3 actually 😉 Our 5-digit logarithm table was a decent book, and everybody had to master it at school. With a slide rule one could do the calculations with 3-digit accuracy at most.
My little joke referred to the arithmetic operation of addition. 🙂
And, of course, a slide rule performs multiplication according to the principle of adding logs.
And, of course, a slide rule performs multiplication according to the principle of adding logs.
Sure. I had a $3 plastic slide rule all through undergrad (it worked fine), and finally was able to get the TI SR-50 in grad school.
But never got an HP, because I couldn't stand RPN.
Same here, but in £ rather than $, of course.
The thing about using a slide rule is that it gives you a better feel for what numbers really mean than when you use a calculator.
You had to have a ballpark idea of what the answer to the calculation was before you actually worked it out using a slide rule.
When calculators came along, some of the uninitiated users made the mistake of trusting what it said on the numerical display.
A slip of the finger on the buttons could lead to an answer that was magnitudes out, but which was blindly accepted!
Getting slide rule answers that are orders of magnitude off comes with the territory.
Not to mention all those esoteric scales that were difficult to figure out.
And in physics we had to use instead a huge desk calculator to get enough significant digits
for our lab work. Sometimes I just ground it out with pencil and paper.
I used to have a nice slide rule collection with some rather expensive models, but had to sell them off
when we last moved. There was just way too much stuff to deal with.
Not to mention all those esoteric scales that were difficult to figure out.
And in physics we had to use instead a huge desk calculator to get enough significant digits
for our lab work. Sometimes I just ground it out with pencil and paper.
I used to have a nice slide rule collection with some rather expensive models, but had to sell them off
when we last moved. There was just way too much stuff to deal with.
I remember using scientific notation.
The slide rule was used for the basic operation and the order of magnitude was found by combining the powers of ten.
You then had to decide if your answer made sense!
Unfortunately, most students at the time didn't seem to have enough sense to figure it out.
Trust me, that situation has only gotten worse - far, far worse - since then.
As part of a recent lab here, students measured a distance I know to be 7.6 centimetres, or roughly three inches. The width of your palm, if you have small hands.
One group of students reported their measurement as 760 metres; another group came up with 0.00076 metres.
It seems nobody in either group had the slightest idea that 760 metres is roughly the length of a ten-minute walk, while 0.00076 metres is about the thickness of your fingernail.
This is in supposedly-Metric Canada, mind you. (I have had equally eye-opening encounters with American students and Imperial measurements.)
As smartphones and tablets are given to younger and younger children, many youngsters are growing up with very little connection to the actual physical world around them. Very few today would have any idea if an apple weighs about 10 grams, 100 grams, or 1000 grams; very few know if a pail full of sand weighs more or less than the same pail full of water. Kids don't build sand-castles any more.
I had to use log tables all the way through three years of coursework for my Bachelor's degree. The rich kids had scientific calculators, but they were banned from university exams, as they gave too large an advantage to wealthy students.
I've read the Nevil Chute book PRR referred to earlier in this thread. The calculations that took forever involved structural stresses in the metal components of a dirigible frame. These were built to the absolute lightest possible weight, for obvious reasons. They were also absolutely enormous, for equally obvious reasons. That presented a very tough structural engineering challenge.
-Gnobuddy
Engineers used to learn how to quickly get "about" the right answer (off by less than an order of magnitude)
for a first approximation, by making a few reasoned estimates.
There is so much math phobia around these days, it's amazing anything ever gets done right.
Then there was the time NASA had a big screw-up when English and metric units were confused.
In 1999, the Mars Climate Orbiter crashed into Mars by miscalculating the force of the thrusters.
for a first approximation, by making a few reasoned estimates.
There is so much math phobia around these days, it's amazing anything ever gets done right.
Then there was the time NASA had a big screw-up when English and metric units were confused.
In 1999, the Mars Climate Orbiter crashed into Mars by miscalculating the force of the thrusters.
That's a point I have repeatedly failed to impress on students. Though FWIW my sticky slide-rule does say 1.3. But in quick-checking a circuit, proposed or repairing, it is vital to be able to look at 2.3k and 1.7k and get "not quite one and a half" instantly. If that agrees with observation, let the error lay and move on. If disagrees, work it out a little closer. "Works" and "don't work" rarely hinge on the 8th decimal place.
I think there is something about a digital readout that makes people tend to believe in it blindly. They don't offer any room for interpretation, the way analogue meters and rulers and pointers did.
With analogue readouts one always had to think, to interpret the reading. "Let's see, that line over there is 2, this one is 3, there are five finer marks in between, so each one must be 0.2. The pointer is roughly over the second mark, okay, that's 2.4-ish."
With digital readouts having no ambiguity, no room or need for interpretation, the larger idea - that one might actually need to think about the numbers critically before accepting them - never comes up at all.
And so when a person who's only ever used digital tools, divides 2 by 3 on a calculator, and comes up with 153476.2231, they tend to blindly accept that.
I used to ask students to calculate the weight of a blue whale (to within an order of magnitude), or the daily total number of cars crossing a given point on a Los Angeles freeway nearby, or the total number of bricks in the classroom walls. Problems which you could not solve exactly simply by punching numbers into a calculator.
The hope was to encourage students to start thinking about orders of magnitude, and about the physical concepts behind math calculations. Not just numbers punched into a calculator, but underlying concepts.
With the whale calculation, for instance, one of the key concepts was to realize that whales float in water - they don't sink like a stone, they don't bob to the surface like Styrofoam. Ergo, they must have pretty much the same density as sea-water.
From there on, getting an order of magnitude estimate of weight is reasonably straightforward - but you still have to figure out what geometric shape (or shapes) to use to roughly approximate a whale's body. (A right circular cylinder was enough to get you to the right order of magnitude, a cone would get you much closer.)
This blind trust in in digital tools sometimes leads to very tragic consequences. Google "Death by GPS", and you will find plenty of sad stories, of suffering and lives lost, by people who trusted their GPS directions a bit too much. While some of these people seem to have acted in ways that were blatantly idiotic (driving into the ocean, for instance, or ignoring the signs and orange cones guarding access to a broken bridge), others could happen to anyone who didn't have a paper map and knowledge of local geography.
This Guardian article offers some examples: https://www.theguardian.com/technology/2016/jun/25/gps-horror-stories-driving-satnav-greg-milner
As an aside, an increasing number of Amazon delivery drivers are unable to find the Shipping/Receiving department at small university I work at, in spite of the large billboards by the side of the road directing them to it. Instead, drivers punch the street address of the University into their GPS, arrive at the main building, and have no idea where to go from there.
Those drivers who get as far as calling me (I purchase some of our equipment from Amazon) typically have no idea which way is north, no idea which street they're on, no idea which cross-street they just passed. They don't even know if they drove past the big fountains, or the Shell gas station. It's as though they had driven there with eyes closed, and had suddenly been ejected from their metal womb onto unfamiliar ground.
In big cities this sort of thing usually won't get you killed. But as the Guardian article shows, in more rural or isolated areas, particularly those with hostile terrain or weather, the GPS can gradually lead you into increasingly severe danger. By the time you realise the trouble you're in, it's too late.
-Gnobuddy
To me it's easier to use this: R1 * R2 / ( R1 - R2 )
where R2 is the value that you need, and R1 is what you have (too large).
If you need 8k and have 10k, then 8 * 10 / ( 10 - 8 ) = 40k to add in parallel.
Of course it's the same equation, just rearranged to be easier to remember and use.
Often you can do the calculation in your head with this equation.
where R2 is the value that you need, and R1 is what you have (too large).
If you need 8k and have 10k, then 8 * 10 / ( 10 - 8 ) = 40k to add in parallel.
Of course it's the same equation, just rearranged to be easier to remember and use.
Often you can do the calculation in your head with this equation.