I say that knowing particular kinds of math, the kind that let you model the world more-precisely, and that give you a theory of error, isn’t like knowing another language. It’s like knowing language at all. Learning these types of math gives you as much of an effective intelligence boost over people who don’t, as learning a spoken language gives you above people who don’t know any language (e.g., many deaf-mutes in earlier times).
The kinds of math I mean include:
how to count things in an unbiased manner; the methodology of polls and other data-gathering
how to actually make a claim, as opposed to what most people do, which is to make a claim that’s useless because it lacks quantification or quantifiers
A good example of this is the claims in the IPCC 2015 report that I wrote some comments on recently. Most of them say things like, “Global warming will make X worse”, where you already know that OF COURSE global warming will make X worse, but you only care how much worse.
More generally, any claim of the type “All X are Y” or “No X are Y”, e.g., “Capitalists exploit the working class”, shouldn’t be considered claims at all, and can accomplish nothing except foment arguments.
the use of probabilities and error measures
probability distributions: flat, normal, binomial, poisson, and power-law
entropy measures and other information theory
predictive error-minimization models like regression
statistical tests and how to interpret them
These things are what I call the correct Platonic forms. The Platonic forms were meant to be perfect models for things found on earth. These kinds of math actually are. The concept of “perfect” actually makes sense for them, as opposed to for Earthly categories like “human”, “justice”, etc., for which believing that the concept of “perfect” is coherent demonstrably drives people insane and causes them to come up with things like Christianity.
They are, however, like Aristotle’s Forms, in that the universals have no existence on their own, but are (like the circle , but even more like the normal distribution ) perfect models which arise from the accumulation of endless imperfect instantiations of them.
There are plenty of important questions that are beyond the capability of the unaided human mind to ever answer, yet which are simple to give correct statistical answers to once you know how to gather data and do a multiple regression. Also, the use of these mathematical techniques will force you to phrase the answer sensibly, e.g., “We cannot reject the hypothesis that the average homicide rate under strict gun control and liberal gun control are the same with more than 60% confidence” rather than “Gun control is good.”
I say that knowing particular kinds of math, the kind that let you model the world more-precisely, and that give you a theory of error, isn’t like knowing another language. It’s like knowing language at all. Learning these types of math gives you as much of an effective intelligence boost over people who don’t, as learning a spoken language gives you above people who don’t know any language (e.g., many deaf-mutes in earlier times).
The kinds of math I mean include:
how to count things in an unbiased manner; the methodology of polls and other data-gathering
how to actually make a claim, as opposed to what most people do, which is to make a claim that’s useless because it lacks quantification or quantifiers
A good example of this is the claims in the IPCC 2015 report that I wrote some comments on recently. Most of them say things like, “Global warming will make X worse”, where you already know that OF COURSE global warming will make X worse, but you only care how much worse.
More generally, any claim of the type “All X are Y” or “No X are Y”, e.g., “Capitalists exploit the working class”, shouldn’t be considered claims at all, and can accomplish nothing except foment arguments.
the use of probabilities and error measures
probability distributions: flat, normal, binomial, poisson, and power-law
entropy measures and other information theory
predictive error-minimization models like regression
statistical tests and how to interpret them
These things are what I call the correct Platonic forms. The Platonic forms were meant to be perfect models for things found on earth. These kinds of math actually are. The concept of “perfect” actually makes sense for them, as opposed to for Earthly categories like “human”, “justice”, etc., for which believing that the concept of “perfect” is coherent demonstrably drives people insane and causes them to come up with things like Christianity.
They are, however, like Aristotle’s Forms, in that the universals have no existence on their own, but are (like the circle , but even more like the normal distribution ) perfect models which arise from the accumulation of endless imperfect instantiations of them.
There are plenty of important questions that are beyond the capability of the unaided human mind to ever answer, yet which are simple to give correct statistical answers to once you know how to gather data and do a multiple regression. Also, the use of these mathematical techniques will force you to phrase the answer sensibly, e.g., “We cannot reject the hypothesis that the average homicide rate under strict gun control and liberal gun control are the same with more than 60% confidence” rather than “Gun control is good.”
Thanks for writing this. I only wish it was longer.