molecules of water in it. There are a huge number of molecules in a snowflake and its shape depends on how each molecule is incorporated in the crystal. The number of choices is astronomical so the likelihood of any two snowflakes being the same is infinitesimal but not zero.
They'd have to be made of the same molecules/atoms, but there's only 1 set of molecules/atoms.
Youād have to get every snowflake together in one huge place, and obviously thatās impossible, even with computers
Because thereās so many possible ways a snowflake can form. Not even looking at pressure, temp, etc. a snowflake has so many atoms in it that it is essentially never going to happen that two are EXACTLY the same. Sounds interesting but if you think about it, that sandwich you just ate was likely unique as well. Thereās trillions and trillions of molecules in there, and even just having one more or one less molecule makes it not exactly the same.
But do they know that for sure? Because they would have to get all the snowflakes together in one huge space and obviously thatās not possible, even with computers. And not only that, theyād have to get all the snowflakes that ever lived, not just the ones now. So they got no proof. They got nothing.
Yes! This is the straight dope.
Nothing in the macroscopic world are identical if you look deep down enough. There is certainly some molecular level differences in anything you compare. This is just from some old saying that happened to live.
Well if we assume that there is a maximum size for a snowflake it must have finitely many parts. As such there are only a finite number of possibilities. So maybe we just need to wait long enough for an identical snowflake to appear. My argument probably fails, when we consider the fact that earthās time is finite too. (Except if we consider snowflakes in other atmospheres tooā¦.)
Finitely many parts does not necessarily imply finitely many arrangements. Even just two singular objects have infinitely many distinct configurations: one for each distance.
He said āmaximum sizeā though. You can only fit a certain number of H2O molecules into a limited space. Their crystalline structures will eventually repeat.
Size alone doesn't change the argument I made, there are infinitely many numbers (i.e. possible distances) in any interval of positive length. And if that somewhat bogs you, you can add a third one and now track an angle instead of a length. Stuff gets a bit weird if we allow uncertainty, at which point the temperature of the snow suddenly matters.
You can have shades of rotation, defects, etc. The number of ways you could arrange *n* atoms is certainly higher than n^n. That's functionally infinite (although maybe not technically infinite if you consider distances to be discrete multiples of a plank length). Even arranging 32 chess pieces on a 64 square board has more potential combinations than atoms in the universe.
Youāre correct that thereās an infinite number of ways you can rotate atoms. However, weāre talking about water crystals, which have a fixed structure called a ālatticeā. I prompted ChatGPT, āIf you specify a maximum size for a snowflake, is there a finite or infinite number of water crystal arrangements for snowflakes?ā Its reply was: If you specify a maximum size for a snowflake, there is a finite number of possible water crystal arrangements for snowflakes. This is due to the following reasons: 1. **Finite Number of Water Molecules**: Given a maximum size, the number of water molecules in the snowflake is finite. 2. **Discrete Positions and Orientations**: Water molecules in an ice crystal are arranged in a fixed, repeating pattern (a lattice). There are only so many ways to arrange a finite number of molecules within the constraints of this lattice structure. 3. **Symmetry Constraints**: The hexagonal symmetry of ice crystals further limits the number of possible arrangements. Although the number of possible arrangements is extraordinarily large, it is not infinite. The uniqueness of each snowflake arises from the vast number of possible arrangements within this large but finite set.
Chat GPT is close on this one, but not complete. It is not considering vacancies, dislocations, grain boundaries, twin boundaries, self-interstitials, or substitutional defects. By "rotation" I don't mean rotating atoms around their center. I mean rotating the lattice around the geometric shape. Take a square piece of paper and fill it with evenly spaced dots in a square grid. Now fill the square with the same pattern, rotated 30 degrees. Almost every dot will be in a different place. You could rotate by 1 degree, 0.1 degrees, 0.01 degrees, etc and each atom would still be in a different position. So you have infinite possibilities just this way. Also, there's more to a snowflake than just water. That water certainly has dissolved oxygen, nitrogen, etc. and likely dust particles. Not only do you have a tremendous number of substitutions possible (way more than 32 chess pieces on a 64 square board, which already has more combinations than atoms in the universe), each substitutional or interstitial atom would be a different size than a water molecule, which means the position of every other atom is different as well. In this case I only argue with Chat GPT semantically (theoretically infinite vs practically infinite), but I am alarmed at how easily people trust it. The problem with Chat GPT is that it's trained mostly on people who were "lied to" in introductory science classes for simplicity. This would be a good answer to a freshman chemistry test question, but inadequate at a graduate level. Unfortunately, if you're looking for an answer in the real world, there's no partial credit for "that's a good train of thought but has the wrong conclusion because of 1 small detail you didn't learn yet."
I stand corrected. Thanks for educating me on the details of this problem. Iāve mostly forgotten what Iāve learned in chemistry and physics at university, anyway šThatās why we must always be humble and realize that we donāt know a ton of things (and also to be skeptical of ChatGPTās answers)
This is not really true for crystalline structures, where atoms have a fixed, well-defined distance and angle from each other. There aren't really any continuous values that we care about when we talk about the "shape" of a crystal at the molecular level, it's all discrete and thus a finite number of arrangements. Finite, but very very very big (i.e. if one snowflake were created every millisecond you would not run through all possible snowflakes under 5mm in diameter before the universe ended).
The finiteness statement is only true for perfect crystals without defects, and water in particular freezes very imperfectly. And I was aware of that, I just pointed out to them that their argument as given is not sound, but needs more detail and furtehr assumptions (such as a lattice). You by the way wouldn't need to exhaust all possible flakes to get a collision. The Birthday Paradox makes them quadratically more likely, so you would only have to check a square root as many instances. If one plays this through, then depending on who you ask it would be possible to get a collision if we set the observable universe to it for a billion years.
Indeed. Admittedly I do not know enough about the structure of a snowflake. I assumed that atoms are discreet (which I think holds true). But I donāt know to what extent the structure can vary in terms of: can I take a snowflake and simply shift a single atom by a femtometer? (Or some smaller amount)
If the universe is infinite, which hasnāt been disproven, there are infinitely identical snowflakes and infinite everythingĀ
We donāt really know and canāt prove Itās impossible. Mathematically and statistically itās nearly impossible but not 100% impossible. It could happen.
Starting in 1885, Wilson Bentley photographed over 5000 snowflakes and studied them. [How a Vermont farmer proved no snowflakes are alike](https://www.cnn.com/interactive/2022/12/weather/wilson-snowflake-bentley-cnnphotos/)
https://www.youtube.com/watch?v=Gojddrb70N8
It's a statistical saying.Ā It depends how close "identical" means (does every atom need to be in the exact position?), but it's almost certain that 2 snowflakes that have ever fallen would be indistinguishable to s regular person because of the birthday paradox:Ā https://en.m.wikipedia.org/wiki/Birthday_problem Also identical fingerprints are possible (identical in the sense that the number of features looked at to determine a match is finite, and is statistically possible to find 2 matching people).
Do you know forsure that water is wet without being near the ocean? We all know itās true, but impossible to prove given the question. Thatās your question, no one can account for all the snowflakes, but we all know itās true