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Wednesday, February 15, 2023

2/15/23 Report - Decoding Mary Queen of Scots Letters. Odd Brick. Distributions and Statistical Reasoning.


Written by the TreasureGuide for the exclusive use of the Treasure Beaches Report.

In my January 24 post, I recommended Poe's The Gold Bug as an introduction to the basics of decoding ciphers. Today I found an article detailing the find and decoding of secret letters written by Mary Queen of Scots. This is much more detailed explanation of how these historic cipher codes were decoded. 

Good read if you are seriously interested, otherwise you might find it too detailed or tedious.

Here is the link.

Lost Secret Letters of Mary, Queen of Scots, Found and Decoded - Archaeology Magazine

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I just noticed something on an old brick I never saw before.  The embossing is on the side of the brick rather than the top.


The second line, I think reads BIRMINGHAM ALA.  I think the first and third line are the same and ends with  ENSON.

If you can find another brick online or anywhere that has the embossing on the edge, I'd like to hear about it.

Also any ideas on what the top line reads.  Thanks for any help.

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During my recent tests, I noticed how much I was using one of the best tools for statistical reasoning = the normal distribution or bell curve.  A frequency distribution of IQs will look something like the following.


If the average was 11, that would be the most frequent score and the more you vary from the average, the scores will decrease in frequency. and fall on curve to either the right of left of the average.  The most the score differs from the average the farther to the right or left it will appear on the curve. This holds for things like IQ or height.  The average IQ is 100 and is the most frequent IQ in representative samples.  110 and 90 are fairly frequent, and scores such as 150 and 50 fall out towards the end of the curve.  Heights are similarly distributed.  Most people will have something close to the average height, and people that are very tall or short will be infrequent.  

Here are three distributions.



Here are three distributions that I'll use for illustration purposes.  The sum of the area under each of the three curves equals one.  The curve on the left has the lowest mean and has the second largest variance or variability.  The purple curve has the largest variance, but for the dark blue distribution, has the least variance.  If these cures represented some measures, such as conductivity numbers, The third would have the highest average, but smallest variance as the numbers closely cluster around the mean.

I didn't do my experiments carefully enough to plot distributions for the conductivity numbers for each coin, but that could be done.  Still if you think about the distribution of the sample numbers, you might find it helpful.

It turns out that the conductivity numbers for the Peace dollar higher on average (37 - 38), with the Kennedy half producing an average in the range of 32 - 34, and the American Eagle gold coin gave an average in the range of 26 - 28.  

The average numbers for the three coins differed by a few points.  If you had average conductivity number of 35 for one coin and 36 for another, that is a small difference, but another thing to consider is the variance.  You would find a very large overlap between the two distributions.  If the averages were farther apart and the distributions narrow, you could more reliably tell the difference between the two coins based upon the conductivity numbers.  It is important to consider not only the mean, but also the variance.  How much do the distributions overlap?  How often might you mistake one for the other when going by the obtained conductivity numbers.  Remember, even the depth can cause more variance.

Two Overlapping Distributions Showing the Large Area of Overlap
When Means Don't Differ by Much.



Few measurements in life are perfect.  You will have some amount of variance and some amount of error.  It is important to consider the variance as well as the mean, and also the shape of the frequency or probability distribution.

I found that when you swept the coil in one direction over a standing coin, that you would obtain numbers that were very different from those obtained from a flat coin.  You could get a different looking distribution.  

I'm going to wrap it up.  All I really wanted to say is an understanding of statistics can help a lot even if you don't do the calculations.  I find myself using statistical reasoning in many ways when thinking about metal detecting and many other topics.

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I will be doing more metal detecting tests in the near future.

Good hunting,
TreasureGuide@comcast.net