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Showing posts with the label math

Tennessee Cave Survey - Caves Described over Time

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I'm often asked, "How many caves are there in Tennessee?" What they are really asking is, "how many caves do we know about in Tennessee?" or "how many caves have been described in Tennessee?" I like to say "described" as opposed to "discovered" since most caves that are newly described were likely known to historic and prehistoric people. Sometimes there is direct evidence to support this. The simple answer to the question is to state the number of caves as it was described in the last Tennessee Cave Survey data release. But a more thorough answer would note that number changes annually. Let's explore just how much it has changed, and maybe speculate on how much it will change into the future. History of Cave Documentation in Tennessee In 1959 Dr. Tom Barr's book, Caves of Tennessee described approximately 500 caves. This was the first attempt to create a single, central source for cave information ...

Shannon Diversity Index in Top Songs by Year

Introduction Can ecological measures be used to glean information about music, and perhaps music trends? This post explores the possible use of the Shannon Diversity Index as a means to understand diversity within the "lyrical ecosystem." Methods A list of List of Billboard Year-End number-one singles (1) was used for the data collection portion of this project. Excluded from the study was 1948's hit, "Twelfth Street Rag" by Pee Wee Hunt. It is an instrumental with no lyrics to study. Length is the song length in seconds as measured by the first video to show up on a YouTube Search, with preference given to anything shown to be "official." Unique words and total words are from song lyrics that were pulled from Google's lyric search. Where lyrics weren't available Genius.com was used. Grunts, moans, yeahs, na-na-nas are all counted if they are found within the lyrics as provided by the stated sources. Words per second is a measure of t...

Coastline Paradox

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A coastline or a shoreline is something that can only be measured with a measurable degree of accuracy. As the measure of accuracy changes, so does the length of the coastline / shoreline. In other words, if I take a yardstick, a ruler, and 30' length of rope to measure the shore, I get three different answers. Each is correct, when stated with what was used to make the measurement. This is a counterintuitive outcome. Geographic Information Systems (GIS) should be able to quite easily measure the length of lines, right? The problem lies within the analysis itself. I can only tell where the shoreline of Dale Hollow Lake is based on known described layers of data with measured limitations. If I artificially inflate those limitations (in this example, I'm increasing distance between vertices) and record the change in shoreline, one can see how the shoreline decreases as the measure of accuracy decreases (distance between vertices increases, shoreline decreases). Same is t...

Male / Female Rule

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Many years ago I made up a rule based on some casual observations. That if someone's name were to end in a vowel, they would tend to be a female. I had guessed this to be correct approximately 80% of the time. Recently, I happened upon a large table of names, and their frequency in the population this morning and wanted to more empirically test my hypothesis. Here's what I came up with. I began be isolating the last letter of each name in Excel and testing to see if it was A, E, I, O, U, or Y. Y is sometimes a vowel, but I lack a good rule to test for this in Excel, so I assumed they were all vowels. This seemed fair since the assumption was made on both male and female datasets. I totaled the frequency occurrence in population column for entries that met the conditions of my vowel test. The male and female datasets totaled to account for 90.05% and 89.94% of their population, respectively. The remainder was assumed to be uniform to the portion I had (assumption of homog...