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| public:t-713-mers:mers-26:concepts_terms [2026/08/18 10:47] – [Working Definition of Intelligence] thorisson | public:t-713-mers:mers-26:concepts_terms [2026/08/22 14:08] (current) – [Correlation, Knowledge, Causation] thorisson |
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| | Correlation | Some factors/variables co-vary when changes in one variable are related with changes in the other, negative or positive. | | | Correlation | Some factors/variables co-vary when changes in one variable are related with changes in the other, negative or positive. | |
| | Correlation: Powerful source of information | Any variables in the world can be measured for correlation (i.e. to see if they are correlated). Only two variables are needed (independent and dependent) for doing correlation studies. | | | Correlation: Powerful source of information | Any variables in the world can be measured for correlation (i.e. to see if they are correlated). Only two variables are needed (independent and dependent) for doing correlation studies. | |
| | Main operating principle behind correlation | There is no causation without correlation. \\ BUT: It is not guaranteed to be measurable. | | | Main operating principle of correlation | \\ There is no causation without correlation. \\ BUT: It is not guaranteed to be measurable (at a particular time using particular means). | |
| | Correlation: Pitfall | Correlation does not imply causation between the variables measured! \\ BUT: ALL correlation that is NOT a coincidence has a cause. | | | Correlation: Pitfall | Correlation does not imply causation between the variables measured! \\ BUT: ALL correlation that is NOT a coincidence has a cause. | |
| | Modeling Correlation | A model that makes use of observed correlation between A and B is only good for prediction, not for manipulation; to be useful for manipulation (goal-directed behavior and planning) it must include the causal direction of the relationship between A and B. | | | Modeling Correlation | A model that makes use of observed correlation between A and B is only good for prediction, not for manipulation; to be useful for manipulation (goal-directed behavior and planning) it must include the causal direction of the relationship between A and B. | |
| | Causal Relations are Invisible | Causal relations do not jump out at us when we observe something unfamiliar because the cause and effect are "spread out" over time -- cause-effect happens over time, as the cause must happen before the effect. | | | Causal Relations are "Invisible" | Causal relations do not jump out at us when we observe something unfamiliar because the cause and effect are "spread out" over time -- cause-effect happens over time, as the cause must happen before the effect. | |
| | Modeling Cause-Effect | Intelligent agents can model cause and effect with many methods; two of them are invention (coming up with a wild idea for the relationship betweeen A and B, e.g. that spirits make people sick) and discovery (through observation and experimentation with A and B, e.g. that unclean surgical knives can bring disease-carrying material between people). | | | Modeling Cause-Effect | Intelligent agents can model cause and effect with many methods; two of them are invention (coming up with a wild idea for the relationship betweeen A and B, e.g. that spirits make people sick) and discovery (through observation and experimentation with A and B, e.g. that unclean surgical knives can bring disease-carrying material between people). | |
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| | \\ 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.// | | | \\ 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.// | |
| | 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. // | | | 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. // | |
| | Causal Relations | A relation between two or more 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) | | | Causal Relations | A relation between two or more entities that makes one predictable from the other. // \\ Examples: If someone flips the light switch, the lights will come on. (Deduction) // If I want the light to shine, I can flip the light switch. (How to achieve a goal) | |
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| | How are they 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. | | | How are they 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. | | | Why does it work? | Because the world's behavior is/seems rule-based. | |
| | Deduction | Mathematical deduction is axiomatic - **always** Boolean (true or false). \\ Scientific deduction is **never** axiomatic - it can always be (potentially) disproven; we say it is //defeasible//. \\ // IRL we do deduction (of the latter kind) all the time, e.g. when picking option B to meet when you already said you cannot do option A.// | | | Deduction | Mathematical deduction is axiomatic - **always** Boolean (true or false), because we give ourselves that it is. \\ Scientific deduction is **never** axiomatic - it can always be (potentially) disproven; we say it is //defeasible//. \\ // IRL we do deduction (of the latter kind) all the time, e.g. when picking option B to meet when you already said you cannot do option A.// (NB: Real-world constraints are non-axiomatic, as they may actually not hold; see 'non-axiomatism' below.) | |
| | Abduction | Mathematical abduction can be completely verified through its axioms. \\ Scientific abduction can always be challenged (bc we will never posses 'the axioms of the universe' -- the entire blueprint for the complete history of everything, so any generalization about it may at any point be found to have exceptions). \\ //IRL: Choosing the side-entrance when we see that the front door is locked (which might still be wrong).// | | | Abduction | Mathematical abduction can be completely verified through its axioms. \\ Scientific abduction can always be challenged (bc we will never posses 'the axioms of the universe' -- the entire blueprint for the complete history of everything, so any generalization about it may at any point be found to have exceptions). \\ //IRL: Choosing the side-entrance when we see that the front door is locked (which might still be wrong).// | |
| | Induction | The best method for verifying induction in mathematics is //mathematical proof.// \\ In science, induction can never be //proven//. This is one reason why scientific theories must instead be formulated in a way that they can be //disproven// (cf. Karl Popper). \\ // IRL: Generalizations are made in the form of rules of thumb all the time; mostly we don't care whether they are always true or not, only how //useful// they are in particular situations for particular purposes.// | | | Induction | The best method for verifying induction in mathematics is //mathematical proof.// \\ In science, induction can never be //proven//. This is one reason why scientific theories must instead be formulated in a way that they can be //disproven// (cf. Karl Popper). \\ // IRL: Generalizations are made in the form of rules of thumb all the time; mostly we don't care whether they are always true or not, only how //useful// they are in particular situations for particular purposes.// | |
| | Analogy | Used by scientists, mathematicians, and average Joe and Jane to come up with new ideas, compare and contrast, and analyze anything the heart desires. | | | Analogy | Used by scientists, mathematicians, and average Joe and Jane to come up with new ideas, compare and contrast, and analyze anything the heart desires. | |
| | Reasoning in \\ Maths vs. Science | Reasoning is different in maths than in science because to do math we //must know all the rules completely up front//. The main role of maths is to inspect what the rules imply. \\ In science //all rules are hidden.// The main role of science is to //uncover the rules//. | | | Reasoning in \\ Maths vs. Science | Reasoning is different in maths than in science because to do math we //must know all the rules completely up front//. The main role of maths is to inspect what the rules imply. \\ In science //all rules are hidden.// The main role of science is to //uncover the rules//. | |
| | Axiomatic vs. \\ Non-axiomatic | In axiomatic reasoning we know for a fact \\ 1. we have the complete set of rules \\ 2. all the rules are true, and that \\ 3. if we strictly follow the rules we will have absolute truth every time. \\ In non-axiomatic reasoning, none of the above holds. \\ //So how is it then that we can reason?// | | | Axiomatic vs. \\ Non-axiomatic | In axiomatic reasoning we know for a fact \\ 1. we have the complete set of rules \\ 2. all the rules are true (by definition), and that \\ 3. if we strictly follow the rules we will have absolute truth every time. \\ In non-axiomatic reasoning, none of the above holds. \\ //So how is it then that we can reason?// | |
| | Empirical Reasoning | For reasoning in the physical world, we must assume that we possibly got things wrong. But //some things are more wrong than others.// To ensure that we use the best knowledge we have for any task X, we must do bookkeeping about //what works and what doesn't in what situations//. | | | Empirical Reasoning | For reasoning in the physical world, we must assume that we possibly got things wrong. But //some things are more wrong than others.// To ensure that we use the best knowledge we have for any task X, we must do bookkeeping about //what works and what doesn't in what situations//. | |
| | Defeasible Reasoning | Reasoning that is based on assumptions and conclusions that can be refuted is called //defeasible reasoning//. | | | Defeasible Reasoning | Reasoning that is based on assumptions and conclusions that can be refuted is called //defeasible reasoning//. | |
| | 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. | | | 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". | | | 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, in practice) 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 not a bug but a //**feature!**:// Exposing the limits of our theories by demonstrating in which contexts they are incorrect allows us to come up with better theories. | | | \\ 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, in practice) 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 not a bug -- it's science's //**central feature!**:// 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==== | ====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.) | | | **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**. \\ //Examples: Rocks. Mountains. Planets.// (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.) | | | 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.) | | | 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.) | |
| | Science vs. Engineering | In science we look for the model; \\ in engineering we mold the world to behave like our model. \\ \\ // Example for science: // \\ [phenomenon] // We see something interesting and call it "**intelligence**". // \\ [model] // We come up with theories for how it works. // \\ [empirical research] // We test the models through systematic creation and evaluation of hypotheses. // \\ [create new models] // We revise the theory. // \\ \\ // Example for engineering:// \\ [model] // We have a theory of intelligence. // \\ [engineering] // We want to build an intelligent system. // \\ [implementation] // We use the theory as a blueprint. // \\ [requirements and theory] // We make sure it behaves to its specifications. // | | | Science vs. Engineering | In science we look for the model; \\ in engineering we mold the world to behave like our model. \\ \\ // Example for science: // \\ [phenomenon] // We see something interesting and call it "**intelligence**". // \\ [model] // We come up with theories for how it works. // \\ [empirical research] // We test the models through systematic creation and evaluation of hypotheses. // \\ [create new models] // We revise the theory. // \\ \\ // Example for engineering:// \\ [model] // We have a theory of intelligence. // \\ [engineering] // We want to build an intelligent system. // \\ [implementation] // We use the theory as a blueprint. // \\ [requirements and theory] // We make sure it behaves to its specifications. // | |
| | Why AI is special | Most research fields rely primarily on either the scientific research approach or the engineering approach. \\ //**AI is special in that it is committed to doing both.**// \\ (Although it does not always operate accordingly.) \\ AI is also the only field of science explicitly committed to the phenomenon of intelligence. | | | Why AI is special | Most research fields rely primarily on either the scientific research approach or the engineering approach. \\ //**AI is special in that it is committed to doing both.**// \\ (Although it does not always operate accordingly.) \\ AI is also the only field of science explicitly committed to the phenomenon of intelligence. | |
| | \\ 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 + 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 obliviously. \\ 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. | | | 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 doubt, therefore 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**. | | | \\ 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 doubt, therefore 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** to us. | |
| | \\ 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. | | | \\ 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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