the old adage, “No two snowflakes are alike” has been used in many different situations throughout history and across literature. It can be a way to communicate the uniqueness of a ‘thing’ or a reminder that every moment is special in its own way.
It is often a touching metaphor. But, I am not a literary scholar. I can’t explicate much. What do I know about metaphors, anyway, I laugh at Jay and Silent Bob.
What I can do, though, is look at math. Numbers are cool! And, to borrow a line from Neil DeGrasse Tyson, “Math is the language of the universe.”
What is snow?
This may be a pretty simple question, but there is a lot to it. Snow isn’t just frozen rain. When rain freezes, it is usually sleet. Snow forms in a particular part of the atmosphere called the Dendritic Growth Zone. That is a space where the air pressure and temperature are just the right way to get dendrites to form. Snow can come in many shapes and sizes, but for this explanation, we will look at what most people consider a “typical” snowflake, the ones with big dendrites.
And you get cool-looking stuff like this:
The branches of a snowflake – six of them – are what make snow so beautiful. The intricate patterns that form are unique each time, because the process that builds them uses a lot of math to manifest each individual outcome. It is a combination of air pressure, air temperature, and time.
Here is a scientific explanation from Cal Tech:
The water molecules have to diffuse through the air to reach the crystal, and this diffusion slows their growth. The farther water molecules have to diffuse through the air, the longer it takes them to reach the growing crystal.
Courtesy: its.caltech.edu
So, snow is just the growth of a water crystal via water vapor that is freezing out over time within a particular environment at a particular level in the atmosphere that involves a very specific set of parameters unique to each individual snowflake.
You can quickly see why each one may look different.
How many different types of snowflakes can there be?
That is a good question. But for the answer, we have to go back to school for a bit.
Because snow forms by water vapor freezing out of the air to form a crystal, it means that these are being built molecule by molecule.
When you have a glass of water on the table, most of those molecules are already bonded together. They aren’t free floating. all 8.36 x 1024 molecules of water are stuck together in the glass.
8.36 x 1024 molecules of water = 836,000,000,000,000,000,000,000,000 molecules
But snow is getting pieced-together molecule-by-molecule. And every molecule of water isn’t exactly the same.
Without getting into the weeds too far, H20 can contain different isotopes of oxygen – either O-16 or O-18 isotopes within the water molecules. The difference in the isotopes can produce subtle differences in how the molecule freezes out and forms bonds.
On top of that one of the two Hydrogen atoms in the molecule can sometimes be swapped for a deuterium isotope. And that can change how it freezes out and forms bonds.
That creates our first math-related suggestion that “no two snowflakes are alike” claim. For more, we go back to Cal Tech
Since a typical small snow crystal might contain 1018 water molecules, we see that about 1015 of these molecules will be different from the rest. These unusual molecules will be randomly scattered throughout the snow crystal, giving it a unique design. The probability that two snow crystals would have exactly the same layout of these molecules is very, very, very small.
COURTESY: ITS.CALTECH.EDU
You may be thinking, wait a snowflake has 1018 water molecules? But a full GLASS of water has 8.36 x 1024 water molecules – those numbers look pretty close.
But they aren’t.
1018 is 1,000,000,000,000,000,000
And, as we pointed out above, 8.36 x 1024 is 836,000,000,000,000,000,000,000,000
So how many different kinds of snowflakes can exist? Well, consider this: According to the Library of Congress, scientists calculate that each winter there are about 1,000,000,000,000,000,000,000,000 (that is a trillion trillions) snow crystals made. And researchers at Cal Tech say, “Even with 1024 [snow] crystals per year, the odds of [the same snowflake occurring twice] within the lifetime of the Universe is indistinguishable from zero.“
The phrase “indistinguishable from zero” is also something I would hear from my girlfriend if I asked, “What are the chances you would be okay with me purchasing a $10,000 82-inch 8K TV?”
