# Half… only sometimes

In a great world of numbers

Heard some people cry, I dunno why.

They lost a lot

Mainly the biggest ones

But a lot of them

Got into a new world

Dunno why.

They were first imprisoned

Then the confused mathemagicians gave them a funny name

They were very ashamed

Until... Some mathemagicians released them from jail... and, at last, they were free

But they were weirdos for everyone except their breed

The mathemagicians were confused...

And people feel the same to this day!

What is this story referring to?

• This is a nice riddle +1. – Smartest1here Jan 7 at 16:51
• Two downvotes? Someone must hate me! – new QOpenGLWidget Jan 7 at 18:37
• (Not the downvoter) Complaining about downvotes in comments isn't going to do anything, and people rarely downvote just because they don't like you. Probably someone thinks this puzzle is low-quality, for reasons that I can't explain to you. Downvotes are not personal. Please stop commenting as if they are. – bobble Jan 8 at 1:34
• Zixuan I would not say you are wrong... personally I find that if I don't like a person on here and I do see their post is low quality, I am ever so the more tempted to press that downvote button. (I gave this puzzle an upvote by the way). The opposite is true, if I like the user and I see his post seems decent. So the moral of the story is to be very careful not to offend people here. – Smartest1here Jan 8 at 1:58
• @zixuanisbadatPuzzling I only see one, not two. – risky mysteries Jan 8 at 5:07

Just an idea from a non-mathemagician, so forgive me is this answer looks naive to you.

I believe this story is referring to

imaginary/complex numbers.

But the same idea could apply to rational vs irrational numbers, it's hard to choose.

In a great world of numbers
Heard some people cry, I dunno why.
They lost a lot
Mainly the biggest ones

This alludes to the square root operation which, by approximately halving the number of digits of (the integer part of) its operand, has a greater impact on big numbers.

But a lot of them
Got into a new world
Dunno why.

This may refer to the creation of imaginary numbers. This new set ("world") of numbers contains the result of applying the square root operator to negative numbers.

They were first imprisoned

"imprisoned" because they were confined into a named category

Then the confused mathemagicians gave them a funny name
They were very ashamed

Wikipedia tells us that imaginary numbers were "originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless"

Until... Some mathemagicians released them from jail... and, at last, they were free

The creation of complex numbers (by Abraham de Moivre, Leonhard Euler or Caspar Wessel, I'm unsure whom to choose). Consequently, imaginary numbers became part of a bigger group and were reunited with real numbers.

But they were weirdos for everyone except their breed
The mathemagicians were confused...
And people feel the same to this day!

Complex numbers may be difficult to comprehend and this category took a long time to be commonly accepted.

• The first lines were about rot13(fdhner ebbg)s, which led to these numbers being created. – new QOpenGLWidget Jan 7 at 17:36
• I'm not able to understand why. So I will let others propose and elaborate on my other possible answer. That was fun anyway. – xhienne Jan 7 at 17:39
• Perhaps it has something to do with $\sqrt{-1}$; i.e $i$? – marsnebulasoup Jan 7 at 20:57
• @marsnebulasoup Oh, I see, thanks. I thought OP was telling me the actual answer was rot13(veengvbany ahzoref). Still, I don't see how the first sentences relate to rot13(fdhner ebbg). There is probably a wordplay that escapes me (English is not my mother tongue). – xhienne Jan 7 at 21:14
• @xhienne - Neither do I...and I am a native english speaker 😑 – marsnebulasoup Jan 7 at 22:15