Snowflake Theory
I just don't think it's an absolute that no two snowflakes are alike.
Something to ponder.
- http://wonderopolis.org/wonder/why-are-all-snowflakes-different/#sthash.1ewgSmC9.dpuf
Quote: HotBlondeI just don't think it's an absolute that no two snowflakes are alike.
Of course its not silly... what sort of a scientist would sit there comparing snow flakes and having to do it real fast too...who would pay him to do it? Its like 'no two persons have the same fingerprints'.
>Something to ponder.
Not really.
Quote: HotBlondeNow that it's getting cold outside I've begun to think about something again that I've thought of in the past. They say that no two snowflakes are alike. But can that actually be true? I can see how most of them can be different, and even 99.99999999% of them (obviously I'm not giving an exact number, but you get what I'm saying.) But is it really mathematically possible to have a bazillion-gazillion snowflakes created since the beginning of time and not one that was created ever matched another one, even if they existed at different times?
I just don't think it's an absolute that no two snowflakes are alike.
Something to ponder.
Search in here for "The Science Thread". We already investigated it =)
+++++++++++1Quote: KeyserSozeIf someone found two identical snowflakes, how many people would really give a damn?
Quote: KeyserSozeIf someone found two identical snowflakes, how many people would really give a damn?
Hulk smash!
(that's how The Hulk feels. Of course, he feels that way about a lot of stuff)
Quote: KeyserSozeIf someone found two identical snowflakes, how many people would really give a damn?
You're missing the point. The point is that it's taught as fact that "no two snowflakes are alike". I'm just saying that maybe it's not a fact after all.
They actually teach that? I always thought it was just a sayingQuote: HotBlondeYou're missing the point. The point is that it's taught as fact that "no two snowflakes are alike". I'm just saying that maybe it's not a fact after all.
Quote: AxelWolfThey actually teach that? I always thought it was just a saying
Jeez, the meeting of two like minds, axelwolf and HB. Can the
universe take the stress without imploding.
Quote: HotBlondeBut is it really mathematically possible to have a bazillion-gazillion snowflakes created since the beginning of time and not one that was created ever matched another one, even if they existed at different times?
Hi HB! Nice to hear from you. I'm with you 99.9999999% on this one. Nobody should make the claim that no two snowflakes have ever been alike unless he has examined every one of them. The expression should be, "It is very unlikely two snowflakes have ever been alike." Or, better yet, "The odds of there having ever been two identical snowflakes are 1 in x." Please substitute the correct number for x. I would love to sink my teeth in into the mathematics of it, but don't know enough about snowflakes.
This annoys me almost as much as maps in a kiosk that don't have an indication saying "you are here."
Quote: KeyserSozeIf someone found two identical snowflakes, how many people would really give a damn?
I find them all the time. Nobody believes me because they always melt by the the time I get them in the house. :-)
Quote: WizardI would love to sink my teeth in into the mathematics of it, but don't know enough about snowflakes.
I'm so glad to hear this!
Ice forms in hexagonal structures, although rarely they can form as triangles, so it would take 6 water molecules to form one "ice unit". As a very rough approximation, a flake contains 10^19 (ten quintillion) molecules of water. I say very rough because we've all seen flakes ranging from the size of a grain of salt, all the way up to the world record of 15". Here in WNY, it isn't uncommon to see them 3" in size.
So, if a "flake" is one of those perfectly formed micro examples that contain 10 quintillion molecules of water, how many molecules do one of the jumbo example contain? And how many combinations can be found in such a number? Can one even comprehend that amount of zeroes?
Add in the fact that said "ice units" form in several different arrangements due to heat and humidity, and even the water itself exists in different formations (most contains Oxygen-16, while 1 in 500 or so contain a molecule of Oxygen-18), and you're talking an amount of combinations (in my ignorant estimate) that eclipses the number of suns in the universe.
Feel free to chew on those numbers, Wiz. If you can manage to ballpark a number of possible combinations, I'll try to ballpark the number of flakes that have fallen since the beginning of time, and we'll have our answer ;)
(While posting this, I looked above and saw Face's post. Mine is another way of thinking about the same thing, so I'll post it as an adjunct.)
I can sit here and look out the window and guarantee you that all the snowflakes falling from the sky are identical, by my view. Next we can hold them up to our eye and say that some of them look different. Then we can isolate some of them, under a magnifying glass, and say that we haven't seen any that are the same....
So lets say that we find two that appear, to our eyes, to be "identical". Are they? Are they really? Do they have the exact same number of water molecules, in the exact same arrangement, or are some missing? Are they "identical" if one of them has one molecule of heavy water, and the other doesn't? (Deuterium exists at 156 ppm on earth.)
Let's go the other direction. What is a snowflake? Does any frozen water in the sky qualify as snow? In that case, let's consider a single molecule of water, frozen, falling from the sky. Wouldn't it be identical to all the other single frozen molecules of water? Snowflakes evolve. Wouldn't there be an incredibly common chance that any 10 molecules of water frozen together would be identical?
IMO, the question in its traditional interpretation is born of old thinking, and it really has no meaning outside of a colloquial one. The only way the term is useful is sarcasm: "Well aren't YOU a special snowflake." In that way, it has a social use.
http://www.its.caltech.edu/~atomic/snowcrystals/
Read this:
http://www.its.caltech.edu/~atomic/snowcrystals/alike/alike.htm
Quote: MoscaLet's talk about scale here. At what level would a snowflake qualify as "identical"? Is it visual? Microscopic? Molecular?
(While posting this, I looked above and saw Face's post. Mine is another way of thinking about the same thing, so I'll post it as an adjunct.)
I can sit here and look out the window and guarantee you that all the snowflakes falling from the sky are identical, by my view. Next we can hold them up to our eye and say that some of them look different. Then we can isolate some of them, under a magnifying glass, and say that we haven't seen any that are the same....
So lets say that we find two that appear, to our eyes, to be "identical". Are they? Are they really? Do they have the exact same number of water molecules, in the exact same arrangement, or are some missing? Are they "identical" if one of them has one molecule of heavy water, and the other doesn't? (Deuterium exists at 156 ppm on earth.)
I take things literally (obviously). "No two snowflakes are the same/identical". Identical means "alike in every way: exactly the same as or equal to something else, or alike in every respect". So if they don't have exactly the same amount of H2O molecules, or are arranged differently in any way, or have just one more O-18 molecule, or whatever, then it's not the same, by definition.
Quote: MoscaLet's go the other direction. What is a snowflake? Does any frozen water in the sky qualify as snow? In that case, let's consider a single molecule of water, frozen, falling from the sky. Wouldn't it be identical to all the other single frozen molecules of water? Snowflakes evolve. Wouldn't there be an incredibly common chance that any 10 molecules of water frozen together would be identical?
There's can't exist "one frozen molecule". One molecule of water can only exist as vapor, and therefore cannot also be a solid.
But I get your point. To that, I say that meteorology defines "snowflake" as "an agglomeration of snowflakes falling as a unit", which would support the idea that the amount of molecules contained therein would have to be numerous indeed to overcome the updrafts of our weather system.
And of course this is just some dumb colloquialism not to be taken seriously. But taking seriously the absurd is precisely why I'm here so often ;)
What we clearly need is:
1. Some information on how many different possible types of snowflakes there could be. We can restrict this to those to the most common size range, like 1/2" or smaller.
2. How many snowflakes have fallen in the history of the earth. We could get at this figure as the produce of number of years * total snowfall in cubic meters * snowflakes per cubic meter. To make it harder, we could factor in the ice ages.
Somebody call Paco.
Quote: HotBlondeYou're missing the point. The point is that it's taught as fact that "no two snowflakes are alike". I'm just saying that maybe it's not a fact after all.
I don't know if you have ever heard the saying "absence of evidence is not evidence of absence" sometimes expressed as "you can never prove a negative".
There are no facts which state that "something never happened". Technically you can only say that something is wildly improbable.
People are always stating that they have proved a negative, or worse yet demanding that such proof be given. Even in legal cases.
Quote: WizardWhat we clearly need is:
...
2. How many snowflakes have fallen in the history of the earth. We could get at this figure as the produce of number of years * total snowfall in cubic meters * snowflakes per cubic meter. To make it harder, we could factor in the ice ages.
This web site claims every year one septillion ( 1,000,000,000,000,000,000,000,000) snow crystals fall from the sky.
The earth is about 4.5 billion years old, although Michelle Bachman may have another opinion on that. So, assuming the same rate of snowfall every year (yes, I know I'm not factoring in ice ages, but let's keep it simple), there would have been 4,500,000,000,000,000,000,000,000,000,000,000 (4.5 * 10^33) snowflakes in the history of the earth.
Now we need to get at the number of different possible snowflakes. Paco?
Quote: Face
Ice forms in hexagonal structures, although rarely they can form as triangles, so it would take 6 water molecules to form one "ice unit".
I could very well understand that on this molecular level, 6 water molecules would condense into a hexagonal symmetric structure. But why are they also macroscopically symmetric ?
I mean, if you add one molecule to the one side of the snowflake, why do the next molecules attach exactly at the other 5 corresponding places, which might be a bazillion times it's own dimensions away ?
Quote: MangoJI could very well understand that on this molecular level, 6 water molecules would condense into a hexagonal symmetric structure. But why are they also macroscopically symmetric ?
I mean, if you add one molecule to the one side of the snowflake, why do the next molecules attach exactly at the other 5 corresponding places, which might be a bazillion times it's own dimensions away ?
But do they? Attach in turn? I would think it far more likely a snowflake would be asymmetrical at any given snapshot point than symmetrical. I think the symmetry would have more to do with the spontaneous transition of liquid to solid when passing either through an area of cold air and/or enough air moving across the molecules to cool them into solid form (such as supercooled rain that then freezes on contact with airplane surfaces), when they become simultaneously and mutually attractive.
After that initial cross-point, any further transitions would be more random as the solid moves through saturated air and randomly encounters similarly near-cooled liquid. There's also the density situation, where snowflakes occupy more volume per cubic than rain/water molecules and are more vulnerable to air movement (lighter, if you will). So the water will hit the snowflake as it falls past and either slightly melt the snowflake and continue or join with the snowflake as a solid in that instant, all depending on ambient conditions.
I think snow tends to happen in concert with much lower humidity simply because snowflakes, once formed, tend to themselves have a cooling effect on the air, which cools the water molecules in turn (like ice cools your tea even as it melts) just enough to make them into snowflake-attachable molecules, which makes the snowflakes larger, which cools the air further, ad infinitum, until the snowflaked air hits a warmer air mass that will de-crystalize the molecules and make them back into water, or the snowflakes hit a solid surface that's cold enough to retain them, or warm enough to melt them.
Quote: MangoJI could very well understand that on this molecular level, 6 water molecules would condense into a hexagonal symmetric structure. But why are they also macroscopically symmetric ?
I mean, if you add one molecule to the one side of the snowflake, why do the next molecules attach exactly at the other 5 corresponding places, which might be a bazillion times it's own dimensions away ?
Locally, the conditions are the same, or close enough to the same that we get symmetry. I believe that they are not all perfectly symmetrical if you look hard at them.
So without doing the math (which was never an exercise in my atmospheric science classes), I'd say it's pretty damned unlikely. The math behind even determining the different combinations of snowflake permutations given the initial conditions is murky at best.
Quote: Wizardthere would have been 4,500,000,000,000,000,000,000,000,000,000,000 (4.5 * 10^33) snowflakes in the history of the earth.
Can somebody, perhaps with Mathematica, calculate the following for me. It is off the scale for Excel, which is not something I say often.
1/[1-0.5^(1/combin(4.5 * 10^33,2))]
Quote: Wizard...1/[1-0.5^(1/combin(4.5 * 10^33,2))]
Let the very small number 1/combin(4.5 * 10^33,2) be called d.
Then ln(0.5^d) = d * ln(0.5).
Then 0.5^d = e^(d*ln(0.5)) which is well approximated, for the very small d, by 1 + d*ln(0.5).
Then 1 - 0.5^d = -d*ln(0.5) = d*ln(2)
The answer is approximately 1 / [d * ln(2)], where d is approximately 2 / (4.5 * 10^33)^2.
So, the answer is approximately 1.46072873 * 10^67.
Quote: ChesterDogSo, the answer is approximately 1.46072873 * 10^67.
Thanks!
If there were this many possible snowflakes, and each was equally likely, there would be a 50% chance of at least one set of identical snowflakes.
Next we need to work on the actual number of possible combinations of snowflakes. Any thoughts anyone?
Quote: WizardThanks!
If there were this many possible snowflakes, and each was equally likely, there would be a 50% chance of at least one set of identical snowflakes.
Next we need to work on the actual number of possible combinations of snowflakes. Any thoughts anyone?
By combination do you mean like snowballs or snowmen?
Quote: petroglyphBy combination do you mean like snowballs or snowmen?
I don't understand the question.
Quote: WizardI don't understand the question.
Sorry Wizard, my humor took over. If you pack snowflakes together [combining snowflakes] you get snowballs etc.
I thought I was funny in a Dilbert sort of way.
You guys are amazing to me with your skills in math, I can't even understand the formulas, questions or answers, but I like to read through.
I have noticed in the few mensa's I've known they were usually too serious to catch witticisms. But they were genuinely good people.
ps I was able to hold off until you solved the problem.
Quote: petroglyphI have noticed in the few mensa's I've known they were usually too serious to catch witticisms.
I have the worst of it. Mensa won't let me in, because I failed the test, and I still don't get a lot of jokes, like yours.
Quote: WizardI have the worst of it. Mensa won't let me in, because I failed the test, and I still don't get a lot of jokes, like yours.
I know how you feel, comedy club wouldn't let me in because I'm not funny, and I got a D in geometry.
Quote: WizardCan somebody, perhaps with Mathematica, calculate the following for me. It is off the scale for Excel, which is not something I say often.
1/[1-0.5^(1/combin(4.5 * 10^33,2))]
Wolfram Alpha.
http://www.wolframalpha.com/input/?i=1%2F%281+-+0.5%5E%281%2FBinomial%5B4.5+10%5E33%2C+2%5D%29%29
Quote: WizardI have the worst of it. Mensa won't let me in, because I failed the test, and I still don't get a lot of jokes, like yours.
I find it hard to believe Mensa won't let you in. Do you not have a pre-95 SAT(1250) or pre-89 ACT(29) score laying around?
http://www.us.mensa.org/AML/?LinkServID=005EB3F7-B83A-44BA-B4FFD5114A1AC31D
Quote: socksI find it hard to believe Mensa won't let you in. Do you not have a pre-95 SAT(1250) or pre-89 ACT(29) score laying around?
Is that all it took? Anyway, no, I don't have such a score *ahem* laying around.
Quote: ChesterDogSo, the answer is approximately 1.46072873 * 10^67.
Let call this the CDN, for ChesterDog number.
I note that the log to the base 2 of CDN is 223.12. The odds of correctly guessing the flip of a coin this many times would be 1 in CDN.
If at every moment a growing snowflake could form in one two directions, then at 223 of such forks we would get to CDN. I tend to think a snowflake goes through a lot more forks in the road in its formation than this. Probably in the thousands.
Nevertheless, it could happen that two flip that coin in the exact same pattern. So, as HB said, we shouldn't say two snowflakes have never been alike.
Quote: socksI find it hard to believe Mensa won't let you in. Do you not have a pre-95 SAT(1250) or pre-89 ACT(29) score laying around?
http://www.us.mensa.org/AML/?LinkServID=005EB3F7-B83A-44BA-B4FFD5114A1AC31D
Hell, I have one of those and I'm an idiot.
http://www.gocomics.com/bc/2013/11/18#.UpYXEI2Hn6Q
http://www.gocomics.com/bc/2013/11/19#.UpYYXI2Hn6Q
There are a couple more in that series.
Quote: DocThere are a couple more in that series.
Look at the dates. Maybe the cartoonist is a forum member.
I didn't know BC was still in publication. I haven't seen it in decades.
There's a bunch more here. It's snowing now, hard
to believe these are the flakes.
http://www.natureknows.org/2013/11/amazing-macro-photography-of-individual.html
Quote: socksI find it hard to believe Mensa won't let you in. Do you not have a pre-95 SAT(1250) or pre-89 ACT(29) score laying around?
Really!?
One freakin' point and I'd have it on the ACT!
EDIT: Pre-89, missed that.
All flakes are 6 sided.
The reason it's so hard to find to alike has to do with how the crystals form. It that wasn't unique enough' snowflakes break when they are falling and when they hit the windshield for example.
