Michael E Hochberg
email: michael.hochberg@umontpellier.fr

A Theory of Intelligences: Concepts, Models, Implications

Keywords: affordance, complexity, crystallized intelligence, difficulty, efficiency, evolution, first principles, fluid intelligence, goals, information, knowledge, life, models, priors, recombination, skills, surprisal, system, uncertainty 1

Intelligence is a human construct to represent the ability to achieve goals. Given this wide berth, intelligence has been defined countless times, studied in a variety of ways and quantified using numerous measures. Understanding intelligence ultimately requires theory and quantification, both of which are elusive. My main objectives are to identify some of the central elements in and surrounding intelligence, discuss some of its challenges and propose a theory based on first principles. I focus on intelligence as defined by and for humans, frequently in comparison to machines, with the intention of setting the stage for more general characterizations in life, collectives, human designs such as AI and in non-designed physical and chemical systems. I discuss key features of intelligence, including path efficiency and goal accuracy, intelligence as a Black Box, environmental influences, flexibility to deal with surprisal, the regress of intelligence, the relativistic nature of intelligence and difficulty, and temporal changes in intelligence including its evolution. I present a framework for a first principles Theory of IntelligenceS (TIS), based on the quantifiable macro-scale system features of difficulty, surprisal and goal resolution accuracy. The key advances of this theory are the partitioning of intelligence into (1) uncertainty reduction ("solving") and goal accuracy ("understanding"); (2) challenges in the forms of goal difficulty and goal surprisal; (3) temporal spaces, including past sources, present proxies, environments and the core system, present and near-future transmission, and distant evolution. The proposed partitioning of uncertainty/solving and accuracy/understanding is particularly novel since it predicts that paths to a goal not only function to accurately achieve goals, but as experimentations leading to higher probabilities for future attainable goals and increased breadth to enter new goal spaces. TIS can therefore explain endeavors that do not necessarily affect Darwinian fitness, such as leisure, politics, games and art. I conclude with several conceptual advances of TIS including a compact mathematical form of surprisal and difficulty, the theoretical basis of TIS, and open questions.

DEFINING INTELLIGENCE

The famous quote "information is the resolution of uncertainty" is often attributed to Claude Shannon 1 . This statement is somewhat tautological since information relates to the inverse of uncertainty. But what Shannon's seminal 1948 article "A mathematical theory of communication" and the above quote more interestingly indicate is that information is a potential: order in the environment that can be perceived, filtered, deciphered, recombined and applied towards a goal. Shannon had previously equated information with intelligence in his 1939 correspondence with Vannevar Bush2 , but as we will see below this is but one (important) element of intelligence. By associating 'the use of information in resolving uncertainty' with 'the resolution of a goal', one arrives at the conjunction: intelligence is the resolution of uncertainty towards the resolution of a goal. One also arrives at the implication that intelligence is an operator that increases information. My objective is to unpack this simple statement towards a more inclusive definition of intelligence and propose the Theory of IntelligenceS (TIS). I do not discuss the evaluation of intelligence in detail, for which the recent overview by Hernández-Orallo [START_REF] Hernández-Orallo | The Measure of All Minds: Evaluating Natural and Artificial Intelligence[END_REF] sets the stage for AI, but also yields insights into animal intelligence and in particular, humans. I do not discuss specifics of different abilities such as creativity, emotional, social and collective intelligence, and physical agility, nor goals such as expression, problem solving and seeking opportunities.

The above and other definitions of intelligence 3 have in common the ability to deal with uncertainty (see Glossary for definitions). Key is the arc of acquiring and using knowledge and skills in new situations. Producing a correct answer to what others would regard as a difficult problem does not necessarily invoke intelligence. Think of a computer simply executing an algorithm to correctly generate the next prime number beyond one inputted by a programmer. The programmer may very well be impressed by the computer's performance, particularly if the answer is rendered in less time than for smaller prime numbers! In this narrow comparative sense, if the programmer did not know that the faster computation was in fact made possible by another programmer surreptitiously updating the computer's internal algorithm, then the computer would appear to the impressed programmer as having learned something from past experience -an indicator of intelligence. This concocted scenario turns out to contain elements -notably relativity and regress -complicating assessments of intelligence.

As we will see below, relativity and regress are central to the larger picture of intelligence. The most familiar demarcation of relative comes from the Turing test -the assessment by a human as to whether a hidden entity (Turing himself took this as a computer) could pass for a human [START_REF] Turing | I.-Computing machinery and intelligence[END_REF]. Beyond the subjectivity of such an assessment and therefore its statistical nature when evaluated by a large sample of observers, the question is whether intelligence is a property completely intrinsic to the entity being assessed. This is the problem of regress. Is a machine programmed to solve a problem no human can solve, intelligent? After all, the machine is just a robot following orders. But if not in the machine, where lies the intelligence? The programmers who wrote the algorithm? Or perhaps the engineers who designed the machine? The person or entity posing the problem in the first place? Or the person who realizes that only this machine can solve the problem? An entity's intelligence necessarily derives -completely or in part -from multiple sources, each of which derives from its own sources, and so on. 4I will refer to computers throughout this essay since they embody what we often associate with intelligence5 : process efficiency and accuracy. Computers and artificial intelligence more generally -even if performing impressive feats from a human perspective -are still far simpler than biological systems and humans in particular [START_REF] Roitblat | Algorithms Are Not Enough: Creating General Artificial Intelligence[END_REF]. The main features added in the huge and fuzzy steps from machine to human intelligence are goal definition, reasoning and flexibility, but also environmental sensitivity associated with active inference [START_REF] Korteling | Human-versus Artificial Intelligence[END_REF]. By virtue of our large brains, problem-solving abilities and planetary dominance, we as humans are arguably ipso facto the most intelligent entities on Earth. But even if correlating with certain definitions of intelligence, brain size, cognitive performance and world influence do not define intelligence. Rather, as discussed below, intelligence is the ability to operate in the relevant world: in ecological parlance, single or multi-dimensional niches, and have the latitude to explore and push the boundaries of these niches.

Intelligent entities have a model of their world 6 . Active intelligence becomes possible when the model has the flexibility to address goals relevant to the entity. Simply possessing a model does not invoke intelligence. Thus, systems from atoms to molecules to gasses, liquids and solids are all governed by physical laws -models of a sort -but these laws, although capable of generating fantastic structures as diverse as crystals, water bodies and stars, are reactive and immutable: at sufficiently macroscopic scales, they always generate a finite number of behaviors. The laws of physics and chemistry can lead to a local reduction in information uncertainty (≈ entropy) and therefore a most primitive instantiation of intelligence, for example in the formation of crystals [START_REF] Damasceno | Predictive Self-Assembly of Polyhedra into Complex Structures[END_REF], [START_REF] Frenkel | Order through entropy[END_REF]. Applying the observation above that intelligence increases information and knowing that overall entropy increases in instantiations ranging from crystal formation to machine computation to biological organism problem solving, we come to the hypothesis that all intelligent systems decrease information entropy in some bounded space strictly relevant to the goal, but increase entropy overall. Minerals, computers and brains assemble information and in doing so, do work.

Laws apply to software employing immutable, deterministic, algorithmic models. Software functions in hardware environments with the user-defined objective of accuracy in goal completion based on data input, the extraction of useful information from the data and information processing by algorithmic models. In so doing, uncertainty is reduced typically in a stepwise forward, lateral or recursive fashion 7 . Goal achievement depends on the capacities and integration of hardware and software. Any given input always results in the same output as long as both software and hardware function are unaffected by random errors and there is no intentional randomness in the algorithm. Thus, a purely unthinking, deterministic computer can meet the barebones definition of intelligence being the resolution of uncertainty towards a goal. To apply broadly across both unthinking and thinking systems a more inclusive and nuanced definition is needed.

A Working Definition

Consider the following working definition A for intelligence:

A: The Use of Knowledge and Data Towards the Achievement of a Goal 8

A makes plain the temporality in intelligence. Uncertainty is reduced or abrogated through how knowledge and data are used towards a goal. The process requires integrating previously acquired knowledge and skills 9 and current data in an existing model towards a future goal10 , producing a desired result. Thus, the model is the pivot that both simulates and predicts. Although complex, the description of A could be considerably expanded (e.g., [START_REF] Chollet | On the Measure of Intelligence[END_REF]), but as developed below, these and other similar definitions can be distilled into a small number of abstract, yet meaningful parameters and processes. Consider Achievement of a Goal, which can be restated as:

B: Goal → y Path → z Result
Regardless of how hard the problem and ingenious the path underlying B, seen from the outside, the system might appear to be a mere reporter. If we could look inside of B in the limit of no computation, then the system is simply using input to find output from an existing list or Goal → Result. When some form of computation occurs, that part of intelligence operating in the latter part of A begins in B at → y : signal processing, simulation, interpretation and understanding, and eventual reformulation of the problem. It then engages in the decided method of computation to → z : predictive processing and checking for decision errors, prediction errors or insufficiency, and decides whether to go back to → y and possibly use what previously appeared to be useless information (or computational methods), or continue on and render the result. Intelligence is reflected in abilities to navigate novel situations so as to winnow alternative paths, extract useful information and detect and not waste time on useless confetti and noise [START_REF] Roli | How Organisms Come to Know the World: Fundamental Limits on Artificial General Intelligence[END_REF].

Minimizing decision and prediction errors through path checking and eventual correction and doing this at different organizational levels is part of what differentiates thinking from non-thinking systems [START_REF] Hohwy | The Self-Evidencing Brain: The Self-Evidencing Brain[END_REF], [START_REF] Tononi | Consciousness: Here, there and everywhere? Phil[END_REF]. Path choices in thinking entities may take the non-mutually exclusive forms of abstraction, stochastic choices, lateral thinking and experimenting new paths, transiently accepting absurdity, counter-intuition or sub-optimality, and looping backwards to revisit previous paths. Thus the prevailing view that trajectories are constrained to affordances (environmentallydependent opportunities and impediments) is an oversimplification of what in reality may be huge sets of alternatives based on the many ways that environments can be informative [START_REF] Roli | How Organisms Come to Know the World: Fundamental Limits on Artificial General Intelligence[END_REF]. Path trajectories become more difficult to predict as goals become more complex and agents less able to resolve goals of a given complexity.

Planning horizons are central to path efficiency and accuracy. In some ways analogous to the "adjacent possible" [START_REF] Kauffman | Investigations[END_REF], non-planned, myopic strategies tend to decrease the predictability of future path nodes and goal outcomes (Figure 1). A myopic path can as such manifest in anything from ingenious routes leading to a satisfactory resolution, to truncated or omitted routes leading to approximate or incorrect answers, to highly reticulated (stupid) routes that may or may not lead to any answer at all. . . or may indeed produce a correct answer. Thus, a tendency towards myopic decisions may either decrease or increase result sensitivity to the path taken depending on the topology of the continuously evolving landscape of alternative paths, such that more than one distinct path might lead to the same result and imperceptible differences among alternative paths may produce very different results. These observations reflect the microscopic basis for the macroscopic Theory of Intelligences proposed below. EXAMPLE 1. To see how parameters and context affect B consider the following example. You are a birder and walking through a forest, bird watching. Your eyes are in the forest canopy. Suddenly you hear a growl in the distance. You freeze and listen. You turn your head from side to side to gauge direction and distance. You estimate that the source is at about 100m, 45°to your right. By the nature of the growl and based on past experience you deduce it is likely a dog, but do not see the dog nor see or hear a possible owner. You wait motionless, now looking for an exit, either a path of escape or a tree to climb. There's no clear path to outrun an attacking dog and the closest tree that will support your weight is 10m in front of you. You quickly realize you are not a good climber, but there is little time to think, since the animal is now running and from the soundbites, it must be in your direction. You spot it and see it is a bear. Without thinking, you execute what you were told when you entered what is in fact a national park: Stand perfectly still. After a few scary minutes the bear leaves. You wait a few more and although in shock, you come away unscathed. Although unverifiable since a specific course of action was taken and no alternative could be tested, this appeared to be an intelligent response relative to others, including ignoring the growl, rolling-up in a ball on the ground, running away when seeing the bear approaching, or flailing at the bear once it was upon you. Your response was based on experience of estimating direction and distance and what an expert informed you to do in case of a bear attack. You now have a great story to tell.

Four Phases

Statement A says that B is embedded in something greater. Specifically, factors preceding and surrounding B predicate what happens in B [START_REF] Roli | How Organisms Come to Know the World: Fundamental Limits on Artificial General Intelligence[END_REF]. Factors preceding B include innate priors, accumulated knowledge and skills. Factors surrounding B are goal context and the environment. These sets of factors have been hypothesized to influence intelligence in complementary yet complex ways [START_REF] Chollet | On the Measure of Intelligence[END_REF]. Thus, what frustrates the descriptions in A and B -and for that matter any multifactorial definition of intelligence -is how each component is weighted in decreeing or quantifying intelligence. In this respect -and again simplifying -a central ambiguity of proposals A and B is the relative importance of marshalling priors, inventing, choosing or being confronted with a goal, articulating the path, and achieving the desired result. Clearly, each phase depends to some extent those preceding it. More interestingly, each phase can depend on predictions of those not having yet occurred. We can therefore further generalize B to how information is accessed, stored, processed and oriented towards a goal:

The main addition with respect to B is that goal → x and path → x ′ can be conditional on priors. Necessities such as food and shelter impose on lower-level priors (e.g., reactions to hunger and fear, and notions of causality), whereas opportunities such as higher education and economic mobility require high-level priors (e.g., causal understanding, learning ability, goal directedness) [START_REF] Chollet | On the Measure of Intelligence[END_REF]. The contingencies of goals and paths on priors -and more generally on stored informationwill figure in the TIS theory presented below.

The Challenge of Modularity

Assuming the inner-workings of a goal-seeking system can be understood, without a theory of intelligence (and even then) there is no objective way to apportion the relative weights among two or more of the phases in C. To better appreciate issues surrounding the modular nature of intelligence, I focus below on the path and the result. Many questions emerge. Is the path-component of intelligence the minimization of prediction errors, computational length, time or energy expenditure? Path simplicity? Understanding the path and why it works? Path creativity? Beauty? What if the path is ingenious, but the result does not meet the goal, due to, for example, either insufficient data or a momentary lapse in thought or processing? There are other possibilities. I may apply someone else's brilliant insight correctly (as might a computer) and swiftly solve a hard problem. Or, I may take an inefficient, reticulated path towards the correct answer. EXAMPLE 2 For illustration, consider two different algorithms available to an entity -an efficient (smart) one and an inefficient (stupid) one -each yielding an answer to the same problem. There are two outcomes for each algorithm. Stupid algorithm, wrong answer (0,0); Smart algorithm, but wrong answer (1,0); Smart, correct (1,1); And yes, especially for multiple choice questions, Stupid, correct (0,1). Undoubtedly, (1,1) and (0,0) are the maximal and minimal scores respectively. But what about (1,0)'s rank compared to (0,1)? If a multiple-choice test, then one gets full points for what may be a random guess and (0,1). If the path taken is judged much more important than the answer, then an interrogator would be more impressed by (1,0) than (0,1).

INSIDE INTELLIGENCE

Difficulty

Active intelligence can only express if there is some degree of difficulty involved in attaining a goal. In the above example, the birder had never before encountered a bear, this increasing surprise and effective difficulty of the situation, but the birder had the tools to assess, react to and resolve her predicament. The solution to the bear problem is actually very simple, don't move and stay silent, but the path to the solution is not at all obvious. In addition to understanding bear behavior, the solution requires overcoming fear. It would be unlikely for the birder to solve the problem based on related experiences. Rather, a short-cut is taken by applying the solution learned when entering the park.

Circumstances can be complicated and cloud the assessment of difficulty, but even should extrinsic influences be eliminated, it is an open question as to whether a first-principles theory of difficulty is even possible. As such, difficulty is the outcome of the intrinsic feature of complexity, the latter being goal characteristics independent of the solver. Loosely speaking, complexity is associated with some combination of path length (decision node number, internode (edge) lengths), multiorder paths (integration of multiple variables, inclusion of higher dimensions), and/or disjoint path grammar (network structure conditional on path segments so far taken). Unless agent capacities are low, dedicated intelligence is not necessary towards simple goals. Similarly, even at high capacity, an agent might waste time addressing extremely complex or complicated goals (but see § §7.2, 7.3 below). Although unexplored to my knowledge, I predict intelligence is most functional in some intermediate range of uncertainties and complexities.

Difficulty can refer to an individual's ability to achieve a given goal in a given context/environment, or be statistical, that is the fraction of agents capable of attaining a given goal in a given context/environment [START_REF] Beckmann | Beyond Psychometrics: The Difference between Difficult Problem Solving and Complex Problem Solving[END_REF], [START_REF] Pelánek | Complexity and Difficulty of Items in Learning Systems[END_REF]. Assuming a gradient in efficient solutions to each of a range of problems (equivalent to graded complexity), problem difficulty is reflected as the distribution in individual abilities for each of the problems and over the range of problems [START_REF] Benedetto | A Survey on Recent Approaches to Question Difficulty Estimation from Text[END_REF], [START_REF] De Ayala | The Theory and Practice of Item Response Theory[END_REF]. Thus, difficulty can be attributed to a single individual or a group of individuals confronting either a single, given goal, or graded sample of goal complexities. A potential issue with attributing difficulty is the extent to which the underlying system has ordered structure and can potentially be understood (i.e., complex), or rather disordered and cannot be understood (i.e., complicated). Intelligence applies to complex systems and (arguably) cannot be meaningfully expressed in complicated ones.

Efficiency and Generality

Intelligence is often evaluated as the result without sufficient regard to how the result was obtained. This is because the path can be complex or reticulated and -importantly as developed belowpartly or completely hidden from observers, whereas the result is the external, process-free, often tightly-packaged product 11 . As a consequence, an observer cannot always appreciate the level of ingenuity (or lack thereof) in the solver's method [START_REF] Stemler | Item Response Theory: Knowing When to Cross the Line[END_REF] -and indeed sometimes the solver can't appreciate it either! 12 Because the ingenuity of a method should negatively relate to the time it takes to complete a task, time is sometimes the only way to infer ingenuity. Ingenuity implies path intelligence, but a better, more measurable metric is efficiency. Efficiency is the tendency towards fewer path nodes and/or less time to achieve a given result (Figure 1C). Moreso than the ambiguous notion of ingenuity 13 , efficiency measures are expected to correlate strongly with the time it takes to achieve a goal.

To the extent that intelligence is reflected in path efficiency and result accuracy, a multi-layered understanding of the path -although fostering accuracy -could compromise efficiency. This is why using short-cuts based on prior knowledge (memory, reflexes, intuitions, skills, etc.) can be superior to needlessly computing or attempting to understand path decisions, be they second-to-second calculations or contemplative future planning [START_REF] Krakauer | The intelligent reflex[END_REF]. A magician, or for that matter a musician, accumulates knowledge and skills and may achieve understanding through learning, training and practice, but once mastered, uses skilled recall (i.e., unconscious automation for magicians; muscle memory for musicians) in execution. This suggests intelligence is both the higher-level knowing when to actively infer and/or reactively recall, and the consequential lower-level applying of one or both strategies. All else being equal there is an expected bias towards already available, fast, cheap memory rather than slower, more uncertain inference and reasoning 14 . This will be revisited below.

To understand efficiency as an indicator of path intelligence consider designed systems such as immutable computers and adaptive artificial systems. At one extreme, a computational device receives input, which might include data and algorithms, and then executes a program, producing output. This is what occurs everywhere from the simplest calculator to powerful but nonadaptive super-computers. At the other extreme (as I write) is the constellation of machine learning, adaptive machine learning, and deep learning [START_REF] Lecun | Deep learning[END_REF]. These systems improve scope and performance by training on what may be huge, but nevertheless finite, databases and/or learning from free experiences. Today's machine learning platforms include AlphaZero (deep learning) that can defeat any human in either Go or Chess. Certain machine learning platforms have been referred to as "pointalistic" [START_REF] Marcus | The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence[END_REF], meaning they are only as good as their trained coverage of the space of possibilities. Indeed, AlphaZeroGo was defeated by a human [START_REF] Marcus | David beats Go-liath[END_REF], but this failing is likely a one-off since (similar to humans) the program can learn to avoid previously unexperienced traps. All else being equal 15 , pointalistic lacuna will be greater for open learning systems such as self-driving cars compared to closed games such as AlphaZeroGo, the former thus requiring the sampling of more experiences and environmental contingencies than the latter for similar levels of performance.

An important mediator of efficiency is the scope of attainable goals. Current AI systems show narrow intelligence relative to humans, since the former are limited to a finite (and usually small) set of specific goals (e.g., [START_REF] Chollet | On the Measure of Intelligence[END_REF]). For example, self-driving cars live in the finite universe of what drivers can ask of a car. Even if there are many intermediate decisions (right turn, speed up, avoid collisions. . . ) leading to the ultimate goal (arriving at designated place), the universe is still the limited set of decisions and goals set for cars.

The modes and implications of generality in intelligence are little understood [START_REF] Chollet | On the Measure of Intelligence[END_REF], [START_REF] Flanagan | The Cattell-Horn-Carroll Theory of Cognitive Abilities[END_REF], [START_REF] Minsky | Minsky's frame system theory[END_REF], but to the extent that predictions from evolutionary ecology apply [START_REF] Futuyma | The evolution of ecological specialization[END_REF], then we might expect 13 Whereas accessing pieces to a puzzle in a stepwise, logical, efficient manner satisfies many definitions of intelligence, path ingenuity has no first principles basis, since it implies taking forbidden, illogical, experimental or random, turns, segments, or jumps to arrive at a priori unexpected trajectories towards a resolution. 14 Although to my knowledge not investigated, the free energy principle would predict an optimum allocation between these strategies. Free energy reduction through Bayesian updating and active inference delimits, gathers, filters and processes information using a world model [START_REF] Parr | Active Inference: The Free Energy Principle in Mind, Brain, and Behavior[END_REF]. Uncertainty is thereby reduced by predicting and anticipating environments and by triaging or even altering environments to better match model predictions. 15 All else is not necessarily equal. The learning curves will ultimately depend on probability distributions of experience types and the consequences of making errors.

greater adaptation and robustness for the limited number of local goals in specialized systems, whereas general intelligence systems should have greater flexibility (interpolation, exploration, extrapolation) to achieve a range of goals, but be subjected to tradeoffs [START_REF] Barbey | Network Neuroscience Theory of Human Intelligence[END_REF] -the latitude to be highly adapted (similar to specialized intelligence systems) on certain important tasks at a cost to performance on other more difficult, more peripheral, or less important tasks. Of course, many systems are not either/or narrow/general -there will be a continuum and the recently launched large language model GPT-4 is a good example of narrow AI having elements artificial general intelligence [START_REF] Bubeck | Sparks of Artificial General Intelligence: Early experiments with GPT-4[END_REF], [START_REF] Wei | Chain-of-Thought Prompting Elicits Reasoning in Large Language Models[END_REF] 16 . Akin to humans and ecological systems more generally, it is therefore reasonable to assume variation in capabilities across task types for AGI systems.

Despite ideas that generality is more advanced than specificity, debates about the importance or superiority of general intelligence risk being sterile, since the evaluation of intelligence needs be in the context of relevant goals [START_REF] Levin | Technological Approach to Mind Everywhere: An Experimentally-Grounded Framework for Understanding Diverse Bodies and Minds[END_REF], that is, the intelligence niche. Intelligence niches can be unidimensional (e.g., find prime numbers) or multi-dimensional (e.g., abilities to hunt and escape predators) and have distinct, fuzzy or discontinuous edges (e.g., difficulty trapping certain prey). Intelligence could be extended by (i) extending capacity niche boundaries (cf. pointillistic [START_REF] Marcus | The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence[END_REF]) or (ii) adapting to novel goal niches (general intelligence). The general intelligence promoting such extensions increases within human lifetimes [START_REF] Chai | Evolution of brain network dynamics in neurodevelopment[END_REF], [START_REF] Shaw | Intellectual ability and cortical development in children and adolescents[END_REF], [START_REF] Tourva | Cognitive correlates of developing intelligence: The contribution of working memory, processing speed and attention[END_REF] and increases through population time [START_REF] Burkart | The evolution of general intelligence[END_REF]. Both phenomena are particularly relevant to the current transition from AI to AGI, where humans are attempting to develop platforms with (human) thinking-like abilities [START_REF] Wang | On Defining Artificial Intelligence[END_REF], and once achieved, it is an open question as to whether such systems could autonomously acquire additional novel capacities.

Black Boxes

Intelligence is making what an observer regards as a difficult problem, look easy 17 . The processes inside the problem-solving system however could be anything from mechanical computation to imaginative reasoning, or some of both. Excepting the simplest systems and those amenable to revealing their inner logic, how can we really know what happens inside? EXAMPLE 3. Consider the quintessential magic trick of the rabbit pulled out of a hat. As in B: Goal, method, result. Only the first and third are known by spectators. The magician appears other-worldly, because he makes a hard if not impossible problem look easy. But the magician's resolution is just appearance: he learned the trick from others and practiced hundreds of times before going on stage. He is effectively a sophisticated pocket calculator doing the same calculation again and again. But should an untrained spectator be asked to do the trick, she may succeed, and indeed, there are several ways to accomplish this illusion [START_REF] Kuhn | Experiencing the Impossible: The Science of Magic[END_REF]. Regardless, the spectator used intellectual flexibility to pull-off this unexpected challenge and she is arguably more intelligent in this respect than the trained magician. If the audience did not know who was who, then the perceived intelligences of the magician and spectator would be equal! Interrogation would suffice to understand the spectator's ingenuity and how the magician simply executed what his magic professors taught him. The magician would have elements of intelligence since he had the capacity to learn the skills enabling the trick. Thus, his performance reveals a past (transmitted) accomplishment, whereas the spectator had to rapidly apply non-specific knowledge to model the sequence of physical and visual illusions to pull-off the trick. Being somewhat destabilized by the sudden challenge, the spectator's detailed decision diagram would likely require more description than the magician's efficient recipe.

The phenomenon of intelligence implies capacities that are not immediately transparent to the observer. This applies both to biological [START_REF] Epstein | The Empty Brain. Aeon[END_REF] and artificial [8], [START_REF] Carabantes | Black-box artificial intelligence: An epistemological and critical analysis[END_REF] systems. System opacity depends on goal difficulty, data availability, the complexity of the system hardware, and the ability of the observer to decipher inner-system states and process causality 18 . Moreover, the Black Box feature of intelligence is not necessarily limited to understanding how and why a given instance of a goal is or is not achieved -it extends to a given goal in alternative contexts or using alternative paths. An example of the latter applying both to humans and AI is the game of chess, where the number of possible legal positions is unimaginably huge (e.g., [START_REF] Steinerberger | On the number of positions in chess without promotion[END_REF]). Observed positions are many orders of magnitudes fewer, constrained by the games actually played and by hypothetical coherent suites of moves (actually played or not). Chess Grandmasters can coarsely describe logic for each move and possible uncertainties regarding alternatives, since a move need factor-in anticipation of the opponent's next moves and one's longer-term strategy. Insofar as moves are a culmination of instinct, knowledge and calculation, it would be laborious if not impossible to describe every detail of what goes through a Grandmaster's mind.

A challenge to understanding efficiency is mapping the inner workings of C, that is → x,x ′ . . . → y . . . → z [START_REF] Stemler | Item Response Theory: Knowing When to Cross the Line[END_REF] and how processes and their structure contribute different attributes in intelligence [START_REF] Barbey | Network Neuroscience Theory of Human Intelligence[END_REF], [START_REF] Duncan | Complexity and compositionality in fluid intelligence[END_REF]. Network neuroscience theory holds the promise of linking network structure and crystallized and fluid components of intelligence [START_REF] Barbey | Network Neuroscience Theory of Human Intelligence[END_REF], but is impractical for dissecting reasoning pathways and short-cuts. A stand-alone or complementary approach is the use of interrogation [START_REF] Cronin | The imitation game-a computational chemical approach to recognizing life[END_REF], where the assessor asks informative questions to evaluate path steps based on what may be some combination of complete/partial, accurate/biased and correct/erroneous answers. Thus, akin to the Turing test, unpacking the Black Box depends on both the assessor and on interactive channels with and in the Black Box. Given a discoverable structure inside the Black Box, determination of its inner-workings would depend on variation in questioning by a single entity of a given ability, or by a population of entities of diverse capacities. To the extent that the Black box is complex, identifying and understanding its inner-workings would require commensurate intelligence on the part of the interrogator(s) [START_REF] Cronin | The imitation game-a computational chemical approach to recognizing life[END_REF].

Limited inference due to the convolution of finite capacities of interrogation with opaque, complex systems has implications for understanding and overseeing AI. Although process in AI is currently generally more accessible than for biological systems -and for humans in particular -humans do not always understand AI decision making [8] . Beyond challenges stemming from deterministic system complexity [START_REF] Thurner | Introduction to the Theory of Complex Systems[END_REF], [START_REF] Zenil | Approximations of algorithmic and structural complexity validate cognitive-behavioral experimental results[END_REF], artificial systems can possess probabilistic components (e.g., in machine learning [START_REF] Ghahramani | Probabilistic machine learning and artificial intelligence[END_REF]). This is true for certain search algorithms (e.g., [START_REF] Pelikan | A Survey of Optimization by Building and Using Probabilistic Models[END_REF]) and can also manifest in hardware and software, the prime example being the emerging technology of quantum computers. Inferring probabilities may enhance task achievement (e.g., [START_REF] Gershman | Computational rationality: A converging paradigm for intelligence in brains, minds, and machines[END_REF]) and in the realm of biology, there is some evidence for stochastic processes in cellular decision-making [START_REF] Balázsi | Cellular Decision Making and Biological Noise: From Microbes to Mammals[END_REF]. Similar to higher-order deterministic system behavior, intelligent randomness 19 could make Turing-like test assessments challenging, such that what appears to be a signature of thinking may in fact be huge, difficult to predict yet hard-wired repertoires.

PAST, FUTURE, PRESENT

Preparedness

The ability to forge a path towards resolution A depends on preparedness. Preparedness includes the priors, knowledge and skills that will form the parametric substrate upon which models feed and articulate, but also the genesis of the models themselves as the ultimate substrate reducing uncertainty in enabling C. Raymond Cattell parsed acquired and active intelligence, defining crystallized intelligence as the ability to accumulate and recall knowledge (much like a computer), and fluid intelligence as abilities to learn new skills and to apply knowledge to new situations (a thinking entity) [START_REF] Cattell | Theory of fluid and crystallized intelligence: A critical experiment[END_REF]. Although an oversimplification of the many factors and interactions forming intelligence discussed by Cattell and others [START_REF] Flanagan | The Cattell-Horn-Carroll Theory of Cognitive Abilities[END_REF], [START_REF] Mcgrew | Cattell-Horn-Carroll cognitive-achievement relations: What we have learned from the past 20 years of research: CHC COG-ACH Relations[END_REF], this basic dichotomy is useful in differentiating the functional significance of storage/recall and active decision making/future planning [START_REF] Parr | Active Inference: The Free Energy Principle in Mind, Brain, and Behavior[END_REF].

The amount and nature of previous experience at an agent's disposal potentially enters into accomplishing each segment of C. It is thus tempting to conclude that intelligence must increase with the quantity, quality and diversity of previously acquired parametric substrate. This will be true to a point [2], but without abilities to parse and apply abundant, contrasting and possibly conflicting information, cognitive load may result in sub-optimal resolution or even failure [START_REF] Dong | How Does Prior Knowledge Influence Learning Engagement? The Mediating Roles of Cognitive Load and Help-Seeking[END_REF], [START_REF] Rey | A Meta-analysis of the Segmenting Effect[END_REF]. This suggests a Goldilocks range of parametric substrate and environmental data for any given solver addressing a given goal (Figure 2). A sham path or an erroneous result occurs when information is either too sparse or too dense. More speculatively, information levels across the Goldilocks range could produce interesting, contrasting outcomes: for example, sparseness producing an inefficient, time-consuming path, to intermediate density giving an efficient, possibly ingenious path, and finally information completeness leading to a rapid, linear path. Fluid intelligence would be most useful with intermediate data/information, whereas the usefulness of crystallized intelligence would generally increase with data/information availability.

Figure 2. The hypothetical effects of data richness on the accuracy of a resolution. Below a threshold (dashed line) data is too sparse to produce an accurate resolution. Increasing data under fixed search permits greater accuracy up to a point, but beyond this, too much data challenges abilities to efficiently parse information (convex curve). The three cases to the left of the fixed search curve represent abilities to bootstrap sparse data so as to increase accuracy. Intelligence corresponds to an increase in both elevation and slope from cases i to iii. The three cases to the right of the fixed search case represent abilities to compress and sort dense or noisy data. Intelligence corresponds to an increase in both elevation and slope from cases iv to vi.

Planning

Intelligence is the ability to set goals and attain these rapidly and efficiently despite constraints. All else being equal, the most difficult goals are either strongly time-constrained or those projected far into the future. The bear encounter is a good example of an immediate problemunfamiliarity, uncertainty of what to do and the necessity to control fear. Goals in the far future on the other hand generate their own uncertainties stemming from either greater challenges or unpredictable future environments. Uncertainty in achieving future goals is reduced through prediction and planning, which tend to optimize information use and foresee and dynamically adapt to environmental conditions, thereby reducing surprises and achieving more efficient paths [START_REF] Maier | An uncertain future, deep uncertainty, scenarios, robustness and adaptation: How do they fit together[END_REF], [START_REF] Walker | Adapt or Perish: A Review of Planning Approaches for Adaptation under Deep Uncertainty[END_REF]. Planning can also reduce goal difficulty by engineering the surrounding environment or altering unachievable goals on-route, meaning, for example, that satisficing may emerge as the most intelligent outcome [START_REF] Bossaerts | Computational Complexity and Human Decision-Making[END_REF], [START_REF] Hayes-Roth | A satisficing cycle for real-time reasoning in intelligent agents[END_REF].

Flexibility and Surprisal

Flexibility is important to fluid intelligence and a hallmark of general intelligence [START_REF] Burkart | The evolution of general intelligence[END_REF]. Flexibility becomes increasingly important to goal resolution as a solver goes from familiar to unfamiliar goals and high to low preparedness. In the bear example, the birder quickly jettisoned the various inferred plans of action and opted for memory of the knowledge provided by an official whom the birder regarded as an expert. The intelligence here is weighing the uncertainty of the birder's own plans and consequences of failure with the more certain, but counterintuitive action advised by the official and trusting that person's expertise. Risk is compounded by the unfamiliar environmental setting, surprise of the situation and time constraint. Flexibility is also important on the path to goal resolution, for example, the capacity to find alternative paths when predicting or encountering a road-block [START_REF] Kabadayi | The detour paradigm in animal cognition[END_REF].

Low preparedness introduces the important notion of surprisal, that is an unfamiliar or unexpected goal, context, or environmental situation. Greater surprisal is usually associated with greater difficulty, particularly if a goal is both complex and unexpected, though some individuals deal well with unexpected challenges and may even achieve better solutions when surprised [START_REF] Ellis | Hidden talents in harsh environments[END_REF]. Simply repeatedly executing the same algorithm towards the same goal in the same environment with the same knowledge reveals nothing more than situation recognition and memory recall 20 .

How does surprisal enter into intelligence? Recall the unthinking computer. It makes path choices based on existing, proximal, immutable, deterministic alternatives 21,22 . The computer might be able to solve problems out of human reach, yet the computer's surprisal level is zero. But if running the optimal routine and quickly producing a correct answer is not an indication of intelligence, then surely the opposite of this -correct answers despite complete surprise, environmental adversity and time-limits -is. This hints at a paradox: more knowledge makes surprise less likely and better equips the entity to handle any remaining surprise. In other words, increased crystallized intelligence tends to reduce the need for fluid intelligence 23 . So, some degree of incompleteness or perturbation is necessary for flexibility in path reasoning -that is fluid intelligence -to be relevant [START_REF] Chollet | On the Measure of Intelligence[END_REF]. Moreover, mastering environments and goals may make an entity appear intelligent, but this is only true insofar as the entity has previously laid the groundwork through accumulated experience and crystallized intelligence. The observer may not be able to discern the actual inner workings behind an accurate resolution.

TEMPORALITY

Regress

An unresolved question is whether intelligence is a de novo property of a system, that is, with no antecedents whatsoever. Clearly non-thinking systems such as calculators and computers cannot create goals or resolve them with imagination, invention and insight. Still, given the inevitability of past sources in AI, biological systems and in humans in particular, it remains an open question of how to attribute potential de novo intelligence beyond apparent invention or the recombination of learned, time-worn knowledge [START_REF] Roli | How Organisms Come to Know the World: Fundamental Limits on Artificial General Intelligence[END_REF] 24 . Thus, consider a human confronting a very difficult problem. If the person were to believe that the problem is soluble by AI, submit the problem to an AI platform and get back an accurate answer, then does what is a routine task for AI reveal intelligence in the human or AI platform, or some of both? Despite challenges in parsing sources, intelligence evolves ( [START_REF] Burkart | The evolution of general intelligence[END_REF] and see below) in biological and artificial systems. This means that phenotypic variants, be they genetically, culturally or technologically based, potentially contribute to future abilities. In the case of human social learning, both established and novel resolutions are the raw material for others to observe, record and emulate, thereby contributing to the diffusion and cumulative evolution of knowledge [START_REF] Roli | How Organisms Come to Know the World: Fundamental Limits on Artificial General Intelligence[END_REF], [START_REF] Henrich | What Makes Us Smart? Topics in Cognitive Science[END_REF], [START_REF] Migliano | The origins of human cumulative culture: From the foraging niche to collective intelligence[END_REF]. In embodying knowledge and its transmission, culture and society are at the foundation of acquired -and what is interpreted as de novo -intelligence. This raises the question of the extent to which the substrates of intelligence such as priors, knowledge and skills are transmitted, that is in the extreme, the receiver is born a 'blank slate' [START_REF] Lawson | The acquisition of biological knowledge during childhood: Cognitive conflict or tabula rasa?[END_REF]. Or, the extent to which facets of intelligence come from genes, the environment and interaction between them. In the extreme case of a non-thinking computer all intelligence is crystallized and stems from those responsible for the hardware and software algorithms and concordance between a user's goals and the computer's abilities. But then, what are the sources of the computer engineer's and programmer's knowledge and skills? Unaccountably large numbers of people through time have ultimately contributed to capacities in each individual computing system and through culture, technology, education systems and society, in each individual human being.

Analogous to vertical regress is the horizontal transmission of factors facilitating intelligence [START_REF] Flinn | Ecological dominance, social competition, and coalitionary arms races[END_REF], [START_REF] Lazer | The Network Structure of Exploration and Exploitation[END_REF], [START_REF] Lucas | The value of teaching increases with tool complexity in cumulative cultural evolution[END_REF], [START_REF] Sterelny | Social intelligence, human intelligence and niche construction[END_REF]. Here, an entity benefits from the contributions of social interactions (e.g., collectives [START_REF] Krause | Swarm intelligence in animals and humans[END_REF]) or from technology (e.g., tools [START_REF] Biro | Tool use as adaptation[END_REF]) and thus the embodiment of shared intelligence can extend beyond the usual notions of the individual [START_REF] Krakauer | The information theory of individuality[END_REF] 25 . Collectives are particularly interesting since they can range from an individual benefiting from or depending on information from one or more others (e.g., outsourcing), to a transient or more persistent group, with or without borders, where individuals exchange information and act towards a goal (e.g., certain primitive social insects), to a division of intelligence labor where different functions in goal attainment are distributed among individuals (e.g., eusocial insects, any corporation). The intelligence substrate provided by these and other proxies could complement, substitute, enhance, or extend an entity's existing facilities [START_REF] Lee | Outsourcing Memory Through Niche Construction[END_REF].

Vertical and horizontal factors are not always independent, since for example technology evolves and a teacher or software engineer, although achieving their skills prior to educating or programming, respectively, do interact with the receiving entity contemporaneously. Back to the computer example above, new hardware and new software can be introduced (horizontally) to an experienced computer, suggesting that problem solving is a dynamic process of interaction among computer, programmer, technological possibilities and human goals.

These dependencies and ameliorations are not static. Whereas both regress and contemporaneous association can increase an entity's intelligence, only the latter can generate a reciprocal dynamic and coevolve with the entity. For example, computers and AI complement or even replace existing intelligence functions in humans, similar in some ways to crystallized mechanisms lessening the need for certain fluid ones. The intelligence symbioses among humans and between humans and technology coevolve through invention (new ideas), recombination (repurposing existing ideas), lateral transfer (information sharing), and sorting and selection (preferences, performance).

Change

Human intelligence changes temporally both in the population and over individual lifetimes. Evidence for changes in population intelligence comes from studies showing increases in IQ scores through time [START_REF] Flynn | Massive IQ gains in 14 nations: What IQ tests really measure[END_REF]. Cumulative invention, learning and their increased accessibility through social networks lead to greater, more general knowledge, innovation, increased skill-sets, and more flexible application to achieving goals [START_REF] Schot | Three frames for innovation policy: R&D, systems of innovation and transformative change[END_REF]. Similarly at the level of human society, culture, urban development and technological evolution [START_REF] Sterelny | Social intelligence, human intelligence and niche construction[END_REF] constitute intelligence resources that enable more ambitious goals.

Evidence also exists for increases in individual crystallized intelligence into adulthood [START_REF] Horn | Age differences in fluid and crystallized intelligence[END_REF], [START_REF] Nisbett | Intelligence: New findings and theoretical developments[END_REF]. Humans gain general intelligence faculties [START_REF] Chai | Evolution of brain network dynamics in neurodevelopment[END_REF] through childhood and adolescence, but they encounter fewer never before seen problems as they age and are less able to maintain processing speeds [START_REF] Salthouse | Consequences of Age-Related Cognitive Declines[END_REF], speculatively suggesting for humans a relative shift from the employment of proxies (parents, social) and memory when very young to fluid (thinking, flexibility) to crystallized (knowledge, skills) intelligence (with more proxies) when old. In other words, even if nuanced [START_REF] Hartshorne | When Does Cognitive Functioning Peak? The Asynchronous Rise and Fall of Different Cognitive Abilities Across the Life Span[END_REF], the accumulation of knowledge and skills enabling goal attainment in a predictable spectrum of environments and contexts anticipates likely future experiences and gradually replaces the necessity to employ novel reasoning 26 .

These elements indicate that intelligence is a dynamic phenomenon through life, both in the definition of and the ability to attain goals. We can modify C to account for temporal feedbacks that ameliorate both crystallized and fluid intelligences and that expand existing and introduce new intelligence niches (general intelligence). Consider system D: where we have not scripted the new arrows with letters, but rather used dots for how goal attainments in the form of results can reinforce future paths taken (crystallized intelligence) and introduce novel setpoints for future goals (general intelligence). Likewise, the dashed line indicates how path experimentation (model flexibility; recombining alternatives) could influence future paths (fluid intelligence) and priors, knowledge and skills (crystallized intelligence). These additions are clearly oversimplifications of the complexity of real feedbacks and interactions, but make the point that even in the absence of significant proxies and environmental inputs, individual experience influences future operations through a selective feedback process.

RELATIVITY

Observer

However defined, intelligence is always relative 27 to zero intelligence, an initial state or an arbitrary reference, benchmark problem or assessment. Arbitrary intelligence metrics can be relative to either a threshold decree (yes/no), a quantitative reference (points), or a statistically-calibrated population distribution on one or more benchmark tests (percentiles). In the first two, relativity stems from an assessor's personal experience or application of a correlate. "He must be intelligent because he answered the hard question correctly" (personal comparison) or ". . . because she has a PhD" (correlate). Respectively, the assessor subjectively calibrated question difficulty (yes/no) or the significance of a label of achievement (PhD). This has implications for assessment value, with the expectation that as an assessor's own cognitive abilities are increasingly limited, the perception of intelligence in others grows, but becomes less accurate. Even should the assessor be a group of individuals leading to greater accuracy through consensus, the problem of the arbitrary nature of references or benchmarks remains.

The relativity problem therefore comes down to the abilities of observers and observed. An example. In 1995, Andrew Wiles published his proof applying to Fermat's Last Theorem. Many people with a university STEM education will know of the conjecture, but few could claim to have even a basic understanding of the proof, and only a vanishingly small number of these had the ability to actually check the proof. This highly skewed distribution of expertise is a reflection of why it took more than 300 years to prove the conjecture despite many attempts. Although Wiles's proof is an extreme example, distributions in abilities to attain non-trivial goals and understand goal attainment is a general expectation in populations. Back to the bear example. It is quite possible that given an extra minute to think, our birder would have climbed a nearby tree. This would be better than running and risking being attacked by the bear, but if up in a tree and the supporting branch were to break with the bear waiting underneath, then the tree-climb could spell the worst possible outcome. The many unknowns of the situation and inability to actually evaluate alternative paths mean that intelligence here is not independent reasoning, but rather low-risk memory recall and the outcome (i.e., the birder is either dead, some degree of scathed, or unscathed). Inferring paths minimizing risk of injury would require a statistical sample of birding situations similar to that in the example; indeed, the advice from the expert at the park entrance was likely based on such a sample. This highlights the statistical nature of outcomes for a given path and outcomes over alternative paths. For the former, a large enough sample of birders following the stand-still strategy would show a distribution in outcomes. This is due to random variables, the two main ones being a complex forest environment and a bear's unpredictable reaction. Not surprisingly, random variables lessen the accuracy of basing intelligence assessments on a single or a small number of events.

Standardization

Standardized assessments of intelligence are based on resolving tasks over a range of difficulties in controlled environments [START_REF] Stemler | Item Response Theory: Knowing When to Cross the Line[END_REF]. Stratified difficulty serves to delimit the transitions from ease (little time consumed; correct answers), to challenge (time consuming; some correct answers), to impossibility (either little or very time consuming; either unanswered, or answered and either incorrect or randomly correct) for a given individual. The accuracy of assessments depends on how problems represent hypothesized components of general intelligence and on the graining of difficulty so as to identify accomplishment thresholds (e.g., [START_REF] Carpenter | What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test[END_REF]). Although reasoning becomes more influential with problem difficulty, the relative contributions of crystallized and fluid intelligence to outcomes as a function of problem difficulty is little understood.

Standardization has an inevitable built-in limitation. Insofar as it attempts to accurately represent certain features of intelligence outside of the test facility and insofar as the test is implemented in a fair, controlled and consistent way across a population of test takers, the latter (environmental control) necessarily limits interpretation of the former (accurate representation). Real-life contexts and environments can be highly variable, differ considerably from sterile testing rooms and standardized test objectives, meaning the relevance of standardized metrics hinge on the assumption that rank problem difficulty reflects real-life goal attainment and does not appreciably change across non-controlled environments for different test takers. Thus, for example, I may perform better than you in stressful environments and you better than me in relaxed environments, but a standardized test cannot control for either. Test scores are often unreliable indictors of achievement in the real world.

A THEORY OF INTELLIGENCES (TIS)

The above discussion only scratches the surface of the concepts and massive literature on intelligence. Despite a multi-factorial, multi-scale and multi-dimensional phenomenon, simplifying assumptions can produce a core framework upon which theory can be developed. My objective below is to propose such a framework and bare bones theoretical models as prototypes for more accurate, general models of intelligence.

Theoretical developments to characterize and predict intelligence are scattered among many disciplines and given the absence of fundamental theory these frameworks are necessarily epistemological. For example LeCun and colleagues focused on learning and the successive resolution of prediction errors in AI [START_REF] Lecun | Deep learning[END_REF] and Chollet developed a theory of intelligence as realized ability relative to prior knowledge [START_REF] Chollet | On the Measure of Intelligence[END_REF]. The contrasts among these and other conceptual, statistical, structural and mathematical models (e.g., [START_REF] Albus | Outline for a theory of intelligence[END_REF], [START_REF] Goertzel | The Structure of Intelligence: A New Mathematical Model of Mind[END_REF], [START_REF] Peraza-Vázquez | A Bio-Inspired Method for Mathematical Optimization Inspired by Arachnida Salticidade[END_REF], [START_REF] Sternberg | Toward a triarchic theory of human intelligence[END_REF], [START_REF] Wang | On Abstract Intelligence: Toward a Unifying Theory of Natural, Artificial, Machinable, and Computational Intelligence[END_REF]) reflect the complexities discussed in the previous sections and the many ways in which intelligence, its correlates and components can be represented in theoretical developments.

The multi-faceted nature of intelligence challenges prospects for a general theory based on first principles. Here I take a macroscopic perspective to propose phenomena that could contribute to such a theory. In more microscopic perspectives, factors in the temporal sequence from access to priors and accumulating knowledge and skills through learning [START_REF] Chollet | On the Measure of Intelligence[END_REF], or prediction error-checking in seeking a goal [START_REF] Lecun | Deep learning[END_REF] are explicitly modeled. The macroscopic theory presented here -the Theory of Intelligences (TIS) -in contrast, considers two higher system-level quantities which are central to the definitions of intelligence developed above. They are reducing uncertainty along a path (i.e., solving) and increasing accuracy in its resolution (i.e., understanding). Importantly, understanding need not evoke higher level thinking, nor even cognitive processes. Understanding is the capacity to causally link the solving process to attainment of goals (i.e., accuracy). Thus, the functioning of a computer program based on logic invokes some form of embodiment of understanding on the part of programmers even though the computer has no emergent understanding per se 28 .

TIS is based on the observation that goals can be attained with little or no insight or computation, and that great solving abilities do not ensure goal realization. Previous theory on cognition partitions goal attainment into perception and action (those these need not be independent, see e.g., [START_REF] Brooks | Intelligence without representation[END_REF]), both of which are optimized by minimizing free energy [START_REF] Friston | The free-energy principle: A rough guide to the brain[END_REF]. TIS generalizes these insights to any uncertainty/entropy-reducing process by positing that both perception and action may enter into either or both of the two partitions: solving and understanding.

Efficiently reducing uncertainty through solving

We assume the goal system is a network of nodes corresponding to information states. The only given information state at the start is the goal g at node n. The remaining nodes are probabilistic possibilities that each depend on successive decisions, analogous to the concept of the "adjacent possible". We do not explicitly model the microscopic processes forging the path through the information network.

The agent enters the network at n=g with stored information (memory) in the form of priors, knowledge and skills and thereafter uses (and possibly recombines) this stored information with (and actively imports) ambient and targeted data through the path nodes to resolution at node n=r. Data importation and information interpretation, understanding and recombination are leveraged in forging the path. They are not explicitly modelled below.

Path intelligence relates to how path decisions -ostensibly to achieve a specific goal -lower the information uncertainty component of the total change in entropy. We assume that entropy change has two parts: the change in information uncertainty ∆U and the total work done. The total work done will include both reduction in information uncertainty -∆U and any additional work in the path to possible resolution (see below). Maximal path intelligence is formally the maximization in uncertainty reduction (towards a putative resolution) and minimization of both information entropy and total work expended.

The change in that part of entropy relating purely to changes in path uncertainty can be represented as:

∆U = U r -U g (1a)
where U g is the initial level of information uncertainty presented by the goal given reference factors (assumed implicit here). These reference factors correspond to an agent in a given context and environment. U r is the level of information uncertainty once a resolution is complete and therefore path intelligence requires U r < U g . Equation (1a) is a gross oversimplification of resolution processes. First, a path will typically have multiple nodes. Each node will depend on the previous path segments taken, current assessments and future predictions over different network scales. Thus, again inspired by the "adjacent possible" [START_REF] Kauffman | Investigations[END_REF], for a highly complex goal, regional and possibly even local network geometry will be difficult if not impossible to predict from the start node n=g and subsequent key junctures in the path. Second and related, equation (1a) considers the resolution of uncertainty as the simple difference from the start to the end of the full sequence of intermediate resolutions. This assumes a linear decent in uncertainty, whereas more realistic non-linear trajectories would reveal that effective difficulty is better represented as some integration of challenges along the path to resolution.

Path intelligence is the efficient reduction in uncertainty along the path to resolution. As above, the work done is both what is useful to ∆U and energy lost in inefficiencies (e.g., the number and optimality of trajectories to U r , time spent (needlessly) evaluating alternative paths. . . ). We assume that work can be expressed as a function of the time T it takes to resolve the goal (even should the resolution be suboptimal or a failure; see below).

Path intelligence, U rg is simply expressed as

U rg = -∆U/ T α (1b)
where T α ≥ 1 and constant α ≥ 0. When α = 0 time and energy do not enter into the assessment of path intelligence. For 0 < α < 1 , fixed in time are of increasingly less importance to path intelligence, whereas for α > 1, increased time and energy expended have an increasingly negative association with path intelligence. Equation (1b) does not explicitly account for the possible influence of efficiency on the path actually taken and vice versa (i.e., ∆U and T α are not explicit functions of one another). Thus, for example, all else being equal, rapid solutions (T → 1) expend little energy, but are also expected to (but not necessarily will) have a negligible influence on uncertainty reduction. We therefore implicitly assume that U and T are functions of one another. Equation (1b) can be expanded to account for uncertainty reduction with each successive node, n=g, g+1,. . .

U rg = -r-1 n=g (U n+1 -U n )/T α (2)
where n is the node in the series from start (n=g=goal set) to resolution (n=r-1=goal resolution). Equation ( 2) reflects both the differential and integrative nature of intelligence. In general, U n will depend on current informational states and predictions of how future decisions will solve adjacent unknowns and bring the system closer to the goal. Although not explored here, a possible way forward is to base path decisions, solving and accuracy checking on key past and current informational states and their predicted futures [START_REF] Friston | The free energy principle made simpler but not too simple[END_REF].

Path intelligence U rg requires that at resolution U rg > 0, and therefore because U rg in (2) is the simple sum of uncertainty differences, uncertainty may increase, decrease or remain unchanged in any subset of the r-g-1 nodes. Equation ( 2) simplifies a process whereby future nodes are contingent on past choices and current inference (e.g., whether a small step in uncertainty reduction is easily found and taken, or a larger step with more difficulty is taken). It also ignores the possibility that path intelligence can be iteratively determined for each node pair (i.e., ∆U is normalized by T α n,n+1 ). Finally, although a satisfactory resolution requires U rg > 0, complete resolution of uncertainty U rg → U g /T α does not ensure goal optimality nor even goal sufficiency, since, for example one may execute a complex series of computations but introduce a numerical error that carries over to the resolution.

Accurately assembling information through understanding

Importantly, reduction in uncertainty does not necessarily result in a resolution that qualitatively matches or quantitatively maximizes a specific goal. Thus, for example, a contestant may be on a treasure hunt and correctly solve all of series of riddles but arrive too late to claim the treasure (i.e., high T α ). Alternatively, the contestant may claim the treasure but achieve this based on luck, outside help or cheating (i.e., partly or completely non-intelligent maximization of -∆U ).

Accurate goal resolution can involve matching a target or maximizing a quantity. An example of the former is the game of chess where each move tends to reduce alternative games towards the ultimate goal of checkmate, but a brilliant move or game does not necessarily result in victory. An example of the latter is maximizing the number of units acquired, for example profits in investments or points in sporting events (where there is both a victory threshold (profit, winning) and quantity beyond (accumulation, self-esteem)). We do not distinguish matching from maximization (or satisficing) in the present study, but rather highlight that resolution could involve one, the other, or some combination of both these objectives.

Cognitive phenomena such as embarking on tangents or transiently pursuing hopeless dead-ends may indeed reduce uncertainty depending on how intermediate tasks and ultimate goals are framed. That is, an accurate resolution to a complex goal requires an understanding of the goal. Understanding may or may not be complete, and can vary during the course of addressing a goal (e.g., there may be a Eureka! moment). Thus, in the game of chess a "gambit" is a path (usually sacrificing a piece) that supposes a deep understanding of the game, despite a transient point and possible positional disadvantage. Although a longer-term strategy, a brilliant chess-piece sacrifice may ultimately fail, with reasons including errors or a blunder in future moves and/or a brilliantly adaptive or unpredictable adversary.

Lowered uncertainty is associated with information gain. Recognizing that this may or may not correlate with goal accuracy, we partition an observable cofactor ∆A of resolution accuracy of information at entry into the goal network A g and accuracy at resolution A r ∆A = A r -A g [START_REF] Balázsi | Cellular Decision Making and Biological Noise: From Microbes to Mammals[END_REF] and that as a cofactor, efficiency is already accounted for in U rg , meaning

A rg = ∆A (4)
In terms of implementation of intelligence measures, isolating (4) as a separate measure differentiates U (black box) from A (the observable result).

Intelligences

Path intelligence and goal resolution may be co-dependent to some extent. Clearly an accurate answer based wholly on understanding is indicative of the path and resolution being tightly connected. Importantly the extent to which U and A are correlated reflects goal simplicity, or goal complexity, but the agent understands how to resolve the goal (it is not difficult). We do not model codependences explicitly and rather I claim that, by definition, difficult goals tend to lower associations between U and A. We also recognize that certain goal types can only be attained if particular path nodes are taken and all nodes are satisfied, whereas other goals have many alternative paths where failure to satisfy a node may or may not impact goal attainment.

As discussed in §5, intelligence is most meaningful if relative to an initial state or a reference, even if the reference is simply zero intelligence. A reference can be either a theoretical or an empirical (population) minimum, mean expectation, maximum or an arbitrary point. Figure 3 illustrates some possibilities. We might for example determine the relevant measures of the outcomes of E and A not to be with respect to starting values U g and A g , but rather the optimally efficient resolution of uncertainty U ′ r /T ′ α and maximum accuracy

A ′ r U ′ r = (U r / T α ) / (U ′ r /T ′ α ) (5a) A ′ r = (A r / A ′ r ) (5b)
However as above, there is no assurance that maximal path intelligence

U ′ r /T ′ α
will yield the optimal goal resolution A ′ r . The reverse is also true: the most accurate resolution to the goal might be attainable via a sub-optimal path U rg . Moreover, it is possible that there is more than one feasible resolution to the goal, in which case there can be many candidate U ′ , A ′ pairs, where one, the other or both of each pair is equal or superior to the path actually taken and/or the final resolution. Figure 3 shows how an entity's U, A pair plots onto a hypothetical universe of achievements. Any one of the points in this universe could serve as a reference and both, one or the other of U and A might be superior to one or more of these references. We can partition the universe into approximate domains, whereby low U, low A corresponds to a random guess or an oblique hunch, low U, high A to an educated guess, high U, low A to a process error leading to a suboptimal or sham resolution, and finally high U, high A being the direction of intelligence.

An evolutionary index. Consider first an intelligence index Ǐe

rg for a single event r,g with respect to an arbitrary reference, denoted Ǔrg , Ǎrg :

Ǐe rg = ψ (U rg / Ǔrg ) (A rg / Ǎrg ) (6)
where ψ ≥ 0 is the magnitude of the achievement and both Ǔrg and Ǎrg are assumed positive. The introduction of ψ reflects utility of attaining the goal and therefore gives goal resolution a functional interpretation. When ψ = 0 achieving the goal is meaningless. Three things to note. First, as above, there is no explicit interaction term. To the extent that nodal changes in U correlate with those in A (e.g., trajectory g →→→ ra in Figure 3), an additional interaction term in eqn. ( 6) would be needed to discount redundancy from principal factor effects. Second, because index Ǐe rg decreases as either U rg → 0 or A rg → 0, this index can be used to reflect the potential for evolution on traits associated with goal resolution. As such (i) a random guess and correct answer U rg = 0 will produce no selection for any underlying intelligence traits and (ii) a brilliant path (maximal U rg / Ǔrg ) and poor resolution (A rg → 0) result in no trait selection either. (Note that equation ( 6) would need to be appropriately modified to accurately model the evolution of traits underlying U and/or A). And third, each of the two terms in parentheses can take on any positive value. Should a term be less than one, then we would expect negative selection on one or more of its underlying traits relative to the arbitrary reference. Greater than one would result in positive selection relative to the arbitrary reference. These and other considerations (e.g., trait linkage) will require future dedicated investigation.

A comparative index. An alternative index for intelligence Ǐc

rg relates to practical measures, whereby the observer weights path α and resolution β components:

Ǐc rg = α (U rg / Ǔrg) + β (A rg / Ǎrg) α+ β ( 7
)
Greater than baseline performance increasingly manifests in [START_REF] Biro | Tool use as adaptation[END_REF] as the relevant coefficient takes on larger values.

Analogous to equation ( 2), expressions ( 6) and ( 7) can be decomposed into a sequence of nodes to produce more microscopic-based measures of intelligence. Thus, a more microscopic perspective would integrate capacities for how crystallized (memory) and fluid (reasoning, inference) mechanisms generate and are arbitrated in alternative strategies to reduce U n and increase A n . These decisions would be based in part on the iterative path and its perceived accuracy leading up to n, and the current assembly of information towards the goal, whilst taking into account how each alternative might influence future decisions along the path (Figure 3).

6.3.3

Incorporating Difficulty and Surprisal. The evolutionary [START_REF] Benedetto | A Survey on Recent Approaches to Question Difficulty Estimation from Text[END_REF] and comparative [START_REF] Biro | Tool use as adaptation[END_REF] indices normalize intelligence with respect to an arbitrary reference or benchmark. In the case of an evolutionary index, the reference could be a mean value of a heritable trait influencing fitness [START_REF] Burkart | The evolution of general intelligence[END_REF]. For the comparative index, the reference could be benchmarked achievements [8], [START_REF] Hernández-Orallo | The Measure of All Minds: Evaluating Natural and Artificial Intelligence[END_REF]. Using concepts developed in earlier sections, goal complexity, surrounding environment and agent ability can be integrated into a measure of intelligence corresponding to task (or goal) difficulty or surprisal as (8) with the minimal value of 0 should the term in parentheses be negative. C y is the complexity of task y and is a function of initial path uncertainty and goal accuracy, E is environmental conditions with E→0 indicating poor and E→1 optimal conditions, and Q max x→y > 0 is the maximum ability of the agent with expertise x to achieve task y in an optimal environment (E = 1). Note that as x deviates from y the task has greater surprisal. When the system achieves its maximum ability for task y, given environmental states, E Q max y = U rg A rg . All else being equal, Q max x→y is expected to decrease as x and y diverge (i.e., greater surprisal). Regardless of whether or not there is surprisal, the term in parentheses is a concise measure of difficulty. Equation ( 8) could be expanded to account for vertical or horizontal influences in abilities ( §4), path dynamics (cf. eqn. 2) and entropies [START_REF] Frenkel | Order through entropy[END_REF], [START_REF] Russo | Learning to Optimize via Information-Directed Sampling[END_REF], and appropriately modified to partition the independent effects of information uncertainty and goal accuracy as in (eqn. 7). Note that if U rg is objectively assessed (i.e., there are no benchmarks, cf. §5.2, and no Black Box, cf. §2.3), then (eqn. 8) is an absolute measure of intelligence (i.e., it is only relative to initial states U g and A g ).

I xy rg = (C y {U g , A g } -E Q max x→y ) U rg A rg
Finally, the potential of proxies such as social interactions and technology can be incorporated to give the general form: [START_REF] Bossaerts | Computational Complexity and Human Decision-Making[END_REF] where P max x→y is analogous to Q max x→y , and in the limit of dependence on proxies alone (P max x→y > 0, E Q max x→y → 0) the system approximates AI. Thus, if (C y {U g A g } -P max x→y > 0) then equation ( 9) is the intelligence of the AI system. Equation ( 9) assumes no environmental influence on proxies and that the use of proxies implicitly may enter into resolution of the path U rg and accuracy A rg . Equation 9 could be modified to account for ability degeneracy associated with proxy robustness [START_REF] Deacon | A degenerative process underlying hierarchic transitions in evolution[END_REF], that is, Q ∝ 1/P .

I xy rg = (C y {U g , A g } -(P max x→y + E Q max x→y )) U rg A rg

CONCLUSIONS

Until recently the study of intelligence has largely focused on psychometrics in humans. With the development of AI and a greater emphasis on interdisciplinarity in scientific inquiry, progress is being made towards theories of intelligence, with the prospect of a general theory based on first principles. Here, I have surveyed recent advances towards conceptual unification of definitions of intelligence, arguing that a general framework needs to recognize scale in the nature of intelligence. This introduces the daunting challenge of explicitly accounting for events and interactions over different system scales, time scales, among different systems, in multi-dimensional heterogeneous environments, and for a diverse range of system goals. The approach taken here is to model intelligence at macroscopic scales based on implicits of information theory and thermodynamics, recognizing the underlying influences of more microscopic states and processes. Importantly, I propose a compact mathematical expression for the concept of goal difficulty, integrating goal complexity, environment and agent maximal ability to the goal, given past experience (i.e., surprisal). Based on model objectives (eqns. 6-9), the Theory of Intelligences proposed here is represented as a central postulate and basic features.

Central Postulate of TIS

Intelligence integrates two fundamental processes: reducing information uncertainty (identifying and solving) and attaining goal accuracy (understanding).

TIS is general, encompassing physical, biological and artificial domains, and in humans in particular, applies to a wide scope of endeavors, including intellectual and physical performance, art, social interactions and political influence.

Basic Features of TIS

7.2a Information and Processing ( §1): Intelligence systems control information. Because external environments require dedicated interpretation and coding, the greater system-environment ensemble manifests at a coarse level as a 2x2 fundamental structure (Figure 4): (1) Information: (1a) External free data and proxies, (1b) Internal free data and stored constructions, and (2) Information processing: (2a) Internal and proxy lower-level receptors, processors, (2b) Higher-level controller and integrator. Implications: Intelligence integrates system, proxies and environment, and codes all three into the greater individual centered on but not limited to the controller [START_REF] Krakauer | The information theory of individuality[END_REF].

7.2b Information Uncertainty and Entropy ( §1): Intelligent systems are dissipative and therefore increase entropy overall, but in the system subsets relevant to goal attainment, information uncertainty is decreased. System and system-environment partitions are only beginning to be understood [START_REF] Friston | The free energy principle made simpler but not too simple[END_REF], [START_REF] Krakauer | The information theory of individuality[END_REF]. Uncertainty (or goal-useful entropy) reduction may manifest as some combination of sorting (i.e., prioritizing), selecting (i.e., eliminating), morphing and/or recombining code. In the extreme of passive intelligence, physical laws express in environments so as to produce locally stable uniqueness, for example, the formation of extremely long-lived inorganic crystals such as diamonds [START_REF] Penrose | Self-reproducing machines[END_REF]. Towards the extreme of active intelligence, intentionality, inference and creativity -together with passive instruments -generate dissipative structures, for example, AI systems or a work of art, leading to entropy in users or admirers, respectively. Implications: Intelligence generates novel objects, pattern, complexity and diversity.

7.2c Development and Complexity ( § §2.2, 3.1, 3.3, 4): Intelligence progressively builds on existing information and novel substrates, including prior achievements [START_REF] Shreesha | Cellular Competency during Development Alters Evolutionary Dynamics in an Artificial Embryogeny Model[END_REF], tending towards greater capacities (efficiency and generality). Greater capacity permits successful encounters with new, more complex goals and therefore the need for enhanced higher-level abilities (e.g., reasoning and inference in thinking systems). Implications: Intelligence accumulates and is cumulative through the development of individuals, collectives, and proxies. Speculatively, capacity categories are expected to manifest in the following (overlapping) sequence (for computers; for humans): execution of laws or recipes (algorithms, programs; DNA expression), contribution of proxies (user, programmer; parents), innate priors (input data compatibility; error checking; nourishment, avoid dangers), acquired knowledge and skills (memory, training in AI; memory, learning, experience), active inference (unknown as present; defining and addressing goals), proxies (computational networks; social interactions, technology). Systems evolve complexity, permitting both increased efficiencies to address attainable goals and extended capabilities to increasingly complex environments and goals [START_REF] Godfrey-Smith | Environmental complexity and the evolution of cognition[END_REF].

7.2d Tradeoffs ( § §2.2, 3, 4.2): Capacities have costs (time, energy), logistical constraints (limited experience) and structural limitations (computational abilities). Tradeoffs emerge which suggest the existence of one or more locally optimal goal resolution strategies. The deployments of acquired skills, novel inference, reasoning and proxies will therefore depend on an agent's evaluation of their relative utilities to achieve goals. Two expected and related tradeoffs are between specialization and generality at a macro level and, correspondingly, between efficiency and exploration at a more micro level. Implications: The interdependencies of intelligence traits and costs and constraints on their deployment will constrain tradeoff surfaces, producing a limited set of intelligence strategy motifs.

7.2e

Relativity and Regress ( § §2.1, 2.3, 3.3, 5): Active intelligence is relative to levels of difficulty and surprisal, that is the integration of the complexity of the goal, agent abilities, the environment and observer perception (arbitrary references). References may include consensual benchmarks, maximal intelligence or zero intelligence. Observer effects can be partially discounted as in equations ( 8) and ( 9), but not completely if perceptual uncertainty remains in the evaluation of the path (i.e., the Black Box). Although not invoking active intelligence, goals without difficulty or surprisal implicitly evoke past intelligence, either in evolutionary adaptations or previous experience and memory. Actively inferring intelligence systems derive certain capacities from the environment, in particular proxies such as social interactions and technology. Implications: There is no known pure, "Boltzmann Brain" of intelligence. More probable would be the sudden emergence of a non-functional object with random features and no intelligent capacities. Similar to the evolution of life [START_REF] Marshall | Formalising the Pathways to Life Using Assembly Spaces[END_REF], intelligence therefore requires some previous assembly beyond purely physical scaffolding.

Status as a Theory

TIS integrates tenets and facts about intelligence. TIS implicits key micro and meso-level concepts at a macro level and can explain different observations. TIS is however limited in not explicitly integrating the causal roles of more microscopic levels and therefore lacks criteria for a general theory. Specifically, the Black Box described in §2.3 is an impediment to a general theory, since caveats are necessary to explain what might appear to be random effects and performances that deviate from expectations (i.e., when E Q max y ̸ = U rg A rg from eqn. 8).

TIS replies to the following:

Why Intelligences? Intelligence signifies the ability to attain goals and therefore maintain and reproduce otherwise dissipative structures, without the necessity of storing huge amounts of information. Storing information in the form, e.g., of memory takes time and energy and given hard to predict environments and the quantity and diversity of future novel challenges, intelligence -if diversified in multiple capacities -is both more efficient and enables exploration of new niches (Figure 4). Partitioning different facets of intelligence underlines the role that uncertainty reduction plays regardless of goal accuracy. The prevailing view that inference (thinking) is necessary and even dominant in intelligence neglects the finer partition of how a processor uses multiple instruments (including inference) in local and regional path resolution and more multiscale integrations towards the global goal (accuracy). I suggest that paths not only function to accurately achieve goals, but as experimentations providing feedback, improvement and therefore both higher accuracy and efficiency for future attainable goals and the necessary latitude to attempt new goal spaces. As such, TIS can explain human undertakings that do not necessarily affect Darwinian fitness, such as leisure, politics, games and art. TIS is therefore applicable to theories of evolution (genetic, cultural, technological) and explains forms of success that are not directly under selection.

Causality. Many theories address the origins of life systems and the evolution of their complexities. TIS in positing that intelligence fosters simplicity (efficiency) on reachable goals, and promotes the evolution of complexity (division of labor) to attain difficult or otherwise unreachable goals, provides a causal framework and therefore a greater understanding of biological assembly and diversification. The empirical facts supporting these claims are (1) on a micro/mesoscale, path decisions are influenced by past experience and influence sequential path decisions and future goals [START_REF] Pearl | The Book of Why: The New Science of Cause and Effect. Basic Books[END_REF], and (2) on a macroscale, natural selection drives responses to needs and opportunities -successful responses (goals met) invoke intelligence. As above, even partly or unsuccessful responses can have an evolutionary effect, suggesting the robustness of intelligence as a primary force in understanding life.

Falsifiability. The main prediction of TIS is that uncertainty reduction and accuracy gain, although expected to be correlated, each involve unique traits. Although the genetics and heritability of these traits are unknown, the traits would affect micro-and meso-scale identification and arbitration of decision alternatives and multi-scale assessments of the accuracy of path decisions and trajectories with respect to the goal. TIS predicts that accuracy is generally increasingly easier to assess as a path is forged, whereas more myopic uncertainty reduction may or may not show a temporal (path) pattern. Evidence to the contrary would falsify TIS, for example, clear views from the start of what accurately attaining a goal entails. (Though in such cases the goal is neither very difficult nor surprising and so active intelligence according to equation ( 8) is not needed). A final test of TIS regards its evolutionary significance, with predictions including (i) impact of intelligence traits on reproductive fitness [START_REF] Burkart | The evolution of general intelligence[END_REF] as evidenced by (ii) assortative mating [START_REF] Plomin | Genetics and intelligence differences: Five special findings[END_REF], and a decline in capacities, particularly fluid capacities, with old age [START_REF] Craik | Cognition through the lifespan: Mechanisms of change[END_REF].

Future Research and Open Questions

TIS is a macroscopic framework that omits explicit consideration of uncertainty and information entropy dynamics as well as the dynamics of system components, controller strategies and interactions with proxies and the environment [START_REF] Crupi | Generalized Information Theory Meets Human Cognition: Introducing a Unified Framework to Model Uncertainty and Information Search[END_REF], [START_REF] Vanchurin | Thermodynamics of evolution and the origin of life[END_REF]. Incorporating these and other features is a daunting challenge and although surely question-dependent, it is currently not clear how these will significantly change our understanding of intelligence.

Future research should address the following questions:

1. To what extent are microscopic processes necessary to understand macroscopic patterns in intelligences?

GLOSSARY

Ability

The potential to successfully apply instruments to complete a task or achieve a goal

Accuracy

How close an achievement is to a goal

Complexity

The structure and dynamics of objects with a function, goal or purpose

Computation

Use of an algorithm to manipulate data and produce information, e.g., a calculation.

Crystallized intelligence

Priors, knowledge and skills that can be applied to goal attainment

Data

Patterns, e.g., numbers, symbols, language. . . that can be processed to become information

Difficulty

The convolution of agent ability, environment and goal complexity

Efficiency

The amount of work required to reduce uncertainty by a fixed amount

Entropy

A change in information content

Environment

Contexts, settings, structures and conditions potentially interacting with a system

Experience

Accomplishing a task resulting in learning

Flexibility

The ability to deal with difficulty or surprise Fluid intelligence Active use of reasoning, invention, creativity applied to goal attainment

Information

Non-random structure of significance

Ingenuity

A creative, unexpected or indescribable method or process towards a goal

Goal

The objective in addressing a challenge or opportunity

Knowledge

Acquired information that may involve understanding, in the form of interrelations, facts or skills

Learning

Gain in knowledge or understanding associated with experience

Model

Abstraction of reality used to simulate situations or make predictions

Path

The choices made in following or forging a (possibly evolving) decision tree

Figure 1 .

 1 Figure 1. Time courses of path node changes for three hypothetical scenarios. Each point corresponds to a transient resolution in the path (potential node changes represented by a continuous line). The magnitude of the node change corresponds to the reduction in information entropy. Goal resolution is indicated by an open circle. A: Monotonic decrease in path node changes leading to an intermediate resolution time. B: Complex trajectory in path node change indicative of the discovery of a more accurate path and a consequential delay in resolution (not shown). C: Efficient path corresponding to a rapid resolution.

Figure 3 .

 3 Figure 3.The space of changes in information uncertainty U and in goal-useful information A. The global optimal solution is denoted ra. Other possible outcomes depending on agent ability and goal complexity are labelled rb, rc, rd and re. Path trajectories can vary in terms of direction, length, and the number of nodes from debut to resolution. The segments g to ra reflect an efficient trajectory and accurate resolution. The agent resolves unknowns and has an actual (e.g., human) or embedded (e.g., AI) understanding of how to attain the goal. The greater number of smaller segments from g to rd correspond to an agent that is both less able to move forward and less accurate in moves. Compound arrows show general directions corresponding to expected outcomes of random guessing, educated guessing, process errors, and intelligence.

Figure 4 .

 4 Figure 4. Schematic diagram of intelligence ecosystem integrating TIS. The SYSTEM phenotype is composed of the CONTROLLER, PROCESSOR and MEMORY. The SYSTEM interacts with the ENVIRONMENT both in setting and addressing GOALS. The extended phenotype are PROXIES such as social interactions, technology and culture. The current SYSTEM is based on past TRANSMISSION and intelligence trait EVOLUTION (not shown), develops and integrates intelligence traits over the SYSTEM's lifetime (not shown), and influences future TRANSMISSION and EVOLUTION. Intelligence resources are augmented by SYSTEM EVOLUTION and possibly SYSTEM-dependent PROXY EVOLUTION and this occasionally produces intelligence innovations[START_REF] Hochberg | Innovation: An emerging focus from cells to societies[END_REF]. Intelligence can be codified in the SYSTEM as phenotypic traits, stored MEMORY and hard-wired or plastic behaviors or active inference. Intelligence can also be codified outside the SYSTEM in (non-mutually exclusive) PROXIES, such as society, culture, artefacts, technology and institutions. TIS is central in bringing the SYSTEM to a GOAL via searching, solving and understanding.

This and related quotes although implied by the 1948 article, are not actually found in the document[START_REF] Shannon | A Mathematical Theory of Communication[END_REF]. A quoted exchange between Shannon and John von Neumann on the terms information, uncertainty and entropy suggest the interrelations of these concepts[START_REF] Tribus | Energy and Information[END_REF].

Container 102, Vannevar Bush Papers, Manuscript Division, Library of Congress, Washington, D.C. See[START_REF] Rogers | Claude Shannon's cryptography research during World War II and the mathematical theory of communication[END_REF].

François Chollet[START_REF] Chollet | On the Measure of Intelligence[END_REF] defines intelligence of a system as "a measure of its skill-acquisition efficiency over a scope of tasks, with respect to priors, experience, and generalization difficulty". Similarly, Pei Wang defines it as adaptation with insufficient knowledge and resources[START_REF] Wang | On Defining Artificial Intelligence[END_REF]. Karl Friston stresses the roles of active inference, planning, curiosity (evaluating alternatives) and resolution of uncertainty[START_REF] Friston | Designing Ecosystems of Intelligence from First Principles[END_REF]. Many have defined intelligence as the ability to plan for and to predict the future. See[START_REF] Legg | A Collection of Definitions of Intelligence[END_REF] for a survey of definitions including theirs: "an agent's ability to achieve goals in a wide range of environments."

Arguably the first glints of intelligence on Earth were the implication of the laws of physics and chemistry in the very first negative entropic systems[START_REF] Schrödinger | What Is Life? The Physical Aspect of the Living Cell ; with, Mind and Matter ; & Autobiographical Sketches[END_REF].

This is related to the ELIZA Effect[START_REF] Dillon | The Eliza effect and its dangers: From demystification to gender critique[END_REF], where humans imbue human-like qualities to functional objects. Similar to the Reverse Turing Test, a Reverse ELIZA Effect is a computer that imbues computer-like qualities to humans.

In the book A Thousand Brains Jeff Hawkins argues that humans have multiple world models[START_REF] Hawkins | A Thousand Brains: A New Theory of Intelligence[END_REF].

It is nevertheless possible that uncertainty remains unchanged or is even increased (stupidity).

Although important contrasts exist, I loosely use the following terms interchangeably: entity, solver, system, individual; goal, problem, task, challenge, opportunity; and process, method, path, computation.

Unless otherwise specified, hereafter I lump the informational concepts of knowledge and priors into the term 'knowledge'. Thus, the important instruments employed in B are knowledge (abstract concepts) and skills (the practical application of knowledge). See[START_REF] Chollet | On the Measure of Intelligence[END_REF] for discussion.

Goals may include the non-mutually exclusive: planning for the future (e.g., goal definition), addressing a problem, challenge or opportunity, or acquiring the knowledge or skills necessary to address future goals. Thus, intelligence extends to knowledge and skill acquisition.

This interesting fact relates to the P vs NP problem. The path to a solution may be very hard to find, but once found, both it and the solution itself appear simple[START_REF] Bossaerts | Computational Complexity and Human Decision-Making[END_REF]. A notable example is exponential increases in difficulty with array size in Sudoku[START_REF] Ercsey-Ravasz | The Chaos Within Sudoku[END_REF].

https://www.britannica.com/science/Dunning-Kruger-effect

But see https://www.nature.com/articles/d41586-023-02361-7

Quote from David Krakauer https://www.samharris.org/blog/complexity-stupidity

This relates to ideas that intelligence is an emergent feature of goal seeking systems (e.g.,[START_REF] Hillis | Intelligence as an Emergent Behavior; or, The Songs of Eden. In Daedalus[END_REF]).

See brief observation in 1955 by McCarthy and colleagues[START_REF] Mccarthy | A proposal for the Dartmouth Summer Research Project on Artificial Intelligence August 31, 1955[END_REF]

This relates to the "AI effect": once a problem is solved and the solution understood its solution is no longer in the domain of intelligence[START_REF] Mccorduck | Machines Who Think: A Personal Inquiry into the History and Prospects of Artificial Intelligence[END_REF].

For example, large language models such as GPT-4 use neural nets to generate output word by word in correct syntax and context, but given that it has no world model, it is not sensitive to possible logical errors and thus does not 'think'.

And therefore non-thinking artificial systems can process data orders of magnitude faster than thinking or non-thinking human beings and for that matter any biological system[START_REF] Korteling | Human-versus Artificial Intelligence[END_REF],[START_REF] Lane | Transformer: The Deep Chemistry of Life and Death[END_REF].

For counter-perspective see[START_REF] Kudithipudi | Biological underpinnings for lifelong learning machines[END_REF].

Moreover, whereas social learning through imitation alone does not create novelty, individual learning in combination with social learning can[START_REF] Mcelreath | When Natural Selection Favors Imitation of Parents[END_REF].

As an interesting tangent, intelligences such as metabolism and immune responses inside individuals -although to some extent plastic and adaptive -are more guided repertoires than intelligences applied by the individual to the (non-coevolving) outside world, which have greater fluid or proxy components.

This concords with the idea of "conjuring the child within us" when referring to creativity in older individuals.

Consider a Boolean definition "true/false". This is not absolute since the result is necessarily relative to a query, which necessarily has a defined reference. For example, "The person did not run 30km/hr. True or false?".

For recent discussion of the debate over understanding in AI Large Language Models, see[START_REF] Mitchell | The debate over understanding in ai's large language models[END_REF].

Path intelligence

Efficiently resolving uncertainty

Priors

Foundations of knowledge, e.g., numeracy, spatial relations, physical properties. . .

Reasoning