BLUEPRINTS OF THE MIND
4.2
Three Levels of Analyses
How should we approach the challenge of understanding the human mind? Is it enough to look at just biology, or behavior, or its function? In this step, we explore a foundational perspective that has shaped cognitive science: the idea that understanding complex systems like the brain requires explanations at multiple computational levels.
When we ask, “How does the brain work?”, our first intuition might be to look at its physical structure – neurons, synapses, neurotransmitters, and electrical signals. One might assume that explaining the brain simply means tracing these physical mechanisms, much like one explains a machine by analyzing its gears and circuits.
The answer must lie in how neurons fire, how they connect, and how their patterns of activity give rise to mental functions. Right?
Not quite. In his foundational work Vision (1982), British neuroscientist David Marr, one of the pioneers in the development of the field of Computational Neuroscience, argued that focusing on the neural level alone cannot explain perception.
“Trying to understand perception by studying only neurons is like trying to understand bird flight by studying only feathers. It just cannot be done. To understand bird flight, you need to understand aerodynamics. Only then can one make sense of the structure of feathers and the shape of wings. Similarly, you can’t reach an understanding of why neurons in the visual system behave the way they do just by studying their anatomy and physiology.”
David Marr, 1982
Marr’s challenged the view that biological mechanisms on their own are no complete explanation. Understanding cognition requires thinking across multiple levels: To truly understand a complex system like the brain, we must consider:
- What is the problem the system is solving, and why?
- How is the problem solved? What are the specific steps that the system uses to solve the problem?
- And lastly, where and how is this physically implemented in the brain?
These levels of inquiry form the basis of what has become one of the most influential frameworks in cognitive science: Marr’s Three Levels of Analysis. Below, we outline each level with two simple examples: addition and color vision.
I. The computational (or functional) level
What is color vision for (what is the goal, why is it useful)?
This level is essentially defining what computation is being done or what problem the mind is solving. Simply put, what are the inputs that the mind is receiving and what is the output (e.g., thought or behavior) that would be desired? As with the previous chapters, it is always important to consider why a problem must be solved from an evolutionary perspective (i.e., how does this help the organism survive and reproduce?).
Addition: The inputs are numbers, and the output is their sum.
Color Vision: The inputs are wavelengths of light striking the eyes, and the output is a color percept. From an evolutionary viewpoint, color supports efficient foraging by helping differentiate ripe from unripe or toxic fruit.
Example color vision
II Algorithmic Level
How is the color vision carried out? What representations and processes are involved? This level specifies how the computation is carried out: what representations are used, and what algorithm processes them. A representation is simply the form in which the actual inputs are used in the algorithm. Regarding the algorithm, if we think about computation like cooking, the algorithm would be the recipe outlining the explicit steps getting us from the inputs (i.e., ingredients) to the output (delicious meal/cognition).
Addition: Numbers can be represented in many formats (Arabic, binary, Roman). A simple algorithm is the familiar digit-wise summation taught in school, carrying over tens when needed.
Color Vision: Here we must define how wavelengths map to color categories (e.g., 530nm -> “green”, 580 -> “yellow”, 555 -> “chartreuse”, etc.). Any algorithm solving color vision must take into account that the light hitting our eyes is the sum of the reflectance and luminance of the observed object and therefore 1) separate the two and 2) normalize for lighting to extract the object color. Because the sensory data conflate these two factors, this is an inherently ill-posed (undetermined) underdetermined problem, which we will revisit later.
III Implementation Level
How are the representations and algorithms physically realised?
Addition: Calculators implement addition through circuits using logic gates.
4-Bit Calculator Built Using Digital Logic Gates
© Cody Wabiszewski, Global Science Network
Color Vision: For color vision, this is how they are embedded into the brain: the neurons, circuits, and physiological mechanisms. Human color vision is implemented through three classes of cone photoreceptors, short (S), medium (M), and long (L) wavelength sensitive, whose relative activation supports trichromatic color perception. Neural circuits in the retina and visual cortex transform these signals into the colors we experience.
IMAGE
The key idea here is that a proper theory of a cognitive process of the mind must be explained at all three of these levels which inherently constrain one another. A theory restricted to one level is incomplete: identifying neural circuits is insufficient without understanding the computational problem they solve, while specifying an algorithm is useless if it cannot be realized in biological tissue.
Once the computational goal is defined, it constrains the range of possible algorithms, which must in turn be feasible within the neural implementation. The figure below summarises these relationships using addition and color vision as examples.
IMAGE Marr’s Three Levels of Analysis with the Examples
Further Reading
If you are curious about whether Marr’s three levels are exhaustive, or how they relate to other multi-level frameworks, see Máté Lengyel (2024), “Marr’s three levels of analysis are useful as a framework for neuroscience.” Lengyel argues for a pluralistic approach that builds on Marr’s original insight while extending it to contemporary computational neuroscience.
References
This step is broadly based on an open lecture by Nancy Kanwisher at the Massachusetts Institute of Technology (MIT), 2018: https://www.youtube.com/watch?v=Di_3pGAveGs
Colombo, M., & Piccinini, G. (2023). The Computational Theory of Mind. Cambridge University Press. https://doi.org/10.1017/9781009183734
{.citation-indented}Marr, D. (1982). Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (Chapter 1). MIT Press.
Gallistel, C. R., & King, A. P. (2009). Representations. In Memory and the computational brain: Why cognitive science will transform neuroscience (Chapter 4). Wiley-Blackwell.
Krakauer, D. C. (2024). The complex world: An introduction to the foundations of complexity science. SFI Press.
Pylyshyn, Z. (1984). Computation and Cognition: Toward a Foundation for Cognitive Science. MIT Press.
Lengyel M. Marr’s three levels of analysis are useful as a framework for neuroscience. J Physiol. 2024 May;602(9):1911-1914. doi: 10.1113/JP279549.
Willshaw DJ, Dayan P, Morris RG. Memory, modelling and Marr: a commentary on Marr (1971) ‘Simple memory: a theory of archicortex’. Philos Trans R Soc Lond B Biol Sci. 2015 Apr 19;370(1666)