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Intelligence (at least as measured by an IQ test) isn't distributed as a bell curve. Bell curves always include negative values, and intelligence can't be nega

by panic 11y ago

Intelligence (at least as measured by an IQ test) isn't distributed as a bell curve. Bell curves always include negative values, and intelligence can't be negative.

thaumasiotes 11y ago
> intelligence can't be negative Asserted without proof. To show this, you'd need to interpret intelligence as something that physically couldn't be negative. I feel safe in saying you haven't done that. In particular, "intelligence (as measured by an IQ test)" can easily be negative, in the sense of yielding a negative IQ score. It would have to be an unrealistically long test, and you'd need way more people than exist in the world, but those problems apply to the tails of actual normal curves too.
- rawnlq 11y ago
  I am really impressed by wolfram alpha's ability to parse my butchered syntax: https://www.wolframalpha.com/input/?i=probability+that+gaussian%28100%2C+15%29+%3C+0 https://www.wolframalpha.com/input/?i=probability+that+gauss... Probability of finding someone with an IQ (as defined as normal distribution with mean 100 and std 15) less than 0 is 1.30839×10^-11
Hobotron1 11y ago
So define 'average' as 0?
hackinthebochs 11y ago
The bell curve distribution is a model. That our metric doesn't include negative values does not contradict its effectiveness. Also someone downstream calculated the probability of seeing a negative value for a normal distribution with 100 mean and 15 sd, the probability is about 1 in 100 billion. And so we don't expect the bell curve model to break down until we reach a population size on the order of 100 billion.
- myg204 11y ago
  Right. Also, in theory, intelligence (or height) can be infinite it if is said it follows a bell curve, but that's sort of impossible too.
static_noise 11y ago
Technically you are correct - the best kind of correct. "The distribution of the measured IQ very closely follows a bell curve." would have been the correct way to formulate.
- madez 11y ago
  To be technically correct is the only way for a statement to be correct. If it's "non-technically correct" it is ill-frased. This debates started by people stating wrong things but still wanting others to understand them.
  - mreiland 11y ago
    While mathematics has for the most part been built up using 2-valued logic, that isn't how humans perceive the world, which is why someone will say something like "you are technically correct", or they'll say "technically that's, but...".
    - madez 11y ago
      It is true that binary logic is not the ultimate logic. However, "technically correct" vs "correct" is not a debate of whether one value of true is enough. The word "technically" is used with "correct" as a rhetoric tool. It seems like they are attacking the truthness of the statement, but in fact they are trying to put the statement into a bigger context. So many people misuse it as such that some even understand it as an attack of the truthness of the statement.
      - mreiland 11y ago
        > So many people misuse it as such that some even understand it as an attack of the truthness of the statement. No, they use it as a device to point out that there is more context around the discussion than whether or not something is true or false (hence my point about 2-valued logic). I could say race is defined by genetics, and while that's technically correct, it adds nothing to a discussion about race relations. This is the context in which people use this term. When people say things like "you're technically correct, the best kind of correct", it's a tongue in cheek way of pointing out the observation is true, but lacks contextual information in order to be useful. This is why it tends to be a joke, in general everyone implicitly understands this.
leni536 11y ago
IQ is defined to be distributed as a bell curve. IQ below 0 is just extremely improbable.
cwhy 11y ago
It depends, Beta(3,3) is also bell-shaped.

by panic 11y ago

Intelligence (at least as measured by an IQ test) isn't distributed as a bell curve. Bell curves always include negative values, and intelligence can't be negative.

thaumasiotes 11y ago

> intelligence can't be negative Asserted without proof. To show this, you'd need to interpret intelligence as something that physically couldn't be negative. I feel safe in saying you haven't done that. In particular, "intelligence (as measured by an IQ test)" can easily be negative, in the sense of yielding a negative IQ score. It would have to be an unrealistically long test, and you'd need way more people than exist in the world, but those problems apply to the tails of actual normal curves too.

rawnlq 11y ago
I am really impressed by wolfram alpha's ability to parse my butchered syntax: https://www.wolframalpha.com/input/?i=probability+that+gaussian%28100%2C+15%29+%3C+0 https://www.wolframalpha.com/input/?i=probability+that+gauss... Probability of finding someone with an IQ (as defined as normal distribution with mean 100 and std 15) less than 0 is 1.30839×10^-11

Hobotron1 11y ago

So define 'average' as 0?

hackinthebochs 11y ago

The bell curve distribution is a model. That our metric doesn't include negative values does not contradict its effectiveness. Also someone downstream calculated the probability of seeing a negative value for a normal distribution with 100 mean and 15 sd, the probability is about 1 in 100 billion. And so we don't expect the bell curve model to break down until we reach a population size on the order of 100 billion.

myg204 11y ago
Right. Also, in theory, intelligence (or height) can be infinite it if is said it follows a bell curve, but that's sort of impossible too.

static_noise 11y ago

Technically you are correct - the best kind of correct. "The distribution of the measured IQ very closely follows a bell curve." would have been the correct way to formulate.

madez 11y ago
To be technically correct is the only way for a statement to be correct. If it's "non-technically correct" it is ill-frased. This debates started by people stating wrong things but still wanting others to understand them.
- mreiland 11y ago
  While mathematics has for the most part been built up using 2-valued logic, that isn't how humans perceive the world, which is why someone will say something like "you are technically correct", or they'll say "technically that's, but...".
  - madez 11y ago
    It is true that binary logic is not the ultimate logic. However, "technically correct" vs "correct" is not a debate of whether one value of true is enough. The word "technically" is used with "correct" as a rhetoric tool. It seems like they are attacking the truthness of the statement, but in fact they are trying to put the statement into a bigger context. So many people misuse it as such that some even understand it as an attack of the truthness of the statement.
    - mreiland 11y ago
      > So many people misuse it as such that some even understand it as an attack of the truthness of the statement. No, they use it as a device to point out that there is more context around the discussion than whether or not something is true or false (hence my point about 2-valued logic). I could say race is defined by genetics, and while that's technically correct, it adds nothing to a discussion about race relations. This is the context in which people use this term. When people say things like "you're technically correct, the best kind of correct", it's a tongue in cheek way of pointing out the observation is true, but lacks contextual information in order to be useful. This is why it tends to be a joke, in general everyone implicitly understands this.

leni536 11y ago

IQ is defined to be distributed as a bell curve. IQ below 0 is just extremely improbable.

cwhy 11y ago

It depends, Beta(3,3) is also bell-shaped.