# [Haskell-cafe] Num instances for 2-dimensional types

Miguel Mitrofanov miguelimo38 at yandex.ru
Mon Oct 5 12:44:46 EDT 2009

```On 5 Oct 2009, at 19:17, Lennart Augustsson wrote:

> Complex numbers are just pairs of numbers,

What about dual numbers? (Yes, I've remembered the term) Aren't they
also just pairs of numbers?

> There may be other ways to define the operations on pairs of numbers
> that makes sense too.

But these aren't the ways to define pairs of numbers, right?

> My real point is that you shouldn't tell others what they should
> regard as numbers and what not.

some interrogation he
reveals that he just renamed Program.hs to Program.exe. Shouldn't we
tell him NOT to do this?

> Being a number is in the eye of the beholder. :)

Yes, and some points of view aren't as good as other. That's why we
have psychiatric hospitals.

>
> On Mon, Oct 5, 2009 at 4:55 PM, Miguel Mitrofanov <miguelimo38 at yandex.ru
> > wrote:
>> No, they aren't. They are polynomials in one variable "i" modulo
>> i^2+1.
>>
>> Seriously, if you say complex numbers are just pairs of real
>> numbers - you
>> have to agree that double numbers (sorry, don't know the exact
>> English
>> term), defined by
>>
>> (a,b)+(c,d) = (a+c,b+d)
>>
>> are just pairs of real numbers too. After that, you have two
>> choices: a)
>> admit that complex numbers and double numbers are the same - and most
>> mathematicians would agree they aren't - or b) admit that the
>> relation "be
>> the same" is not transitive - which is simply bizarre.
>>
>>
>> Lennart Augustsson wrote:
>>>
>>> But complex numbers are just pairs of numbers.  So pairs of numbers
>>> can obviously be numbers then.
>>>
>>> On Mon, Oct 5, 2009 at 4:40 PM, Miguel Mitrofanov <miguelimo38 at yandex.ru
>>> >
>>> wrote:
>>>>
>>>> Lennart Augustsson wrote:
>>>>>
>>>>> And what is a number?
>>>>
>>>> Can't say. You know, it's kinda funny to ask a biologist what it
>>>> means to
>>>> be
>>>> alive.
>>>>
>>>>> Are complex numbers numbers?
>>>>
>>>> Beyond any reasonable doubt. Just like you and me are most
>>>> certainly
>>>> alive.
>>>>
>>> _______________________________________________