Two articles about nothing
July 8, 2018 2:54 PM   Subscribe

Humanity’s discovery of zero was “a total game changer ... equivalent to us learning language,” says Andreas Nieder, a cognitive scientist at the University of Tübingen in Germany. But for the vast majority of our history, humans didn’t understand the number zero. It’s not innate in us. We had to invent it. And we have to keep teaching it to the next generation. Other animals, like monkeys, have evolved to understand the rudimentary concept of nothing. And scientists just reported that even tiny bee brains can compute zero. But it’s only humans that have seized zero and forged it into a tool.
posted by Johnny Wallflower (24 comments total) 36 users marked this as a favorite
 


Wait, this isn't about Seinfeld?
posted by Quackles at 3:50 PM on July 8, 2018 [1 favorite]


I was hoping nobody would comment on this in a slight collective sense of comedy.
posted by transient at 4:22 PM on July 8, 2018 [8 favorites]


One of our own wrote a book on zero (which I enjoyed immensely even before I knew it was written by a mefite).

“When you ask [a child] which number is smaller, zero or one, they often think of one as the smallest number,” Brannon says. “It’s hard to learn that zero is smaller than one.”

But unfortunately "zero is the loneliest number" doesn't have the right meter.
posted by TedW at 4:25 PM on July 8, 2018 [5 favorites]


Aren't you going to look silly when mods delete Harvey Kilobit's and Quackles' comments, transient?

I like the fact that due to zero existing and negative numbers therefore also existing, there is a sense in which:

1 + 2 + 3 + ··· = -1/12
posted by axiom at 4:29 PM on July 8, 2018 [2 favorites]


”So they put out a series of sheets of paper that had differing numbers of objects printed on them. Using sugar as a reward, the researchers taught the bees to always fly to the sheet that had the fewest objects printed on it.”

Wow this is an amazing thing to figure out too. Do bees like doing things like this or do they prefer sniffing through flowers? That’s what I’d like to find out next.

Metafilter: Using sugar as a reward, the researchers taught the bees to always fly to the sheet that had the fewest objects printed on it.
posted by bleep at 4:30 PM on July 8, 2018 [4 favorites]


Hey Sumerians thanks for nothing.
posted by Lutoslawski at 4:47 PM on July 8, 2018 [22 favorites]


Personally, I'd rather train bees to always fly to people whose pictures I show them and sting them on the top of their penises.

But that's me.
posted by delfin at 5:06 PM on July 8, 2018 [5 favorites]


Delfin, you would enjoy the season 3 episode of Black Mirror called “Hated in the Nation.”
posted by ejs at 5:12 PM on July 8, 2018 [1 favorite]


Much ado about nothing - if you don't like Seinfeld, how about Shakespeare? (sorry)
posted by blue shadows at 5:38 PM on July 8, 2018 [1 favorite]


EMPTY SET PROBE TRIAL
She’ll simply ask the kids to pick the card with the fewest number of objects. When a card with nothing on it is paired with a card with one object on it, less than half the kids will get the answer right


Not sure I agree with their police work there......it is not true that the empty set has fewer objects than a card with n objects, if I remember my set theory right.
posted by thelonius at 5:45 PM on July 8, 2018 [1 favorite]


The computer you’re reading this article on right now runs on a binary — strings of zeros and ones. Without zero, modern electronics wouldn’t exist.

You know, we only use zero and one to represent the two voltage levels in a digital signal by convention. You could just as easily have used any other two symbols, like one and two, or A and B, or black and white, or cat and dog.

Kaplan walked me through a thought exercise first described by the mathematician John von Neumann. It’s deceptively simple.

Imagine a box with nothing in it. Mathematicians call this empty box “the empty set.” It’s a physical representation of zero. What’s inside the empty box? Nothing.

Now take another empty box, and place it in the first one.

How many things are in the first box now?

There’s one object in it. Then, put another empty box inside the first two. How many objects does it contain now? Two. And that’s how “we derive all the counting numbers from zero … from nothing,” Kaplan says. This is the basis of our number system.


[pedantry]That's not exactly how von Neumann constructed the natural numbers from set theory. The real process is to start with nothing on your table, and at each step put a copy of everything on your table into a box and put that box on the table. In this way, we know that any two boxes' contents are distinct from each other, which is important because in set theory, two sets are equal if their contents are identical, and a set cannot contain multiple copies of any object.[/pedantry]

But at any rate, the idea of constructing the natural numbers by starting from a base number (in this case, zero) and applying a successor operation (i.e. adding one) was well established before von Neumann was born. And there's nothing requiring that the starting number be zero; depending on the context, it may be preferable to start with one instead, and exclude zero from the natural numbers.
posted by J.K. Seazer at 5:49 PM on July 8, 2018 [12 favorites]


"a binary"

That can't be right.
posted by humboldt32 at 6:28 PM on July 8, 2018


*heads back to the Charles Seife book."
posted by aspersioncast at 6:46 PM on July 8, 2018




1 + 2 + 3 + ··· = -1/12

I'm confused. That series does not converge so you can't make any meaningful statement about it. What an I missing?
posted by rdr at 9:08 PM on July 8, 2018


I'm confused. That series does not converge so you can't make any meaningful statement about it. What an I missing?

Numberphile explains, using a method that's a little... suspect, but easier to follow than using Zeta function regularization. Ramanujan summation comes to the same conclusion.
posted by axiom at 9:45 PM on July 8, 2018


1 + 2 + 3 + ··· = -1/12

I'm confused. That series does not converge so you can't make any meaningful statement about it.


You can't take an ordinary meaningful sum of a divergent series, but that is far from saying that you can't take any meaningful sum. There are many different ways of assigning precise definitions to certain divergent series, and some of them, like zeta function regularization, have found applications in theoretical physics.

In this sense, divergent series are similar to negative numbers. Summation methods for divergent series were invented out of a desire to meaningfully and precisely manipulate and assign values to infinite series even when they don't necessarily converge. Similarly, at first, people did not know how to make sense of subtracting a larger quantity from a smaller one. However, once you start writing quantities and algebraic manipulations symbolically, you eventually realize that, no matter what x and y are, x - y behaves just like any other number. So even if x is less than y, the number that x - y represents must have some meaning, even if it doesn't correspond with our ordinary intuition of numbers representing a physical amount of something. Of course, if x can be less than y, then x can also be equal to y, and thus we get zero.
posted by J.K. Seazer at 10:25 PM on July 8, 2018 [2 favorites]


Things like that sum are what make me highly suspicious of mathematicians.
posted by runcibleshaw at 10:30 PM on July 8, 2018 [9 favorites]


previously
posted by infini at 3:40 AM on July 9, 2018 [1 favorite]


My favourite formulation of the concept of zero remains the one by Douglas Hofstadter:
  • Genie is a djinn.
  • Every djinn has a meta (which is also a djinn).
  • Genie is not the meta of any djinn.
  • Different djinns have different metas.
  • If Genie has X, and each djinn relays X to its meta, the all djinns get X.
Of course by now you recognise "Genie" as a tongue-in-cheek symbol for "zero." But let us temporarily suspend this belief, and notice this. For these axioms to be really about natural numbers, they must be able to support arithmetic operations that follow something called "intuition". By "intuition" I mean a core collection of properties that are so desirable that they must be preserved when we clarify what we mean by "plus", "times", "equals-to", etc. For example:
"There exists a [special djinn for addition], such that for any djinn x, x plus the [special djinn for addition] is x herself."
(This is just one of the intuitive pearls that we have to clutch. There are more regarding multiplication and equality, etc.)

It turns out that the only way to have both, i.e. the bullet-points and the "intuition" of arithmetic, is to have
Genie as the [special djinn for addition], among others. The only interpretation of the djinns that is also "arithmetically-intuitive" is not merely about the natural numbers, they essentially must be the natural numbers, with Genie as Zero, the meta of Genie as One, etc.
posted by runcifex at 6:45 AM on July 9, 2018 [2 favorites]


“When you ask [a child] which number is smaller, zero or one, they often think of one as the smallest number,” Brannon says. “It’s hard to learn that zero is smaller than one.”

As a person who has taught several kids to count (but not a professional educator) and then add, I think this statement is very problematic as proof of anything greater than the way we teach children to count. First of all, most counting for children starts at 1, not a zero unless you specifically push 0 as a starting point, more out of habit than anything else. And it's not really 'counting' at first either, it's just listing of numbers for games like hide and seek or for counting food and whatnot.

I'm not disputing that 0 is a hard concept to teach children because it kind of is. It can really only be done via subtraction. For instance you can't start at 0 swing pushes or at 0 when counting for hide and seek because the 0 represents the same thing as 1 swing pushes, which is conceptually incorrect. If I were a professional educator, I'd go even further actually, and not represent 0 as the smallest number, and go into negatives. That numbers can go backwards really blows kids' minds.
posted by The_Vegetables at 6:50 AM on July 9, 2018


Numberphile explains, using a method that's a little... suspect

More than a little. Essentially the same reasoning can be used to demonstrate that 2 = 4.
posted by flabdablet at 8:57 AM on July 9, 2018


I'm not disputing that 0 is a hard concept to teach children because it kind of is.

I taught it to our little one in the course of explaining how to play Snakes and Ladders.

She'd regularly count 1, 2, 3, 4 ... as she moved her game piece, but she'd always say "1" while tapping the piece on the square she was already on.

So I got her to think about how far she was moving, and she quickly got the idea that after a dice roll she always had to move somewhere, and that the smallest number of squares she could possibly move was 1, so the very next square on the board from where she was already was the square she had to touch her game piece on when she said "1".

Then we played a variant where I prepared a die by whiting out the spots on the 6 face, so that if the blank face came up you just missed a turn without moving at all.

Then I got her to think about how far she was moving when she missed a turn, and she readily agreed that she wasn't moving at all. So then we had a conversation about the way the distance we moved after a roll was the same as the number of spots shown on die; and then we had a conversation about how to write down the number of spots as a digit.

For ⚀ write 1; for ⚁ write 2; for ⚂ write 3; for ⚃ write 4; for ⚄ write 5 - and at that point it just seemed completely natural to have another digit - 0 - that we could write when the top face had no spots at all.
posted by flabdablet at 9:24 AM on July 9, 2018 [9 favorites]


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