Galactic Mathematics

[NinjaPuppy]

Sorry, but it's above my pay grade.

[NinjaPuppy]

[SydneyPSIder]

[NinjaPuppy]

[SydneyPSIder]

Is there a quick algorithm to divide any number by 11? There is a 10% GST on everything here, and to figure out the ex GST price involves taking 10/11 of the item. 1/11 is the GST amount itself.

[SydneyPSIder]

Very interesting. They seem to be algorithms devised as an artefact of positional numbering and base 10 (or base anything). I assume it only works that way for 11? Not 12 or 13 etc?

I suspect we are taught arithmetic the way we have been as the same algorithm works for any length of numbers, although it might take longer and can't be done easily in our heads or via a quicker algorithm. I guess the methods are broken down into steps that are within our capability, i.e. you just need to know the times tables to 10 to be able to perform multiplication of larger numbers...

GST is a goods and services tax, basically a sales tax like VAT.

[SydneyPSIder]

[SydneyPSIder]

a-ha, very interesting. in effect, for numbers > 5, you are subtracting from 10.

the techniques certainly are interesting for doing quick arithmetic on large numbers. remember the days when they used to have rooms full of people with slide rules doing the calculations for various physics projects etc, just before modern computers really took off -- they were all replaced with a Univac in the end. I know floating point processors also use 'shortcuts' to operate using lookup tables and the like to do various types of calculation. The more we use spreadsheets, the less we do manual arithmetic -- and we don't trust our own answers anyhow...

[SydneyPSIder]

How have you determined a different value for pi than the one that has been calculated to a trillion decimal places as an exercise?

I just wanted to say it reminded me of another conceptual mathematical area I struggled with. Complex numbers are used in electrical theory to emulate circuit behaviour under AC, which is even more bewildering lol.

Not sure about the real numbers math replacement.

[SydneyPSIder]

that jain thing really does not sound like the hundreds of pages of notes and proofs I took down in Calculus and Linear Algebra classes.

[SydneyPSIder]

Quite funny. The proofs, collectively, are one of the reasons we can differentiate and integrate and solve engineering problems. I was quite good at doing second order partial derivatives once upon a time, calculating the volume of spheres with cylinders drilled out of them using functional partial derivatives mathematically rather than by measurement.

The trouble with 'Vedic mathematics' is that it's just a bunch of tricks that let you come up with simple arithmetic answers a bit quicker -- some Indian guys have spent the past 2,000 years observing and studying patterns of positional notation and coming up with a couple of shortcuts in all that time, but nothing more. Basic arithmetic is only useful for accountancy. No calculus, no more advanced mathematics. None of it means anything if you're trying to launch a satellite and do some meaningful calculations. Clearly in the information age calculators and spreadsheets have pretty much superseded the need for Vedic shortcuts just to add up a few numbers. To make is a mark of pride is a bit sad, really.

Is it 0.0526315789473684 ? Through long division or Windows 'calc'.

[SydneyPSIder]

You need to demonstrate all of the above. But I don't doubt that with a lot of work it might be possible to come up with alternative computational methods for those sorts of transformations. However, the symbolic logic of performing calculus would not change, simply the method of calculation -- similarly to how slide rules and logs used to be used to speed up calculations before computers became widespread and were obviously very fast and very accurate.

I did it by running 'calc' and pressing the buttons '1/19='. Computer algorithms did the rest.