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Difference between Vertical and Horizontal Complexity

7 min read

From: jimruttshow8596

In developmental psychology, the concept of hierarchical complexity is a key focus, distinguishing it from simpler forms of complexity. This framework helps to understand how human cognition and skill develop over a lifetime [00:02:49].

Defining Hierarchical vs. Horizontal Complexity

Horizontal Complexity

Horizontal complexity refers to increasing the amount of the same type of task at the same level of difficulty [00:06:36]. It’s about performing more of the same kind of task without fundamentally altering the nature of the task itself [00:06:38].

  • Example: Tying a thousand shoes in half an hour [00:07:14].
  • Example: Taking an elevator from the lobby to the seventh floor, where each step (standing, pressing button, waiting) is a discrete sequence of tasks at roughly the same level of difficulty [00:11:25]. The tasks are disjoint and don’t significantly affect each other [00:11:45].

Vertical (Hierarchical) Complexity

Hierarchical complexity describes the qualitative growth in complexity, where lower-order capacities are integrated into fundamentally new, more complex tasks [00:06:44], [00:09:01]. It involves “non-repeating recursions” where higher-order actions organize and transform lower-order actions to produce new, non-arbitrary organizations that couldn’t be accomplished by the lower orders alone [00:35:30], [00:35:50]. Once lower-order elements are integrated into a higher-order element, they are no longer the same elements they were before [00:37:34].

  • Example: Making a shoe, which is hierarchically more complex than tying shoelaces [00:07:07].
  • Example: Disassembling, replacing a part, and reassembling a lawnmower engine, where every move depends on previous moves and requires ancillary skills like organizing parts mnemonically [00:11:55]. This requires coordinating sensory-motor systems with abstract conceptual understanding and descriptive language of parts [00:13:51].

Historical Context and Key Figures

The concept of hierarchical complexity has a long history in psychology:

  • Early Shades: Found in the works of James Mark Baldwin and Herbert Spencer, and even in natural philosophies of mind [00:04:15].
  • Jean Piaget: His 1923 publication, The Language and Thought of the Child, marked a significant emergence of the construct [00:04:02]. Piaget was interested in how universal laws of logic and mathematics emerge from evolution and human experience [00:23:37].
  • Neo-Piagetian Consensus: In the 1980s and 1990s, a consensus emerged among researchers, leading to a formal definition of developmental stages across the lifespan [00:04:36].

Hierarchical Integration and Skill Development

Hierarchical complexity is a ubiquitous process in skill development, creating new skills from prior existing ones [00:08:13].

  • Lower-order skills integrate into higher-order skills: Before tying a shoe, a child needs to manipulate individual laces and understand notions of tension at a muscular level [00:08:25]. This mastery is then applied to the higher-order skill of tying a knot [00:08:42].
  • Sensory-Motor to Representation:
    • Infants first develop single sensory-motor actions (e.g., focusing on a face [00:43:00]).
    • They then coordinate actions (e.g., looking with reaching to knock something off a table [00:43:08]).
    • Further coordination leads to sensory-motor systems (e.g., coordinating looking, reaching, grasping, bringing to mouth, and drinking [00:43:17]).
    • Eventually, a sprawling array of sensory-motor schemes gets integrated into a single representation, like “bedtime” [00:14:55]. This emergence of representations (semiotic function) is considered miraculous because it allows for summarizing dense lower-order material [00:15:04], [00:47:32].
  • Representations to Abstractions:
    • Individual representations (e.g., “bedtime,” “dinner time,” “TV time”) are then brought together [00:15:42].
    • This leads to abstractions, such as “quality family time,” which generalizes across multiple representations [00:15:47]. Abstractions integrate many examples of representations and cannot be directly pointed to in the world like representations can [00:50:17].
  • Abstractions to Principles: Further integration leads to principled understanding, akin to John Rawls’s “justice as fairness,” integrating different fields of ethics into a single theory of justice [01:09:31]. This allows for making rules about the making of rules [01:10:40].

Relationship with Chunking and Working Memory

The concept of hierarchical complexity is closely related to “chunking,” a term used in computational linguistics and neuroscience [00:16:11].

  • Chunking: As individuals gain more life experience, they can load more information into a single term. For example, the word “complexity” carries a huge history of depth and nuance for someone who has studied complexity science for years, unlike for a novice [00:16:41].
  • Scale of Chunking: Hierarchical complexity proposes a definable scale of chunking. Chunking sensory-motor systems differs from chunking multiple theories into a higher-order theory [00:17:33].
  • Working Memory as a Driver: A common hypothesis suggests that the remarkably small short-term memory (e.g., Miller’s 7 +/- 2 chunks [00:27:33]) is a driving function for hierarchical complexity [00:28:04]. To work on more difficult problems, individuals must make chunks larger, enabling them to hold more complex information simultaneously in working memory [00:27:57].
  • Epistemic Motivation: Beyond the working memory bottleneck, a deeper “epistemic motivation” (the need to understand, not just succeed) also drives the processing of information through this bottleneck [00:29:50].

Broader Implications of Hierarchical Complexity

Hierarchical complexity is not just a psychological construct but a pervasive property of information across the biological spectrum [00:19:02].

  • Cosmological Evolution: It can be seen as part of a larger story of cosmological evolution, where complex entities emerge from simplicity (e.g., atoms forming molecules, cells forming multi-cellular organisms, organisms forming ecosystems) [00:19:55], [00:21:00].
  • Fractal Property: The development of skills shows a fractal-like property; closer examination reveals constructions and levels within levels [00:42:38].
  • Societal Demands: The evolution of societies, particularly with industrialization and digital technology, has placed greater demands for hierarchical complexity on citizens [00:56:30]. This has created a “complexity gap” between societal demands and individual capacities [00:54:17].

Application in Education and Leadership

The formal definition of hierarchical complexity allows for operationalization in educational contexts and research [00:09:36].

  • Lectica Assessments: Theo Dawson’s Lectica assessment system uses psychometric tools (like the Rasch model) to create standardized assessments of cognitive development [01:14:01].
    • These assessments analyze open-ended human performance (e.g., linguistic responses) to determine the deeper hierarchical structure being expressed [01:13:24].
    • Unlike traditional standardized tests that simply pass or fail, Lectical assessments are diagnostic, identifying what a person understands and suggesting the “next best thing” for them to learn to continue their growth in hierarchical complexity [01:15:46].
  • Leadership Development: Lectica’s work in business, particularly with intelligence agencies and municipalities, focuses on identifying and developing leaders [01:18:23].
    • A “complexity gap” exists between leadership roles’ task demands and leaders’ capacities, often manifesting in deficits in perspective-taking, perspective-seeking, and perspective-integration [01:19:22].
    • Assessments can pinpoint where these deficits occur, guiding specific learning sequences for leaders [01:23:42].
    • The aim is to promote leadership development rather than just hiring/firing, providing detailed diagnostic reports [01:24:06].

Warnings Against Misapplication

It is crucial not to oversimplify or misapply hierarchical complexity:

  • Individual Classification: It is inaccurate to assign a person a single hierarchical complexity level [00:59:18]. Instead, a specific task accomplished by a person can be assigned a level [00:59:23]. A person may exhibit different levels of complexity in different skill domains (e.g., highly complex in physics but sensory-motor in small engine repair) [00:34:31], [01:00:04].
  • General Intelligence (IQ): While hierarchical complexity correlates with general intelligence (Spearman’s G), IQ tests are summary statistics based on narrow indices [00:59:02]. They radically oversimplify human psychology and can create a “demi-reality” where people are categorized by a single number [01:00:29].
  • Cultural Evolution: Applying hierarchical complexity to cultural evolution to suggest that ancient cultures are “childlike” or less complex than modern ones is a misapplication [00:54:34]. While the complexity required for social coordination can evolve (e.g., from kinship ritual to complex constitutional law), this doesn’t mean the individual experiences or “humanity” of people in earlier cultures were less complex [00:52:45].
  • Political Misuse: Using hierarchical complexity for political activism or as a “social sorting mechanism” can lead to misuse and become a “bludgeon,” similar to how IQ tests were historically used [01:05:51]. Responsible use requires rigorous measurement and ethical training for practitioners [01:06:21].

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