# A Brief Introduction to Ancient Counting Systems for the Non-Mathematician

The below link is to a pdf version of the illustrated 54 page booklet I wrote, A Brief Introduction to Ancient Counting Systems for Non-Mathematicians.  It is an introduction and beginner’s guide to ancient counting systems, including Inuit (Eskimo), Greek, Hebrew, Babylonian, Chinese, Mayan, Egyptian, Armenian, Asian rods, the quipu and abacus.  This primer is intended for the non mathematician, so the reader can learn to read and understand numerals in several languages.  While some ancient systems are difficult at first to comprehend, many are simple to learn.  For example, the ancient Asian rod system, that calculates using physical rods or sticks, is remarkably similar to our system.   The quipu, a string necklace-like device used by the Mayans and pictured to the right, is also easy to learn.  On the other hand, the Inuit and Babylonian systems, while numerically sound, are significantly different than what our brains are used to.  I’ve long said that two of areas of study that will change how one views the universe, areas that bend the mind and reveal your narrowness of one’s thoughts and assumptions, are visual illusions and foreign numeral systems.  The ancient mathematicians could take a different and foreign path to end up at the same, correct answer as you, revealing that your method of thinking isn’t the only method.

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# The Infrared Camera and Art Authentication

This is my infrared camera that I use in authentication. It’s a normal over-the-counter Fuji digital camera, except it had the inside infrared blocking filter removed. As with x-ray machines, infrared cameras allow you to see through layers of paint on a painting. It shows a different layer of paint than an x-ray machine.  It is also commonly used to identify alterations and  restoration and to see writing that has nearly faded away with time and wear.  Unlike x-ray machines that shoot dangerous radiation, infrared viewers are harmless as they detect radiation, or light, that is already there (at the infrared frequency) and transforms it to a visual image. As it’s an otherwise normal digital camera, you can snap the infrared image and download it onto your computer. Some non-human animals, including certain snakes, can see infrared light, but humans cannot and require a converter. Geese can see longwave ultraviolet light (commonly known as black light) that we cannot, and the black light is another tool authenticators use. As you can see, authentication and forgery detection involves looking an an item in different ways, including in ways outside our natural eyesight. X-rays can go as far as to identify the specific chemicals and their amounts in an item, such as in the paint on a painting.

If the topic intrigues you, the following is a link to a pdf primer to forensic light, covering visible, infrared and ultraviolet.  It shows how it works, the history and interesting facts, and how you use can use the tools in forgery detection, arts and crafts (glow in the dark drawings and mobiles, infrared art photography) and more.

Forenensic Light: A Beginner’s Guide (87 pages, illustrated, pdf)

Hidden writing revealed on a 1922 game used baseball bat. The grease pen text, faded to unreadable to the naked eye but seen with the infrared camera, was written by a worker at the famed bat manufacturer Hillerich & Bradsby of Louisville Kentucky when the Philadelphia Athletics player returned the broken bat to receive new ones.  Hillerich & Bradsby used the broken bat as the model to make the new ones, and kept it in their vaults.  Bats with this type of manufacturer’s writing are often referred to as ‘side written’ (the writing is always along the side of the barrel)’ or ‘vault written.’  The text gives the player’s name, team and the date the bat was returned, and helps in authenticating the bat as game used by the player.  Baseball bats, uniforms and other equipment shown to be used in Major League Baseball games fetch top dollar from collectors.

Infrared photo of my parents’ toy fox terrier, Jack. Frances Bacon-esque, no?

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