The assumption of a random (Gaussian) distribution is a theoretical tool used to model chance variables. The times of death of people and the times when conditions are ripe for rainbow-viewing at a given location seem somewhat random/chancy. But if we do not agree they are random, or at least involve a major random component, then we're taking on the far bigger burden of demonstrating non-random patterns in their occurrence. In the case of rainbows, obviously, there are *some* non-random patterns in terms of the time of day, and certain rainy seasons, when they are more likely. But within those timeframes they seem to follow a roughly Gaussian pattern.

I think the word "gaussian" does not mean what you think it means

A random variable can be distributed in different ways:

- Gaussian distribution means (roughly) that multiple measurements (for instance, of an electric current) will gather around an average value within a certain deviation, with a specific shape which is mathematically defined. In fact, a gaussian shape with a very small deviation is kind of "spoiling" the randomness, as one single value becomes the most probable!

- A uniform distribution means all results are equally probable, like in gambling in a roulette: all numbers should have the same probability of wining. I would never ever gamble in a roulette which has a gaussian distribution: they are cheating!!

- You can even make up an "inverted gauss" distribution, where all values are equally probable, except those around an average value and deviation defined by an "inverted gauss shape"

- The number of different rainbows that can appear for a certain fixed period of time can be modeled using a Poisson distribution (

https://en.wikipedia.org/wiki/Poisson_distribution)

- The number of cards guessed using Zener cards (

https://en.wikipedia.org/wiki/Zener_cards) can be modeled using a binomial distribution (

https://en.wikipedia.org/wiki/Binomial_distribution)

Now, you can statistically model the location where a rainbow can be seen using latitude and longitude.

If you say that they are both gaussian distributions it means that there is a very specific point where rainbows are seen more likely than others, and the further you move away from that point, less likely is to see one. That's what "gaussian" means. (or you could use an "inverted gaussian" to say it is the least likely spot to see a rainbow). Either case, that itself would deserve a research, without the need of a Queen passing. It means that would be a special location for some reason.

I don't see any reason to suppose the distribution has to be different than uniform (i.e. same probability at Buckingham than London Eye, Windsor, Greenwich, Salisbury or wherever). It is

*random*, but not neccesarily

*gaussian*.

I fully understand your point, and I have myself already outlined its gist in the OP as well as many posts since. If rainbows appeared very frequently and at random all over Britain, say virtually every other September afternoon an hour or two before sunset, the Buckingham Palace and Windsor rainbows would (no disrespect intended to any a believer), objectively speaking, lose their symbolic significance. In fact, it would be sufficient to demystify these rainbow appearances by simply demonstrating how they occur

*at those two locations* quite regularly at those times in September

But based on the low frequency of Buckingham Palace rainbows using our rough photo search (thanks to

@deirdre) as a tentative starting point, that doesn't seem to be at all the case.

You should compare that frequency to other "non remarkable" sites, not stick to a single value. Also, basing your statistics on photo search can lead you to wrong conclusions. It depends on :

- weather/sun conditions to create a rainbow

- People around to see it

- People having a camera to take a picture.

- People uploading it to internet.

I don't expect the frequency of being able to see rainbows from Whitechapel to be significantly different. However, I kind of think Whitechapel is not as photogenic as Buckingham. Also, some places may usually be more crowded than others, increasing the probability that someone takes a picture that is later uploaded to internet.

I think the proper scientific approach is thinking the other way around. The places where the rainbows appeared at 1830s are *factually known*. Buckingham and Windsor.

Places where rainbows

**were reported** to appear at 1830 are known. Places where rainbows appeared but

**were not reported** are not, because the focus of attention was at the other places. You are looking at a single spot, ignoring others.

The *real phenomenon* for which there are two rival *theoretical* *explanations*. These locations are, factually, her chief residences and seats of reign.

Balmoral is factually the place where the passing occurred.

They're not a theoretical criterion. For awe-inspiring rainbows to appear there at 1830 hrs when her death was announced, and when mourners were gathered there, *seems* like a remarkable coincidence.

I wouldn't expect mourners to gather at London Eye. But I expect they could also see the rainbow.