What’s wrong with ‘diamonds’ in the language of maths?
In a word, it’s hard to know.
But a new article in the journal PNAS by two American mathematicians makes clear why: the numbers themselves have been changed to represent different types of mathematical particles.
In fact, the mathematical terms used in the new article – like “bounded” and “exponential” – have been replaced by “exponential”, which is how you write it in everyday English.
“A new mathematical term is used for the addition of two terms that are in fact different types,” wrote lead author Christopher Burt, a mathematician at the University of Florida.
The term “expansion” is used instead, meaning that it describes the addition between two numbers of the same type.
“The number 4 is expanded by 4 and the number 2 by 2,” he explained.
“This is the case for the following: 3, 2, 5, 4, 3.
The addition of these two numbers to 4 is 4, and the addition to 2 is 2.
This is the same as adding 4 and 2 to 5.”
Burt said that he and his colleagues found this “unusual” change when they looked at how the mathematics of 3D space, and of 2D space and 3D time, was being used in a computer game.
“We were looking at the way in which the game engine was being built, and in the case of 3DS Max, we noticed that the number of objects on the screen was being dynamically set by the user,” he told Al Jazeera.
“There was an increase in the number and then a decrease in the size of the objects that were being displayed on the field of view.”
This change is also evident in the way the maths of 3ds Max is being used.
“It’s pretty clear that a new mathematical form has been introduced to the game, and it’s a new form that is actually being used,” Burt added.
“So we’re seeing the addition being done on the fly.
The user is choosing which numbers are being added.”
Maths and maths is not the only area of the world that is being impacted by the new mathematical language.
In the UK, for example, the British government is currently in the process of re-branding the official language, which includes the words “economy” and a new word “government”.
Burt and his team at the UK Mathematics Institute think that this re-design is a good move, but they say that the language is not entirely satisfactory.
“If we have an attempt at a new language, it is going to be a big project and not necessarily a good fit,” he said.
“I would rather see the language change so that it is compatible with the current state of mathematics, rather than trying to change the entire language.”
This article was originally published on Al Jazeera and can be reproduced here.