As we became proficient in mathematics we noticed that some of the operators had inverse effects on numbers. For instance, subtraction was the inverse of addition thus you could take 10+4 = 14 and reverse the effect with subtraction; 14 -4 = 10. Next, they looked for an inverse to multiplication and came up with division. When it came to exponentiation however they had to search for a while for its inverse.<\/p>\n
Finally, in 1614 John Napier published a book entitled Mirifici Logarithmorum Canonis Descriptio<\/i> (Description of the Wonderful Rule of Logarithms<\/i>). The logarithm is the inverse of the exponent, where 10 to the 3rd power is 1000, the logarithm base 10 of 1000 is 3. Logarithms had several interesting properties.<\/p>\n
If you added two logarithms together you obtained the logarithm of the number that was the product of the two original numbers. For example, the logarithm base 10 of 100 is 2 and the logarithm base 10 of 1000 is 3. If we add the two logarithms, 2 + 3 = 5, we find that 10 to the 5th power is 100,000 as is 100 * 1000. Similarly, when you subtract two logarithms you get the logarithm of the number that you get when you divide the two original numbers; 5-2 = 3 thus 100,000 \/ 100 = 1000. This fact allowed for the invention of the slide rule, which was what all the geeky engineering types used before they had computers.<\/p>\n
I’m going to generate some figures to illustrate this next feature of logarithms but in the mean time, bear with me as I describe it. A plot of an exponential function on a standard Cartesian grid starts with a very shallow slope which increases rapidly until it has a very steep slope that approaches infinity. When you plot the same function on a grid where the x axis is graduated in logarithmic intervals, the exponential curve becomes a straight line. This makes it easy to identify exponential functions when you don’t know their formula. You plot the raw data on a logarithmic grid and if you see a straight line, the function is exponential.<\/p>\n
Like I said, I’ll add some figures to illustrate what I’m talking about tomorrow and we will continue on our adventure.<\/p>\n
Sweet dreams, don’t forget to tell the people you love that you love them, and most important of all, be kind.<\/p>\n","protected":false},"excerpt":{"rendered":"
As we became proficient in mathematics we noticed that some of the operators had inverse effects on numbers. For instance, subtraction was the inverse of addition thus you could take 10+4 = 14 and reverse the effect with subtraction; 14 -4 = 10. Next, they looked for an inverse to multiplication and came up with … Continue reading “The Future Explained, Part 2”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[31,181],"tags":[],"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=\/wp\/v2\/posts\/612"}],"collection":[{"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=612"}],"version-history":[{"count":7,"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=\/wp\/v2\/posts\/612\/revisions"}],"predecessor-version":[{"id":619,"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=\/wp\/v2\/posts\/612\/revisions\/619"}],"wp:attachment":[{"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=612"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kellie.wildroseandbriar.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}