>> (Seriously - why the hell does anybody in the modern era need to be 
>> fluent at long division?
> 
>   No such thing as useless knowledge.

Knowing how to do long division is not useless.

Practicing long division over and over and over and over again, for many 
years on end, is a completely waste of time IMHO. Once you know how to 
do long division, you know how to do long division. What possible 
purpose could there be in spending years doing it over and over again?

>   How many people thought high-school math classes were boring and useless,
> until they fell in love with POV-Ray?

Maybe we should make POV-Ray more popular? Maybe it would make a good 
teaching aid! ;-)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On Fri, 04 Jul 2008 07:23:13 -0400, Warp wrote:

> Invisible <voi### [at] devnull> wrote:
>> (Seriously - why the hell does anybody in the modern era need to be
>> fluent at long division?
> 
>   No such thing as useless knowledge.

How many angels can dance on the head of a pin? ;-)

>   Is it really so that in the US, the UK and other places everybody has
> to explicitly fill out tax forms each year, specifying all their income,
> tax reductions, etc?

In the US that is the case if you make over a certain amount in the 
year.  There are a handful of different forms based on how complex your 
income situation is, too; 1040EZ is pretty straightforward, the full 1040 
form is a bit more complicated.  Many people have to have an accountant 
do their taxes.

>   Here in Finland all that is automatic: You receive a pre-filled form
> with all your income, tax reductions, etc. already put in. If everything
> is correct, you don't have to do anything about it. Only if there's
> something not in the form already (for example some significant payment
> which has not been notified to the tax officials, or something which is
> worth tax reductions) you'll have to add it to the form and return it.

A lot of the information that goes onto the US tax form comes from other 
forms; automating the information from employer W2 forms and 1090 forms 
is something that *could* be done if there were sufficient funding and 
motivation at the IRS to automate it instead of sending us a million 
pieces of paper with the information on it.

We've done our taxes electronically the last several years, so at least 
the chances of a calculation error are drastically reduced.  Ironically, 
my dad discovered the early onset of his alzheimer's while doing the 
taxes one year - he caught himself going back for the same information 
over and over and over and over again and decided to get tested.

Jim

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On Fri, 04 Jul 2008 12:30:38 +0100, Invisible wrote:

> Either way, laughing at me isn't helping anything, is it? :-P

At some point you're bound to learn to laugh at yourself.  ;-)

But more to the point, you demonstrated McKean's Law, as described on 
Wikipedia as:

"Any correction of the speech or writing of others will contain at least 
one grammatical, spelling, or typographical error"

(aka Skitt's Law)

While not precisely what happened here, it's that type of irony; even 
you've got to appreciate the irony and see the humour in it. ;-)

Jim

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>> (Seriously - why the hell does anybody in the modern era need to be
>> fluent at long division?

Ever tried dividing one polynomial by another?  A useful skill if you're 
doing Laplace transforms and stuff that need polynomials in certain forms. 
Without knowing how to do long division with numbers, you'd be stuffed to 
try and divide a polynomial.

>  Is it really so that in the US, the UK and other places everybody has
> to explicitly fill out tax forms each year, specifying all their income,
> tax reductions, etc?


or if you have some "special" items, like company car, shares, working 
abroad, or basically anything that is non-standard.

>  Here in Finland all that is automatic: You receive a pre-filled form
> with all your income, tax reductions, etc. already put in. If everything
> is correct, you don't have to do anything about it. Only if there's
> something not in the form already (for example some significant payment
> which has not been notified to the tax officials, or something which is
> worth tax reductions) you'll have to add it to the form and return it.

Which is essentially what you do on the UK form too, if you get one. 
Everyone gets a "P60" form that tells you how much income you got and how 
much tax you paid over the last year.  You simply copy&paste those two 
numbers onto your tax return form.  The rest of the tax form is for other 
items.  I suspect a lot of people simply leave 90% of the form blank (there 
are many many optional sections).

It can get complicated if you are a family, paying a mortgage with two kids 
at university, have a company car and shares in the company you work for. 
You just need to sit down and read through the guidelines carefully to work 
out which numbers to put in which boxes.  Of course, many people just pay 
someone else to do it for them who is much more familiar with the system.

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>>> (Seriously - why the hell does anybody in the modern era need to be
>>> fluent at long division?
> 
> Ever tried dividing one polynomial by another?

No.

And you know why?

Because I don't know what polynomial division actually "is" yet.

(Remember: I've never been taught algebra. I just read books when I have 
time...)

> Without knowing how to do long division with numbers, you'd be 
> stuffed to try and divide a polynomial.

I didn't say you don't need to know how to do long division - I said you 
don't need to spend 3 years practising it for several hours per day.

>>  Is it really so that in the US, the UK and other places everybody has
>> to explicitly fill out tax forms each year, specifying all their income,
>> tax reductions, etc?
> 
> In the UK it's only if you pay tax in the highest band (earn more than 

> working abroad, or basically anything that is non-standard.

Thanks for clarifying that. I was wondering myself!

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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>>   No such thing as useless knowledge.
> 
> How many angels can dance on the head of a pin? ;-)

I'm going to have to Google this one, aren't I? :-P

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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> Because I don't know what polynomial division actually "is" yet.

Opposite of polynomial multiplication.

(x^3+3x^2-4x)/(x^2-x) = ???

> I didn't say you don't need to know how to do long division - I said you 
> don't need to spend 3 years practising it for several hours per day.

It makes things later in life, assuming you go on with studying maths, a lot 
easier.  At university I used to cringe at the people who used their 
calculators so often to do what they really should be doing in their head. 
When you are tackling a large problem it is a huge advantage do be able to 
do at least the basics very quickly in your head.

> Thanks for clarifying that. I was wondering myself!

Since I'm living in Germany I don't pay UK tax anymore, but I asked them to 
repay me some bank interest tax (it was a relatively small amount, like 


because I didn't return it by the deadline (even though the deadline had 
passed by the time I got the form!!!).


long time and a lot of effort - not sure if that was a profitable use of my 
time though!

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On Fri, 04 Jul 2008 12:34:19 +0100, Invisible wrote:

> Practicing long division over and over and over and over again, for many
> years on end, is a completely waste of time IMHO. Once you know how to
> do long division, you know how to do long division. What possible
> purpose could there be in spending years doing it over and over again?

Some people need more practice than others.

Jim

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On Fri, 04 Jul 2008 13:10:46 +0100, Invisible wrote:

>>>   No such thing as useless knowledge.
>> 
>> How many angels can dance on the head of a pin? ;-)
> 
> I'm going to have to Google this one, aren't I? :-P

LOL, you're learning. ;-)

Jim

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>> Because I don't know what polynomial division actually "is" yet.
> 
> Opposite of polynomial multiplication.
> 
> (x^3+3x^2-4x)/(x^2-x) = ???

As I understand it, the product of two polynomials is a formula that 
produces the same result as running the two polynomials and then taking 
the product of their answers. And this product is guaranteed to always 
be a polynomial.

It is not immediately clear to be that the quotient of two polynomials 
is necessarily a polynomial.

>> I didn't say you don't need to know how to do long division - I said 
>> you don't need to spend 3 years practising it for several hours per day.
> 
> It makes things later in life, assuming you go on with studying maths, a 
> lot easier.  At university I used to cringe at the people who used their 
> calculators so often to do what they really should be doing in their 
> head. When you are tackling a large problem it is a huge advantage do be 
> able to do at least the basics very quickly in your head.

Hell, I can't even multiply numbers in my head!

I'm good at understanding principles and elligant mathematical theories. 
I'm not good at memorising vast amounts of unstructured data.

And if you think your experience was bad, imagine being in a room full 
of undergraduates and finding that only 2 of them know what "logarithm" 
means. (Obviously one was me. The other one was that crazy rugby player 
from Manchester. I remember at the time feeling quite guilty for 
assuming he was stupid just because has acted like a complete psychopath 
all day long...)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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