# Center for Analysis and Design of Intelligent Agents

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##### Karl Popper

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## Lecture Notes

### Concepts

 Theory (Icel. 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.” Hypothesis (Icel. tilgáta) A prediction about the relationship between a limited set of phenomena, as explained by a particular theory. Data (Icel. gögn) Typically “raw numbers” – only contain low-level semantics Information (Icel. upplýsingar) Processed and prepared data – “data with a purpose” Randomness It is hypothesized in quantum physics that the universe may possibly be built on a truly random foundation, which means that some things are by their very nature unpredictable. Randomness in the aggregate, however, does seem to follow some predictable laws (c.f. the concept of “laws of probability”). Sampling Sampling theory uses statistics to tell us (a) how many random measurements we need to make to make a prediction about a whole group of which they are members and (b) how reliable the results are given the particular methods of sampling and recorded variations in the data. \\(Notice: not the same as Nyquist's sampling theorem, which states that to capture a waveform accuractly in digital form you need to sample it at twice its frequency.) Empiricism All knowledge comes through the senses Deduction (Icel. afleiðsla) “The facts speak for themsevles”. In deduction it's impossible for the premises to be true and the conclusion to be false. “You've got the facts, all you have to do is put them together, draw a natural conclusion.” Usually goes from the general to the particular. Induction (Icel. aðleiðsla, tilleiðsla) A generalization from a set of observations. Generalization can be about a class of observed phenomena or about a particular unobserved phenomenon that is part of the class. Experiment Typically refers to the most powerful method of science, the comparative experiment. There are other reliable ways of studying the world, and they can be scientific if one realizes their limits. Tautology (Icel. klifun, hringskýring) A 2-part sentence where the second part sounds like a logical conclusion of the first part but is simply a restatement of it. Example: “All Icleanders love shopping — because it's fun!” The key to the advancement of scientific knowledge. The ability of individuals and groups to create “coherent stories” of how phenomena in the world are connected and produce rigorous models that support the stories is a necessary condition for scientific progress.

### Science: Historical Beginnings

 Greek philosophers Roughly 2000-3000 years ago Plato, Aristoteles (his pupil) and Socrates (a big influence) – provided the beginnings of modern philosophical thought, which later became modern philosophy and science. Roger Bacon (1214 – 1294) English philosopher. One of the earliest proponents of the scientific method (empiricism). Descartes (1596 - 1650) French philosopher. Enormous influence on math (inventor of analytic geometry), science, philosophy of mind and philosophy in general. “I think, therefore I am.” “Cogito ergo sum.” Sir Francis Bacon (1561 - 1626) English philosopher. Influential proponent of the scientific method. Galileo Galilei (1564 - 1642) Italian philosopher and polymath. Influence on the use of quantitative measurements and the use of math. Karl Popper (1902 - 1994) Philosopher. Most famous for his claim that theories can only be tested through the falsification of hypotheses. Book: The Logic of Scientific Discovery (1959) Thomas Kuhn (1922 - 1996) Philosopher. Most famous for his theory of scientific change as intermittent challenges to the status quo. Book: The Structure of Scientific Revolutions (1962)

### Falsification of Hypotheses

 Very powerful method Given theory X, if one can deduce a relationship that has to hold between A and B, where A and B are the domain of a particular theory, and that relationship is falisifed through an experimental procedure that can be replicated by anyone, then obvioulsy theory X has been disproven. Problem Although scientific knowledge is the most reliable knowledge there is, most scientific theories at any point in time are theories in flux. Theories in flux Counter to what many think, theories almost never pop out complete and finished. The become assembled piece by piece, until there are so few pieces left that someone figures out the full picture. In the mean time, however, it is easy to falisfy hypotheses based on the theory, which, in the early stages, may not be much of a theory. Science builds theories The theory - hypothesis distinction is a convenience. In reality this is a continuum. Which means that theories are in various forms of growth. Conclusion We need a mixture of methods during the development of theories.

### Why We Need Statistics & When to Use it

 When building theories: We go from the particular to the general The path of induction: We make observations and draw conclusions Statistics are inappropriate in the early stages of scientific work When we are trying to “wrap our brain around a problem” When to use statistics When trying to uncover relationships between phenomena using measurements of particular limited observations. To have an idea of the generality of a few isolated results, we use statistics. Statistics is essential for any usability study, because it makes it easy to extrapolate results from experimental data with human subjects. It is essential when we want to generalize from particular observations done with imprecise measuring devices and/or under condtitions where we cannot control all independent variables. Randomness Key concept in statistics

### Why We Need Simulation and When to Use it

 Simulation Simulations are the newest methodology that science offers in our study of the (natural) world Theories Explains the connections between things in the world Relation between theories and simulations Before a model can be built and a simulation can be done we need a theory that tells us how things relate to each other When to use simulation When the complexity of that which is to be modeled/understood becomes so great that mathematical models are intractable and hypothesis falsification would take decades, centuries or millenia.

### The key to the advancement of scientific knowledge

 Theory: The coherent story The ability of individuals and groups to create “coherent stories” of how phenomena in the world are connected and produce rigorous models that support the stories is a necessary condition for scientific progress. Support of evidence The strongest form of evidence is rigorous hypothesis testing using scientific experimentation: clearly thought-out tests of the claims that naturally fall out of the Theory to be tested. It helps if the hypotheses concern unexpected results. Creating hypotheses Use both induction and deduction Creating experiments Use logic and tradition Executing experiments Use care Interpreting results Use rationality. Follow the data! (“Follow the duck, not the theory of the duck.”)

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