This article explores analogism and creativity, starting with a detailed investigation into IQ-test style analogy problems and how both the brain and some new artificial neural networks solve them. Next we analyze concept map formation in the cortex and the role of the hippocampal complex in establishing novel semantic connections: the neural basis of creative insights. From there we move into learning strategies, and finally conclude with speculations on how a grounded understanding of analogical creative reasoning could be applied towards advancing the art of rationality.
- Under the Hood
- Conceptual Abstractions and Cortical Maps
- The Hippocampal Association Engine
- Cultivate memetic heterogeneity and heterozygosity
- Construct and maintain clean conceptual taxonomies
The computer is like a bicycle for the mind.
- - Steve Jobs
The kingdom of heaven is like a mustard seed, the smallest of all seeds, but when it falls on prepared soil, it produces a large plant and becomes a shelter for the birds of the sky.
- - Jesus
Sigmoidal neural networks are like multi-layered logistic regression.
- - various
The threat of superintelligence is like a tribe of sparrows who find a large egg to hatch and raise. It grows up into a great owl which devours them all.
- - Nick Bostrom (see this video)
Analogical reasoning is one of the key foundational mechanisms underlying human intelligence, and perhaps a key missing ingredient in machine intelligence. For some - such as Douglas Hofstadter - analogy is the essence of cognition itself.
Steve Job's bicycle analogy is clever because it encapsulates the whole cybernetic idea of computers as extensions of the nervous system into a single memorable sentence using everyday terms.
A large chunk of Jesus's known sayings are parables about the 'Kingdom of Heaven': a complex enigmatic concept that he explains indirectly through various analogies, of which the mustard seed is perhaps the most memorable. It conveys the notions of exponential/sigmoidal growth of ideas and social movements (see also the Parable of the Leaven), while also hinting at greater future purpose.
In a number of fields, including the technical, analogical reasoning is key to creativity: most new insights come from establishing mappings between or with concepts from other fields or domains, or from generalizing existing insights/concepts (which is closely related). These abilities all depend on deep, wide, and well organized internal conceptual maps.
In a previous post, I presented a high level working hypothesis of the brain as a biological implementation of a universal learning machine, using various familiar computational concepts as analogies to explain brain subsystems. In my last post, I used the conceptions of unfriendly superintelligence and value alignment as analogies for market mechanism design and the healthcare problem (and vice versa).
A clever analogy is like a sophisticated conceptual compressor that helps maximize knowledge transmission. Coming up with good novel analogies is hard because it requires compressing a complex large body of knowledge into a succinct message that heavily exploits the recipient's existing knowledgebase. Due to the deep connections between compression, inference, intelligence and creativity, a deeper investigation of analogical reasoning is useful from a variety of angles.
It is the hard task of coming up with novel analogical connections that can lead to creative insights, but to understand that process we should start first with the mechanics of recognition.
Under the Hood
You can think of the development of IQ tests as a search for simple tests which have high predictive power for g-factor in humans, while being relatively insensitive to specific domain knowledge. That search process resulted in a number of problem categories, many of which are based on verbal and mathematical analogies.
The image to the right is an example of a simple geometric analogy problem. As an experiment, start a timer before having a go at it. For bonus points, attempt to introspect on your mental algorithm.
Solving this problem requires first reducing the images to simpler compact abstract representations. The first rows of images then become something like sentences describing relations or constraints (Z is to ? as A is to B and C is to D). The solution to the query sentence can then be found by finding the image which best satisfies the likely analogous relations.
Imagine watching a human subject (such as your previous self) solve this problem while hooked up to a future high resolution brain imaging device. Viewed in slow motion, you would see the subject move their eyes from location to location through a series of saccades, while various vectors or mental variable maps flowed through their brain modules. Each fixation lasts about 300ms, which gives enough time for one complete feedforward pass through the dorsal vision stream and perhaps one backwards sweep.
The output of the dorsal stream in inferior temporal cortex (TE on the bottom) results in abstract encodings which end up in working memory buffers in prefrontal cortex. From there some sort of learned 'mental program' implements the actual analogy evaluations, probably involving several more steps in PFC, cingulate cortex, and various other cortical modules (coordinated by the Basal Ganglia and PFC). Meanwhile the eye frontal fields and various related modules are computing the next saccade decision every 300ms or so.
If we assume that visual parsing requires one fixation on each object and 50ms saccades, this suggests that solving this problem would take a typical brain a minimum of about 4 seconds (and much longer on average). The minimum estimate assumes - probably unrealistically - that the subject can perform the analogy checks or mental rotations near instantly without any backtracking to help prime working memory. Of course faster times are also theoretically possible - but not dramatically faster.
These types of visual analogy problems test a wide set of cognitive operations, which by itself can explain much of the correlation with IQ or g-factor: speed and efficiency of neural processing, working memory, module communication, etc.
However once we lay all of that aside, there remains a core dependency on the ability for conceptual abstraction. The mapping between these simple visual images and their compact internal encodings is ambiguous, as is the predictive relationship. Solving these problems requires the ability to find efficient and useful abstractions - a general pattern recognition ability which we can relate to efficient encoding, representation learning, and nonlinear dimension reduction: the very essence of learning in both man and machine.
The machine learning perspective can help make these connections more concrete when we look into state of the art programs for IQ tests in general and analogy problems in particular. Many of the specific problem subtypes used in IQ tests can be solved by relatively simple programs. In 2003, Sange and Dowe created a simple Perl program (less than 1000 lines of code) that can solve several specific subtypes of common IQ problems but not analogies. It scored an IQ of a little over 100, simply by excelling in a few categories and making random guesses for the remaining harder problem types. Thus its score is highly dependent on the test's particular mix of subproblems, but that is also true for humans to some extent.