" I also have a couple of slide rules, which I bought in 1969, they are still in regular use, and the batteries haven't worn out yet. One of the great things about slide rules that even calculators don't do well, is that they can present you with a range of quotients to choose from, since every division calculation on a slide rule automatically displays all other simultaneous numerators and denominators with the same quotient. When I worked in the telecommunications industry planning for telecommunications traffic growth, making long-term, short-term, and seasonal forecasts for network traffic, that was extraordinarily useful. "

"I didn't phrase that well. Imagine you want to calculate 6/5. Set cursor to 6 on the D scale. Move the slide so that 5 on the C scale is now also on the cursor. If you scan along to 1 on the C scale, it is lined up with 1.2 on the D scale, so 6/5 is 1.2. But notice that if you now slide the cursor anywhere on the slide rule, the numbers under the cursor line on the D and C scales are always in the same ratio, 1.2. Moreover, if you look at the A and B scales, you now have the same ratios in squares."

I told you earlier Alex, that i had not used my slipstick since I took it out of its box to show my grandson; well, that is no longer the case, because I took it out a short while ago to see what you meant with regard to obtaining the same quotients. Thanks for your later explanation, but let me say there is nothing profound about this at all. They are simply examples of the many functions that were always taught regarding use of the slide rule. Thanks for the explanation. Dugald.

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QUOTE (Samjohn @ 19th Nov 2014, 06:16pm)

Thanks for your later explanation, but let me say there is nothing profound about this at all. They are simply examples of the many functions that were always taught regarding use of the slide rule. Thanks for the explanation.

I'm sure it's not profound, of course, but the idea of having a range of values displayed in this way is something you can't easily do on most calculators, and likewise for multiplying by a constant. When I was working out traffic flow through telephone exchanges in order to work out when new extension equipment would be required, this was very useful. That was the only point being made here.

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QUOTE (DannyH @ 19th Nov 2014, 01:11am)

Hello TeeHeeHee ... I know you meant it tongue in cheek, Regards to All

Danny Harris

Glad to see I can give someone a laugh on here Danny As for tongue in cheek, well, considering that my first ever day at School was at St Joseph's (in Blantyre) until the Police found me and took me home, everything which followed with this wee *banned word* (priddy dig perhaps? ) had to be said tongue in cheek.

--------------------

Wait a minute ... I've got my eye on a burd.

... Some try to tell me thoughts they cannot defend ...

I'm sure it's not profound, of course, but the idea of having a range of values displayed in this way is something you can't easily do on most calculators, and likewise for multiplying by a constant. When I was working out traffic flow through telephone exchanges in order to work out when new extension equipment would be required, this was very useful. That was the only point being made here.

Just prior to leaving the teaching profession I was looking after a maths class for the maths teacher. The class was doing calculations I think in trigonometry. They were hunched over their calculators and when I suggested they try doing it "By hand" they thought the task impossible. Wayne the maths teacher produced old a set of old Napierian log tables and proceeded to astound them. At the same establishment I found an abandoned slide rule that when I was using my Woolworths bought 6 shilling slide rule, would have been beyond the means of even the maths teachers.

Talking of calculators in exchanges, the head tech in one of the exchanges I worked in asked me to solve a complicated puzzle pertaining to mathematics using quadratic equations. All attempts to solve the question ended in failure. I asked him why he would ask me to solve when he was obviously more adept at maths that myself. He explained that the puzzle was from an old Chinese almanac some 1500 tears old and as I was studying Chinese at the time I would have more insight into the subject matter. As I knew the Chinese had no knowledge of Algebra that the problem was not one of equations. The Chinese had the Soroban (jap) abacus so I drew out an abacus indicated the required fields by filling in the circles and leaning others blank and solved the problem in a few minutes.

I would advocate the broad teaching of internalized calculation. However except in a doomsday situation it does not have a great real of relevance due to the massive influx of electronic data management. It is possible to purchase calculators cheaper that some good lead pencils. I have paid as little as $6 for a scientific calculator that has functions above and beyond my needs and abilities.

I remember my director of studies when I was post graduate, he was initially a professor of mathematics, telling me he had only ever used quadratic equations 4 times in his life. Yet in Scottish schools they were considered the "Holy Grail" of algebraic competence.

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Fascinating story about the Chinese abacus.

I wonder if maybe your erstwile mathematician DS was more pure than applied maths, where he recalled only four occasions on which to use quadratic equations. It's true that the average school wean will never have a single occasion to use a quadratic equation for the rest of his life once he's outside the school gates, though that's not true of anyone involved in the sciences, engineering and applied mathematics. You can't do anything with motion, for instance, and not come up against quadratics : projectile motion, and anything to do with gravity, has quadratic equations in time in just about any situation. In electrical and electronics, quadratics appear when resistors are in a circuit. Quadratics appear in navigation, when you have to acccount for water currents. If you are working with areas, whether on farmland or factory metal pressing, quadratics appear. A quadratic can also sometimes be a good approximation to something more complicated, where a quadratic is easier to manipulate. I guess it all depends on which walk of life you end up on.

Thinking about log tables, that's what we had at school. Even though there were slide rules, our classes had to use look-up tables for trigonometry, squares, roots, and logarithms. Understanding how logarithms work is a good basis for understanding how slides rules work, since essentially a slide rule converts a multiplication into an addition, and it's logarithms that are being added via the slide rule. I wouldn't want to go back to using tables, but I could if I had to.

I wonder if maybe your erstwile mathematician DS was more pure than applied maths, where he recalled only four occasions on which to use quadratic equations. It's true that the average school wean will never have a single occasion to use a quadratic equation for the rest of his life once he's outside the school gates, though that's not true of anyone involved in the sciences, engineering and applied mathematics. You can't do anything with motion, for instance, and not come up against quadratics : projectile motion, and anything to do with gravity, has quadratic equations in time in just about any situation. In electrical and electronics, quadratics appear when resistors are in a circuit. Quadratics appear in navigation, when you have to acccount for water currents. If you are working with areas, whether on farmland or factory metal pressing, quadratics appear. A quadratic can also sometimes be a good approximation to something more complicated, where a quadratic is easier to manipulate. I guess it all depends on which walk of life you end up on.

Thinking about log tables, that's what we had at school. Even though there were slide rules, our classes had to use look-up tables for trigonometry, squares, roots, and logarithms. Understanding how logarithms work is a good basis for understanding how slides rules work, since essentially a slide rule converts a multiplication into an addition, and it's logarithms that are being added via the slide rule. I wouldn't want to go back to using tables, but I could if I had to.

Prior to entering university in Australia I was employed as a fault linesman for many years with Telecom. During my schooling there, I was obliged to calculate stresses related to cross bracing and straining on carrier pole routes and was even obliged to construct, and dismantle runs of aerial cable. the mathematical side was easy for me as in Scotland we covered most of this in physic before third year (albeit horses dragging barges along canal banks). On leaving line school my first job was to dismantle the last remaining aerial route in the Melbourne area.The point I am trying to make is that there has been a tendency not to embrace technological advantage in institutions where those in charge have a fear that those coming up will have an advantage over them in their access and familiarity with the "new". I was working for Telecom for at least 12 years before I even touched a computer. It was not until I left the computers were standard in trucks and all our test instruments were digitalised. However reliance on these things was never a full substitute for experience, insight and intuition from years spent being as good as one could get at their particular skill. There is a brave new world out there in terms of electronic processing media but my worry is that the "Deus ex Maccenae" will eventually devour it's disciples. After years of accumulating top end power tools to construct furniture, in my dotage I have returned to doing all furniture construction by hand tools only. It is a quieter and more satisfying way of doing things but unless you are in the Krenov class or Jimmy Carter (yes he is a furniture maker) you will not make a living from it. However when calculating measurement I always use an electronic calculator.

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You're right GQ, this post took quite a tour on various subjects.

St Cuthbert's Primary started at 09:00 and went to noon for the little ones, then to 15:30 for the majority finally going on until 16:00 for the about-to-be Eleven Plussers. Trying to accustom them to Secondary Hours I suppose.

St. Cuthbert's built a swimming pool and allowed some to try it out a week before the official opening. I was the first ever kid to get wet. The obligatory "dirty feet inspection" only served to heighten the excitement of hitting "the big pond". I could swim like a fish before trying the new pool out (courtesy of Woodside Baths) so I was an exception to the flounderers who couldn't. The school did teach a basic swimming and floating program. Remember the gravestone-shaped pink styrofoam boards as flotation devices and the newbies dogpaddling behind them?

Later on in life I used to off of the high board at Kirkintilloch several times per visit. Quit when the headaches started.

St. Augies (as I'm sure you remember well) was 09:00 'till 16:00 and Night School was (I think) Tuesdays and Thursdays 17:30 until 20:30. Correct me please if wrong.

Calculators: Still have my Sinclair Electronics Calculator that does not have a square root key.

St. Augies: I knew very few who had a Slide Rule. For the most part, we used Logarithmic Tables. I still have mine.

Sometimes calculators are referred to as computers (at least here in Canadar). The very first computers were people who used printed tables to calculate the fall of artillery shot. To this day computers (as we now know them) still cannot multiply nor divide. They simply add and/or subtract rapidly to synthesize multiplication and division functions. Mental Arithmetic:

Wife and I usually calculate shopping bills to the penny before hitting the checkout and announce the price to somewhat startled and bemused cashiers. It's not the first time we've ever heard the phrase, "How'd you do that?" when handing over exact cash. Our reply is usually along the lines of, "Mental Arithmetic." That's sometimes alarmingly followed by the cashier asking, "Wow, is that like a new Math or something?". Really.

Full circle and back to topic; was school lunchtime 12: to 13:30?

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Held prisoner in Scotland from 1953. Escaped to England in 1970 then to Homeland Canada in 1980.

I astounded a teenage cashier by calculating a simple bill in my head. She thought I was some kind of mathematician. The young lady was not dull. However the calculation I explained to her by isolating 10s and then 5s and the remainder of single cents. I was more astounded than she was that no one had taken the trouble to explain these things to her at school.

The new "limo" I purchased last year, not content to provide a manual, had a second manual for the touch screen or voice activated computer and satellite relay and can answer your Bluetooth phone automatically. I am beginning to feel redundant and I am not looking forward to driverless cars!

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