h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

It is worth mentioning, I think, that mathematicians seem to make some bizarre connection between mathematics and arithmetic. The latter, of course, is an ancient and highly refined means of torturing schoolchildren through the mindless repetition of simple problems in addition, subtraction, multiplication and division.

The connection between mathematics and arithmetic, of course, is spurious. Of course mathematics uses some numbers and, when it cannot be avoided, plus or minus signs. However, its operations go into the wholly fantastic, using unknown or imaginary values to express unknown or imaginary concepts which can only exist in some unknown or imaginary world. Arithmetic, on the other hand, stubbornly continues using the same old basic operations, over and over, in a procedure meant to break the will of the student. Any knowledge or understanding of the theory behind this repetition is coincidental.

Aha! Somebody who has mentioned that most useless invention. . .imaginary numbers. It seems to me, (one of the many uninformed) that imaginary numbers are what mathmeticians use to make an equation work when it doesn't. By putting in an imaginary number, 99% of the population become confused and uninterested and think that the person must be incredibly intelligent. The point is that imaginary numbers are IMAGINARY, thus they do not exist in 'real' terms (this is where it goes a bit hazy), and if they don't exist, what is the point of them being there? They have no effect and the equation doesn't work. Now as long as this doesn't affect the simple laws of physics that keep me stuck to the ground with gravity etc. etc., then they can continue to use them and feel really clever.

Bollocks. Yes imaginary numbers can make your head hurt, and they can look like some mathematician yanked something out of his butt to make the equation work, but the fact is that electronics uses them quite a bit to get the phase that they need. In fact most of physics is totally tied to the idea of imaginary numbers, they are explicit in most equations. And while we can deride physicists for being lost bunglers with their head in the clouds, the computer you type on would not of existed had not solid state physicists not had imaginary numbers in their bag of tricks.

Physicists are also lazy bastards too. Even thought the offcial pull of gravity is 9.8...m/s/s (meters per second per second) - when doing equations they get lazy and pretend it's actually 10m/s/s.

As for teh mention of arithmetic - there is an area of math called 'Arithmetic Sequences' here using the formula tn=a+(n-1)d (where 'a' is the first term, 'd' is the distance between terms and 'n' is the term you're looking for) you can calculate any number in a sequence where the numbers increase in regular intervals. FOr eg. in the sequence 1, 4, 7, 10... the 21st term would be 121.

Alright then can we turn this into a Did You Know sort of forum?
Did you know that if you multiply 111,111,111 by itself you get 12345678987654321?
For non maths types that number is counting up to nine and back down to one again.

I don't really know about the did you know part but I am quite impressed that imaginary numbers make my computer work. Does this mean my computer can imagine things? Or am I just taking the piss? Basically I don't understand them and no number of lecturers can make it work for me (and I've had a few). I'm happy to be ignorant as long as things keep working.

There seems to be some confusion here. While it's true that mathematics is the creative bit and arithmetic is the bit with the basic operations (all just adding up really), counting is concerned with the rather plain and boring real world and is therefore physics or accountancy.

Why do you claim that imaginary numbers are any more imaginary than, say, negative numbers? They've just been given an unfortunate name. Do you suppose irrational numbers keep storming out saying "You just don't understand me!"

Oooh. This is getting a bit like one of those moral problems that sixth formers (11th Graders?) get set.

You are in a balloon and you have a Physicist, an Accountant and a Theoretical Mathematician - the balloon is losing height over a shark infested sea - who should you throw overboard?

I have several answers:

The Theoretical Mathematician - cos then you wouldent be in this mess.

All of them

The Accountant - cos you need the Physicist to figure out velocity and trajectory and all that kind of stuff to get the balloon down, and teh Mathematician to do his sums.

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Have you ever imagined a world without hypothetical questions?

Do you mean this world or some other world?

have you ever hypothesised a world without imaginary questions???

Maybe

Answer: Note that the theoretical mathematician might not have a clue about the balloon stuff: properly theoretical maths is nothing to do with calculating things. The physicist might have a reasonable chance of working out why they're about to plummet just as they crash down.
Basically, chuck over the accountant. He's probably the richest, so there's an opportunity for some social justice.