Is Every Snowflake Unique?

Simon Allan

No. And also yes.

On a purely physical level, in 1988, researcher Nancy Knight found two virtually identical snowflakes.

The paper is called ‘No two alike?’, and was published in the Bulletin of the American Meteorological Society (Issue 69). Here is the image of the snowflakes taken from the paper:


Image Credit: NCAR

I could just leave it at that and knock off for lunch, but I’d like to think I’m more professional than that, so it’s worth delving into the topic a bit more.

Snowflakes form when very cold water comes into contact with a dust grain or pollen particle. The water coats the particle and freezes into an ice crystal. The newly-formed ice crystal can no longer be held up by the buoyancy of the air, so it falls. As it falls, more water and water vapour freezes onto the crystal, building it up in size. If the air between the cloud and the ground is below freezing, the snowflake will be preserved and continue to grow.

In terms of the crystal structure of snow, there are entire academic papers dedicated to the physics and chemistry of snowflake structures and diversity.

Most snowflakes start as a simple hexagonal structure, but many factors exist which can change how the crystal grows from there. Crystal temperature as the snowflake falls, the altitude at which the snowflake is formed, the speed it falls, the snowflake’s overall trajectory, variations in the diameter of the particle the water condensed onto, differences in the clouds, drop collisions and vapour pressure in the clouds all control how the crystal structures form.

Lower vapour concentrations cause a snowflake to grow more slowly and produce less intricate shapes. The shapes we most associate with snowflakes form more readily in higher vapour concentrations, or in colder conditions (like the ones found in high altitude cirrus clouds). Larger snow crystals can have more diversity in patterns than smaller crystals.

All these factors control how diverse snowflakes can be. Estimates of crystal diversity vary from 500 different types (cited from the paper linked above), to 30,000. A diversity curve for snowflakes, adorably called the mitten curve, is basically impossible to observe.

To get around this problem and determine the likelihood of crystal similarity, an approximation for snowflake uniqueness, called the Feller’s approximation, attempts to calculate the probability all crystals in a snow cloud are unique. In large snowstorms, there are enough crystals so that some crystals stand a good chance of looking like copies.

Taking all the snow that may have ever fallen to Earth, the Feller’s approximation tells us that two indistinguishable crystals almost certainly existed.

The only problem is, this is virtually impossible to disprove.

On a molecular level, the ‘impossible to prove’ problem exists for the opposite reasons.  Two molecularly different snowflakes could very easily look alike under a microscope.

Kenneth G. Libbrecht, a physicist at Caltech who has an interest in pattern formation of ice (and actually made two identical snowflake crystals in a lab), argues:

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.  Even with 1024 crystals per year, the odds of it happening within the lifetime of the Universe is indistinguishable from zero.

Thus, at some very pure level, no two snow crystals are exactly alike.


While there’s no way to prove if snowflake doppelgangers exist, snow has many wide reaching impacts on the climate of the entire globe.  

Even if there aren’t unique snowflakes, those small crystals are tiny cogs in an amazingly complicated climatological system that affects the entire planet. Perhaps that’s the real magic of snow.

Or maybe it’s just the excuse to stay in with hot drink, or snowball fights in the Peaks.

Does Homeopathy Work?

Simon Allan

In 2015, the small Lothian Health Board in the Scottish Lowlands was taken to court by a 73-year-old woman with arthritis. The health board had taken the decision to stop funding homeopathic treatments. The woman had called for a judicial review of their choice, and the courts came down firmly on the side of the health board, stating:

“…A different decision, namely, to continue spending money on a service whose efficacy was not established, would have been unreasonable”

This may seem something of a deathblow to homeopaths, however support for alternative practices remains widespread. Known homeopath Prince Charles recently thrust the topic back into the limelight after proposing homeopathy be used to treat animals to combat overuse of antibiotics on farms. Ever popular Health Secretary Mr Hunt is rumoured to have supported it (Mr Hunt has since denied this). Labour leader Jeremy Corbyn’s support, at time of writing, stands unwavered. Should it?

L0057834 Mattei's electro-homeopathic treatments, Bologna, Italy, 187

Image Credit: Wikipedia Commons

The term homeopathy was coined by a German physician named Christian Friedrich Samuel Hahnemann in the 1700s. He based his ideas on the “Principle of Similars,” – literally like cures like. The reasoning was simple enough: if, in large doses, a substance creates symptoms, in lower concentrations it will remove them. The more diluted a substance, the more effective at removing the symptoms it’ll be. Fortunate, considering most original homeopathic compounds are toxic. One common designation is “NC”, where C signifies that a substance is diluted by a ratio of 1:100 and N stands for the number of times the substance has been diluted. In the least diluted form, the one advocated by Hahnemann (30C), the ratio of active ingredient to water is 1:1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

For perspective, one molecule of active substance in a 30C homeopathic remedy would require more than all the atoms in the solar system. Homeopaths will navigate around this inconvenience by stating water retains a “memory” of the active substance. This is crap. America’s National Institutes of Health (NIH) points out that the key concepts of water memory in homeopathy are inconsistent with the fundamentals of chemistry and physics. Tim Minchin more humorously notes:

“It’s a miracle! Take physics and bin it! Water has memory! And whilst its memory of a long lost drop of onion juice is infinite, it somehow forgets all the poo it’s had in it.”

A fact still trotted out regularly by defenders of homeopathy is its initial success in apparently treating illnesses. Indeed, one London hospital practicing homeopathy had far fewer deaths than conventional hospitals in the area in treating 19th century cholera outbreaks – a staggering score against the conventional medicine of the time. Of course, with the benefit of 20/20 hindsight, the higher death rates in conventional hospitals can be chalked up to poor practices – bloodletting is not remembered for its illness curing capabilities, after all. Homeopaths will also point to treatments such as radiation therapy to treat cancer, antivenom, or the original smallpox vaccine as proof of the “like cures like” concept. But in the face of modern medicine, the above examples of antivenom and radiation therapy have been subjected to the rigour of randomised control trials to prove their safety and effectiveness (oncologists don’t throw cancer patients into nuclear reactors with crossed fingers).

Studying the efficacy of homeopathy, the NIH states, is difficult. Shockingly, it’s hard to examine the effects of a medicine when that medicine has little to no active ingredient beyond just placebo. Some of the more comprehensive reviews of homeopathy include a 2002 systematic review (or study of studies) in the British Journal of Clinical Pharmacology, and a 2005 meta analysis in the Lancet, where researchers compared trials of homeopathic and conventional medicines. In large, well-designed trials, there was no evidence of homeopathy being more effective than placebo.  Another review, released by the National Health and Medicine Research Council (NHMRC) said just as much. As did a 2010 House of Commons report into the matter.

The NHS Choices website echoes these sentiments, but goes on to say:

“Two NHS hospitals provide homeopathy, and some GP practices also offer it”

Do you agree this should be the case?