Architecture, constraints, and behavior

Neuroscience and Robust Control

A recent claim (7) is that human motor control is better explained as a robust rather than optimal controller, an explanation with a long tradition in neuroscience. Controllers optimal, on average, to only additive noise can be arbitrarily fragile to other uncertainties (21), motivating the development of robust control theory (22⇓–24). Robust control is risk-sensitive, optimizing worst case (rather than average or risk-neutral) performance to a variety of disturbances and perturbations. Robust control theory formalized and extended best practice in control engineering and coincided with a massive expansion into active control in robots, airplanes, automobiles, smart weapons, communication networks, etc. Therefore, robust control is now ubiquitous but hidden, evidenced largely by what does not happen, such as skids, stalls, crashes, missed targets, dropped packets, etc. Similarly, most CNS activities are hidden from conscious awareness (4⇓–6), implementing the sensing, decision-making, and actuation necessary for robust control in complex environments.

Control theory makes strong predictions about how robust circuits must necessarily be implemented largely independent of the device technology, all perfectly consistent with observations in neural circuits (1). Such claims are easily checked by experts in math, but hopefully, they are intuitively plausible to neuroscientists generally. In particular, any natural parameterization of functional control circuits (e.g., lobster somatogastric ganglia) (1) is well-known to be large (high dimension), thin (even higher codimension), and nonconvex (24). If it were otherwise, engineering design would be much easier. As a simple analogy to explain these terms, consider a 2D piece of paper with lengths that are large by some measure sitting in a 3D square box of comparable lengths. The larger that these lengths are, the smaller that the fraction of volume that the paper will occupy in the box is. Therefore, the paper can be both large and thin as a fraction of the box volume. If the paper is bent or wrinkled, then it is also nonconvex within the box, because most straight lines between two different points on the paper will not remain in the paper.

An even simpler example is the set of words in most languages, which is large but vanishingly thin as a fraction of all possible meaningless sequences of letters. There are 9! = 362,880 different permuted sequences from just the nine distinct letters adeginorz, roughly the total number of English words, but only organized is a word. Humans would have some difficulty checking this claim, but computers do so easily (and make formidable Scrabble opponents). The set of English words is, thus, large and thin. The set of functional parameter values of any circuit will also typically be large but vanishingly thin and nonconvex in the set of all possible (mostly nonfunctional) circuits. This fact is largely independent of the notions of function, circuit, or parameter, provided that they are sufficiently complex and realistic. Much of engineering theory is devoted to constructing special (higher-dimensional, nonphysical, and abstract) parameter embeddings that are convex and thus, algorithmically searchable for robust and functional design values. This idea that robust systems are large but thin and nonconvex in the space of all systems is a theme discussed below.

Another general feature of control systems is hard limits on robustness and efficiency (20). If the brain as controller has evolved to control action, then conscious thought may be, in some sense, a late evolutionary addition or byproduct (6⇓⇓⇓⇓⇓–12). Both robust control theory and experimental evidence suggest that complex internal dynamic models are needed to resolve ambiguities in noisy sensations as well as plan for uncertain action, all in an uncertain, perhaps hostile, environment. When these models are implemented in slow neural hardware, management of the resulting delays almost certainly requires a heavily layered organization, a concept central to the network architecture emphasized here. (Delay has little ill effect if there is truly no uncertainty, because then, open-loop control is adequate; however, this ideal is never seen in practice.)

Pain and reflexes illustrate the sophisticated interplay of central and peripheral control, and fast action receives priority. Fast, thick, myelinated, general purpose sensory fibers initiate withdrawal from painful stimuli, whereas slow, thin, specialized fibers provide delayed, but detailed, information about the source of pain. This pattern is seen throughout the organization of the nervous system, and throughout behavior, we see this mix of reflex (fast, automatic, hidden, and expensive) and reflect (slow and conscious), with reflex receiving priority in resources. The acquisition of skill (playing instruments, ball sports, chess, reading, etc.) involves shifting down into fast reflex processes that start high and slow. Indeed, the more expert that we are in an activity, the less that we necessarily rely on conscious processes to perform, and such evidence for layering is found everywhere (4⇓–6).

If brains are doing robust control using internal models, then illusions may be intrinsic. What reaches conscious awareness is the state of a simulation, not a direct perception of the world (9⇓⇓–12). However, seeing is believing, because what we see is not only a remarkably robust, integrated, dynamic state estimate of the external world blending multiple senses but one that automatically focuses attention on information that we need to take robust actions. That we can be almost arbitrarily fooled is one of the many unavoidable tradeoffs of our physiology, evolution, and brain architecture. Therefore, it is equally true that seeing is dreaming, which is known from a variety of well-studied illusions (3), dreams, and hallucinations. Functional losses because of CNS lesions (4, 6) are often highly specific and reproducible, making us aware of myriad unconscious processes that were previously taken for granted and showing that our internal simulations use a distributed and parallel implementation to mitigate the effects of hardware delays. The extreme gain and loss of capabilities in savants also suggest powerful but constrained simulation capabilities.

Computer and Control Technology

Modern robust control systems are typically implemented using digital hardware and software, and most computers are embedded in this way and thus, are permanently hidden. Examples are ubiquitous from antilock brakes to automated collision avoidance to global positioning systems in cars to fly by wire aircraft. Networks and cloud computing that connect the relatively fewer (but still billions worldwide) personal computers and smart phones have hidden routers and servers that control the flow of packets and files. The internal mechanisms are again manifest largely in the rarity of crashes, losses, errors, and failures and in the catastrophic nature of rare crashes. However, despite enormous progress, robots struggle to navigate the real world as effectively as rodents or even insects, and computers continue to fail in Turing tests, although in fascinating ways that reveal much about both humans and computers (42). This enormous, hidden, cryptic complexity, driven by robustness, is both the greatest initial obstacle in using advanced information and control technologies as metaphors for biology and also ultimately, the key to important insights and theories (16, 19).

As a starting point, human memory layering seems to be very different from computers, which is shown by various syndromes, lesions, and laboratory studies (6) as well as competitions pushing the extremes of human memory (14). A standard technique among competitors memorizing sequences of meaningless symbols is to embed them in previously prepared complex and vivid 3D dynamic simulations (called palaces) that can then be replayed to retrieve the symbols. For example, such methods allow experts to memorize a single pack of 52 shuffled playing cards with no errors in less than 22 s. Palaces are reused after the memories are actively purged. This finding illustrates that humans can repurpose innate (dynamic, modal, and grounded, etc.) simulation capability in lower layers for purely symbolic higher-layer memory and (it is claimed) the lack of real alternatives for rapidly storing and retrieving large amounts of symbolic data (14). That it works so poorly is perhaps less remarkable than that it works at all.

Computers have opposite memory capabilities from humans in that massive amounts of purely symbolic, meaningless data are nearly instantaneously found, stored, searched, and retrieved, and as a result, Google is now a verb. This finding is possible, because computers and networks have, arguably, the canonical layered architecture in engineering from very-large-scale integration (VLSI) chip design to the transmission control protocol/internet protocol (TCP/IP) protocol stack (16, 19), and a brief look at such architecture is a rich source of insights. Near the bottom is analog circuitry that is exquisitely organized (extremely large/thin/nonconvex) to create digital behavior when interconnected appropriately but at the expense of speed and efficiency. These analog and digital hardware layers are functionally distinct but physically coincident. Importantly, these hidden layers and interfaces are fundamental to the more obvious plug and play modularity that they enable.

Many devices can be built purely out of hardware, but a software layer gives much greater flexibility at even more expense of speed and efficiency. As with the digital layer and its analog substrate, software only exists when embodied in hardware, but because software can be moved across hardware platforms, it also has an existence that transcends any individual physical instantiation. Software is a very special organization of hardware, and similarly, digital hardware of analog circuitry, but no simple terminology captures the full richness of this layering. Nevertheless, there are no mysteries here, just an impoverished language for description. Software, also, is richly layered. An operating system (OS) often has a kernel layer that manages and virtualizes the various hardware resources for higher-layer application programs. For example, the hardware memory typically has its own separate layering of memories from small, fast, and expensive to large, slow, and cheap. This layering is within the hardware, and therefore, it is orthogonal to that of analog to digital to software.

By managing the use of layered memory cleverly, the OS kernel can provide applications programs with a virtual memory that has nearly the speed of the fastest hardware, with the cost and size of the cheapest hardware. Such virtualization is a familiar and essential element of layering. Therefore, applications can use abstractly named variables and higher-level languages, and the kernel then translates these names into virtual addresses and ultimately, physical addresses; however, the name to address translation process is hidden from the applications. This OS architecture provides a variety of robustness features from scalability of the name and virtual address spaces to resource sharing between applications to security of the physical memory from application failures or attacks.

At the most basic level, the Internet TCP/IP protocol stack extends the functionality of the OS kernel across the network to multiple machines, allowing much broader resource sharing and creating the illusion to users of near infinite resources. Unfortunately, TCP/IP was designed decades ago not as a general purpose platform but primarily to be robust to physical attacks on hardware in relatively small networks with trusted users running minimal applications. It did this brilliantly, especially compared with the alternatives at the time, but modern use is largely the opposite. Hardware is more reliable than software, which is more trustworthy than users, and the network is large and supports a bewildering range of applications. In essence, TCP/IP is not strongly layered enough. It lacks a modern naming and virtual addressing mechanism, leading to problems with security, performance, scalability, multihoming, and mobility for which resolution is hotly debated even among experts (43). That TCP/IP is in some ways inadequate is less surprising than that it works at all given the astonishing change that it has enabled.

TCP/IP is an example of how architectures that are well-designed for extreme robustness can create evolvability as a side benefit, perhaps the essential benefit of good architectures and the focus of the rest of this paper. Networked and embedded control computers may ultimately be a good source of metaphor and theory for neuroscience, because we know exactly how the system behavior depends on the technical details, and a rich and growing body of mathematics formalizes the insights (19). Unfortunately, these details are, by design, largely hidden from users, and although experts will find the previous discussion trivial and obvious, many readers may not. Also, despite abundant relevant tutorial material on computer architecture (less on networks), there is little discussion on which of its features arose from fundamental design vs. historical accidents of rapid evolution. For these reasons, we explore some additional case studies that are transparent and familiar but illustrative of the fundamental concepts of complexity, architecture, layering, and robustness.

Layered Architectures Simplified

Clothing and textiles represent a simple case study in network architecture and the role of robustness and layering, with paper as a special case. Although clothing may seem a frivolous illustrative example, it is based on many levels of complex technologies and reveals universal organizational principles, with details that are easily accessible to nonexperts. On the surface, each clothing module or garment (coat or socks) looks fairly similar, hiding chemical and physical differences in weave, elasticity, water-resistance, breathability, UV protection, and even insect repulsion. The constraints imposed by fashion trends on the success of clothing as a technology illustrate important points but will be deemphasized, and our consideration of the architecture of an outfit focuses more on essential function and robustness in harsh environments. The basic function of clothing is protection, providing comfort over a wide variety of external (weather and temperature) and internal perturbations (physical activity). Like other complex systems, complexity in clothing is driven by robustness to extremes more than by need to provide minimal function. Human skin seems optimized by evolution for dissipating heat during endurance running in the tropics (44⇓–46), and it offers little protection compared with heavy fur. Clothing provides that protection when needed.

Four fairly universal layers exist within textile architecture: (i) fibers that are spun into (ii) yarn or thread, which are woven or knitted into (iii) cloth that is sewn into (iv) garments. Cotton fibers are about 12–20 μm in width and several centimeters in length, roughly comparable with large neurons but with very different morphologies; 1 kg cotton has less than 1 billion fibers, large but still much less than the number of neurons in 1 kg brain, and the way in which fibers are interconnected is much simpler than neurons. Thus, in this simple but easily understood example of layering, the properties of textiles are not obvious from those properties of fibers. Tens to hundreds of fibers are spun into yarn and thread of essentially arbitrary length, which are woven or knitted into cloth that is nearly 2D and sewn into garments, also of arbitrary size.

This layered construction is much simpler, but it parallels analog to digital hardware to software and the polymerization of metabolic building blocks to macromolecules that assemble into networks and cells. In all of these examples, the layered architecture illustrates universal principles of organization and protocols for construction. Each layer has the large/thin property for which functional alternatives are almost unaccountably numerous but are nevertheless a vanishingly small fraction of all possible (e.g., random) configurations. Each layer must be exquisitely organized to produce the layer above it, which is not necessarily physically distinct. Garments are functionally distinct from the fibers from which they are physically composed, which is the same for cloth and yarn.

The complexity of the textile architecture is driven by robustness tradeoffs, because all of the layers from fiber to cloth can be completely collapsed to make paper, a nearly random connection of fibers with no intermediate layers. Paper is an extreme example of a degenerate special case of a layered architecture. Here, degenerate simply means that the constraints that define the architecture are relaxed or removed entirely. Additionally, with minimal additional complexity, paper can be sewn into specialized but unavoidably fragile garments. This finding makes clear that the complex internal, hidden layering is only for robustness and is not needed for minimal functionality, because paper can easily stand in for cloth in idealized environments. Similarly, small bio-inspired networks of metabolites and enzymes can be used to manufacture valuable chemicals, but they lack the robustness and evolvability of whole organisms. The overall textile architecture has persisted for many thousands of years (the bacterial cell for billions of years), whereas technologies within layers evolved rapidly.

One feature of the fiber to garment (i.e., garment/sew/cloth/weave/thread/spin/fiber) layered architecture is that it is robust enough that we can temporarily defer its study and focus on something even simpler, which is how individual garments are also layered to make outfits. Outfits for harsh environments typically have three kinds of layers. The outer shell layer protects from wind and water, the middle or insulation layer provides warmth, and the inner or base layer is comfortable next to the skin and keeps it dry. These three layers each are composed of garments, which have within them the fiber to garment layers. Therefore, the garment to outfit layering and the fiber to garment layering are, in some sense, orthogonal, although there is no standard terminology. This finding illustrates an almost trivial but nevertheless crucial feature of organized complexity. Because this overall architecture is intrinsically so robust, we can temporarily take 1D (fiber to cloth layering) for granted and view it as a platform for another simpler dimension of clothing, but one that also connects with more popular views of modularity, while still introducing some essential elements of architecture.

Layering of garments to make outfits is one obvious architectural feature of clothing providing robustness to environments. These modular layers are physically distinct (unlike fiber to cloth) and can be shed or reincorporated as needed. This finding has obvious parallels with software. Good programming practice includes breaking large algorithms into smaller subroutines with simple interfaces; this modularity is more familiar but less fundamental than the layering of analog to digital hardware to software that makes it possible in the first place. In the absence of robustness requirements, the necessary engineering aspects of architecture can recede, and clothing can become considerably simplified or elaborate (as dictated by fashion). In perfect environments, little or no clothing is required.

Similarly, even the most complex architectures allow for much simpler degenerate special cases (analogous to paper) under idealized circumstances. Tradeoffs abound within each layer in fabric, weight, cost, durability, and fasteners, etc. With changes in technology or conditions, garments can become obsolete or evolve (e.g., body armor and Velcro, etc.). Highly optimized, robust, and efficient garments that are finely specialized for a specific layer, body part, and individual are typically fragile to other uses (other layers, body positions, or wearers of different size and shape) and may be costly. Simple wraps or rags are very versatile but at best, yield outfits that are fragile to environment and movement. Most garments fall between these extremes.

If we knew nothing about the layering of garments, we might learn little from observing intact outfits, but we could begin reverse-engineering the architecture through lesions or knockouts in controlled experiments. These experiments might require harsh experimental conditions and perhaps, appropriately instrumented crash dummies. Damage or loss of a garment layer can cause very specific loss of robustness: outer layer to wind and/or water, middle layer to cold, and inner layer to comfort. Changes to fiber types, yarn, or sewing could be lethal at different levels, revealing their functional role. Most informative would be small changes with large consequences, such as unraveling a seam to reveal the role of sewing in garment construction or disruption of a weave or knit to reveal its role in cloth integrity.

Architecture as Constraints That Deconstrain

The view of architecture as constraints that deconstrain (17, 18) originated in biology, but it is consistent with engineering (16) and illustrated by clothing. A robust architecture is constrained by protocols, but the resulting plug and play modularity that these shared constraints enable deconstrain (i.e., make flexible) systems designed using this architecture. Constraints give a convenient starting language to formalize and quantify architecture and ultimately, a mathematical foundation (19). Concretely, consider a given wardrobe that is a collection of garments and the problem of assembling an outfit that provides suitable robustness to the wearer's environment. Three distinct but interrelated types of constraints are universal in clothing as in all architecture (16): (i) component (garment) constraints, (ii) system (outfit) constraints, and (iii) protocol constraints. Therefore, in combination, diverse, heterogeneous components (garments) that are constrained by materials and construction combine synergistically (through protocols) to yield outfits that satisfy system constraints not directly provided by any single component. We will use outfit to describe a functional, robust set of garments, and heap (Craver uses aggregates) (47) to describe a random collection not required to have any other system features.

The protocols that constrain how garments make outfits are simple and familiar, and a minimal view is that each of g garment categories (e.g., socks, sweaters, coats, boots, and hats) is constrained to a specific layer and body position and thus, to a specific and essentially unique location within an outfit. Suppose, for simplicity, that a wardrobe has n garments of each type for a total of ng garments. If any of the n garments of a specific type can be part of an outfit, then there are a total of F = n^g possible outfits. For example, for n = g = 10, there are ng = 100 total garments but 10¹⁰ (10 billion) distinct outfits that obey the layered architecture. However, there are 2^ng subsets or heaps of ng garments, and therefore, if protocols are ignored, the number of unconstrained garment heaps is vastly larger. For n = g = 10, there are 2^ng > 10³⁰ such heaps, and therefore, heaps chosen without regard to protocols have a vanishingly small chance of being outfits (another example of large/thin).

The discussion of clothing so far provides only a static view of architecture. In reality, the core of good architecture is ability to facilitate change over many timescales, including overall architecture (millennia), manufacturing technology (centuries), garments (decades), and outfits (daily). This example can be expanded to hint at the dynamic and control dimensions of both us and our clothing. Well-constructed outfits respond so automatically to movement that wearers can normally ignore the hidden internal complexity that makes this possible, just as we do the control of movement itself.

The roughly minute to hour timescales needed to assemble outfits also illustrate the role of dynamic control within architecture. The most obvious control is the actual forward assembly of a specific choice of g garments into a layered outfit. Most of the protocols that govern this process are readily learned by children, although specialized garments may require complex control (e.g., bowties and shoe laces). Ideally, the protocols are complete enough that any outfit made that obeys them will automatically satisfy system constraints (this is rare in engineering, because it is hard to design protocols with such guarantees). Humans easily visualize (simulate) what an outfit will look like from seeing the separate garments, but often, they still need to try them on to be sure of details of fit and appearance. Our simulators are robust but imperfect.

More subtle and complex (and less easily learned) is the backward process of choosing these garments to match the day's specific systems constraints, which are most dependent on weather and the wearer's activities. This process takes simulation to another level. Because layering allows dynamic reconfiguring of an outfit in real time, this backward selection control or management process potentially interacts with forward assembly control on all time scales. The backward process of choosing components is typically much more complex (and less obvious) than the forward assembly process, and this process can lead to confusion about the role of control and feedback in architectural design. Hopefully, in this concrete example, the processes are obvious, even if the language for describing it is inadequate.

On longer time scales (days to decades), the user might assemble a wardrobe of garments, again guided by the overall architecture by which garments make outfits. Manufacturing technologies can change on year to century timescales but must both reflect the architecture and only slowly change aspects of it. New technologies (such as spandex and Velcro) relax component constraints and allow new systems without fundamentally changing the architecture of clothing, which has persisted for millennia. Here again, in the engineering context, robustness largely drives complexity, because without changing system and component constraints, the protocols and control processes for connecting and reconciling them could be vastly simpler (e.g., standardized uniforms).

Bowties, Hourglasses, Pathways, Flows, and Control

Another aspect of constraints that deconstrain is the relatively small diversity in the protocols and processes that connect layers and enable vastly greater diversity in the materials that constitute a layer. This aspect of architecture can be visualized as a bowtie or hourglass (depending on whether layers are visualized horizontally or vertically) (27). For example, the fairly universal, homogeneous process of sewing (the bowtie knot or hourglass waist) takes an almost unaccountably greater and extremely heterogeneous diversity of cloth (fanning in to the knot) into an even greater diversity of garments (fanning out of the bowtie). Similarly, the reactions and metabolites of core metabolism are largely universal, connecting extremely diverse layers of catabolism to moderately diverse biosynthesis. The basic processes and codes underlying transcription and translation are highly conserved, but the specific genes and gene products are extremely diverse.

After the diverse garments sewn from cloth become components in the layered outfit architecture, they are categorized into the much less diverse types of garments and assembly protocols that, in turn, make a hugely diverse set of outfits. Threads and yarns are more diverse than the few canonical weaves, knits, or knots that create diverse textiles. The least diversity is in the fibers (from plant, animal, mineral, and synthetic origins) and the spinning processes that make yarn and thread. (What are vastly diverse are the geographic origins of these fibers.) Thus, the great diversity and heterogeneity within each layer also varies among layers, and it even depends on the categories used to define diversity. Garments (or cells) are unaccountably diverse and deconstrained when viewed in detail as the result of the garment/cloth/yarn/fiber (or DNA/RNA/protein) architecture but much less so when viewed as satisfying system constraints of that architecture, the component constraints of the outfit architecture, or the constraints on cells or cell types. The protocols between layers are typically more fixed and much less diverse by any measure than the layers that they connect.

Because they are the fixed points in robust architecture, when protocols are subject to attack, the system can fail catastrophically. Seaming is the protocol that sews fabric into garments, providing structure and function. Seams make the important difference between wraps and clothes, but they are the main source of clothing's fragile robustness. If the seam connecting the shoulder to sleeve unravels, a coat is useless. The greatest fragility of universal knots/waists is that they facilitate hijacking and attack by parasites and predators. Viruses hijack cellular transcription/translation machinery, and predators exploit the fact that they share universal and essential metabolic building blocks with their prey. In neuroscience, the role of dopamine in a robust and flexible reward system (knot of the bowtie) is fragile to hijacking by addiction (5). The stitches used in seams are not as tight as fabric weave and therefore, seams are internalized and often protected by lining, illustrating how good architectures allow hiding of necessary fragilities as much as possible. Our skulls, cardiovascular system, blood–brain barrier, and immune systems similarly protect fragilities of our brains to trauma, intense activity, and infection at the expense of the overhead to maintain them.

In both textiles and biology, obvious natural pathways and flows of materials and information assemble systems from components. Indeed, depicting these architectures in terms of pathways rather than layers has been the dominant view in science (and until recently, in engineering as well). Although not inconsistent with layering, the emphasis on a pathway view has limited our understanding of control, complexity, and robustness. Although the interplay between computational complexity, constrained optimization, and robust control has been deeply explored in the last decade, with broad applications including the Internet (19), power grids, and systems biology, no universal and accessible taxonomy for describing these various flows and their various complexities has emerged, even within engineering.

We already saw that the backward process of deciding on an outfit that satisfies the constraints of a given activity and environment is vastly more complex than the forward process that assembles the outfit from a set of garments. Similarly, the feedback control (e.g., of looms and sewing machines) within each layer of textile manufacturing is vastly more complex than the forward flow of materials from fibers to textiles. Additional complexity comes from the backward flow of textile design that turns constraints on textiles into specifications on the manufacturing processes as well as the supply chain management of the resulting process in response to customer demand.

Biology has similarly complex feedbacks. There are 10 times as many fibers feeding back from the primary visual cortex to the visual thalamus as there are in the forward flow (6). Wiring diagrams that include both autocatalytic (e.g., of ATP, NADH, etc.) and control feedback in metabolism are so much more complex than the usual depictions of relatively simple tree-like flows of metabolites that they are rarely drawn in detail except at the level of small circuits. Even complete wiring diagrams do not reflect the true complexity of control (20). The control of transcription and translation is vastly more complex than the basic forward polymerization processes themselves. Although we have no difficulty understanding the basic nature of these feedbacks and their roles in these specific architectures, the lack of an adequate language to generalize and/or formalize is still a roadblock, especially because engineering jargon is domain-specific and heavily mathematical.

Hidden Complexity, Illusions, and Errors

Related but important research themes can be mentioned only briefly while recapping the main points. For example, the emphasis on dynamic and mechanistic explanations in the philosophy of neuroscience (47⇓–49) is compatible, is complementary, and hopefully, can help lead to a more coherent and consistent shared language, which is desperately needed. The dangerous illusions and errors that plague individuals are often amplified by institutions, and this finding is relevant to engineering as well, because policy and politics often trump technology (39). Arguably, the most dangerous and pervasive of popular illusions is that our actions are unconstrained by hard tradeoffs, a problem increasingly acute in everything from teaching evolution to dealing with global warming. A unique case study in human error, because it is entirely within science, is the genre of research that has dominated mainstream literature for decades under the rubric of new sciences of complexity and networks (NSCN). NSCN is relatively new in neuroscience, but it already has an appealing narrative (50) and extensive and accessible reviews (51, 52). Claims that NSCN has been a success in other fields (50⇓–52) are supported by impact factor measurements, but NSCN has led to persistent and systematic errors and confusion that show no sign of abating (refs. 16 and 30⇓–32 and references therein). Although the goals of NSCN research are somewhat consistent with our goals, particularly in neuroscience, the methodology is not. Most concepts and terminology in NSCN do not overlap with control theory, but those terms that do overlap can have opposite meaning. A thorough discussion is beyond the scope of this paper, but a simple instance is illustrative.

Engineered and biological systems necessarily make ubiquitous use of nonlinearity, recursion, feedback, and dynamics, which in NSCN, are almost synonymous with unpredictability, fractals, self-similarity, or chaos (16). In engineering, quite the opposite is true. For example, the amplifiers in the sensors and actuators that enable robust controllers are necessarily extremely nonlinear. Digital computers are recursive and also extremely nonlinear (i.e., switching using transistor amplifiers in hard saturation) but are the most repeatable complex systems that we build. Ironically, to a naïve observer, the analog behavior of the billions of transistors (each much smaller and simpler than a neuron) per chip in a computer might seem bewilderingly noisy, chaotic, and unpredictable, with no hint of the almost perfectly robust, repeatable digital behavior that results at the interfaces and that engineers use to build systems. Of course, this finding is exactly the purpose of the very special large/thin/nonconvex organizations that constitute digital/analog and other forms of layering. This finely tuned, hidden diversity and complexity underlying robust systems are also the opposite of complexity in NSCN, which emphasizes minimally tuned, mostly random interactions of large numbers of homogeneous components that yield surprising emergent self-organization and order for free (50⇓–52).

Recall that, in the clothing example, for a fixed number of garment types g, the number of outfits F = n^g is constrained to polynomial growth in the number n of each garment type, whereas all possible heaps grow exponentially in n. A related source of confusion in biology is whether biology is fine-tuned vs. robust, as if these types were mutually exclusive. There is robustness in the large (polynomial growth) sets of structured and functional networks and fine-tuning that makes these sets a thinly small subset of the vastly larger (exponential growth) set of random nonfunctional networks. Highly evolved biological systems are large/thin and both fine-tuned (obey strict and far from random protocol constraints) and robust. Indeed, this finding is the essence of constraints that deconstrain and a necessity, not a paradox. The connection between the large/thin feature of neural circuits (1) and robust control is even deeper, which is sketched above.

In a completely different direction, research on human evolution has recently exploded in both depth and accessible exposition (44⇓–46), and the picture emerging is also complementary and compatible to ours. Compared with other great apes and top predators, humans are physically weak and slow with thin skin, no protective fur, and small guts that digest raw food poorly, all possibly fragile side effects of evolved robustness to running long distances in hot weather (46). When paired with even minimal technologies of weapons (e.g., simple sticks and stones), fire (for cooking, protection, and warmth), and teamwork, we go from helpless prey to invincible top predators (45), whose main threat then comes from other, similarly equipped humans. Our layered biological architecture of brain to mind is now augmented by layered technological architectures such as fiber to garment to outfit, metal to tool, weapon, machine, analog to digital, hardware to software, all of which expand the cognitive niches (44) in which we can robustly function. We have now eliminated our fragilities to our environment but replaced them with new and potentially catastrophic fragilities of our own making.

The tradeoffs that we see throughout these architectures and systems between efficiency and robustness, as well as between robustness to various different perturbations, are necessities and not accidents, although choices are still abundant within the resulting constraints. Versions of such tradeoffs can be formalized and made mathematically precise (20), and SI Text presents a simplified tutorial on the mathematics and model systems. More speculative but plausible is the claim that layered architectures are also necessary to effectively balance these tradeoffs, which is evidenced by their ubiquity in biology, physiology, and technology. That is, inner/lower layers are large/thin/nonconvex and must remain hidden within the system for robustness. For example, inner and middle garments must remain hidden behind the outer shell to provide comfort and warmth in a harsh environment, whereas the middle and outer layers must be segregated from skin for comfort. Because each garment maintains a separate identity that can be easily recovered by disassembling an outfit (or heap), this finding is perhaps the paradigm for modularity (51), but it is a very special case and on its own, quite misleading without considering the protocol and component constraints.

The component constraints on garments within the shell/insulation/base layering of outfits depend on material properties that derive from the orthogonal garment/cloth/yarn/fiber layering of textiles. In these orthogonal layers, garments are very special large/thin/nonconvex organizations of fibers/threads that must lose their individual identity. Loose threads (disobeying protocols even minimally) make garments fragile. Similarly, cells are a special organization of macromolecules, digital hardware of analog circuitry, software of hardware, brains of cells, and perhaps, minds of brains. If the brain is layered at the highest modular level (6, 15), roughly analogous to outfits/garments, then there is an orthogonal layering of tissues down to cells down to macromolecules that occurs within each of the macro brain layers, analogous to the garment to fiber layering.

In all of these layered architectures, the virtualization of the lower layer resources is an illusion that can be maintained almost perfectly in normal operations of minds, outfits, machines, and computers. The hidden complexity is primarily needed to create this remarkable robustness and evolvability, not minimal function, and it is only revealed by pushing systems to their extremes by perturbing the environment or components in lower layers outside the constraints that the systems evolved to handle (3⇓⇓–6). After the layered architectures are in place, both our minds and software are free to rapidly evolve independently given the right environment, although the large differences between digital and brain hardware imply very different constraints (6). This plasticity is one of the main benefits deconstrained by the constraints of the bowtie/hourglass protocols that create the layering (17, 18, 27). The mind/brain layering is much more complex than the most complex current technology of embedded and/or networked software/hardware/digital/analog, but the latter would be utterly incomprehensible without the right conceptual framework, mathematics, and tools, most of which are still unknown or relatively new to neuroscience (7). We hope that the connections between neural and technological architectures will help to demystify some aspects of this complex continuum.