Calculator Accuracy & Usefulness

[Matt Agajanian]

Hi all.

Humour me, if you will, please.

Although HPs, TIs, Casios and Sharps were not like they are today in 2015, how vital, useful, essential were these scientific & programmable calculators in technical, scientific disciplines in the past even though they had 10 digit displays, limited algorithms, and, in TI's case 13-digit calculating precision at most?

Further, how useful, essential, reliable, etc. were HP Spice/Spike, Woostocks, V'Gers (yes, Voyagers), 41s in real engineering disciplines with their 10-digit accuracy?

Thanks in advance

[Dwight Sturrock]

I pulled my dad's old British Thornton slide rule out last night and multiplied a few numbers. I would say calculators were definitely an improvement in accuracy over that!

[Dave Britten]

I think in many cases, having greater precision is a benefit not so much because you actually need that many figures in the result, but to minimize the chances of rounding errors creeping into the figures you do need. I can't imagine trying to use something scientific with fewer than 10. (See: Sinclair Scientific)

[Les Bell]

(05-23-2015 11:42 PM)Matt Agajanian Wrote:  how vital, useful, essential were these scientific & programmable calculators in technical, scientific disciplines in the past[?]

They weren't essential, but they were incredibly useful. I grew up with the slide rule in school, and then got my first calculator as a second-year engineering (actually, cybernetics) student. The difference was staggering - not so much in terms of accuracy, as in eliminating the effort of keeping track of the decimal point. Replacing manual addition and subtraction was pretty cool, too. After that, access to logs and exponentiation was cream on top.

Mind you, the first time I submitted an assignment with 10-digit precision in the answer, I got marked down and was subjected to a stern lecture on the nature of measurement error, accuracy and precision.

[Garth Wilson]

I do electronics circuit design in my job. I don't remember ever needing anywhere near ten digits. I usually keep my HP-41cx on ENG 03 display mode. I started with the slide rule too (1970's), and the reason for moving to a calculator was that the slide rule was not programmable.

[d b]

HP forum tip: don't try to imagine a programmable slide rule while drinking red wine. Thanks Garth.

[Csaba Tizedes]

(05-24-2015 01:37 AM)Garth Wilson Wrote:  I do electronics circuit design in my job. I don't remember ever needing anywhere near ten digits. I usually keep my HP-41cx on ENG 03 display mode. I started with the slide rule too (1970's), and the reason for moving to a calculator was that the slide rule was not programmable.

Totally agree, but I started my engineering work only in 2005.
My calculators tipically in ENG3 mode and it's normally enough for all the calculations.
If I don't want to disturbed with too many digits, the ENG2 is the great mode and I use for the fourth digit the CLEAR PREFIX (on my 15C) or SHOW (32SII).
It means three significant digit always visible, that is 0.1% precision at least. In normal engineering (mechanical) this is far enough.

[Tugdual]

We don't need very deep accuracy simply because the measurement systems already include this concept in the real life. You don't measure bacteria sizes in km and/or the distance in between galaxies in mm.

[Paul Dale]

(05-24-2015 09:28 AM)Tugdual Wrote:  We don't need very deep accuracy simply because the measurement systems already include this concept in the real life. You don't measure bacteria sizes in km and/or the distance in between galaxies in mm.

Doesn't everyone use attoparsecs per microfortnight?

Then there is the nanoacre.


Pauli

[peacecalc]

And what is about financial calculations?
Not only engineers use a calculator.

[Tugdual]

(05-24-2015 12:13 PM)peacecalc Wrote:  And what is about financial calculations?
Not only engineers use a calculator.

On a financial calculator, 1+1=2.5 with interest and taxes, why would you need accuracy for that sort of calculations?

[CR Haeger]

Hp15c made me 34.56372% more productive in my Mech Eng studies in the 1980s.

Seriously though, I turned it ON during or shortly after my brain finished booting up.

In my field, ENG 3 mode is sufficiently precise for almost all math encountered. For the others, I make a younger Engineer figure it out.

[peacecalc]

Quote:Tugdal wrote:

On a financial calculator, 1+1=2.5 with interest and taxes, why would you need accuracy for that sort of calculations?

Maybe you not, but may be an accounting clerk.

[SlideRule]

.Measure with a micrometer.
..Mark with a Crayon..
...Cut with a chainsaw...

BEST!

SlideRule

[ttw]

Bond and mortgage computations often need high precision. Also, naïve implementations of variance computation can need high precision.

[Les Bell]

(05-24-2015 09:59 AM)Paul Dale Wrote:  Doesn't everyone use attoparsecs per microfortnight?

Then there is the nanoacre.

I was very fortunate to have Prof. J. E. Gordon, author of "The New Science of Strong Materials" and "Structures: or Why Things Don't Fall Down" as my materials science lecturer. Gordon was something of a classicist - he actually got the university to award combined degrees in Engineering and Classics, and ran final-year projects such as building a Greek palintonon, a kind of classical high-tech crossbow.

I believe he coined the SI unit of beauty, the milliHelen, which he defined as "that face which would launch one ship".

[Dave Shaffer]

[/quote]
I believe he coined the SI unit of beauty, the milliHelen, which he defined as "that face which would launch one ship".
[/quote]

Not sure what epoch you refer to, but I invented/used this term back in the early '70s (and could enlist friends to back me up, if necessary).

However, it's pretty obvious, too.

[Les Bell]

(05-25-2015 02:50 AM)Dave Shaffer Wrote:  Not sure what epoch you refer to, but I invented/used this term back in the early '70s (and could enlist friends to back me up, if necessary).

However, it's pretty obvious, too.

Gordon was an active engineer and scientist from the 1930's onwards, and I got the impression he'd been using the line for many years when I heard it in 1973 or so - but as you say, it's pretty obvious and independently "discoverable".

[Joe Horn]

The millihelen may have first been suggested by Isaac Asimov. Published references to it exist from the 1960's and possibly earlier. A hilarious number of further details about the "Helen" unit of beauty may be found here: http://en.wikipedia.org/wiki/List_of_hum...uty:_Helen

[Claudio L.]

(05-24-2015 09:28 AM)Tugdual Wrote:  We don't need very deep accuracy simply because the measurement systems already include this concept in the real life. You don't measure bacteria sizes in km and/or the distance in between galaxies in mm.

Reading this thread it gives the impression that in engineering there's no need for precision. Far from reality!
Engineers don't only use "measured" quantities. We also use complex algorithms with thousands of computations.
Just try an ODE (Runge-Kutta anyone?), do a shootout at various precisions and see where it takes you when you are thousands of tiny steps away from the boundary condition.
We can take the final result and only use a few digits, and we can round the input to a few digits, but all intermediate calculations NEED some precision or it'll be a disaster. Changing the third digit on the boundary condition might get you off only by 5% or so, but after a thousand steps, you'll be an order of magnitude off if you only use 3 digits at every step.

Surveyors are a good example: they use exclusively measured quantities, yet they were historically desperate to get more precision: multiple measurements with the tape, compensating for the temperature of the tape, compensating for the sag, compensating for the stretching of the tape due to axial stress, etc. are just examples of how much they needed that precision in the past. Today, they use GPS to get an accuracy within 1 cm anywhere on earth. Satellites are orbiting 20200 km above earth, and within 1 cm you need to operate with numbers of the order of 2 020 000 000 cm, that's 10 digits bare minimum right there.

In electronics, engineers need to count 'ticks' of clocks that are gigahertz in frequency. Lots of digits there. Transmission of signals needs accurate clocking (GPS receivers are again a good example).

Old engineers with slide rules didn't have to deal with this, or simply couldn't even if they wanted to. These examples are a consequence of the gradual increase in precision over the years, of which early calculators were a very important part.

Some areas of engineering need more precision than others, but for sure calculators with more precision (and later computers) enabled a LOT of progress.