Galactic Mathematics
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Re: Galactic MathematicsSorry, but it's above my pay grade.
Re: Galactic Mathematics
It means that I don't have what it takes to understand any of the topic.
Re: Galactic Mathematics
There are some mental arithmetic shortcuts that I can see in there, but there may be some more tricks. e.g. 24 x 11 = 240 + 24 = 264 i.e. just put a 0 on the end of the 24 and add another 24. There might be an even quicker way. I also realised a while ago that multiplying a number by 5 can be done more quickly by just halving it mentally, then shifting it 1 decimal place. The other larger multiples I can't see a quick way through though.
Re: Galactic Mathematics
My head my explode.
Re: Galactic MathematicsIs 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.
Re: Galactic MathematicsVery 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.
Re: Galactic Mathematics
I sort of see what you mean, it's a little like getting expertise in anything, say in database or something, things become more second nature after a while. I used to struggle for a bit with engineering and physics formulas etc in terms of really understanding the underlying concepts and the relationship between them, although I could recite the actual formula and use it to get a correct result. Vedic maths seems to be tricks of the positional numbering system and almost accidental patterns that can be observed. Although the Western arithmetic methods are a bit clunkier, the same method works for anything, including other base systems, without a lot of thought involved. Fibonacci is certainly a patterned sequence. Not sure how the calculation of pi is wrong, or its decimal representation, especially to 6 decimal places, as it is a verifiable ratio which can even be measured graphically as the ratio of the diameter of a circle to its circumference. This reminds me of another conceptual mathematical area I struggled with, probably out of lack of interest, which is imaginary numbers, and the famous formula 'e to the i pi = 1' (or ) which (amazingly?) unites the major mathematical entities of interest into a single identity statement  e, i, pi, 1 (unity) and the negative number concept. http://en.wikipedia.org/wiki/Pi#Complex ... d_analysis
I'm not sure that was the intent, rather that a simple, repeatable and consistent algorithm could be used by anyone to get the correct result.
hmm, not sure about that one, 6, 8 and 9 are multiples of 2, 3 and 4, but 7 is a prime number and therefore not a multiple. unless it is simple addition of 5 and 2 or similar.
No, GST is basically a VAT  'value added tax'  which claims to tax a process of production from beginning to end where value is added by someone's labour. It applies to the provision of both physical goods and services. So a doctor charges 10% GST for a consult. A food vendor who has prepared food on the premises, cooks it, and sells it, also remits 10% GST to the govt for the value added in making the food from raw materials. In the case of goods, GST is added from the beginning of the production process, but all intermediate producers claim full 'GST credits' or offsets as they go, i.e. they are effectively GST exempt, until the product is sold to the final consumer who is slugged with the final 10% on the finished product. I assume US statebased 'sales taxes' are similar. It is a socalled 'indirect tax' in that it does not tax income, but those sorts of definitions are pretty arbitrary. It is also an example of a flat tax, and is therefore somewhat regressive. However, it catches a slice of the services pie rather than just goods, thus broadening the govt's tax base. In Australia, it replaced 'wholesale sales tax' on goods which had differential rates of tax and was harder to define, administer and collect and helped avoid rorting via reclassifications of goods to a lower rate. The VAT in Britain has gone up several times due to govt fiscal crises, and is approaching 20%, whereas the Oz GST has remained at 10% which at least makes the maths easier. All this assumes the necessity and inevitability (like death) of some sort of system of taxation to run the machinery of state.
Re: Galactic Mathematicsaha, 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...
Re: Galactic MathematicsHow 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.
Re: Galactic Mathematicsthat jain thing really does not sound like the hundreds of pages of notes and proofs I took down in Calculus and Linear Algebra classes.
Re: Galactic MathematicsQuite 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'.
Re: Galactic MathematicsYou 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.
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