6 ms·

I’m pleasantly surprised that nobody started the discussion on whether zero is odd or even ;-) https://en.wikipedia.org/wiki/Parity_of_zero https://en.wikipedia

I’m pleasantly surprised that nobody started the discussion on whether zero is odd or even ;-) https://en.wikipedia.org/wiki/Parity_of_zero https://en.wikipedia.org/wiki/Parity_of_zero

eru 3y ago
I find it hard to understand how someone can be confused about that. But I dimly remember talking to people with this confusion in the past.
- contravariant 3y ago
  It's apparently confusing enough that if you ban odd license number plates then the cops don't want to arrest anyone whose license plate ends in 0 because they're not sure if it is even or not. At least that was the case in Paris in 1977, when they alternated between odd/even license plates every day to limit the number of cars.
  - eru 3y ago
    Interesting. Do you have a source for that?
    - Snarwin 3y ago
      It looks like bans for odd/even license plates were used in Paris in 2014 [1] and 1997 [2], but not before then. However, a similar scheme was used to ration gasoline in the US during the 70s [3]. The only source I can find for the claim about police confusion is the one cited by Wikipedia [4], whose reliability I'm inclined to doubt based on the 1997/1977 discrepancy. [1] https://www.npr.org/sections/thetwo-way/2014/03/17/290849704/to-clear-its-air-paris-tests-odd-or-even-driving-days https://www.npr.org/sections/thetwo-way/2014/03/17/290849704... [2] https://www.wired.com/1997/09/paris-smog/ https://www.wired.com/1997/09/paris-smog/ [3] https://www.npr.org/sections/pictureshow/2012/11/10/164792293/gas-lines-evoke-memories-oil-crises-in-the-1970s https://www.npr.org/sections/pictureshow/2012/11/10/16479229... [4] https://en.m.wikipedia.org/wiki/Odd%E2%80%93even_rationing#Dealing_with_0 https://en.m.wikipedia.org/wiki/Odd%E2%80%93even_rationing#D...
      - contravariant 3y ago
        The wikipedia article matched my vague recollection of the event, but if they got the year wrong then it may as well just be a rumour at this point.
      - eru 3y ago
        Thanks!
- travisjungroth 3y ago
  Please don’t take this as defending this thinking. I’m just guessing at how someone could get to this confusion. I can see how you’d get there by thinking of numbers as a thing for counting. Even numbers give you piles of two without one left over. Zero fails the first condition since it gives you no piles at all. But it doesn’t leave a pile of one, so it’s not really odd, either. If you ever find yourself confused in this way about definitions consider: is this definition serving me? Could I adopt a different definition that’s used by people really good at this sort of thing? (Zero is even because any integer n that can be formed by 2k for integer k is even, and that can be formed by 2k+1 is odd. 2x0=0)
  - eru 3y ago
    Yes, it all boils down to definitions. Definitions that have 0 as an even number work well in math. For most people's daily life, it doesn't really matter which category zero would fall under (as they never really eg consider dividing zero items evenly between people.) So their (implied) definitions can be all over the place.
    - deleted 3y ago
      [deleted]
  - Joker_vD 3y ago
    I am fairly certain I can split an empty pile into two empty piles, without a remainder.
    - sbarre 3y ago
      Hmmm by definition an empty pile is not a pile though, is it? So there's nothing to split? ;-)
      - Joker_vD 3y ago
        And an empty plate is not a plate, also by definition? Okay, sure.
- layer8 3y ago
  One might even say it's odd.
- latexr 3y ago
  The thing that gave me pause the first time I thought about it (it was during a test so I couldn’t ask or check) was that if zero is even, that means (despite numbers being infinite) there’s one more even number than odd numbers. I also knew that 1 is not prime, even if logically it should be. Its definition specifically states a prime number needs to be greater than 1. So that means mathematics sometimes has exceptions for numbers inside a definition. Given that, it’s not immediately obvious that zero would be even. It wouldn’t be odd either, that was out of the questions, but it could be neither.
  - eru 3y ago
    > The thing that gave me pause the first time I thought about it (it was during a test so I couldn’t ask or check) was that if zero is even, that means (despite numbers being infinite) there’s one more even number than odd numbers. Thanks to Hilbert's Hotel you can re-arrange the numbers to have an arbitrarily larger or smaller overhang of even or odd numbers. https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gra... > I also knew that 1 is not prime, even if logically it should be. Its definition specifically states a prime number needs to be greater than 1. So that means mathematics sometimes has exceptions for numbers inside a definition. The definition I use is that a prime number needs to have exactly two distinct divisors. No need for any special cases in this definition. (The motivation for this somewhat strange definition is so that factoring any positive number, including 1, into a multiset of her prime factors is unique. If you redefine the prime numbers to include 1, prime factoring is not unique. Of course, you could still make everything work out in the end: you just need to declare that your new-prime factoring is unique up to the multiplicity of 1s. Just like eg standard decimal numbers don't change if you add leading 0s, new-prime factoring would not change if you add factors of 1. You can do math with almost any arbitrary definitions, if you add enough exceptions and explanations in your theorems to work around the rough edges in your definitions.)
    - latexr 3y ago
      > Thanks to Hilbert's Hotel That makes no difference to the numbers that exist, it only changes which ones you count for the duration of that thought experiment. > The definition I use is that a prime number needs to have exactly two distinct divisors. No need for any special cases in this definition. You’re still making up a special case with the explicit goal of excluding a particular number. It’s a roundabout definition that requires more thought and will be lost on most people which don’t already know the regular one.
raverbashing 3y ago
This is the kind of discussion that matters only for the very theoretical edge cases or for the pop-math inconsequential discussions 0 is even I mean, it is the first phrase on the linked fine article: > In mathematics, zero is an even number.
Viliam1234 3y ago
Is that article about the IEEE 754 positive zero, or negative zero, or both?
- Mountain_Skies 3y ago
  When I was a junior developer fresh out of college, another junior and I noticed a bank sign with the temperature showing to be -0 degrees. We made a few comments about Two's Complement and felt a bit smug in our superiority over the manufacturer of the sign. Decades later I read an article about how -0 degrees is a standard in civil meteorology for "below freezing but rounded up to zero". Though it took a while to learn, it was a good lesson in making assumptions about standards in other domains.
  - deleted 3y ago
    [deleted]
vitiral 3y ago
I particularly liked this bit > Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the "most even" number of all. in the arena of even one-up-man-ship, zero wins.
codeflo 3y ago
I always found it funny that this is printed as a reminder text on Magic the Gathering cards that care about even or odd values: https://scryfall.com/card/iko/88/extinction-event?utm_source=mw_MTGWiki https://scryfall.com/card/iko/88/extinction-event?utm_source... But thinking about it, I have no doubt that Wizards found out this confusion is somewhat widespread during playtesting, and printing a short reminder was an easy fix.
Klaus23 3y ago
I asked a few LLMs whether zero is an even or odd number to see how they fared on such a widely misunderstood question: LLAMA 2 7B: 3x even, 2x neither LLAMA 2 13B: 1x even, 4x neither LLAMA 2 70B: 1x even, 4x neither GPT 3.5: 20x even despite trying to trick it Mistral 7B: 1x even, 3x neither, 1x even+neither?! Mixtral 8x7B: 8x even, 2x neither
- Klaus23 3y ago
  It seems that it is not a matter of size or processing power, but a fundamental problem of bad training data that bakes these misconceptions into the model. OpenAI is probably using a better filtered dataset and may even be able to remove some of the more common errors through alignment and fine-tuning. I experimented a bit more and it seems that Mixtral is better than Mistral when it comes to common misconceptions. There has probably been some improvement in the training data.

I’m pleasantly surprised that nobody started the discussion on whether zero is odd or even ;-) https://en.wikipedia.org/wiki/Parity_of_zero https://en.wikipedia.org/wiki/Parity_of_zero

eru 3y ago

I find it hard to understand how someone can be confused about that. But I dimly remember talking to people with this confusion in the past.

contravariant 3y ago
It's apparently confusing enough that if you ban odd license number plates then the cops don't want to arrest anyone whose license plate ends in 0 because they're not sure if it is even or not. At least that was the case in Paris in 1977, when they alternated between odd/even license plates every day to limit the number of cars.
- eru 3y ago
  Interesting. Do you have a source for that?
  - Snarwin 3y ago
    It looks like bans for odd/even license plates were used in Paris in 2014 [1] and 1997 [2], but not before then. However, a similar scheme was used to ration gasoline in the US during the 70s [3]. The only source I can find for the claim about police confusion is the one cited by Wikipedia [4], whose reliability I'm inclined to doubt based on the 1997/1977 discrepancy. [1] https://www.npr.org/sections/thetwo-way/2014/03/17/290849704/to-clear-its-air-paris-tests-odd-or-even-driving-days https://www.npr.org/sections/thetwo-way/2014/03/17/290849704... [2] https://www.wired.com/1997/09/paris-smog/ https://www.wired.com/1997/09/paris-smog/ [3] https://www.npr.org/sections/pictureshow/2012/11/10/164792293/gas-lines-evoke-memories-oil-crises-in-the-1970s https://www.npr.org/sections/pictureshow/2012/11/10/16479229... [4] https://en.m.wikipedia.org/wiki/Odd%E2%80%93even_rationing#Dealing_with_0 https://en.m.wikipedia.org/wiki/Odd%E2%80%93even_rationing#D...
    - contravariant 3y ago
      The wikipedia article matched my vague recollection of the event, but if they got the year wrong then it may as well just be a rumour at this point.
    - eru 3y ago
      Thanks!
travisjungroth 3y ago
Please don’t take this as defending this thinking. I’m just guessing at how someone could get to this confusion. I can see how you’d get there by thinking of numbers as a thing for counting. Even numbers give you piles of two without one left over. Zero fails the first condition since it gives you no piles at all. But it doesn’t leave a pile of one, so it’s not really odd, either. If you ever find yourself confused in this way about definitions consider: is this definition serving me? Could I adopt a different definition that’s used by people really good at this sort of thing? (Zero is even because any integer n that can be formed by 2k for integer k is even, and that can be formed by 2k+1 is odd. 2x0=0)
- eru 3y ago
  Yes, it all boils down to definitions. Definitions that have 0 as an even number work well in math. For most people's daily life, it doesn't really matter which category zero would fall under (as they never really eg consider dividing zero items evenly between people.) So their (implied) definitions can be all over the place.
  - deleted 3y ago
    [deleted]
- Joker_vD 3y ago
  I am fairly certain I can split an empty pile into two empty piles, without a remainder.
  - sbarre 3y ago
    Hmmm by definition an empty pile is not a pile though, is it? So there's nothing to split? ;-)
    - Joker_vD 3y ago
      And an empty plate is not a plate, also by definition? Okay, sure.
layer8 3y ago
One might even say it's odd.
latexr 3y ago
The thing that gave me pause the first time I thought about it (it was during a test so I couldn’t ask or check) was that if zero is even, that means (despite numbers being infinite) there’s one more even number than odd numbers. I also knew that 1 is not prime, even if logically it should be. Its definition specifically states a prime number needs to be greater than 1. So that means mathematics sometimes has exceptions for numbers inside a definition. Given that, it’s not immediately obvious that zero would be even. It wouldn’t be odd either, that was out of the questions, but it could be neither.
- eru 3y ago
  > The thing that gave me pause the first time I thought about it (it was during a test so I couldn’t ask or check) was that if zero is even, that means (despite numbers being infinite) there’s one more even number than odd numbers. Thanks to Hilbert's Hotel you can re-arrange the numbers to have an arbitrarily larger or smaller overhang of even or odd numbers. https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gra... > I also knew that 1 is not prime, even if logically it should be. Its definition specifically states a prime number needs to be greater than 1. So that means mathematics sometimes has exceptions for numbers inside a definition. The definition I use is that a prime number needs to have exactly two distinct divisors. No need for any special cases in this definition. (The motivation for this somewhat strange definition is so that factoring any positive number, including 1, into a multiset of her prime factors is unique. If you redefine the prime numbers to include 1, prime factoring is not unique. Of course, you could still make everything work out in the end: you just need to declare that your new-prime factoring is unique up to the multiplicity of 1s. Just like eg standard decimal numbers don't change if you add leading 0s, new-prime factoring would not change if you add factors of 1. You can do math with almost any arbitrary definitions, if you add enough exceptions and explanations in your theorems to work around the rough edges in your definitions.)
  - latexr 3y ago
    > Thanks to Hilbert's Hotel That makes no difference to the numbers that exist, it only changes which ones you count for the duration of that thought experiment. > The definition I use is that a prime number needs to have exactly two distinct divisors. No need for any special cases in this definition. You’re still making up a special case with the explicit goal of excluding a particular number. It’s a roundabout definition that requires more thought and will be lost on most people which don’t already know the regular one.

raverbashing 3y ago

This is the kind of discussion that matters only for the very theoretical edge cases or for the pop-math inconsequential discussions 0 is even I mean, it is the first phrase on the linked fine article: > In mathematics, zero is an even number.

Viliam1234 3y ago

Is that article about the IEEE 754 positive zero, or negative zero, or both?

Mountain_Skies 3y ago
When I was a junior developer fresh out of college, another junior and I noticed a bank sign with the temperature showing to be -0 degrees. We made a few comments about Two's Complement and felt a bit smug in our superiority over the manufacturer of the sign. Decades later I read an article about how -0 degrees is a standard in civil meteorology for "below freezing but rounded up to zero". Though it took a while to learn, it was a good lesson in making assumptions about standards in other domains.
- deleted 3y ago
  [deleted]

vitiral 3y ago

I particularly liked this bit > Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the "most even" number of all. in the arena of even one-up-man-ship, zero wins.

codeflo 3y ago

I always found it funny that this is printed as a reminder text on Magic the Gathering cards that care about even or odd values: https://scryfall.com/card/iko/88/extinction-event?utm_source=mw_MTGWiki https://scryfall.com/card/iko/88/extinction-event?utm_source... But thinking about it, I have no doubt that Wizards found out this confusion is somewhat widespread during playtesting, and printing a short reminder was an easy fix.

Klaus23 3y ago

I asked a few LLMs whether zero is an even or odd number to see how they fared on such a widely misunderstood question: LLAMA 2 7B: 3x even, 2x neither LLAMA 2 13B: 1x even, 4x neither LLAMA 2 70B: 1x even, 4x neither GPT 3.5: 20x even despite trying to trick it Mistral 7B: 1x even, 3x neither, 1x even+neither?! Mixtral 8x7B: 8x even, 2x neither

Klaus23 3y ago
It seems that it is not a matter of size or processing power, but a fundamental problem of bad training data that bakes these misconceptions into the model. OpenAI is probably using a better filtered dataset and may even be able to remove some of the more common errors through alignment and fine-tuning. I experimented a bit more and it seems that Mixtral is better than Mistral when it comes to common misconceptions. There has probably been some improvement in the training data.