Center for Analysis and Design of Intelligent Agents

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[[/public:t-713-mers:mers-23:main|T-713-MERS-2023 Main]] \\
[[/public:t-713-mers:mers-23:lecture_notes|Link to Lecture Notes]]

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====== INTRODUCTION ======

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|  EMPIRICAL REASONING  | Defeasible / non-axiomatic reasoning where the data, rules, and results are restricted to the physical world.  |

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==== Working Definition of Intelligence ====
|  The (working) \\ Definition of \\ Intelligence \\ Used in This \\ Course  |   \\ \\  **Adaptation with insufficient knowledge and resources** \\ -- Pei Wang \\ \\     |
|  'Adaptation' | means changing strategically in light of new information.      |
|  'Insufficient' | means that it cannot be guaranteed, and in fact, can never be guaranteed to be sufficient to guarantee that goals are achieved. The reason it cannot is that an agent in the physical world can never know for //sure// that it has everything needed to achieve its goals.     |
|  'Knowledge' | means information structures (about target phenomena) that allows an agent to predict, achieve goals, explain, or model (target phenomena).      |
|  'Resources' | means that it cannot be guaranteed, and in fact, can never be guaranteed. The reason they cannot is that we don't know the 'axioms' of the physical world, and even if we did we could never be sure of it.     |
|  Another way to say \\ 'Adaptation under Insufficient Knowledge & Resources'  |  \\ "Discretionarily Constrained Adaptation Under Insufficient Knowledge & Resources" \\ -- K. R. Thórisson \\ \\ Or simply **Figuring out how to get new stuff done**.  \\ \\   |
|  'Discretionarily constrained' adaptation | means that an agent can //choose// particular constraints under which to operate or act (e.g. to not consume chocolate for a whole month) -- that the agent's adaptation can be arbitrarily constrained at the discretion of the agent itself (or someone/something else). Extending the term 'adaptation' with this longer 'discretionarily constrained' has the benefit of separating this use of the term ‘adaptation’ from its more common use in the context of natural evolution, where it describes a process fashioned by uniform physical laws.     |


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====Correlation, Knowledge, Causation====
| Correlation  | Some factors/variables co-vary when changes in one variable are related with changes in the other, negative or positive  |
| Correlation: Powerful tool  | Any variables in the world can be measured for correlation. Only two variables are needed (independent and dependent) for doing correlation studies  |
| Main operating principle behind correlation  | There is no causation without correlation  |
| Correlation: Pitfall   | Correlation does not imply causation between the variables measured!  |
| Quasi-experimental designs  | Purpose: Where true experimental design is not possible, approximate it.  \\ If direct control over dependent/independent variables is not possible.    | 
| How it works  | 1. One-shot case study (no control group) \\ 2. Single group pre- and post-test (minimal control) \\ 3. ABAB: Single-group repeated measures (slightly less minimal control)  | 
| Limitations  | Much greater uncertainty as to the internal and external validity of the quasi-experiments than true experimental designs  |

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==== Science, Technology, Philosophy, Mathematics ====

|  Philosophy  | A systematic investigation into any phenomenon. \\ Fundamental motivation: Deepened understanding of our place in the universe. \\ Fundamental driving principle: Human reasoning and creativity. \\ Fundamental organizing principle: Schools of thought; methods of reasoning. \\ //When you hardly know anything about a phenomenon, yet insist on getting to the bottom of it, philosophizing gets you started.// |
|  Induction  | The cognitive act of generalizing from experience. //Example: Socrates is a man. Socrates died. Hence, all men will die.//  |
|  Science  | A systematic investigation into phenomena in the natural world susceptible to physical experimentation. \\ Fundamental motivation: Reliable knowledge of the world. \\ Fundamental driving principle: Induction. \\ Fundamental organizing principle: Controlled comparative experiment. \\ //When you embark on improving your understanding of a phenomenon with measurable/quantifiable variables, through comparative experiments, you are applying the **scientific method** ("doing science").//  |
|  Engineering  | Effort to construct things using relevant knowledge (often state-of-the-art scientific models/theories - see below), systematic methods, and relevant technology. \\ Fundamental motivation: Control of human environment. \\ Fundamental principle: Design. \\ Fundamental organizing principle: Methodical application of known procedures and methods. \\ //When you embark on changing or improving any aspect of your environment, working towards the implementation of a well-defined end product, through an application of best known practices, you are doing engineering.//  |
|  Technology  | Tools and techniques for getting things done. Fundamental principle: Composition, design, engineering.  |
|  Deduction  | The cognitive act of following preconceived rules to their inevitable implication. // Example: All men are mortal. Socrates is a man. Hence, Socrates is mortal. //  |
|  Mathematics  | A systematic study of quantity, numbers, patterns, and their relationships. Fundamental principle: Deduction. \\ //When you embark on clarifying the behavior and nature of quantifiable domains, using axiomatic rules and proofs, you are doing mathematics.//  |
|  Causal Relations  | A relation between two entities that makes one predictable from the other. // Examples: If I flip the light switch, the lights will shine. (Deduction) // If I want the light to shine, I can flip the light switch. (How to achieve a goal)   |

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==== Empirical Science (or just 'science') ====

|  Empiricism  | The claim that "the world is its own best model" - that is, no matter what our preconceived notions of how the world works are, the world is the ultimate judge of that.  |
|  'Empiricism' the term  | The term comes from Greek ('empeiria'), meaning "experience". Descartes put it best when asking the question "How can I be sure that I exist?" when he answered with the no-famous phrase "I think, therefore I am".   |
|  Empiricism in science  | Modern science takes the idea of empiricism to its ultimate conclusion: Let's find the **best** way to create the **most reliable** way of creating **trustworthy knowledge** about the world.   |
|  Comparative experiments  | ...are the key form that this creation has taken, but in fact many other forms of reliable knowledge creation, besides controlled comparative experiments, are in use. The key to them is the systematic categorization and estimation of the uncertainty of the information they produce. By knowing these, the trustworthiness of the knowledge produced can be assessed, and appropriate action taken when the knowledge is used.  |
|  The Content of Scientific Knowledge  | ...is essentially rules about the causal behaviors and relations of things. Causality is a way to extract compact knowledge about any complex system that contains regularities. It works for the physical world because the physical world is highly regular.   |

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==== Causation ====

|  What it is  | A relation between entities in the physical world that allows us to achieve goals and predict events.  |
|  Why it's important  | The comparative experiment ("the scientific method") is based on the assumption that such relations exist, i.e. that the world has regularities.  |
|  How it relates to logic  | If causal relations are rules, and the world has regularity, then the world is rules-based. Reasoning is the method of following logic when working with rules. It means we can reason about the world.  |
|  Types of \\ (basic) \\ causal relations  | A->B & A->C : A causes B and C. \\ A->B->C : A causes B and B causes C \\ [A+B]->C : A and B together cause C. \\ A->C, B->C : Both A and B are sufficient to cause B. |
|  Time and Causation  | The temporal relation between cause and effect is strict on time: Effects cannot happen before causes.   |


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====Reasoning====

|  What is Reasoning?  | A systematic way of thinking about implications.  |
|  How is it done?  | Via processes that observe rules.   |
|  What are the main types?  | Deduction: All men are mortal. Socrates is a man. Hence, Socrates is mortal \\ Abduction: How did this come about? (Sherlock Holmes)   \\ Induction: What is the general rule?  \\ Analogy: 'This' is like 'that' (in 'this' way).  |
|  How is it used in science?  | In empirical science to unearth the "rules of the universe".  \\ In mathematics as axioms. \\ In philosophy as a way to construct arguments. \\ In computer science to write code.  |
|  Why does it work?  | Because the world's behavior is/seems rule-based.  |

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====Scientific Research Concepts / Definitions====

|  Theory (isl. kenning)  | "A set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena." [[http://dictionary.reference.com/search?q=theory|REF]] \\ A theory is a relatively big explanation, covering several phenomena, often through a single principle, or a set of simple principles.  |
|  Hypothesis (isl. tilgáta)  | Is a prediction about the relationship between a limited set of phenomena, typically formulated as measurable variables, as explained by a particular theory.  |
|  Data  | Typically "raw numbers" -- only contain low-level semantics.  |
|  Information  | Processed and prepared data. \\ Data organized at more than one level of detail. \\  "Data with a purpose."   |

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==== The Scientific Method: The Comparative Experiment (ísl. samanburðartilraun) ====	 
|  Identification, description and formalization of phenomenon  | Observation and description of a phenomenon or group of phenomena. |
|  **Hypothesis**, null-hypothesis  | Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation. Null-hypothesis of a hypothesis is the claim that it is false - i.e. that some relationship that it proposes does **not** hold. |
|  Creation of **experimental setup** to test hypothesis  | Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations. |
|  Performance of experiment, collection and analysis of results  | Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments. Basic assumption: Repeatability	Can be repeated by anyone anywhere  |
|  **Repeatability** requires formal framework  | Detailed description, clear goals, clear (limited) scope, hence the formalities in their execution  |
|  Key idea: **Comparsion**  | Baseline collected in same experimental setup without any other intervention by experimenter  |


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====Theories of the Scientific Method (Philosophy of Science) ====	 
|  A scientific theory predicts  | A good scientific theory can be used to predict (known and unknown) results.   |
|  A scientific theory is a spotlight  | A good scientific theory tells us where to look for interesting things; the more detailed the theory the more detailed should be its predictions and the more narrow its spotlight (specific suggestions for new investigations).   |
|  A scientific theory can produce new hypotheses  | A good scientific theory helps us do more experiments by being a source of hypothesis creation.   |
|  A scientific theory provides control  | A good scientific theory gives us control over the phenomenon it addresses that we would otherwise not have.  |
|  A scientific theory **explains** ("tells a coherent story")  | A good scientific theory explains how data is related. The more **completely** and the more **simply** it explains things, the better the theory.  |
|  A scientific theory gives us the big picture  | A good scientific theory relates together, in a coherent way, some part of the world -- in general the bigger the part, the better the theory.   |
|  Occam's Razor  | A good scientific theory cannot be simplified; it is the shortest and most accurate explanation of a phenomenon. Einstein is quoted as saying: "A theory should be as simple as possible, but not simpler".   |
|  A scientific theory can be **disproven**  | A scientific theory or hypothesis is a statement that is //disprovable//. To count as "scientific" a theory //must// be disprovable. For this there must exist some measures and actions that are //possible// (in theory, but better yet, practic) whose results would possibly - should the measurements come out a particular way - disprove the theory. \\ Applying this criterion strictly means that //all scientific theories to date have been disproven - i.e. proven incorrect.// \\ This is a //feature// of science (not a bug): Exposing the limits of our theories by demonstrating in which contexts they are incorrect allows us to come up with better theories.   |


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====Scientific Method: Independent of Topic====
|  **Phenomenon**  | The world is filled with "stuff". Anything is a "thing" - even "nothing" is a thing (a concept in our minds, which is represented as neural patterns and potential for behavior). We can group any arbitrary collection of things and call it a **phenomenon**. //Example: A rock. A mountain. A planet.// (If I say that I want to study //"thingamajigs"// - something you've never heard of - I will first have to list some of the major ways in which thingamajigs can be identified. In fact, this is a good idea anyway, so as to be clear and consistent about what it is that one is studying.)   | 
|  The scientific method is independent of topic...  | One can study **any phenomenon** with the scientific method, including claims of telepathy; selection of topic is independent of method -- there is nothing inherently "unscientific" about studying any subject. (Close-mindedness //is//, however, very unscientific.) \\ In other words, given that science gets us the most reliable ("best") knowledge to build on at any time, we should take it seriously. But not so seriously as to exclude the possibility that it's wrong. (Because in fact we already know that **all** scientific knowledge is wrong -- i.e. every scientific theory to date has limits to its scope that we know of.) |
|  How can we trust our knowledge?  | The scientific method is a **General Way of Producing Trustworthy Knowledge.** It is independent of topic. Therefore, it can also be used for AI systems. (In fact, it can easily be argued that something very similar to the scientific method is happening when humans learn cumulatively -- with a few caveats that we will carefully cover in this course.)   |

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====Models====
|  What it is  | A model is a "cartoon" of a phenomenon -- an information structure that captures the most important (preferably all the important) aspects of a phenomenon in question.  | 
|  All scientific theories present a model  | No matter how explicit or implicit, all scientific theories are models of the world. //Best known example: E=mc^2//   | 
|  Science vs. Mathematics  | Mathematics is **axiomatic**: Some a-priori premises are (and must be) assumed. \\ Science is non-axiomatic: We do not know the full set of rules that govern the universe, and we will never know.   |
|  Science vs. Engineering  | In science we look for the model; \\ in engineering we mold the world to behave like our model.  |
|  \\ Science + Math  | We strive to make scientific theories (models of the world) mathematical because of the //compactness, precision,// and //specificity// this can give us. However, it is not guaranteed solely through the use of math because //a model must detail how it maps to the thing it is a model of//. If this is not done properly the math provides //no benefits//. \\ Mapping a model to its reference: A good scientist does it properly; a bad scientist does it sloppily; the wannabe ignores it happily. \\ Bottom line: Being mathematical is //no guarantee// for good science - it is neither necessary nor sufficient.   |
|  Science + Engineering + Math: The Holy Trinity  | The three fields so defined support each other: Building better scientific models helps us engineer better; engineering better helps us build new tools for doing science better. Both are bootstrapped by philosophy and clarified through math. |
|  \\ The universe: Nothing is given  | How do we know that the sun will come up tomorrow? What evidence do we have? Can we prove it mathematically that the sun will come up tomorrow? \\ The only thing we know for sure is that we can perceive things in the world and that "I am here now". (This principle is most famously captured by Rene Descartes who wrote "I think, therefore I am".) \\ But since that perception is provided/generated by the same universe that we want to claim "exists" through those senses, using those grey cells, we cannot possibly know **for sure** what that really is, and hence whether it can be trusted. \\ Therefore, the universe is (and cannot be anything but) **non-axiomatic**.   |
|  \\ Computer Science  | A creative mix of empirical science, engineering and mathematics. \\ Direct testing of applications and programs; user studies.  \\ Models and simulations. \\ Logical and mathematical proofs.   |


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