But it must change the language

Posted Jan 13, 2015 19:27 UTC (Tue) by cesarb (subscriber, #6266)
In reply to: But it must change the language by Wol
Parent article: Type hinting for Python

> But this is all computer science stuff. Why can't we just have numbers that are numbers :-)

For which definition of number? N? Z? Q? R? C?

> Try looking at the problem from a "real world" perspective, not from a theoretical mathematical perspective, sometimes ... :-)

All of these except perhaps C come from the "real world".

In related news: the Lua language, which had previously used "float" for everything, now has both 64-bit "int" and "float" in the just released 5.3 version. See these slides: http://www.inf.puc-rio.br/~roberto/talks/ws2014.pdf (found at https://news.ycombinator.com/item?id=8874766).

But it must change the language

Posted Jan 13, 2015 20:40 UTC (Tue) by mpr22 (subscriber, #60784) [Link] (2 responses)

Even complex numbers relate to the physical world; analysing alternating-current electrical systems without them is painful.

But it must change the language

Posted Jan 13, 2015 22:19 UTC (Tue) by mathstuf (subscriber, #69389) [Link] (1 responses)

Yep. The geometric interpretation of multiplication by sqrt(-1) is a turn of π/2 radians. "Imaginary" is a really poor name for them since it really just comes from the lack of an imagination by mathematicians when they were first being investigated. Likewise, quaternions can be viewed as an axis on a sphere with an "up" vector off of the oriented radius. I haven't worked with octonions enough to have a real-world example for them (and since their algebras start to break down anyways, they're much harder to conceptualize as well). Wiki suggests they're used in things such as string theory and other (relativity-related) physics subfields though.

But it must change the language

Posted Jan 14, 2015 0:35 UTC (Wed) by gracinet (guest, #89400) [Link]

I think the naming is historically due to Cardano's trick of assuming existence of « imaginary » solutions of the auxiliary 2nd degree equations that are used for solving 3rd degree equations in the case where the discriminant is negative, in a trick that must have looked incredibly artificial at the time. *That* was thinking out of the box !

The geometric interpretations came much later, and while useful in countless cases, it's just one way to think about complex numbers, that's not adapted to all settings.

Anyway, getting back on topic, sorry.