In Comes IQ
When the concept of Intelligence Quotient arose it was based on this approximation.
Each human being has a number that quantifies their intelligence relative to a fixed norm, and, although this number may vary from testing to testing and over the course of years, it varies only within a small statistical deviation and is essentially determined at meiosis, when the DNA is assembled for that human.
Experiments and studies supported the validity of IQ as a measure of intelligence. Others refuted the concept. It was ethically questioned on the ground that it fostered intellectual elitism. There were legislative discussions regarding discrimination on the basis of IQ.
Andrew Niccol's brilliant 1997 motion picture, Gattica, starring Ethan Hawke, Uma Thurman, and Jude Law, dramatically examined the question of genetic determinism.
Research overturned the elitist belief that IQ is purely a mater of pedigree. The current evidence-based perspective is that from six months old to adolescence, nurture dominates over genetics.
Nonetheless, during the 20th Century, IQ rose to become a common household term. People knew, for example, that Albert Einstein was supposed to have had an IQ greater than 200. How that was calculated, since he never took an IQ test, few have stopped to scrutinize.
Unlike the single number used to gauge intelligence, college boards gauge achievement using a vector of numbers.
- Command of evidence
- Ability to express ideas
- Following of language conventions
- Problem solving
- Essay writing
It is interesting that a set of numbers are used to gauge academic achievement yet all the complex genetic and educational factors that impact a person's intelligence are rolled up into a one-dimensional number.
- Within the complex genetics, circuitry, and chemistry of the human brain is there some single factor that determines the intelligence of an individual?
- Does one factor eclipse and render irrelevant all other factors that are known to affect how smart a person is?
- Does each person have a glass ceiling on personal growth and education that is locked in by their mid-teens?
- Is this what people really believe?
Today, Peter Norvig's word frequency table places
IQ among words like
defect at the 96.9 percentile position in terms of frequency of use. This linguistic fact is strong evidence that our culture responds to these questions with, "We buy IQ."
In Comes The Singularity
Now the concept of The Singularity can be reduced to this.
Humans will work on artificial intelligence diligently, causing the peak level of intelligence of an artificial variety to increase. Once the intelligence of an artificial variety exceeds the intelligence of humanity, the artificial intelligence will gain control over humans to guarantee the perpetuation of its own existence and continued self-development.
The Singularity concept relies on a very specific pair of propositions. (Using pseudonyms)
The intelligences of Abby and Beth are fully represented as scalars (1-D) not vectors (multidimensional) and therefore can be directly compared.
If the intelligence of Abby is greater than the intelligence of Beth, Abby will gain control over Beth and exploit her.
In Comes Proof of the Limits of Proof
The dominant enlightenment philosophies of humanism and determinism, that the intellectual pursuits of men will grow to dominate all things, were challenged in the early 20th Century by the work of two people.
- Heisenberg proved, and there has been no credible refutation, that one cannot accurately measure two determining extensible quantities of a particle at the same time and therefore any mathematical treatment of Bohr's model of the atom must be based on probabilities, not the certainty of mechanical phenomena.
- Gödel proved two things (a) That a formal mathematical system cannot be relied upon to indicate the truth or falsehood of every statement that can be made formally, and, more importantly, (b) no formal system can, though its own formalisms, establish its own consistency via proof.1
This uncertainty appears in linguistic expressions like, "Ricky doesn't test well," when Ricky's test score is below expectation (again using a pseudonym). There is scientific validity to these sayings because neural activity cannot be measured in natura (in natural life). We must bring the subject into the lab to measure their neural activity, which disturbs the neural activity of the subject under study, just as the electron in Heisenburg's thought experiment.
Applying Gödel's thinking, human intelligence cannot construct a formal system to determine inconclusively that human intelligence is can be expressed as a scalar, can be expressed as a vector, or even exists at all.
We cannot, via intelligence, formally prove that intelligence is self-consistent.
In Comes Genetics
Research has recently revealed that, of 12,000,000 human single-nucleotide polymorphisms (SNPs) examined, 336 have been found that significantly correlate with human intelligence, and those 336 SNPs implicate 22 independent genes.2, 3 It is also likely that additional intelligence related genes will be discovered as research continues.
Even if there are no further independent genetic determinants of human intelligence found, twenty-two genetically distinct, independent degrees of freedom define the variable features of human intelligence. An important conclusion then falls directly from this research.
A scalar, such as IQ, cannot possibly describe the permutations of genes that human intelligence.
At least a 22-dimension vector is required to represent the multifaceted features of an individual's intelligence.
Putting the Proof Together
Although the MAGNITUDE of a vector can be greater than the MAGNITUDE of another vector (without first taking the absolute value of the vector) it is mathematical nonsense to say vector X (of 22 dimensions) is greater than vector Y (of 22 dimensions).
We also lack any evidence-based reason to apply an absolute value to the vector. A pure root mean squared calculation (RMS) would mean that human intelligence is a Cartesian hyper-cube of 22 equally weighted traits. There is no evidence to validate the idea that the mathematical inventions of Descartes should be applied to genetic traits.4
All these traits are situational anyway, arising out of specific environmental challenges during evolution. For instance, trait number 9 may produce an intelligent response in one scenario and trait numbers 11 and 17 together may produce an intelligent response in another scenario.
So without creating some basis for mapping the traits to the scenarios where they are important in survival, problem solving, or human advancement, it is NOT MATHEMATICALLY SENSIBLE to say that Abby is or is not smarter than Beth (using the previous pseudonyms).
Neither can we say that a machine named Polycharp is smarter than Abby. Consequentially, what is described above as The Singularity cannot possibly be singular.
We have only three logical possibilities. Only one can be true, but which one?
- The genetic research is flawed.
- The concept of The Singularity is flawed.
- The logical inference laid out in this question is flawed.
The Unpredictability of Cybernetics
The proposal that has been suggested in the literature is that the detailed workings of human intelligence may not fit into the network size of the human cerebral cortex. That is a reasonable line of scrutiny. Just as particle physics and the complexities of the biosphere may always require computer analysis and be visible only through the lens of statistics, so may be the case with human cognition.
Adding the work of Heisenberg and Gödel and it only gets worse. Even a computer model of the twenty-two or more dimensions of human intelligence may be as elusive as physical quanta, further confining the evaluation of intelligence to statistical treatment.
These factors place the interplay between human beings and machines (cybernetics) firmly within the realm of the unpredictable.
Super-intelligence May Face the Same
It may be that some higher intelligence that exists in the universe or some superior artificial intelligence we invent can both fathom human intelligence and predict the course of cybernetics. However, that greater intelligence may eventually be confronted with the same issue. Such beings may not have the intellectual capacity to fully fathom their own intelligence or predict their own cybernetic destiny.
Returning Back to the Main Question
Regardless of the predictability of cybernetics, it is reasonable to ask,
"Is the singularity concept mathematically flawed?"
 Assuming the twenty-two or more traits involved in human intelligence should be aggregated via an RMS function would be as subjective (and ridiculous) as applying RMS thusly: F2 = b2 + b2, where F is fun, b is blonde, and B is blue-eyed, because fashion magazines sold contact lenses and hair color products to a primarily brown-haired, brown-eyed population by depicting blue-eyed blonds having fun.