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Language is an imperfect model for representing ideas. Million is close to billion, linguistically. Certainly not off by a power of 1000 in the space of languag

Language is an imperfect model for representing ideas. Million is close to billion, linguistically. Certainly not off by a power of 1000 in the space of language. I’m surprised the author is just coming to this realization.

dec0dedab0de 4y ago
That would be interesting, if we had to use longer words. Like officially change billion to gagillion. Only two extra letters, but it feels bigger Edit: I originally had one extra letter, thanks jrd79
- snewman 4y ago
  I'm not sure this would help. The error was likely in thinkspace, not a literal typo. The real problem is when people toss around numbers without deeply understanding them. I don't think there's any simple fix for that. You simply can't reliably funnel information through a channel as narrow as a single number, nor the equivalent short phrase of number words.
- jrd79 4y ago
  Two extra letters. Numbers matter :).
- kbutler 4y ago
  One extra? Maybe bbillion pronounced b-billion would be better. And to add confusion, note that UK English had 1e6 million 1e9 thousand million 1e12 billion (million million) I think this has mostly consolidated to the US usage now
neither_color 4y ago
In Spanish you literally say "thousand million" to mean billion so it's very unambiguous.
- eequah9L 4y ago
  In languages that use short scale, you say "milliard" to mean "billion". You say "billion" to mean "trillion". It's very confusing and a frequent source of errors in translation. Every time I see the Czech word for "billion", I have to think about whether they mean 10^9 or 10^12.
praestigiare 4y ago
They are not, nor is million/billion the main point of the article.
LeifCarrotson 4y ago
If you can't trust language users to be accurate enough to represent a power of 1000, you can't really represent concepts which differ by a thousand, or by a thousandth! There are times when people are communicating approximations and feelings, where imperfection is fine, and times when they're communicating precise, technical, numeric concepts where an imperfect model is insufficient.
- deleted 4y ago
  [deleted]
Cthulhu_ 4y ago
It's imperfect if used inaccurately. The fact that the words million and billion is only one letter apart isn't really relevant IMO. I mean a single letter turns an innocuous word into a rude insult, which suddenly wouldn't be a simple mistake anymore.
- simulate-me 4y ago
  It's not only about the letters. "Million" and "billion" are both numeric concepts. Numeric concepts are only a small subset of things expressible by language. So million and billion are close because they are spelled similarly and they deal with the same conceptual "thing." Duck and Fuck don't occupy the same conceptual category, so the distance between the two words is large despite being spelled similarly. One interesting application of neural networks is the creation word embeddings. ML models are trained to place words in a vector space, which is useful for measuring distance between words, performing arithmetic on words, or finding the closet word. Using an embedding allows your to formalize the "distance" between words, and perform fun tricks like King + Woman = Queen.
  - moate 4y ago
    >> So million and billion are close because they are spelled similarly and they deal with the same conceptual "thing. Citation needed. Is this based on any sort of formal linguistic/anthropological reasoning or just like, your opinion? Also, the article's whole point is "people are bad at numbers" and your argument that "linguistically, all numbers close" isn't really true. Why don't rhyming words in English feel "close"? Also, "duck" and "fuck" are both verbs involving a thing you would do with your body, so why isn't that closeness? If you're going to point out that language feels arbitrary by making arbitrary points, you're going to be "right" but you're not actually saying much. Language can be both specific and arbitrary (it's a means of expressing both objective and subjective concepts) so an argument in favor of doing your best when seeking to be objective seems pretty reasonable.
    - simulate-me 4y ago
      I'm not making an arbitrary point. The end of my comment mentions word embeddings, which are learned from analyzing language and its usage in an unsupervised manner. You can use a word embedding to measure similarity between words. For instance, I just downloaded a pre-trained model of Stanford's GloVe embedding that was trained on 840 billion (yes, billion with a b) tokens. The cosine similarity can be used to measure how close two words are in the embedding. The cosine similarity of million and billion is 0.89. The similarity of duck and fuck is 0.27. The data indicates million and billion are much more similar than duck and fuck. This result is intuitively obvious to me, which this article illustrates. Even if the resulting sentence is not factually true, a true-sounding sentence can be constructed by taking a sentence with the word million and replacing it with the word billion (in a majority of cases). This isn't true with duck and fuck, and duck is a noun and a verb used in generally different contexts than the word fuck.
jeliotj 4y ago
Is there another way than language to represent ideas?
karaterobot 4y ago
> Language is an imperfect model for representing ideas. That may be so. But, the New York Times can't use that as a excuse for making simple mistakes, nor do I think it wants to. Language is primarily what it relies on to represent ideas. Accurate description of the world through language is the core of its value proposition to subscribers.
karmakaze 4y ago
> [...] exceeded half a million known virus cases. > “Half a million known virus cases”, huh? During the Omicron peak, the US alone exceeded that many cases every day. Clearly they meant half a billion. I wonder if the New York times knew exactly what they were writing. Both of course are technically correct. And billions/trillions/etc get into unfamiliar/meaningless territory for some with a million being the largest meaningful number so could have more emotional impact as a headline.

dec0dedab0de 4y ago

That would be interesting, if we had to use longer words. Like officially change billion to gagillion. Only two extra letters, but it feels bigger Edit: I originally had one extra letter, thanks jrd79

snewman 4y ago
I'm not sure this would help. The error was likely in thinkspace, not a literal typo. The real problem is when people toss around numbers without deeply understanding them. I don't think there's any simple fix for that. You simply can't reliably funnel information through a channel as narrow as a single number, nor the equivalent short phrase of number words.
jrd79 4y ago
Two extra letters. Numbers matter :).
kbutler 4y ago
One extra? Maybe bbillion pronounced b-billion would be better. And to add confusion, note that UK English had 1e6 million 1e9 thousand million 1e12 billion (million million) I think this has mostly consolidated to the US usage now

neither_color 4y ago

In Spanish you literally say "thousand million" to mean billion so it's very unambiguous.

eequah9L 4y ago
In languages that use short scale, you say "milliard" to mean "billion". You say "billion" to mean "trillion". It's very confusing and a frequent source of errors in translation. Every time I see the Czech word for "billion", I have to think about whether they mean 10^9 or 10^12.

praestigiare 4y ago

They are not, nor is million/billion the main point of the article.

LeifCarrotson 4y ago

If you can't trust language users to be accurate enough to represent a power of 1000, you can't really represent concepts which differ by a thousand, or by a thousandth! There are times when people are communicating approximations and feelings, where imperfection is fine, and times when they're communicating precise, technical, numeric concepts where an imperfect model is insufficient.

deleted 4y ago
[deleted]

Cthulhu_ 4y ago

It's imperfect if used inaccurately. The fact that the words million and billion is only one letter apart isn't really relevant IMO. I mean a single letter turns an innocuous word into a rude insult, which suddenly wouldn't be a simple mistake anymore.

simulate-me 4y ago
It's not only about the letters. "Million" and "billion" are both numeric concepts. Numeric concepts are only a small subset of things expressible by language. So million and billion are close because they are spelled similarly and they deal with the same conceptual "thing." Duck and Fuck don't occupy the same conceptual category, so the distance between the two words is large despite being spelled similarly. One interesting application of neural networks is the creation word embeddings. ML models are trained to place words in a vector space, which is useful for measuring distance between words, performing arithmetic on words, or finding the closet word. Using an embedding allows your to formalize the "distance" between words, and perform fun tricks like King + Woman = Queen.
- moate 4y ago
  >> So million and billion are close because they are spelled similarly and they deal with the same conceptual "thing. Citation needed. Is this based on any sort of formal linguistic/anthropological reasoning or just like, your opinion? Also, the article's whole point is "people are bad at numbers" and your argument that "linguistically, all numbers close" isn't really true. Why don't rhyming words in English feel "close"? Also, "duck" and "fuck" are both verbs involving a thing you would do with your body, so why isn't that closeness? If you're going to point out that language feels arbitrary by making arbitrary points, you're going to be "right" but you're not actually saying much. Language can be both specific and arbitrary (it's a means of expressing both objective and subjective concepts) so an argument in favor of doing your best when seeking to be objective seems pretty reasonable.
  - simulate-me 4y ago
    I'm not making an arbitrary point. The end of my comment mentions word embeddings, which are learned from analyzing language and its usage in an unsupervised manner. You can use a word embedding to measure similarity between words. For instance, I just downloaded a pre-trained model of Stanford's GloVe embedding that was trained on 840 billion (yes, billion with a b) tokens. The cosine similarity can be used to measure how close two words are in the embedding. The cosine similarity of million and billion is 0.89. The similarity of duck and fuck is 0.27. The data indicates million and billion are much more similar than duck and fuck. This result is intuitively obvious to me, which this article illustrates. Even if the resulting sentence is not factually true, a true-sounding sentence can be constructed by taking a sentence with the word million and replacing it with the word billion (in a majority of cases). This isn't true with duck and fuck, and duck is a noun and a verb used in generally different contexts than the word fuck.

jeliotj 4y ago

Is there another way than language to represent ideas?

karaterobot 4y ago

> Language is an imperfect model for representing ideas. That may be so. But, the New York Times can't use that as a excuse for making simple mistakes, nor do I think it wants to. Language is primarily what it relies on to represent ideas. Accurate description of the world through language is the core of its value proposition to subscribers.

karmakaze 4y ago

> [...] exceeded half a million known virus cases. > “Half a million known virus cases”, huh? During the Omicron peak, the US alone exceeded that many cases every day. Clearly they meant half a billion. I wonder if the New York times knew exactly what they were writing. Both of course are technically correct. And billions/trillions/etc get into unfamiliar/meaningless territory for some with a million being the largest meaningful number so could have more emotional impact as a headline.