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How I "Discovered" Logarithms

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crashsite

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My analytical skills are pretty good but, my math has always been pretty poor. Sometimes I think maybe it's the way it's taught. I was aware of logarithms but, was balled up in definitions and such from math classes.

Here's where the clarity of logarithms came into focus for me and maybe it will be of help to others.

About the time the scientific pocket calculator came out, I was futzing around and had an idea to try. I know that squaring a number is multiplying it times itself and that when the number is 10, raising it to a power gives a number with the same number of zeros as the exponent used (10 to the 6th = 1,000,000) but, what would happen if I tried to make that exponent something other than a whole number? I was expecting an error if I raised 10 to say, the 2.35 power.

To my surprise, instead of an error, I got a number. What's more, it was between 100 and 1000. At that point I must have had an epiphany because I wondered what would happen if I put my result into the log10 thingie. Of course (though it wasn't so obvious to me then), I got back my original numver of 2.35.

I instantly "got it". A logarithm is simply the exponent of 10 with the whole number defining the range (between 100 and 1000 in my example) and the decimal part defining the actual numeric value.

Thinkng I must have stumbled into something so obvious it was common knowledge, I showed it to another technician (not an engineer) and his exact response was, "Is that all there is to it?". Even to this day, I keep expecting that there MUST be more to it than that but, I'll be darned if I can figure out what it may be.

Later, I found out that those are called, "common logarithms" and there are others, especially the natural logarithms. But, they all made a lot more sense once I discovered just what they are.
 
You will be amazed when you get to play with a slide rule. They rock.

We (me+wife) made magic rulers when our kids were young. My eldest is now doing a double maths degree.

Mike.
 
...Thus, my slide rule is STILL virtually unused...

Pommie said:
You will be amazed when you get to play with a slide rule..

I have done that and tried to "design" one. I quickly discovered the "binary" nature of it. You have the same linear distance from 1 to 2, 2 to 4 and 4 to 8 but, then you need to wrap back around to 1.6 and that means knowing where 10 is on the scale, to stay in the decimal system. People who are good at math probably think that's pretty easy to figure out but, it completely stumped me.

The poor (mostly 3-place) resolution and the need to still manually figure out the decimal point made me glad for the electronic calculator!
 
The hearth

Nigel Goodwin said:
Never liked slide rules, but always loved logarithms - in fact I stole my school log book when I left! :p

Yeah, I finally threw away my old log book the last time I moved. But, on cold, winter nights still wish I had it since one log is pretty much the same as another to my wood stove.

We had a guy at work named, John Briggs who we used to tease when we discovered there was something called, Briggsian Logarithms. To this day I have no idea what a Briggsian Logarithm is or where it would be used.
 
Have you never heard of google?

Henry Briggs -- Britannica Online Encyclopedia
English mathematician who invented the common, or Briggsian, logarithm. His writings were mainly responsible for the widespread acceptance of logarithms
 
Days of Yore

Nigel Goodwin said:
Have you never heard of google?

Well...I knew John Briggs back in the early '80s and didn't think to consult with Google at the time (I guess I was already behind the power curve even before Al Gore invented the internet) and hadn't really thought about Briggsian Logarithms until I joggled it, just yesterday, out of some obscure convolution of my withered brain.
 
Last edited:
Actually Al Gore didn't invent the Internet and he never has claimed to have done so.
**broken link removed**
 
Hero999 said:
Actually Al Gore didn't invent the Internet and he never has claimed to have done so.
**broken link removed**

Yes, yes, we know. Now, here's the real shocker. There never really was a "man from Nantucket" (of course, there have been many men from Nantucket but, just not the one you always hear about).

But, steering back to null...

I knew that the only linear scale on a slide rule is the log scale and I tried to figure out how to use that to maake "my" slide rule but, without any really exact numeric alignmnets (like whole numbers aligning) I couldn't get a good interpolation. But, it did serve to improve my empirical understanding of logarithms so, I don't consider the effort wasted.
 
I thought that most people on here would understand logarithms as they come into so many areas of electronics.

A good example of logarithms is the stock market. It has typically grown 10% per annum. Plot this on a linear scale and you get an exponential graph. Plot on a logarithmic scale and it's a straight line. When it varies from the logarithmic line you should worry.

Mike.
 
Danger, Will Robinson...

Pommie said:
I thought that most people on here would understand logarithms as they come into so many areas of electronics.

A good example of logarithms is the stock market.

I'm living proof of the danger of making such an assumption. I was in electronics pretty much all my working life but, as a technician (which I preferred the work) rather than as an engineer. Mostly because of my poor math skills. I could easily envision where the trains would be as they headed toward each other in algebra class but, something in my brain just doesn't "see" the algebraic equation. I work mostly by simple math, iteration and visualization.

It's pretty obvious that many (perhaps most) on here are well versed in math but I also see posts where it's at least possible that some people might get some benefits from some tips and tricks better suited for us math morons.

Trust me, the stock market gives me plenty to worry about, logarithms or not!
 
crashsite said:
It's pretty obvious that many (perhaps most) on here are well versed in math but I also see posts where it's at least possible that some people might get some benefits from some tips and tricks better suited for us math morons.

Trust me, the stock market gives me plenty to worry about, logarithms or not!

i do agree with that one
math is importand and verry handy but i am not a guru in it and liked the practical side a bit more

i discover now deeper in the theory side of things and can relate them to real situations and experiances which is kinda cool end very intressting

about stocks
thats analithical information emotional interpetated

a behavior specialist would probably do better than an analist

Robert-Jan
 
Yes, rvjh. Sometimes I think the signs of the zodiac may be more applicable to stock picks than logarithms. Voodoo dolls and tea leaves may also help.
 
forecasting by zodiac sign will require some more mathematics isn't it
i heard that our ears also work in logarithmic scale;)
 
Ears

kep said:
forecasting by zodiac sign will require some more mathematics isn't it
i heard that our ears also work in logarithmic scale;)

Yes, both our ears and eyes have a logarithmic response (which, in addition to the brain and adaptability to sound and light makes us virtually unable to accurately quantify either thus making us rely on instrumentation).

But, our ears also have another related aspect. Our ear canal and outer ear tend to form an exponential horn, leading to the eardrum. And, it's a horn that we can extend even further by cupping our hand around our ear or using an olde timey ear trumpet (as in, "Eh, what's that you say, ya young whippersnapper?").
 
The musical scale is also logarithmic.

Scientists even say that fate of the universe will be logarithmic; the theory of heat death one of an exponential decay.
 
crashsite said:
Yes, both our ears and eyes have a logarithmic response (which, in addition to the brain and adaptability to sound and light makes us virtually unable to accurately quantify either thus making us rely on instrumentation).

Back in the fourth or fifth grade in school, our teacher explained to us kiddies for the first time how our ears have a logarithmic response to sound (although they avoided the big words). So I put my hand up and asked if our eyes also had such a response. There ensued such a din of laughter from my fellow classmates, resulting in such intense embarassment in me that I had asked the supreme stupid question of the month, that I never pursued it further and never heard an answer until today. I feel finally free of a great burden. Obviously it was this trauma, suffered at an early age, that sent me on my quest to seek the truth about how things work, ultimately culminating in my being a somewhat adequate engineer. Interesting connections.
 
Elementary Education...perhaps, too elementary...

RadioRon said:
Back in the fourth or fifth grade in school, our teacher explained to us kiddies..

It's a verifiable fact that, when it comes to science, the only thing dumber than a 4th or 5th grader is a 4th or 5th grade teacher.
 
crashsite said:
It's a verifiable fact that, when it comes to science, the only thing dumber than a 4th or 5th grader is a 4th or 5th grade teacher.

I agree 100% with that
 
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