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ArishMell · 70-79, M
'Tis a curious thing... regarding Number Two.
I was introduced to logarithms as arithmetical calculating tools way back in the 4th of Primary School in 1962, when I was still 10; though possibly as our teacher's own extension to the syllabus.
They remained the universal hard-sums technique, along with their slide-rule equivalent, until about the end of the 1960s / early-1970s, when electronic calculators started to appear. One or two fellow-students had them in our last Year or two at school; while most of us were still using slide-rules.
I can still use both log tables and the slide-rule, with a little revision; yet - and this is what is odd - I did not understand them until well within the last twenty years! And then only when work and a some private study outside that, meant I needed understand deciBels; hence coming back round to understanding what logarithms actually are.
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What does Napier's equation tell us? That to multiply two numbers, add their logarithms; then the product is the antilogarithm of that sum. Divide by subtracting the logs. This extends to it being simple to calculate awkward powers and roots: multiply or divide the log of the original number by the index. (This is ordinary numbers and logs, both to base-10: I don't know my way around Hyperbolic Logarithms and have never used them.)
I do not know if they are still published at all, but at one time you could very easily buy books of look-up tables of logarithms & antilogs, trigonometrical constants, etc. Scientific calculators are programmed with them (or with their generating functions?).
I was introduced to logarithms as arithmetical calculating tools way back in the 4th of Primary School in 1962, when I was still 10; though possibly as our teacher's own extension to the syllabus.
They remained the universal hard-sums technique, along with their slide-rule equivalent, until about the end of the 1960s / early-1970s, when electronic calculators started to appear. One or two fellow-students had them in our last Year or two at school; while most of us were still using slide-rules.
I can still use both log tables and the slide-rule, with a little revision; yet - and this is what is odd - I did not understand them until well within the last twenty years! And then only when work and a some private study outside that, meant I needed understand deciBels; hence coming back round to understanding what logarithms actually are.
+++
What does Napier's equation tell us? That to multiply two numbers, add their logarithms; then the product is the antilogarithm of that sum. Divide by subtracting the logs. This extends to it being simple to calculate awkward powers and roots: multiply or divide the log of the original number by the index. (This is ordinary numbers and logs, both to base-10: I don't know my way around Hyperbolic Logarithms and have never used them.)
I do not know if they are still published at all, but at one time you could very easily buy books of look-up tables of logarithms & antilogs, trigonometrical constants, etc. Scientific calculators are programmed with them (or with their generating functions?).
ArishMell · 70-79, M
@Sazzio LOL!
Far from it. I was always a slow learner and Maths was one of my weakest subjects - as my post hints.
I understood logarithms eventually, some 30-40 years after leaving school, by a rather indirect route that gave a physical anchor to my thinking.
I had had to think of my own way around the problem - and if there is one thing most mathematics text-books dismally fail to do, it is to explain the mathematics they illustrate.
Similarly with Calculus.
Although Calculus was taught in the Fifth Form of senior school, as part of the GCE O-Level Mthematics syllabus, I could not grasp Differentiation until a chance encounter in a geology club lecture probably thirty years later. Shown a numerical technique for analysing river gradients, something inspired me to write the simple formula in calculus notation. It dawned on me this was a sort of very basic differentiation, and so finally twigged what that term actually means, hence what it is doing! Its anchor was the real thing - the gradient of a stream flowing down sloping countryside.
Conversely, when I hopelessly tried A-Level Maths, I found 3-dimensional graphs easy because I could relate their abstract, algebraic (x, y, z) co-ordinates to the Ordnance Survey maps' NGR and altitude points with which I was already familiar.
I've not had that lucky break with Integration though....
And as for Matrices..... Luckily I have never needed use these arcane abstractions! A scientist told me a typical use for them was in her work - solving gigantic blocks of simultaneous equations with 100 and more unknowns. The computer does the number-milling, of course, but she still needs understand the application and method. Not exactly everyday arithmetic for we lesser mortals trying to keep up with petrol prices or baking cakes!
The Maths I use now, rather than ordinary Arithmetic, is largely limited to simple geometry and mensuration, with trigonometry and pi occasionally.
'
Some with no head for numbers seem to take a perverse pride in it; almost boasting about being innumerate. I have no time for that. I accept many of us need know only simple weights, measures and money arithmetic. That's fair; but not a reason to sneer at Maths as a whole. Being no "Child Genius", or even just good at Maths, wrecked my dreams of becoming a professional scientist or engineer as both disciplines are highly mathematical. I did work in these, but at semi-skilled shop-assistant level.
Far from it. I was always a slow learner and Maths was one of my weakest subjects - as my post hints.
I understood logarithms eventually, some 30-40 years after leaving school, by a rather indirect route that gave a physical anchor to my thinking.
I had had to think of my own way around the problem - and if there is one thing most mathematics text-books dismally fail to do, it is to explain the mathematics they illustrate.
Similarly with Calculus.
Although Calculus was taught in the Fifth Form of senior school, as part of the GCE O-Level Mthematics syllabus, I could not grasp Differentiation until a chance encounter in a geology club lecture probably thirty years later. Shown a numerical technique for analysing river gradients, something inspired me to write the simple formula in calculus notation. It dawned on me this was a sort of very basic differentiation, and so finally twigged what that term actually means, hence what it is doing! Its anchor was the real thing - the gradient of a stream flowing down sloping countryside.
Conversely, when I hopelessly tried A-Level Maths, I found 3-dimensional graphs easy because I could relate their abstract, algebraic (x, y, z) co-ordinates to the Ordnance Survey maps' NGR and altitude points with which I was already familiar.
I've not had that lucky break with Integration though....
And as for Matrices..... Luckily I have never needed use these arcane abstractions! A scientist told me a typical use for them was in her work - solving gigantic blocks of simultaneous equations with 100 and more unknowns. The computer does the number-milling, of course, but she still needs understand the application and method. Not exactly everyday arithmetic for we lesser mortals trying to keep up with petrol prices or baking cakes!
The Maths I use now, rather than ordinary Arithmetic, is largely limited to simple geometry and mensuration, with trigonometry and pi occasionally.
'
Some with no head for numbers seem to take a perverse pride in it; almost boasting about being innumerate. I have no time for that. I accept many of us need know only simple weights, measures and money arithmetic. That's fair; but not a reason to sneer at Maths as a whole. Being no "Child Genius", or even just good at Maths, wrecked my dreams of becoming a professional scientist or engineer as both disciplines are highly mathematical. I did work in these, but at semi-skilled shop-assistant level.