Here are some thoughts about numeracy as compared to literacy. There is a tl;dr at the end.
The US supposedly has 95% literacy rate or higher. An 14yo english-speaker in the US is almost always an english-reader as well, and will not need much help interpreting an “out of service” sign or a table of business hours or a “Vote for Me” billboard. In fact, most people will instantaneously understand the message, without conscious effort—no need to look at individual letters and punctuation, nor any need to slowly sound it out. You just look, scan, and interpret a sentence in one automatic action. (If anyone knows a good comparison of the bitrates of written sentences vs pictograms, please share.)
I think there is an analogy here with numeracy, and I think there is some depth to the analogy. I think there is a possible world in which a randomly selected 14yo would instantly, automatically have a sense of magnitude when seeing or hearing about about almost anything in the physical world—no need to look up benchmark quantities or slowly compute products and quotients. Most importantly, there would be many more false and misleading claims that would (instantly, involuntarily!) trigger a confused squint from them. You could still mislead them about the cost per wattage of the cool new sustainability technology, or the crime rate in some distant city. But not too much more than you could mislead them about tangible things like the weight of their pets or the cost per calorie of their lunch or the specs of their devices. You could only squeeze so many OoMs of credibility out of them before they squint in confusion and ask you to give some supporting details.
Automatic, generalized, quantitative sensitivity of this sort is rare even among college graduates. It’s a little better among STEM graduates, but still not good. I think adulthood is too late to gain this automaticity, the same way it is too late to gain the automatic, unconscious literacy that elementary school kids get. We grow up hearing stories about medieval castle life that are highly sanitized, idealized, and frankly, modernized, so that we will enjoy hearing them at all. And we like to imagine ourselves in the shoes of knights and royalty, usually not the shoes of serfs. That’s all well and good as far as light-hearted fiction goes, but I think it leads us to systematically underestimate not only the violence and squalor of those conditions, but less-obviously the low-mobility and general constraint of illiteracy. I wonder what it would be like to visit a place with very low literacy (and perhaps where the few existing signs are written in an unfamiliar alphabet). I bet it would be really disorienting. Everything you learn would be propaganda and motivated hearsay, and you would have to automatically assume much worse faith than in places where information and flows quickly and cheaply. Potato prices are much lower two days south? Well, who claimed that to me, how did they hear it, and what incentives might they have to say it to me? Unfortunately there are no advertisements or PSAs for me to check against. Well, I’m probably not going to make that trip south without some firmer authority.I can imagine this information environment having a lot in common with the schoolyard.
My point is that it seems easy to erroneously take for granted the dynamics of a 95% literate society, and that things suddenly seem very different even after only a minute of deliberate imagination. It is that size of difference that I think might be possible between our world and an imaginary place where 8-year-olds are trained to become fluent in simple quantities as they are in written english.
Tl;dr: I think widespread literacy and especially widespread fluency is a modern miracle. I think people don’t realize what a total lack of numerical fluency there is. I’m not generally fluent in numbers—in general, you can suggest absurd quantities to me and I will not automatically notice the absurdity in the way I will automatically laugh at a sentence construction error on a billboard.
Here are some thoughts about numeracy as compared to literacy. There is a tl;dr at the end.
The US supposedly has 95% literacy rate or higher. An 14yo english-speaker in the US is almost always an english-reader as well, and will not need much help interpreting an “out of service” sign or a table of business hours or a “Vote for Me” billboard. In fact, most people will instantaneously understand the message, without conscious effort—no need to look at individual letters and punctuation, nor any need to slowly sound it out. You just look, scan, and interpret a sentence in one automatic action. (If anyone knows a good comparison of the bitrates of written sentences vs pictograms, please share.)
I think there is an analogy here with numeracy, and I think there is some depth to the analogy. I think there is a possible world in which a randomly selected 14yo would instantly, automatically have a sense of magnitude when seeing or hearing about about almost anything in the physical world—no need to look up benchmark quantities or slowly compute products and quotients. Most importantly, there would be many more false and misleading claims that would (instantly, involuntarily!) trigger a confused squint from them. You could still mislead them about the cost per wattage of the cool new sustainability technology, or the crime rate in some distant city. But not too much more than you could mislead them about tangible things like the weight of their pets or the cost per calorie of their lunch or the specs of their devices. You could only squeeze so many OoMs of credibility out of them before they squint in confusion and ask you to give some supporting details.
Automatic, generalized, quantitative sensitivity of this sort is rare even among college graduates. It’s a little better among STEM graduates, but still not good. I think adulthood is too late to gain this automaticity, the same way it is too late to gain the automatic, unconscious literacy that elementary school kids get.
We grow up hearing stories about medieval castle life that are highly sanitized, idealized, and frankly, modernized, so that we will enjoy hearing them at all. And we like to imagine ourselves in the shoes of knights and royalty, usually not the shoes of serfs. That’s all well and good as far as light-hearted fiction goes, but I think it leads us to systematically underestimate not only the violence and squalor of those conditions, but less-obviously the low-mobility and general constraint of illiteracy. I wonder what it would be like to visit a place with very low literacy (and perhaps where the few existing signs are written in an unfamiliar alphabet). I bet it would be really disorienting. Everything you learn would be propaganda and motivated hearsay, and you would have to automatically assume much worse faith than in places where information and flows quickly and cheaply. Potato prices are much lower two days south? Well, who claimed that to me, how did they hear it, and what incentives might they have to say it to me? Unfortunately there are no advertisements or PSAs for me to check against. Well, I’m probably not going to make that trip south without some firmer authority.I can imagine this information environment having a lot in common with the schoolyard.
My point is that it seems easy to erroneously take for granted the dynamics of a 95% literate society, and that things suddenly seem very different even after only a minute of deliberate imagination. It is that size of difference that I think might be possible between our world and an imaginary place where 8-year-olds are trained to become fluent in simple quantities as they are in written english.
Tl;dr: I think widespread literacy and especially widespread fluency is a modern miracle. I think people don’t realize what a total lack of numerical fluency there is. I’m not generally fluent in numbers—in general, you can suggest absurd quantities to me and I will not automatically notice the absurdity in the way I will automatically laugh at a sentence construction error on a billboard.