The arrogance here is breathtaking.
Have you ever considered that maybe people who know more than you have come to the conclusion that what you consider the bad definition is actually the good one, by the criteria that matter, and vice versa?
Have you ever considered that maybe people who know more than you have come to the conclusion that what you consider the bad definition is actually the good one, by the criteria that matter, and vice versa?
I get how it's fun for intellectual people to come up with new definitions for things that expand our knowledge and understanding of the universe, and tease people who have the old simple understanding with seemingly impossible quandaries. But I would like the emphasize that I think this teasing is counterproductive. It leads people to believe mathematicians operate in a field that is fully disconnected from reality. Either take the time to explain how you define your construct, so they can truly appreciate the usefulness and ingenuity of the equation, or use different symbols and present it as a valuable yet opaque contribution to practical mathematics by showing its applications. Both cases will yield the much deserved admiration.
Problem with what you're saying: Hundreds and Hundreds of years of history and tradition and the sheer knowledge that's been built up in the current way we do Maths.
Another problem: It's not teasing if the ideas are actually complicated. Which this one most certainly is.
Another problem: Not all Math is practical and applied, some of it almost certainly operates in a field that is "disconnected from reality".
Another problem: Your solution of using different symbols has the same problem as XKCD standards.
Another problem: "Regular people" is vague. People fear math for a reason. They can suck at it.
Another problem: This idea is also fairly old. So your part about "old simple understanding" also doesn't hold true.
Only thing we can agree on: Math can suck at communicating ideas if you're not used to it and/or don't have the context and knowledge.
Scientific American is targeted at educated laypeople. The author's job is to communicate with that target audience. And it absolutely is a tease to use a headline that, to that audience, will come over as a bizarre indication that they're actually clueless.
Oh we can definitely agree to that
> that what you consider the bad definition is actually the good one
Sum is pretty much well defined for different sets used in mathematics. In none of them the sum of infinite positive numbers is a negative number.
Here's a definition for a bad definition: it is ambiguous
if i have a circle of circumference 5
the sum of 1+2 is equal to both 3 and -2.
sum continues to work in the same in your circle (Commutativity, Associativity, Identity element and a + 1 is the next successor of A)
The point is, in "the universe" most of "infinity" are actually finite circles that you can travel along "infinitely" - because you eventually arrive back where you started.
and -1/12 just means 1/12 to the left before you get back where you started moving right.