discussion "Not fit for purpose"

[Gern]

You want a calculator with RPN mode. In that, you would do 2 + 2 ÷ 2 with the desired answer being 2 as 2 2 + 2 ÷ — that is: here’s the number 2, here’s another 2, now add them; here’s another 2, now divide the previous outcome by that. Whereas for the outcome of 3, you would need to do: 2 2 ÷ 2 +. There is no need to remember which operation goes first: whichever you put first, goes first.

Really, it’s one of those things that I wish were taught in primary schools rather than the confused mess of the order in which to apply operators, that needs mnemonics in order for people to remember them.

I've not seen this RPN system before, but it strikes me as being just an alternative way of doing calculations either sequentially - just like the old fashioned bog standard calculator, or in 'scientific' order. You - the operator - are still left with the problem of deciding which method of entry will give you the answer you need rather than the answer the machine decides you need.

Incidentally, the article you have linked to also makes the point that this method is more difficult to learn.

I do agree that the idea of sequencing multiple calculations is a skill that needs to be taught early, but my jury is still out on which method is best - sequential or scientific. Both are equally valid and will give the correct answer if used properly, although sequential calculation does seem slightly more natural.

 

[Gern]

Hi Dave
i understand all of your points here, and think the issue lies with the rigid application of the BODMAS concept. To me, maths is a language, and to work through a string calculation carrying out certain operands before others is absolutely counter intuitive. BODMAS seems to exist to allow lazy question compilation. It has no real basis in logic. In your first example the answer given by the syntax as written is, and only can, be two. To me, if I am supposed to get three as an answer I have to read the “sentence” backwards! If the question is to generate an unambiguous answer it must be compiled more accurately, as Laurie indicates.

I agree that sequential calculation seems more natural, but wasn't BODMAS introduced originally as an attempt to clear up any possible ambiguity?

 

[Gern]

Interesting put in my computer calculator it comes up with the correct answer.
Laurie

Which computer calculator are you using Laurie? My PC has two types of calculator - the normal default one (sequential) and a scientific one (BODMAS). They give different answers.

 

[Gern]

I'm getting a nose bleed!

Thank heaven I made enough pennies for an early retirement simply by knocking nails into bits of wood.

The only calculation I ever needed was if I could finish a roof in time before the British Legion Bar opened.....:thumb2:

Nice to see some of us old farts using maths as it was originally intended - to give us usable, practical answers to everyday problems!

 

[Gern]

But can you still spell BOOBS on it?

And 5407708! Read it upside down.

 

[Gern]

My biggest bug-bear as a result of modern education is the total lack understanding around Metres Squared and Square Metres.

I got asked that a few times by various tutors in the vocational subjects at college. Alas, it's not really a maths question. It's English and just a matter of semantics. None of them could tell me that they used the terms unambiguously - ie always using metres squared when talking about the area of a shape 2m x 2m = 4 metres squared. If they can't be consistent, why should I be?

 

[Gern]

Hi Dave
i understand all of your points here, and think the issue lies with the rigid application of the BODMAS concept. To me, maths is a language, and to work through a string calculation carrying out certain operands before others is absolutely counter intuitive. BODMAS seems to exist to allow lazy question compilation. It has no real basis in logic. In your first example the answer given by the syntax as written is, and only can, be two. To me, if I am supposed to get three as an answer I have to read the “sentence” backwards! If the question is to generate an unambiguous answer it must be compiled more accurately, as Laurie indicates.

You have a good point Tim, but why then do we supply our kids with tools that use both methods, one which will give a correct answer and one that gives a wrong answer? And how about tools that don't give an answer at all?

 

[Gern]

I've not seen this RPN system before, but it strikes me as being just an alternative way of doing calculations either sequentially - just like the old fashioned bog standard calculator, or in 'scientific' order. You - the operator - are still left with the problem of deciding which method of entry will give you the answer you need rather than the answer the machine decides you need.

Incidentally, the article you have linked to also makes the point that this method is more difficult to learn.

I do agree that the idea of sequencing multiple calculations is a skill that needs to be taught early, but my jury is still out on which method is best - sequential or scientific. Both are equally valid and will give the correct answer if used properly, although sequential calculation does seem slightly more natural.

I meant to ask. How do you enter 2 2 + 2 ÷ ? Is it 2 space 2 space + space 2 space ÷ ? If so, that''s a lot of extra buttons to push. If not, how do you distinguish between 2 2 and 22?

And would this interfere with the idea of space notation when writing ordinary numbers?

ie 102 represents 1 hundred + 0 tens + 2 units. We wouldn't write it as 1 space 2. With printed numbers I suppose that could work, but it would be an absolute nightmare for handwritten calculations. Anyone with poor writing would be unable to distinguish between 1 2 and 12.

 

[Tim Marlow]

You have a good point Tim, but why then do we supply our kids with tools that use both methods, one which will give a correct answer and one that gives a wrong answer? And how about tools that don't give an answer at all?

For the same reason we teach them SI units, then ignore them in real life, or standard chemical notation, and use old archaic names. Try finding 10M HCl in a builders merchants. No chance! You’ll probably find 3.5N spirit of salts though. It even happens in scientific establishments and with scientific chemical suppliers. It is just not seen as really important. When I started work at Porton I had to take myself back to school to find out what “normals” were! I had only ever been taught molarity as a measure of chemical concentration so didn’t have a clue what it was.
For another example, ask almost anyone how long a centimetre is and they will say ten millimetres. The answer is really one hundredth of a metre because the metre, not the millimetre, is the base SI unit of length.
Last example, how many times have you been asked to fill in your weight on medical forms? The correct answer should be given in Newton’s, because weight is a product of mass and gravity. What they really want is your mass, which is given in Kilos! Weight changes minutely depending upon height above sea level, mass is a constant.
BODMAS only seems to have appeared in mainstream teaching once early calculators were coomonplacel. These crude early devices could only carry out instructions as they were keyed in by the operator, so this was brought forward to ensure consistency during use. Before that it was the domain of those interested in that part of mathematics.
By the way, my phone and IPad both give the “BODMAS correct” answer to your question…..so at least their electronic appendage is correct according to standard tuition, if not to logic as I was taught it.
Really interesting subject, by the way!

 

[dave]

Although we had calculators at school, we were taught with slide rules and were only allowed to use calculators in the O’level year. The idea being we knew how to do the calculations and how to do rough estimates so we knew if the calculator gave a stupid answer.
you would also be suprised how high you can stack chairs, the year above me on their last night stacked all the chairs from the assembly hall into a massive pyramid in the quadrangle, took a photo, and put the chairs back. Left the photo on the headmasters place at breakfast.

 

[Nicko]

Although we had calculators at school, we were taught with slide rules and were only allowed to use calculators in the O’level year. The idea being we knew how to do the calculations and how to do rough estimates so we knew if the calculator gave a stupid answer.
you would also be suprised how high you can stack chairs, the year above me on their last night stacked all the chairs from the assembly hall into a massive pyramid in the quadrangle, took a photo, and put the chairs back. Left the photo on the headmasters place at breakfast.

Sounds like you went to one of those 'posh' schools Dave..... :smiling2:

Nick

 

[Guest]

I've not seen this RPN system before, but it strikes me as being just an alternative way of doing calculations either sequentially - just like the old fashioned bog standard calculator, or in 'scientific' order. You - the operator - are still left with the problem of deciding which method of entry will give you the answer you need rather than the answer the machine decides you need.

But isn’t that problem impossible to remove? It eventually always boils down to:—

Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?

Incidentally, the article you have linked to also makes the point that this method is more difficult to learn.

I read that too, and I wonder if that is because literally everyone in the world who ever learned to do arithmetic, was first taught so using the traditional method. There’s no way to test that, unfortunately, other than teaching a couple of schools worth of kids to use RPN from the start, I suppose.

Which computer calculator are you using Laurie? My PC has two types of calculator - the normal default one (sequential) and a scientific one (BODMAS). They give different answers.

FWIW, the system calculator on macOS in both standard, scientific and programmer modes says 2 + 2 ÷ 2 = 3, as does Spotlight (the system’s search tool that has a calculator built in too).

If they can't be consistent, why should I be?

To show people how it should be done. I generally refuse to lower myself to someone else’s standards if they’re clearly making mistakes, instead using terminology etc. correctly in my replies. If that confuses them, then maybe they’ll learn something. (Of course, it’s possible all they’ll learn is that they think I’m wrong )

Last example, how many times have you been asked to fill in your weight on medical forms? The correct answer should be given in Newton’s, because weight is a product of mass and gravity. What they really want is your mass, which is given in Kilos! Weight changes minutely depending upon height above sea level, mass is a constant.

That, though, is a result of scientific understanding moving on but not units. Go back a few hundred years and not even scientists realised there was a difference between weight and mass, so the gram was defined as a weight — when later on, it dawned that what it was actually defining, is a mass.

Also, since this is essentially a thread about pedantry: in the SI, names of units are not capitalised — the name of the unit is newton. not Newton

 

[Tim Marlow]

Also, since this is essentially a thread about pedantry: in the SI, names of units are not capitalised — the name of the unit is newton. not Newton :smiling3:

Not me buddy, autocorrect got that one wrong!

 

[Tim Marlow]

That, though, is a result of scientific understanding moving on but not units. Go back a few hundred years and not even scientists realised there was a difference between weight and mass, so the gram was defined as a weight — when later on, it dawned that what it was actually defining, is a mass.

Going further into pedantry …
Actually, the gram was defined as a volume of water, not a weight per se, and it’s adoption in the metric system was predated by the understanding of mass by about 100 years……

 

[Dave Ward]

Strange that metric system was brought up. As a design engineer, I worked for a British Company, we were totally metric, and I was tasked with designing a gas engine conversion - we made diesel engines, so I had to do different pistons etc etc. As a diesel, there were no spark plugs, or electric ignition system, so I had to work up a system from scratch. I value engineered everything, even going for over specced bearings, as they were the cheapest I could find. It worked nicely, looked elegant & was within budget. UNTIL our US subsidiary started bleating about metric bearings! What was the cheapest bearing in Europe was one of the most expensive in the US, and they had to have a certain percentage of American produced parts to qualify as 'US Made' . The US was geared up to large diesels, and I had to redo the design to use clunky parts designed for engines 3 times the size! All because the US is one of the 3 countries in the world that have not accepted the metric system! ( The other two are Liberia & Myanmar! ). The design looked terrible, patched together with oversized parts - I always kept quiet when anyone asked who has designed the monstrosity! Consolation was that it worked pretty well!
Dave

 

[Guest]

I'm getting a nose bleed!

Thank heaven I made enough pennies for an early retirement simply by knocking nails into bits of wood.

The only calculation I ever needed was if I could finish a roof in time before the British Legion Bar opened.....:thumb2:

Well said 570.
453 still using the stick system to measure.
Few would know what I was talking about I feel .

 

[dave]

Sounds like you went to one of those 'posh' schools Dave..... :smiling2:

Nick

Not that posh, back in the day it was a workaday boarding school for children of military officers, doctors, farmers etc., most of the cars picking up at the end of term were Ford Cortinas and the like.

 

[Guest]

Going further into pedantry …
Actually, the gram was defined as a volume of water, not a weight per se

As the weight of a volume of water:

Gramme, le poids absolu d'un volume d'eau pure égal au cube de la centième partie du mètre , et à la température de la glace fondante.

 

[Tim Marlow]

But as it would have been used by measuring other materials as a standard, and using a balance beam as a comparison tool, gravity is taken out of the equation. It therefore becomes mass by default because the definition given is that of an amount of substance…ergo its “mass”.

 

[Nicko]

I think this thread is a good measure of the weather being too hot for sticking bits of plastic together and painting them......

Nick