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Misfits and balance

My notion of balance comes from thinking about Alexander's misfits. The information here is drawn from [Sal10].

Misfits introduced by Alexander in Notes on the Synthesis of Form [Ale64] (NSF).

  • Novel approach to design problems.
  • Misfit: a mismatch between the capacities of and expectations on a form in a specific context.

He also introduced two “cultures” of designing:

  • unselfconscious cultures designed primarily through a heritage of craft and artisanship where reflection and systematization were largely absent.
  • modern selfconscious cultures that reflect and systematize intensively.
  • While there are benefits in selfconscious designing, one also gives up advantages of unselfconscious designing.
    • The responsiveness of unselfconscious design to externalities (the exigencies of the context and problem at hand) has given way to a more internalized and abstract perspective.
    • He sees this as problematic because the internalizations are imperfect.

Alexander's work on misfits has not been as popular as his other work.

  • I think that a modified view of misfits plus systems thinking can lead to new ways of thinking about design.

Formal logic in NSF

Set theory is used extensively in NSF. I have found some problems with its use there:

  1. Alexander assumes the existence of the universal set.
    • However, the universal set is excluded from every standard set theory, because its inclusion makes set theory invalid1).
  2. Godel proved that no formal system can be both complete and valid [Hof79].
    • There is no evidence of a completeness proof of Alexander’s logic. An incomplete theory is one in which there are some true statements that cannot be proved true within the theory.
    • Thus, it appears that Alexander’s work is neither valid nor complete.
  3. Alexander’s logic appears to be a many-sorted, first order logic.
    • Every many-sorted logic has an equivalent one-sorted logic. One-sorted logics tend to be more stable and reliable, and more easily computed) than many-sorted logics.
    • Alexander appears to have never translated his work to one-sorted form for the sake of establishing a completeness proof.

Alexander's work is not invalidated by these 3 problems, but because of these problems, the formal aspects of Alexander's work are unreliable by modern standards and are ignored in developing the idea of balance.

What is a Misfit?

NSF gives no direct definition of misfit, but rather a number of characteristics scattered over several passages.

  • Alexander writes about “requirements or misfit variables”
    • This suggests some equivalence between the two terms.
    • Although Alexander nearly always uses the term misfit, the text is best understood by reading misfit variable.
    • The difference between misfit variables and requirements is that misfits simply describe a situation, whereas requirements constitute directives to the designer to address misfits to the extent described by constraints (either boundary constraints or minimization constraints).
  • Alexander also refers to a misfit (variable) as relating to an ensemble, which is the combination of a given form and the context in which it exists. This is very important because it connects a misfit variable to a particular situation.
    • That is, misfits are always situated; this connects to John Gero's situated design.

That misfits are really variables is important but easy to overlook.

  • A variable has two elements: a named property, and a value for that property.
    • If the variable’s value is “bad,” then it is a misfit.

The goal of designing, then, becomes the changing of the values of misfit variables so that they are no longer “bad.”

  • This is reinforced by the partitioning and clustering tasks in NSF.
    • Networks of related misfits are mathematical graphs.
    • Partitioning and clustering builds a hierarchy such that the root of the hierarchy is the design problem as a whole.
    • The network is one of misfits, or requirements, so the network is a model of the design problem.
  • The design problem is not something under the designers’ control.
    • But its model (as requirements/misfits) may change as the designers' understanding improves over time.
    • Excluding changes arising from the imperfect knowledge and reasoning of human designers, the problem itself remains fixed (i.e. invariant).
    • If the problem changes because of external influences on the existent ensemble (also not under the designers’ control, but quite possible in the real world), then the original problem no longer exists and the designers must essentially begin again.
    • Simplifying assumption: assume here that these kinds of changes do not occur.
  • Therefore, if the problem is fixed, then the misfit network must also remain fixed.

The designers’ goal, however, is to eliminate the misfits.

  • If we eliminate the misfits, and the misfits are the network, then we must change the network.
  • This contradicts the previous statement: we cannot change the network if it must remain fixed.

We can resolve the contradiction thus:

  • The nodes in the network are variables.
  • Misfits are just bad values of those variables.
  • So, to eliminate a misfit, one must change the content of a node, not the node itself.
  • This removes misfits while keeping the network itself fixed.

Another problem: misfits represent only the “bad” aspects of ensembles.

  • So a network of misfits forms on a partial representation.
    • “Good” aspects of ensembles will not be part of the misfit network.
  • But the good aspects are likely coupled to the misfits, just as misfits are coupled to one another.
  • So changing the values of misfit variables could adversely influence those good aspects.
  • But the misfit network will not capture those influences.

Address this by capturing as “fitness” variables any property of an ensemble, not just those with bad values.

  • The resulting network now has some variables with “good” values and others with “bad” values, and the coupling between all of them will be captured as well.
    • So when a variable with a bad value is improved, the coupling information in the network can be used to make sure variables that have good values are not adversely affected.

Now we can describe the network as representing forces at work in a situation that must be resolved, or balanced, by a design.

  • The network graph describes how well balanced a form is with respect to a context, including both its good and bad aspects.
    • Conveniently, this viewpoint is quite consistent with Alexander’s work on pattern languages [AIS77].

There Is Always a Form

Misfits motivate designing, so misfit identification (and existence) must precede design.

  • From this, one may argue that Alexander’s approach ignores the possibility of highly innovative design or invention.
    • The argument hinges on asserting sufficiently innovative designs have no preceding form.

However, the author believes that there is always a preceding form.

  • This form is the way that we do things now, that we find inadequate, and that we address by innovation.
    • That is, even for highly innovative forms, there is also a preceding (but substantively different) form.
  • Example: palm pilot requirements case study. The Palm Pilot was a highly innovative product; its preceding form was a leather-bound paper agenda.
    • The preceding form was not a PDA but still shared aspects of functionality with it.
    • The innovations in the Palm Pilot were driven by the need to compete with the preceding form.
  • Thus one must focus on the function of the preceding form, not its structure.
  • The extant form is used to understand how the required function is not being fulfilled.
  • These shortcomings are the misfits, and they drive the design of a new form.

In high innovation, it may be difficult to identify/separate the predecessor form within the context.

  • Solve this by applying systems thinking:
    • Entities are marked by boundaries.
    • Boundaries are where properties change.
  • So identifying an entity means identifying key properties and then finding where they change.
    • Even the act of drawing different boundaries can be enough to inspire innovation.
    • Example: while the first attempts to build flying machines typically used flapping wings to generate both lift and thrust, success came relatively easily once new functional boundaries were drawn in the situation such that lift (via wings) and thrust (via propellers) were separated.

The Palm Pilot was not the first PDA to be designed, but it was the first to be successful.

  • This is because its designers found the right balance point (in context) between all the factors that influence its success: cost, size, functionality, complexity, etc.
  • To find an appropriate balance point, one must identify the appropriate systems, which in turn drives the identification of proper misfits.

The Problem of Form and Requirements

In NSF, Alexander refers often to an example of a kettle, and gives a rather extensive list of requirements that a kettle should satisfy. One of them reads “…should have a handle that….”

  • Alexander assumes that the kettle has a handle – thus implying that at least one design decision has been made (that there must be a handle) by the time the requirements were specified – even though specifying the requirements is supposed to precede designing.
  • This is a logical contradiction.
    • There may have been constraints on the kettle design problem requiring a handle, but this is not indicated in the text.
    • This kind of logical contradiction is common in NSF; the kettle’s handle is just one example of it.
  • More appropriate requirements would be functional, not structural.
    • They would be more appropriate because they would make no assumptions about form.

Two examples of how this might have been done for the kettle’s handle include:

  1. [The kettle must be such that] a person can easily carry/lift the kettle.
    • This begs questions about the capacity of the users, how far and how often they carry/lift the kettle, etc.
    • Such questions should be answered with constraints.
  2. [The kettle must be such that] a person can pour the kettle’s contents.
    • This begs questions about the position/location of the thing receiving the poured contents with respect to the kettle and its user, the rate of pour, etc.
    • These should be answered with constraints too.

Thus, Alexander’s requirements are not good ones.

  • The lack of good requirements undermines his argument.

One can recover and refine the overall process as follows.

  • Clients and users do not really know what they want. Designers serve that purpose. Clients and users are very good, however, at identifying what is wrong in how things are.
  • This is precisely what misfits are for, so they are ideal for capturing what clients and users find wrong with the current situation.
  • However, designing requires production of form to suit function. See below for a sketch of such a process.

Abstract Categories of Requirements

Alexander correctly observes in NSF that requirements are in practise often grouped according to abstract concepts like “safety” or “durability,” and that such categorization is not helpful because it is arbitrary and constructed entirely by the needs of the designers rather than the needs of the situation for which the designers work.

  • The arbitrary nature of the categorizations that designers impose only obscure the nature of the problem, which exists independent of the designer.
    • The designer only recognizes the problem.

Alexander also correctly observes that categorizations should be driven by the available information and not by the designers’ needs or beliefs of what the categorization “should be.

  • One may think of this as “evidence-based design.”
  • While the act of re-balancing a situation through design will naturally include the designers' experience and perspective, the forces to be balanced must be those observed to exist in the extant ensemble/situation.

Decomposing Misfit Networks

Per Alexander, the purpose for decomposing misfit networks is: “We now have a graph G(M,L) which represents the design problem. …to solve the problem, we shall try to decompose the set M in such a way that it gives us a helpful program for design.”

  • i.e., decomposition helps guide designers to a solution.
  • However, all attempts to do this (by Alexander and others since), involve cutting certain links between misfits in the network graph to construct the needed hierarchical structure.
  • This means some relationships are ignored.
    • Significant effort is made to identify the “weakest” relationships – those that, if removed, are least likely to invalidate the network as a representation of the design problem.
  • The graph is cut where (a) the smallest damage to the network, and (b) the greatest decrease in complexity, can be achieved.
  • The complexity of the algorithms arises from the need to identify those specific cuts.

This approach is problematic.

  • There is no way to know a priori what the impact of any change to a problem definition will be on the fitness of a designed solution.
    • Alexander emphasizes that design should be led by the evidence.
    • So to ignore information simply for the benefit of the designer seems inappropriate.
    • Demonstrable intractability might be one excuse to do this, but not such demonstration is made in NSF.

A possible solution is to develop a hierarchy of systems based on functional interactions.

  • Higher level functions emerge from, but are not necessarily produced by, constituent subsystems.
  • This requires describing properties of entities in the situation in functional terms.
  • It does not impose arbitrary structures (e.g., the kettle's handle) on the problem. More on this below.

Alexander in NSF gives 2 criteria for what constitutes a good misfit network decomposition

  1. A good decomposition allows one to find “constructive diagrams” for each subset of misfits individually.
    • This is analogous to encapsulation
    • It's also part of systems thinking wherein subsystems can be swapped so long as interfaces are the same.
    • Alexander also writes that a subset of misfits must “cohere somehow” and suggest “a physical aspect or component of the form.”
      • I believe Alexander intends a functional coherence: misfits in a set must all be functionally connected – which in turn would suggest kinds of forms.
      • In this interpretation, systems, being functional entities, clearly fit well in Alexander’s approach.
  2. A “useful” decomposition must be such that the representation (i.e., constructive diagrams) of a combination of two subsets of misfits must be “derived…in some simple way” from the representation of the two subsets.
    • This suggests that there must be a relatively straightforward superposition of representations to combine two sets of misfits.
    • This in turn suggests that all the requirements/misfits must be known before a design solution is started.
    • This is not usually possible because many requirements of lower level solution elements (e.g., the parts and sub-assemblies of a physical product) are derived from a combination of higher-level requirements plus design decisions that were made earlier in the process.
      • This coevolution of problem and solution [DC01] is necessary because every design decision alters the specifics of the design problem.

However, it appears that Alexander is following a waterfall model.

  • EG: He writes in NSF that a decomposition must occur entirely before solutions are sought. This is not a good way of proceeding with design.
  • We can salvage this with a systems-based hierarchy.
    • If we focus on only the requirements of one system at a time, and design as much as possible for it before moving to its subsystems, then we can implement co-evolution.
    • Alexander’s misfit-based approach can be applied to each level in turn.
  • Thus, a systems-based approach to misfit organization satisfies both of the requirements set forth in NSF for acceptable decomposition methods.

Another problem: Alexander’s method of combining subsets of misfits.

  • It ignores that some properties of combined subsets are neither endemic nor constituent of the subsets.
  • Rather, these properties emerge from the combination itself.
  • Emergent properties are very important for design.
  • A systems-based approach treats these properties by associating them only with particular systems and not necessarily with their sub- or super-systems.
    • EG: the drive train of an automobile enables the emergence of a key property of the automobile (its ability to move) without providing the property per se.
    • But without the engine, that key property is not available.

Relative Independence of Requirements

Reconsider Alexander's example of the requirements for a kettle.

  • ”…must be comfortable…“ and ”…must be economical to heat.“
  • Alexander wonders about their apparent independence, writing that it is hard to see if and how they relate.
  • Requirements can appear uncoupled but still become coupled in a specific design.
    • This is because the structure of the design may cause coupling to emerge only in that context.
    • From Suh’s Axiomatic Design [Suh90], one can decouple/uncouple requirements by choosing the “right” design.
    • That is, truly uncoupled requirements depend on both the requirements and the design solution.
    • For the kettle: requirements that explicitly mention structure, e.g., the kettle’s handle, create structural coupling that may not be present if the requirements were first treated functionally.
    • This could explain the uncertainty that Alexander expressed in NSF.

The distinction between functional and structural aspects is also evident in Alexander’s own words:

  • “Some sets of misfits, in view of their interactions, seem naturally to belong together, and, taken as units, suggest physical form very strongly.”
  • If there is a justifiable reason for using a certain form that causes requirement coupling, then so be it.
  • Better still to be given the choice of deciding whether such a form is in the best interest of the designed object’s users.
  • To ensure that the designer at least has the opportunity to choose, it is important to distinguish between the form and the function – particularly in the requirements (or misfits) – so that coupling is not artificially introduced.

Balance, Misfits, and Systems

The concept of balance can help address the problems noted in preceding sections. Designing as balancing provides a sketch of a design process based on balance.

Example: NSF's kettle

  • Consider the kettle as a single system.
    • That is, we do not refer to its constituents, only to the kettle as a whole.
  • The number of its basic functional requirements are very few:
    • to allow water to enter it,
    • to heat the water it contains, and
    • to allow the water in it to come out.
  • The extents of these functions are specified with contextual constraints.
    • EG: the amount of water contained by the kettle depends on how it is to be used.
      • If its capacity is not consistent with its use, then the design is not balanced.
      • To re-balance it, either
        • the kettle’s capacity must be changed, or
        • the kettle must be re-tasked to a different context.
  • Since the kettle’s purpose is to provide hot water, we can describe its major functional elements (subsystems) as:
    • an access system (to get water into and out of the kettle),
    • a heating system,
    • a containment system, and
    • a control system (to control the kettle’s dynamic behaviour).
    • These subsystems interact to produce the required overall functions of the kettle.
  • At the level of subsystems, further balancing will be required, but only for interactions between specific subsystems.


Sal10. a F.A. Salustri. 2010. Misfits, Balance, Requirements, and Systems: thoughts on Alexander's Notes on the Synthesis of Form. Proc 2010 Conference of the Design Research Society. Montreal. (link)
Ale64. a C. Alexander. 1964. Notes on the synthesis of form. Havard University Press.
Hof79. a D.R. Hofstadter. 1979. Godel, Escher, Bach: An Eternal Golden Braid. Vintage Books.
AIS77. a C. Alexander, S. Ishikawa and M. Silverstein. 1977. A Pattern Language: Towns, Buildings, Construction. Oxford University Press, London.
DC01. a K. Dorst and N. Cross. 2001. Creativity in the design process: co-evolution of problem–solution. Design Studies, 22(5):425–437.
An invalid theory is one that yields false positive results (i.e. the theory can prove true statements that are in fact false).
research/misfits_and_balance.txt · Last modified: 2020.03.12 13:30 (external edit)