How to measure embodied intelligence?

Embodied intelligence (EI) summarizes design approaches that give robots efficient physical interaction with their surrounding environment. EI has, to date, found an extensive descriptive treatment yet lacks universal metrics. Could we quantify EI? What would be the EI analog to intelligence quotient (IQ) in humans? We first suggest an intelligent unit (intel-unit) as the smallest entity that displays program execution beyond simple stimuli-responsiveness. The emergence of EI by situatedness of encoded physical agents in an environment is explored in three case studies. First, an awn of a wild oat – a non-living structure in nature that satisfies all robot’s descriptions – is analyzed in terms of material-level intelligence. Next, a jocular quantitative scale found with a popular gadget – the ‘fortune teller fish’ – is given treatment in the EI context. Finally, the learned and summarized EI principles are tested on a well-known object with perceived intelligence yet lacking a consensual robotic description – a knitted woollen sweater. We confirm the necessity of treating environment interactions in expressions and definitions of EI, as situatedness is central in defining functionality. Universal metrics would identify non-intuitive representations of EI and lead from empirical to model-based design of unconventional robots. Robots that engage situatedness provide a physical interface to artificial intelligence, similar to our bodies communicating with our brains.


Introduction
Intelligence, either 'biological' or 'artificial,' appears as a nebulous entity without size, shape, or weight.Modern 'cloud' computation further disarrays the idea of the physical embodiment of intelligence -almost rightfully so.First, let's ask how intelligence manifests itself in the physical world.Any machine computation in today's convention entails physical electron transactions in arranged field-effect transistors to algorithmically process information.The code and information are stored similarly: as an increased electron density in gates of tiny electronic capacitors forming memory arrays.Thus, even artificial intelligence (AI) is conditionally embodied, as it does have a traceable physical representation.We could localize the AI, yet the users barely know (and it hardly even matters) if a particular AI algorithm is physically being executed on their smartphone or a server cluster across the ocean.Even probabilistic machine learning algorithms reach a comparable outcome in any syntactically compatible computation device, regardless of their physical location or working principle.Indeed, AI is inevitably situated, but it very seldom engages situatedness.Remarkably, synaptic transactions in the brain appear to emerge from hard-wired neurons; yet only to be connected to a situated network of neurons throughout the body, constituting a certain level of EI.
All fields in science benefit from having objective traceable metrics that allow reliable comparison between the works of different scientists, may they be as fundamental as the meter for length or as complex as IQ.Quantification (or quantitation), central to the scientific method, 1292 (2023) 012002 IOP Publishing doi:10.1088/1757-899X/1292/1/012002 2 entails the act of measuring (including counting) to transform human sensory observations and experiences into numerical values [1].Inevitably, EI, as any intelligence, is highly contextual and arguably subjective, yet systematic metrological approaches are essential for comparison or benchmarking.A reproducible (i.e., precise) and valid (i.e., accurate) quantification process must be operationally definable.
Indeed, When considering intelligence, the path of quantification is far from straightforward.Human intelligence, for example, generally attributed to cognitive ability, is measured by one's ability to perform a given task based on reasoning, quantified by a standardized score, i.e., intelligence quotient (IQ) [2].Although a single underlying construct, i.e., the general intelligence factor (g), has been used to quantify abstract thinking, theories on the existence of multiple intelligences have been postulated [3].As a result, scientific consensus on the standardization of measuring human intelligence is still an open question.
Quantification of artificial intelligence (AI) has shown the importance of having an adequate understanding of the quantifiable subject.The quantification of AI has changed in time due to a better understanding of objectives and human intelligence as the main comparing element, creating an iterative loop [4].Turing test [5] was the first quantification of machine intelligence by evaluating if a human evaluator can reliably distinguish a human and a machine in a natural language conversation.The Turing test has shortcomings as the list of possible expressions of AI has expanded (e.g., problem-solving, decision making, learning [6]), and other tests (such as ImageNets test [4]) have been devised to comply with these expressions.
Although intelligence quantification is already challenging in the biological domain, let's ask an even intriguing yet practically essential question: could we measure embodied intelligence?
In an attempt to isolate embodied intelligence (EI), let's exercise our brains to define the smallest physical unit (with a finite size and shape, thus embodied), the intel-unit, that we recognize and accept as physically intelligent.Isolation of intel-units gives us the first practical tool for measuring EI -by counting.
In the quest for an intel-unit, let's first observe robots that we currently associate with intelligence.In the literature, we are first obstacled by the terms 'smart' or 'intelligent' materials that actually refer to stimuli-responsiveness.As a representative example, would material's swelling (i.e., increase in volume and dimensions) upon exposure to water vapor suffice for intelligent behavior?As an argument in favor, a piece of hygroscopic material displays the highest possible degree of multi-and combined functionality (a cornerstone in soft robotics narrative), as it detects humidity and reacts to it to a defined extent at a molecular level.It appears like a perfect closed-loop control!Yet, treating swelling as an act of computation is barely convincing to anyone.
A higher swelling rate hardly makes one hygroscopic material more intelligent than another.In a similar line, extensive parameters such as weight are hardly any better candidates as intelligence metrics.Yet, sometimes we perceive 'material intelligence,' whereas the connection of this concept to measurable material parameters is not straightforward.The structure in which the material is arranged gets us warmer.Yet, a physical parameter such as fiber density, analogous to transistor count in a microprocessor, barely directly scales with intelligence.If a parameter scales in meters, it probably does not in intelligence.For intelligence comparison, we should look at the program code instead, not trivial in material-encoded robots.
Although anything that could be called a conventional EI robot is still to be established, the most unconventional robots are probably the best to be isolated for exploring the extent of the validity of theoretical assumptions.We consider it safe to assume that a structure with EI also shares the minimum defining requirements for any robot: sensing, actuation, and execution of code.Vice versa, the presence of an executable code of any description could define a finite level of intelligence.

Case studies 2.1. Case study 1: awns of wild oat
The awns of wild oat appear to satisfy all requisites of a robot.As they detach from the plant, the seed-carrying awns are non-living structures that execute a program aimed at better seed dispersal and plantation [7,8].The awns react to humidity by twisting their helical structure made of hygroscopic fibers of cellulose.Indeed, the swelling of awns upon exposure to a humid environment and the kinematic amplification of movement by a twisted structure is generally well-understood from a physics and material science point of view at the structural and molecular level.Yet, the microarrangement of linear actuators for joint rotational actuation barely attests to any description of intelligence.The movement per se governs sensing and actuation, but apparently not the code.So, where is intelligence in an awn?Indeed, when an awn would be observed in an isolated condition, for example, fixed by its base in a humidity chamber, we could easily observe its complex kinematic choreography.The code gets apparently deciphered, but it does not make much sense.However, when exposed to a highly diverse natural environment at the soil surface, the twisting awns interact with the surrounding structures (such as plant debris or roots) so that the likelihood of burying the seed would statistically increase [9].Situatedness defines the mission plan of awn-robots.The program code is next to impossible to decipher without considering the environment.Situatedness appears to be a defining aspect of embodied intelligence, manifested by algorithms that produce environment-dependent results.The program code for EI entails, per minimum, three interconnected levels: materials + structure + situatedness in an environment.In isolated conditions, the choreography, although extremely elaborate for its simple structure, is deterministic.Thus, awns fixed on a lamp do not suffice for deciphering of the encoded seed dispersal mission.
One pair of awns, or actually an attached pair of awn-carrying florets (Figure 1), appears a good candidate as an intel-unit.Upon disassembly of an awn-robot, all its components would react to stimuli (humidity) (using energy harvested from the environment for movement).Yet, it would break the program code to an undecipherable level.The robot's parts apparently make calculations, yet not in a strategically meaningful way.One pair of awns is a minimum unit that embodies intelligence.
The awn-bearing wheat seeds deploy in pairs, allowing the individual awns to temporarily cross-entangle and suddenly release the energy collected during the entanglement phase, enabling fast movements.Such function is not apparent ex-situ but becomes evident when random interactions with the environment necessitate stimuli in a broad frequency spectrum.Equally important is the inter-robot, i.e., between two awns of a seed pair, interaction: the awns do not have any interconnection than a rigid structural link that holds them together.The awns experience a rich interaction mediated by the random interactions at the robot's surface.Consequently, the environment not only contributes to the code and acts as a randomizer.The awn's code exemplifies the engagement of intrinsically random interactions for defined action.
Two situated awn pairs (each intel-unit, as suggested above) pose an intriguing perspective.In addition to facilitating random interactions, the environment appears to interconnect different intel-units for intelligent cooperation.Thus, for intelligent cooperation, the intel-units may interact internally or externally.In this example, information transfer between intel-units occurs via the robot-environment interface.Randomized interaction between intelunits is much richer and more potent than being strictly 'connected' would allow.
Remarkably, in a wild oat, we could not evidence intra-robot information transfer in any more sophisticated form as simple delivery of force through mechanically bonded units, as the same fibers that sense humidity express their swelling response locally.Indeed, we isolated an intelligent agent with only local expression of responsiveness but displaying intelligence as a whole.
The awn's code does not involve decision-making by combining information from multiple inputs.Indeed, a practical embodied computer can be highly robust, well-evidencing Occam's razor concept for the simplest solution to win! 2.2.Case study 2: the 'fortune teller fish' The awns gave us the first evidence of EI quantification: by counting intel-units.Can we identify and isolate an example for continuous scale as well?Unexpected occurrences may teach us more than established ones!We note that our example of a continuous-scale EI is familiar to most readers -yet probably unrecognized as such: the commercially available 'novelty' product -"The Fortune Teller Fish" (Figure 2).Under this name, this popular magician requisite dates back at least two centuries.Today, similar products, probably by several manufacturers, are available in numerous retail stores.For those not yet come across one, a "miracle fish" exhibits different morphologies upon exposure to a wet palm.The more sweat on the palm, the more pronounced the morphological effect is.The 'miracle fish' is made from regenerated cellulose -a hygroscopic polymer sodium polyacrylate that bonds and retains water molecules.The swelling and drying cause changes in the shape of the molecules, which in turn bring the particular fish-shaped film to move its 'head', 'tail,' sides or curl up entirely.Remarkably, the product's packaging is accompanied by a scale that associates different movements with the participant's temperament, behavior, or mood.For example, held in a palm, the moving tail is for indifference, the moving head indicates jealousy, turning over is interpreted as falsehood, etc.The process is probably slightly empirical to be called a proper 'measurement,' yet an explicit scale provides more than a binary result.
Just like fish in nature needs water to survive, the 'fortune teller fish' needs some water to serve some insights into how to measure embodied intelligence.The polymer (the subject) is not intelligent per se.A sensing and actuating feedback loop is formed upon exposure to a wet surface (i.e., situated in an object, the environment).Through sensing, the perceiving subject and perceived object conclude a primary form of intelligence.Notably, the material of the 'fish' and its specific shape is essential to the code: the thickness and morphological features of higher (the tail) or lower (the head) determine curling patterns.The fish material, shape features, and the situatedness on top of a wet palm, could be seen as an intel-unit.
Intriguingly, instead of a palm, similar curling could be achieved above any humid surface, allowing us to observe the repetitive closed-loop interaction between (in)animate objects, similar to connected intel-units described in the first case study.It looks like the description of its behavior could be readily accepted and even fully described based on simple control theory.Yet, a loop may form as well elsewhere.When the 'fish' is held on a palm of an anxious participant (we can assume a palm more sweaty than in a relaxed state), the curling of the 'fish' visually announces anxiety, thus generating even more moisture on the palm (the environment).In this case, the temperament of the participant dictates the state of the natural environment situated on the palm forming a closed-loop information exchange with the 'fish.'

non-binary lookup table for interpretation of water-mediated information exchange on a wet palm
The nature of the environment, whether natural or simulated, determines the number of curls the fish would make, which plays an essential role in recognizing the nature of the loop, open or closed.

Case study 3: a woollen sweater
A woollen sweater is a well-comprehensible everyday item; yet, in our quest for unconventional robotics, let's assume here (provocatively) that a sweater also has the qualities of a robot!Among known robot descriptions, the presumed intelligence of a sweater is safe to be qualified as embodied.Arbitrary at first sight, applying robotic conventions to an unexpected item may bring light to the boundaries of EI.
To understand the nature of its intelligence, let us first zoom into a single woollen fiber -the essential bits being the cuticle and the cortex.The outermost surface of the fiber consists of overlapping cuticle cells that repel water, thanks to a chemically-bonded waxy coating.The cortex comprises two types of cells -ortho-cortical and para-cortical, each with a different chemical composition.The expansion of cells is moisture-dependent.The difference in expansion causes the fiber to 'crimp' or curl, allowing the wool to trap millions of tiny still air pockets, providing insulation.Consequently, a lightly-damped woollen sweater becomes crimper and, thus, warmer.An interplay between humidity-responsive materials and their hierarchical structure gives rise to complex behavior when situated in an environment.
A 'single' fiber on its own probably does not manifest the sweater's embodied intelligence.The cross-interactions between adjacent fibers, the arrangement of entangled fibers into bundles, and the number of loops made thereof already give us sufficient input to quantify the degree of warmth.How is it, however, connected to the goal of intelligence?For example, in coarser fibers, the para-cortical and ortho-cortical cells are arranged more randomly, providing less crimp, hence less warmth.A loosely-knit sweater with finger-sized holes would fail to give warmth to the wearer compared to that of a tightly-knit sweater.In both cases, the sweater still fails to decipher its final goal of intelligence.The presence of and experience by a wearer is a central consideration here.Unless coupled with the environment (i.e., in part the wearer's body), the sweater's qualification and quantification of intelligence are inconspicuous.For example, depending on the environment (dry or moist air; calm or sweating), the sweater executes a relevant code, keeping the wearer warm or warmer.Slightly similar to the 'fish' in the previous case study, human emotions and subjective perceptions are a part of the environment descriptions.The environment, in turn, constitutes an essential component of EI, as discussed above.
So, where is the intel-unit of a sweater located?Questioning the uncertainty, one might still argue the sweater as a whole represents a single intel-unit, and most rightfully so.As a single entity, a woollen sweater establishes a specific fiber arrangement and bridges the information exchange between the wearer and the environment.If this entity is cut in half -a piece of woollen cloth would merely display responsiveness to stimuli (humidity) locally by the fiber's inherent properties and arrangement.However, it would fail to decipher its mission of intelligence, a.k.a execution of the program code.The sweater code is written into the material by arranging the thread by knitting and sewing (Figure 3).The hierarchical nature of textiles implies a combination of defined and repeating elementary units for total code formulation.Specific knitting patterns define building blocks yet do not suffice as intel-units.One can practically program any form of code into the sweater to deploy pre-defined functions.However, the style of programming the code (encoding) is, obviously, much different than what is conventionally understood in digital coding [10,11].To understand this, let us look into the making of a woollen sweater from a hierarchical perspective.Starting from the origin -wool, while situated in a specific environment, such as on a sheep, expresses material-level intelligence necessary to regulate humidity and keep the sheep warm.Once the fleece is scoured off from the sheep, followed by carding and combing the felt and twisting it into yarn, one can add different levels of 'material intelligence' that define the responsiveness of the material (strength, friction, etc.).Finally, when the fibers are knit into a sweater, a program consisting of loops as mesoscale building blocks is executed.Knitting determines the final set of properties -shape, size, and specific interaction with the wearer.One can alter the code without changing the core material (fiber).Similar to both previous case studies, the material, structure, and environment work in unison in defining the sweater code.By taking into account -the environmental variables, the wearer's body, and the arrangement of fibers to interact and exchange information from and to the wearer, the intended program can be indeed encoded (at least altered) by modifying only the fibers or only the arrangement of fibers.The processing steps applied throughout the wool's journey from sheep to sweater bring changes to its macroscopic structure beyond recognition, yet the reshaped (and resituated!) intelligent agent performs a remarkably similar mission in negotiating the cold weather.A changed situatedness thus may require an unrecognizably different structure to encode a similar behaviour.
Indeed, different wool types do create an empirically felt difference.Well-pronounced in a sweater, the adaptive properties can assume a central role in material-level EI.As an observation, the sweater's interaction with the wearer's body allows it to conform to its shape with extensive wearing and learning, manifesting bidirectional, environment-mediated communication between intel-units (one of which being the sweater, the other may be the wearer).The intelligent loop between the wearer and the environment could be fragmented into functional feedback keeping the wearer warm and emotional feedback that may be determined by protective heritage signs, symbols, and colors that could provide emotional support and protection.The fiber properties can measure the former, functional intelligence, for instance, by analyzing the sheep breed and the climatic variables that influence the fiber to be either more adaptive to the climatic fluctuations or not.Additionally, one could measure the yarn and its mechanical properties, quantify the degree of warmth dependent on the knit and seater patterns, and measure felting that occurs with wearing.Traditional craft techniques appear to have definite signs of intuitive EI engagement.
How could we measure a sweater's embodiment of intelligence?In countable intel-units, the previous discussion reached a unity result.Could we quantify the sweater's emotional intelligence as a function of time?Could we measure emotional support expressed by wearing protective colors and heritage symbols [12]?Yet a compiler for implementing specific tasks in a thread is still to be developed.

Conclusion
We explored the origin and essence of EI in three case studies (Figure 4) at (or probably exceeding) the consensual boundary of robotics.In all cases, the elementary (bio)material (micro)structure, chemistry, and responsiveness are generally well-accessible to scientists to characterize quantitatively.We intuitively assume some degree of EI in each of the three examples.Yet, even with the complete (mechanical and chemical) blueprint in our hands, we struggle to decipher any meaningful EI code.In two of the latter case studies, the macroscopic arrangement of biomaterial is entirely defined by humans, so the blueprint is original.Consideration of situatedness in and interaction with the environment provided the necessary link.In none of the analyzed cases, we could identify more than one intel-unit, suggesting the environment as a universal relay between individual intel-units.For consistency, it probably makes sense to consider humans as individual intel-units in communication with other intelligent agents, be it even a sweater around the body or a 'fish' on the palm.Randomizing the effect of the environment may reason difficulty in establishing analytical, causal relations between the code features and the product, especially when the outcome is of emotional or otherwise subjective nature.The naturally occurring robot -the wheat awn -confirmed the universal nature of EI and the inability to decipher its code ex-situ.After identifying, a broad and systematic understanding of EI principles enables us to approach design at an entirely new level, functionally combining robotics, biology, and cultural heritage.

Acknowledgments
This research was supported by the Estonian Research Council grant PRG1498, PRG1084, H2020 project TWINNIMS (Grant agreement 857263), and the Estonian Centre of Excellence in ICT Research.

Figure 1 .
Figure1.Hygrochoreography of wild oat's awns.Awns made of twisted hygrpscopic fibers respond to humidity change by fast and extensive movement.In isolated conditions, the choreography, although extremely elaborate for its simple structure, is deterministic.Thus, awns fixed on a lamp do not suffice for deciphering of the encoded seed dispersal mission.

Figure 2 .
Figure 2. Non-binary scale for EI.The gadget 'Fortune Teller Fish' is accompanied with a non-binary lookup table for interpretation of water-mediated information exchange on a wet palm

Figure 3 .
Figure 3. Encoded wool.Reshaping and re-situating a responsive biomaterialwoolas a new intelligent agent.In a new situatedness, the wool macrostructure is changed beyond recognition, yet encodes a remarkably similar program.

Figure 4 .
Figure 4. Case studies for EI.Synthetically or naturally encoded biomaterials express their mission when situated in an environment.Three levels -materials, structure, and environment considered together form an intel-unit.