Logarithms and Anti-logarithms

[DarloRich]

I have no idea what those words mean. I do about Tacitus and Oliver Cromwell.

 

[Mcr Warrior]

I have no idea what those words mean. I do about Tacitus and Oliver Cromwell.

Classically educated?

 

[Gloster]

I took my O-Level Maths in late 1975 and competence with log tables of various types was definitely required. I trimmed my copy of the book so that when you opened it you could see down the right-hand edge of the book what each page covered; a bit like an old address book. We had been using log tables ever since I moved from prep. school to public at thirteen in 1973, and possibly had at least an outline of how they worked even before that. It was also normal to use slide rules for calculation, although I think that by the time I took (and failed) the Additional Maths O-Level in the summer of 1976, calculators were permitted for simple calculations, although not for working out more complicated matters such as cos, tan, etc. Anti-logarithms, if I ever studied them, have completely passed from my mind.

 

[ABB125]

Classically educated?

As opposed to "properly" educated?

 

[Xenophon PCDGS]

Classically educated?

If he was, I too am of that particular ilk, as I was in the Classics stream from the Lower Fourth up to the Upper Sixth taking both Greek and Latin. The school had still boarders in those days who were all in the Classics stream, as they were intending to study for the priesthood and my school was seen as having had a very long tradition in that respect. As such, instead of being in the theology lessons, I was allowed to sit in at an extra Mathematics lesson in the year above.

 

[DelW]

... I have never forgotten those words of our teacher and wonder if there are contributors on this website who were introduced to these at age 11 and if they used them in their later lives in employment.

Yes and yes.

As an engineer, setting-out roads and bridges in the early 1970s, I used them daily to calculate the whole circle bearing and distance between pairs of co-ordinates. Since these were 8-digit numbers, of which we needed to use at least six, we had books of 7-figure log and trig tables, which were hardback books about 30 - 40mm thick. (I finally discarded our last office copy during a move in about 2006.)

In about 1974 I bought a four-function calculator (for £30, equivalent to several hundred pounds now), which automated part of the process but still needed the tables for trig functions and square roots. Not until 1976 could I buy a scientific calculator when they became relatively affordable at around £50, although that was a week's gross salary for a graduate engineer. They didn't become company-issue until 1977, by which time I was setting out part of the M25, and even then one Casio was shared among an office of six or eight engineers.

When using hand calc's, the calculations would take rather longer than did the fieldwork to set out the points you'd calculated. Nowadays the calculations take fractions of a second in Excel.

 

[MotCO]

I took my O-Level Maths in late 1975 and competence with log tables of various types was definitely required. I trimmed my copy of the book so that when you opened it you could see down the right-hand edge of the book what each page covered; a bit like an old address book. We had been using log tables ever since I moved from prep. school to public at thirteen in 1973, and possibly had at least an outline of how they worked even before that. It was also normal to use slide rules for calculation, although I think that by the time I took (and failed) the Additional Maths O-Level in the summer of 1976, calculators were permitted for simple calculations, although not for working out more complicated matters such as cos, tan, etc. Anti-logarithms, if I ever studied them, have completely passed from my mind.

I took O Level maths in 1973 and A Level in 1975, and was not allowed to use calculators. So the cut-off for exams seems to be around 1974/1975.

== Doublepost prevention - post automatically merged: 26 Oct 2021 ==

Nope. Electronic calculators had by then become available. Thank you Mr. Casio.

My first calculator was a Sinclair Cambridge - cost £80 if I recall in around 1973. So it would be thank you Mr Clive Sinclair (RIP).

 

[Lloyds siding]

If you used a Sinclair calculator then after a couple of iterations of log/anti-log...you would have the wrong answer....they rounded to an appallingly low number of significant figures!
Thank heavens for Commodore!

 

[DarloRich]

Classically educated?

Correct - a proper, civilised education. None of this perverted mathematics nonsense.

 

[MotCO]

If you used a Sinclair calculator then after a couple of iterations of log/anti-log...you would have the wrong answer....they rounded to an appallingly low number of significant figures!
Thank heavens for Commodore!

A Snclair Cambridge could not do square roots, except by going through a guess and see type operation

 

[Ediswan]

They didn't become company-issue until 1977, by which time I was setting out part of the M25, and even then one Casio was shared among an office of six or eight engineers.

Casio fx-29 by any chance ? That model was very popular at the time.

 

[AM9]

A Snclair Cambridge could not do square roots, except by going through a guess and see type operation

Par for the course with Sinclair. The first version of ZX81 firmware reckoned that the square root of 0.5 was 1.35. I originally assembled the board as a kit, buit when I sent it back to Sinclair for the ROM change they swapped it for a new factory-built one. The first real calculator that I handled was an HP-35. Couldn't get used to RPN, (reverse polish notation).

 

[306024]

I took my O-Level Maths in late 1975 and competence with log tables of various types was definitely required. I trimmed my copy of the book so that when you opened it you could see down the right-hand edge of the book what each page covered; a bit like an old address book. We had been using log tables ever since I moved from prep. school to public at thirteen in 1973, and possibly had at least an outline of how they worked even before that. It was also normal to use slide rules for calculation, although I think that by the time I took (and failed) the Additional Maths O-Level in the summer of 1976, calculators were permitted for simple calculations, although not for working out more complicated matters such as cos, tan, etc. Anti-logarithms, if I ever studied them, have completely passed from my mind.

Sounds very familiar, apart from my school was a comprehensive My recollection of doing Maths O-level in 1975 and Additional Maths O-level in 1976 is that calculators were not permitted by the examination board we had. Logarithms were part of the syllabus, I remember answering an exam question using them, but that was the last time in my life I did. I had a slide rule, but only used the edge of it for drawing a straight line.

Then doing A-levels in 1978 calculators were permitted, but you had to write on the exam paper whether you used one or not. I didn’t for my maths A-level, but did for my further maths A-level. No idea how that was taken into account when marking the exams.

 

[Ediswan]

My first calculator was a Sinclair Cambridge - cost £80 if I recall in around 1973. So it would be thank you Mr Clive Sinclair (RIP).

When new, more like £20-25. At the price you mentioned, maybe thinking of ZX80 ?

 

[Bevan Price]

Does anyone remember the mechanical calculators used by some workplaces before electronic calculators became available. Early models were "hand-cranked", but later models were electrically powered. They only did basic arithmetic, and got confused if you told them to divide by zero - to stop them required you to switch off the electric power.

For example, see here:

Monroe

Monroe calculators were first produced in 1912, and, so far as the hand-cranked machines are concerned, didn’t change much in the next 50 years, except that they got smaller. They work on a …

mechanicalcalculators.wordpress.com

 

[biko]

Never heard of antilogarithms until I read this thread, but clearly it is because I am too young (graduated this year). I am however quite familiar with logarithms and exponents and actually used them today at work!

Correct - a proper, civilised education. None of this perverted mathematics nonsense.

The one doesn't exclude the other! I am an engineer but attended a grammar school where I was fortunately taught both about logarithms and Tacitus.

 

[DelW]

Casio fx-29 by any chance ? That model was very popular at the time.

Having just looked at a picture of one, it might well have been. It certainly had the same slide switch for angle setting, as I remember wasting much of a day trying to find a mistake in my calc's, only to find eventually that *someone* had moved the switch to grads. No one would admit to it though.

In 1978 I bought a Casio fx-2000, with an LCD display, whose long battery life meant I could carry it out on site in my donkey jacket pocket. I still have that one, and it was still in working order when I put some new batteries in it a few years ago.

 

[Ediswan]

Par for the course with Sinclair. The first version of ZX81 firmware reckoned that the square root of 0.5 was 1.35. I originally assembled the board as a kit, buit when I sent it back to Sinclair for the ROM change they swapped it for a new factory-built one. The first real calculator that I handled was an HP-35. Couldn't get used to RPN, (reverse polish notation).

Sinclair were not the only suppliers with maths bugs. In the 1980s, work had an expensive HP machine where the results to a mathemtical model were not making sense. This was eventually tracked down to -0.1 x -0.1 giving the answer -0.01 (wrong sign). The fix was not to enter those as initial conditions, the exact numbers never occured otherwise. Then there was the Intel floating point bug.

I like RPN. Works best with a multi-line display where you can see the top few items on the stack.

 

[Peter Sarf]

I was taught how to use logarithmic tables, probably whilst studying O'Level Mathematics in 1977. I have never needed to use them and had a Calculator at that time - A Sinclair model iirc. What has been useful is the understanding of the logarithmic scales. I have recently inherited a book of logarithmic tables that I recall my Grandfather showing me. My father used to use a slide rule.

 

[DelW]

Does anyone remember the mechanical calculators used by some workplaces before electronic calculators became available. Early models were "hand-cranked", but later models were electrically powered. They only did basic arithmetic, and got confused if you told them to divide by zero - to stop them required you to switch off the electric power.

For example, see here:

Monroe

Monroe calculators were first produced in 1912, and, so far as the hand-cranked machines are concerned, didn’t change much in the next 50 years, except that they got smaller. They work on a …

mechanicalcalculators.wordpress.com

We used them at university in around 1972-3, but I've never used one for real. I think they must have been quite expensive, as our tutors never let them out of their sight.

(Edit) Ours were unlike the Monroe ones as they didn't have rows of buttons. IIRC the numbers were set by vertically sliding levers on the front panel.

 

[MotCO]

When new, more like £20-25. At the price you mentioned, maybe thinking of ZX80 ?

I thiught it sounded expensive - you are probably right.

 

[swt_passenger]

Having just looked at a picture of one, it might well have been. It certainly had the same slide switch for angle setting, as I remember wasting much of a day trying to find a mistake in my calc's, only to find eventually that *someone* had moved the switch to grads. No one would admit to it though.

In 1978 I bought a Casio fx-2000, with an LCD display, whose long battery life meant I could carry it out on site in my donkey jacket pocket. I still have that one, and it was still in working order when I put some new batteries in it a few years ago.

That prompted me to check my 1985 Casio fx361. I don’t think I’ve looked at it since I got a decent phone calculator, but it’s seemingly still going ok on its original batteries. Bargain…

 

[DelW]

That prompted me to check my 1985 Casio fx361. I don’t think I’ve looked at it since I got a decent phone calculator, but it’s seemingly still going ok on its original batteries. Bargain…

Testament to Casio's build quality! It's not surprising that they were more successful than Sinclair, since with all due respect to Sir Clive's ingenuity, reliability was never a strong point for them.

 

[Ediswan]

Does anyone remember the mechanical calculators used by some workplaces before electronic calculators became available. Early models were "hand-cranked", but later models were electrically powered. They only did basic arithmetic, and got confused if you told them to divide by zero - to stop them required you to switch off the electric power.

I don't recall them in use. I do recall listening to an episode of R4 "The Museum of Curiosty" and shortly after spending around £400 on a Curta Type II.

 

[Peter Sarf]

I took O Level maths in 1973 and A Level in 1975, and was not allowed to use calculators. So the cut-off for exams seems to be around 1974/1975.

== Doublepost prevention - post automatically merged: 26 Oct 2021 ==



My first calculator was a Sinclair Cambridge - cost £80 if I recall in around 1973. So it would be thank you Mr Clive Sinclair (RIP).

Thats it you have jogged my memory two models Sinclair Cambridge and Sinclair Oxford. I ended up with one of each. One was larger and had more functions iirc - Oxford. The Cambridge was originally my sisters. I remember the larger one I had ate batteries. I ended up buying a large 9V battery which somewhat defeated the portability of the thing.

 

[DynamicSpirit]

As an engineer, setting-out roads and bridges in the early 1970s, I used them daily to calculate the whole circle bearing and distance between pairs of co-ordinates. Since these were 8-digit numbers, of which we needed to use at least six, we had books of 7-figure log and trig tables, which were hardback books about 30 - 40mm thick. (I finally discarded our last office copy during a move in about 2006.)

I pity whoever was tasked with doing the calculations for the tables in that book/checking that they were correct.

 

[AM9]

Does anyone remember the mechanical calculators used by some workplaces before electronic calculators became available. Early models were "hand-cranked", but later models were electrically powered. They only did basic arithmetic, and got confused if you told them to divide by zero - to stop them required you to switch off the electric power.

For example, see here:

Monroe

Monroe calculators were first produced in 1912, and, so far as the hand-cranked machines are concerned, didn’t change much in the next 50 years, except that they got smaller. They work on a …

mechanicalcalculators.wordpress.com

In the very earliest days at work, there were two main types of mechanical calculators: Comptometers that were repetitive adders like the Monroe and Plus Adders that had 6 columns of buttons nubered 1-5 and 7 total numbers indicated. See here Entering digits higher than 5 required two key presses which one got quite adept at the key combinations for.

 

[MotCO]

Does anyone remember the mechanical calculators used by some workplaces before electronic calculators became available. Early models were "hand-cranked", but later models were electrically powered. They only did basic arithmetic, and got confused if you told them to divide by zero - to stop them required you to switch off the electric power.

For example, see here:

Monroe

Monroe calculators were first produced in 1912, and, so far as the hand-cranked machines are concerned, didn’t change much in the next 50 years, except that they got smaller. They work on a …

mechanicalcalculators.wordpress.com

Were they Comptometers? We hired someone to add up all our stock sheets for the year end acounts and they used a comptometer. They literally punched the numbers 12 times or whatever to multiply something by 12.

 

[DynamicSpirit]

On the subject of calculators, I still have on my desk - and regularly use - a Casio fx-570, which I believe I purchased in the early 1990s. It's still going strong. I also have no recollection of having ever needed to change the battery - which I find pretty amazing.

A couple of years ago, I bought an fx-991ES PLUS, out of curiosity to see whether a modern calculator was any easier to use. Although the newer one has a bigger screen that displays intermediate steps and is therefore useful if I'm doing a rare extended calculation with brackets and stuff (the old one just displays a single number), I actually find I prefer the old one for simple calculations - slightly fewer button presses.

 

[DelW]

I pity whoever was tasked with doing the calculations for the tables in that book/checking that they were correct.

IIRC the original purpose of Charles Babbage's Difference Engine was to produce accurate mathematical tables, as the human compiled ones of that era were notoriously full of mistakes.