Difference between revisions of "Logarithmic Scale and the Slide Rule"

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[[Image:Sliderule006.png|center|border|1450px]]
 
[[Image:Sliderule006.png|center|border|1450px]]
The logarithmic scales are widely used in science and other applications. For example, the well known pH scale is logarithmic since <math>pH=log_{10}[H^+]</math> where <math>[H^+]</math> denotes the concentration of positive hydrogen ions in the solution.
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The logarithmic scales are widely used in science and other applications. For example, the well known pH scale (a measure of acidity) is logarithmic since <math>pH=-log_{10}[H^+]</math> where <math>[H^+]</math> denotes the concentration of positive hydrogen ions in the solution.
  
  
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==='''The Logarithms, Its Discovery and Development'''===
 
==='''The Logarithms, Its Discovery and Development'''===
  
This section, though embedded in this page as a sub section, stands equal to an independent article and hence, I direct you to [[The Logarithms, Its Discovery and Development]]. Having found a very thin but immensely interesting volume, [http://www.archive.org/details/johnnapierinvent00hobsiala ''John Napier and the Invention of Logarithms, 1614 --- A Lecture''], by [http://en.wikipedia.org/wiki/E._W._Hobson Ernest William Hobson], I was fascinated by logarithm's history and its subsequent development into what we know today. The book is a very concise and succinct volume that presented how John Napier delivered his original ideas. It is an absolute a pleasure to read because it translated Napier's arguments and thoughts into relatively modern mathematical symbols and notations and at the same time preserved and revealed Napier's ingenuity.  
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This section, though embedded in this page as a sub section, stands equal to an independent article and hence, I direct you to [[The Logarithms, Its Discovery and Development]]. Having found a very thin but immensely interesting volume, [http://www.archive.org/details/johnnapierinvent00hobsiala ''John Napier and the Invention of Logarithms, 1614 --- A Lecture''], by [http://en.wikipedia.org/wiki/E._W._Hobson Ernest William Hobson], I was fascinated by logarithm's history and its subsequent development into what we know today. The book is a very concise and succinct volume that presented how John Napier delivered his original ideas. It is an absolute a pleasure to read because it translated Napier's arguments and thoughts into relatively modern mathematical symbols and notations and at the same time preserved and revealed Napier's ingenuity. In the redirected page, most of the ideas are from the above mentioned book and another wonderful book by Lancelot Hogben, [http://books.google.com/books?id=0ms4xyvhxbQC&printsec=frontcover&dq=mathematics+for+the+million&source=bl&ots=kBvshhk9k6&sig=RQ1bJOSi1ByS_Ep-gpK6kSkG2_0&hl=en&ei=m5UbTMPeNML88AakvNijCQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDIQ6AEwAw#v=onepage&q&f=false Mathematics for the Million: How to Master the Magic of Numbers]. In addition, I have supplied some additional proofs and necessary information for understanding. Though a thorough understanding of the books requires some careful thoughts and deliberate ruminations, in the end, you will find that you will appreciate logarithms a lot more than you did before. However, you should not be intimidated and discouraged by the section, in which case you should continue to the next section.
  
In the redirected page, most of the ideas are from the above mentioned book and another wonderful book by Lancelot Hogben, [http://books.google.com/books?id=0ms4xyvhxbQC&printsec=frontcover&dq=mathematics+for+the+million&source=bl&ots=kBvshhk9k6&sig=RQ1bJOSi1ByS_Ep-gpK6kSkG2_0&hl=en&ei=m5UbTMPeNML88AakvNijCQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDIQ6AEwAw#v=onepage&q&f=false Mathematics for the Million: How to Master the Magic of Numbers]. In addition, I have supplied some additional proofs and necessary information for understanding. Though a thorough understanding of the books requires some careful thoughts and deliberate ruminations, in the end, you will find that you will appreciate logarithms a lot more than you did before. However, you should not be intimidated and discouraged by the section, in which case you should continue to the next section.
 
  
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==Other Scales on the Slide Rule and How They Were Constructed==
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Should I even talk about this?
  
==Other Scales on the Slide Rule and How They Were Constructed==
 
 
==Operating Principles==
 
==Operating Principles==
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Knowing that 99% of those who read this page won't even have a slide rule, I have found a [http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html Virtual Slide Rule] from the internet so that you could play around with this and try out the operations described below.
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==='''Multiplication'''===
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==='''Division'''===
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==='''Squaring'''===
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==='''Taking Square Root'''===
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==='''Calculating <math>a^x</math> and <math>\sqrt[x]{a}</math>, where <math>x</math> is arbitrary.'''===
 
==Zenith and Downfall==
 
==Zenith and Downfall==
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I kind of talked about it in the introduction section. But I will discuss in a little detail here.
 
==What is the point of all this?==
 
==What is the point of all this?==
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Why is is so important to learn about this?
  
  
[http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html Virtual Slide Rule]
 
 
|other=Algebra
 
|other=Algebra
 
|AuthorName=IBM
 
|AuthorName=IBM

Revision as of 13:12, 18 June 2010

Inprogress.png
150 Extra Engineers
150 extra engineers thumb.jpg
Field: Algebra
Image Created By: IBM
Website: Global Nerdy --- Tech Evangelist Joey deVilla on software development, tech news and other nerdy stuff

150 Extra Engineers

This was a picture of an IBM advertisement back in 1953.


Basic Description

This was a picture of an IBM advertisement back in 1953 during an age when "computer" referred to human who did calculations and computation solely. The advertisement boasted that


"An IBM Electronic Calculator speeds through thousands of intricate computations so quickly that on many complex problems it's just like having 150 Extra Engineers. No longer must valuable engineering personnel...now in critical shortage...spend priceless creative time at routine repetitive figuring. Thousands of IBM Electronic Business Machines...vital to our nation's defense...are at work for science, industry and armed forces, in laboratories, factories and offices, helping to meet urgent demands of greater production."


Doesn't one just want to go back to that age when engineers were in "critical shortage" and "If you had a degree, you had a job. If you didn't have a job it's because you didn't want one." Oh well...


Notice that in the picture, in addition to the lack of women engineers back in those days, the male engineers almost all have receding hairlines (possibly due to constant overwork and the disproportional allocations of oxygen and other nutrients between brain cells and scalp skin). It was also typical of the male engineer to be defined by a standard uniform: "white shirt, narrow tie, pocket protector and slide rule." I need to do footnote here. But I don't know how. Yeah! Pocket protector! I did not know what it is until I saw the picture in the Scientific American Article, When Slide Rule Ruled, by Cliff Stoll, who is a brilliant engineer, physicist and educator, and whose TED talk is both hilarious and inspiring. However, it is neither Cliff Stoll, nor the pocket protector that I want to talk about. (It is just a thing that, despite making the engineers look very geeky and very attractive in author's opinion, protected their shirt pockets from being worn out so quickly due to the numerous engineering essentials they had in there.) Rather, it is the ruler looking stuff that is the engineer's hand that I want to talk about. The Slide Rule.


Born into the digital and automatic age, hardly anyone of our generation ever gets to know anything that is analog or manual. Not only that, we hate to have anything to do with stuff that is analog. We have been cultured to base our life and happiness on gadgets that allow us to access the world and all the information with a finger tip. We don't realize that in fact, things that are analog laid the foundation for our modern society and ushered us into the digital age. Slide Rule is one of "those analog things". In the pre-computer age, it was one of those ingenious tools that enabled engineers, mathematicians and physicists to do calculations, and because of it, we have witnessed the erections of skyscrapers, harnessing of hydroelectric power, building of subways, advancement in the aeronautics, beyond that, it helped us won the WWII, sent astronauts into the space (as a matter of fact, a Picket 600-T Dual base Log Log slide rule was carried by the Aopollo crew to the space and moon should the on-board computers fail) and eventually, hastened its own demise.

A More Mathematical Explanation

Note: understanding of this explanation requires: *Algebra

Logarithm and logarithmic Scale

This section is not to preach you on logarithms since you are we [...]

Logarithm and logarithmic Scale

This section is not to preach you on logarithms since you are well familiar with its properties. Rather, I will simply introduce logarithmic scale which is less mentioned and understood but widely used and essential to the construction of a slide rule.

We are familiar with the linear scale, namely the equally divided scale, from the number 0 to whichever number as shown in scale A. We then use the identity x=log_22^x to relabel scale A to produce scale B. Then what we do to transform the linear scale to logarithmic scale is simply to take away the log_2, turning scale B to scale C. Calculating the numbers on scale C, we end up with scale D.

Sliderule001.png


Now, notice that the given numbers are equally divided but the differences between consecutive numbers are not the same. Our goal is to produce a logarithmic scale that has all the integers from 1 to 8. For example, if we want the number 3 on scale D, there will be a number x on scale A that corresponds to the number 3 on scale D. We have <template>AlignEquals




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About the Creator of this Image

International Business Machines (IBM) is a multinational computer, technology and IT consulting corporation headquartered in Armonk, North Castle, New York, United States. IBM is the world's fourth largest technology company and the second most valuable by global brand (after Coca-Cola). IBM is one of the few information technology companies with a continuous history dating back to the 19th century. IBM manufactures and sells computer hardware and software (with a focus on the latter), and offers infrastructure services, hosting services, and consulting services in areas ranging from mainframe computers to nanotechnology.


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