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In "Eugenics: A Reassessment" Richard Lynn writes:
The intelligence level of the population would be expected to stabilize at its theoretical maximum of around 200 after six or seven generations.
The "intelligence level" here refers to IQ.
Lynn's work has been criticized in many ways. What I am interested in specifically whether there is a theoretical maximum for IQ and whether its value is 200. Have any other scientists commented on this point?
Considering IQs as a normal distribution the order of magnitude of the chance of a 100 point deviation is 10^-11. There is many more distinct coding DNA sequences than 10^11 (not sure about phenotypes) so it is not inconceivable that higher IQs would exist.
There are a few ways that you could answer this question.
First, IQ is defined with a mean of 100 and a standard deviation of 15. But this is a normative score and relative to a given target population typically defined by time, geography, and various inclusion criteria. In particular, IQ scores have increased over time (i.e., Flynn effect). So by this definition, the meaning of a 200 IQ has changed over time. That said, you could pick a date and place (e.g., 1900 United States or the year 2000 United States) to define as the normative sample and that would give you a normative metric to work with.
You then have the issue of conceptualizing the standard deviation of intelligence. In general, there is a reasonable basis for assuming that such psychological traits are roughly normally distributed. But presumably, quantifying this as the high end is more difficult.
More generally, conceptualizing and measuring intelligence at the very high end is challenging. Most normal measures of intelligence max out at about 3 standard deviations above the mean (i.e., around 145). They generally would not be very reliable at distinguishing a 145 from a 160 IQ person.
It is also not immediately clear whether just making intelligence tests harder is sufficient to validly measure intelligence at the very high end. But it is presumably the starting point. Nonetheless, these difficulties in measurement and definition make conceptualizing a theoretical maximum quite difficult.
Another approach to this question is to consider geniuses throughout history. E.g., Einstein, Leonhard Euler. You will sometimes see projected IQs for such figures. It seems likely that these people who achieved eminence in highly cognitively demanding fields had very high intelligence. But disentangling intelligence, domain specific abilities, devotion to their discipline, training, disposition, and good fortune is challenging. So in general, determining whether they had a 150 or 180 IQs or something else is difficult.
More generally, presumably the eugenics argument is that humans are modifiable through selective breeding (and related processes), genetic modification, and possibly technological and pharmaceutical augmentation. This presumably opens up a whole, and potentially scary, world of possibilities for cognitive enhancement.
Another perspective to this question comes from artificial intelligence research. Presumably, as such technologies evolve to replicate and exceed more of what we consider to be uniquely human functionality, we may be better able to judge what is the conceptual limit of intelligence of any entity (biological or otherwise).
IQ is a human constructed / defined concept in which a person answers various questions under a time limit and they are given a number derived from the way they answered the questions.
If we take some specific IQ test (to hold constant, for consistency), and observe that people get different numbers as they take the test, then I don’t think there can be recourse to a strong law of the universe as to why a “human” could not answer the questions faster or more accurately, except regarding:
the definition of a “human”
the range of numbers the IQ test allows (in its scoring rules)
For example, perhaps it could be argued that in order to add some numbers, there has to be some physical system carrying representations of those numbers and performing an actual physical process - a transformation or a “computation” - to produce the output, their sum. Maybe a neuroscientist would know the maximum speed at which the physical brain is able to carry out such an operation (however it does that). For example, maybe the speed of electricity in the brain, neural actions, or the speed of light, and also taking into account the size of the task (the number of computations needed to obtain the result).
As you suggested about DNA, the possibility that we are not strictly concerned with what kind of thing is doing the test, makes the physical limit described above seem possibly to be relevant to answering the question instead of dismissably ideal. If you wanted to ask specifically about biological forms close in similarity to currently existing ones, it’s still basically the same type of question, just bounding the set of possible “thinking” systems to certain physical types (i.e., brains, with various parameters and constraints on what they’re like).
So, in some way, while a good question, it may have the issue that it is tautologically self-answering, because it depends on how you interpret it, or what you mean. If an IQ test is some test, the theoretical maximum of performance of whatever will be taking the test will simply be by whatever you choose to allow to take the test, in your thought experiment.
The question of a “score” also trivially depends on the scoring conventions of the test itself; so, again, trying to lay down some assumptions to make the question something more concrete and definite and not as flexible, you probably mean something like mental / neural / cerebral capability, where IQ is just meant to be an attempt at observing that.
So the question is more about if there any known physical hard limits to the functioning of “the” brain - which is actually the respective brains of a number of different people. So I think - as you indicated - the real question might be the probability of any particular brain being born, right now, or at some time, given the brains and the DNA of the people living and reproducing at that time. A brain with some aspects like Ramanujan’s might be less common; someone else’s more. At that point, I think we should ask neuroscientists and evolutionary biologists how DNA interplays with the architecture of brains, and try to come up with an estimate for how likely a certain functional substructure with particular “performance” characteristics would be.