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| public:e-217-prog-2010-1:thorisson-simulation-1 [2010/03/24 15:53] – thorisson | public:e-217-prog-2010-1:thorisson-simulation-1 [2024/04/29 13:33] (current) – external edit 127.0.0.1 |
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| | Simulation | A model of a process that can transform an initial state to a future state. S -> S' | | | Simulation | A model of a process that can transform an initial state to a future state. S -> S' | |
| | Scientific Method | In Western science, the usage of a set of principles that facilitate the production of reliable knowledge | | | Scientific Method | In Western science, the usage of a set of principles that facilitate the production of reliable knowledge | |
| | 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. | | | Theory (isl. kenning) | Explain the connections between things in the world. \\ “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, as explained by a particular theory | | | Hypothesis (isl. tilgáta) | Is a prediction about the relationship between a limited set of phenomena, as explained by a particular theory | |
| | Experimental design | “A planned interference in the natural order of events" | | | Experimental design | “A planned interference in the natural order of events" | |
| | Sample: Subject selection from a “population” A representative subset, drawn from a population, of the phenomenon we are studying. | Typically you can't study all the individuals of a particular subject pool, so in your experiment you use a sample and hope that the results generalize to the rest of the subjects. \\ Examples: \\ a. Siggi, Maggi and Biggi representing human males. \\ b. 10 lakes representing all freshwater on the Earth's surface. \\ c. rust on bottom of doors representing the overall state of an automobile. \\ A sample should be randomly chosen to (1) minimize spurious correlations and thus (2) maximize the generalizability of the results of measuring only a small subset of the phenomenon. | | | Dependent variable(s) | These are "the things we want to measure", e.g. the speedup seen with the new word processor. \\ Values are measured during and/or after the experiment. | |
| | Sample Distribution | If you sample data many times it may not always give the same result. \\ Example: If you measure the temperature repeatedly over a full day, the values you get will not be identical, they will be distributed. | | | Independent variables | These are factors that need to be controlled for the results to be more intelligible. Example: If we want to study the efficiency speedup seen by a new multi-cultural word processor we would want to have all or some of the cultures represented when we do the study. \\ We select their **values** - the values are known when we start an experiment. \\ Any independent variable must have at least 2 levels (values), so its effect can be evaluated. | |
| | Normal distribution | The Bell Curve. Also called Gaussian Distribution. \\ {{:public:e-217-prog-2010-1:bellcurve1.jpg|Bell Curve}}\\ [[public:e-217-prog-2010-1:thorisson-simulation-1:NaturalBellCurve|See picture]] | | | Sample: Subject selection from a “population” A representative subset, drawn from a population, of the phenomenon we are studying. | Typically you can't study all the individuals of a particular subject pool, so in your experiment you use a sample and hope that the results generalize to the rest of the subjects. \\ Examples: \\ a. Siggi, Maggi and Biggi representing human males. \\ b. 10 lakes representing all freshwater on the Earth's surface. \\ c. rust on bottom of doors representing the overall state of an automobile. \\ A sample should be randomly chosen to (1) minimize spurious correlations and thus (2) maximize the generalizability of the results of measuring only a small subset of the phenomenon. | |
| | Data | Typically “raw numbers” – only contain low-level semantics | | | 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"). | |
| | Information | Processed and prepared data | | | Sample Distribution | If you sample data many times it may not always give the same result. \\ Example: If you measure the temperature repeatedly over a full day, the values you get will not be identical, they will be distributed. | |
| | Statistics | Mathematical methods for dealing with uncertainty | | | Normal distribution | The Bell Curve. Also called Gaussian Distribution. \\ {{:public:e-217-prog-2010-1:bellcurve1.jpg|Bell Curve}}\\ [[public:e-217-prog-2010-1:thorisson-simulation-1:NaturalBellCurve|See picture]] | |
| | | Data | Typically “raw numbers” – only contain low-level semantics | |
| | | Information | Processed and prepared data | |
| | | Statistics | Mathematical methods for dealing with uncertainty | |
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| ====Where Simulation Fits In Science==== | ====Where Simulation Fits In Science==== |
| | Challenges | a. Grounding Simulations \\ b. Detail \\ c. Abstraction | | | Challenges | a. Grounding Simulations \\ b. Detail \\ c. Abstraction | |
| | Grounding | The connection between a simulation (model) and reality | | | Grounding | The connection between a simulation (model) and reality | |
| | Complexity | How complex should we make a model/simulation? | | | Complexity | How complex should we make a model/simulation? More complexity ≠ more explanatory power | |
| | Abstraction | How abstract can we make things? \\ What is the difference between simulating market behavior by modeling every individual consumer, versus modeling the market behavior grossly as "percent of those who buy"? | | | Abstraction | How abstract can we make things? \\ What is the difference between simulating market behavior by modeling every individual consumer, versus modeling the market behavior grossly as "percent of those who buy"? | |
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| | Exogeneous variables | Independent variable that affects a model without being affected by it, and whose qualitative characteristics and method of generation are not specified by the model builder. An exogenous variable is used for setting arbitrary external conditions, and not in achieving a more realistic model behavior. For example, the level of government expenditure is exogenous to the theory of income determination. [[http://www.businessdictionary.com/definition/exogenous-variable.html|REF]] | | | Exogeneous variables | Independent variable that affects a model without being affected by it, and whose qualitative characteristics and method of generation are not specified by the model builder. An exogenous variable is used for setting arbitrary external conditions, and not in achieving a more realistic model behavior. For example, the level of government expenditure is exogenous to the theory of income determination. [[http://www.businessdictionary.com/definition/exogenous-variable.html|REF]] | |
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| ==== When to Use Simulation ==== | ==== When to Use Simulation ==== |
| | When dealing with complex causal relationships | In systems such as societies, ecosystems, minds, a complex relationship exists, sometimes at many levels of detail, between phenomena. | | | Simulation | Simulations are the newest methodology that science offers in our study of the (natural) world. | |
| | When developing theories | Simulations help in formulating hypotheses about causal relationships, and thus. | | | 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 tying together many disconnected theories | Simulation can help tie disconnected theories together (theory generalization). | | | For visualizing mathematical models | When mathematical models are too complex to calculate in other ways. | |
| | As a tool for thinking about phenomena | In complex systems such as | | | When dealing with complex causal relationships | 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. \\ In systems such as societies, ecosystems, minds, a complex relationship exists, sometimes at many levels of detail, between phenomena. | |
| | | When developing theories | Simulations help in formulating hypotheses about causal relationships, and thus helps scientists create theories. | |
| | | When tying together many disconnected theories | Simulation can help tie disconnected theories together, even from different scientific fields (theory generalization). | |
| | | As a tool for thinking about phenomena | When studying complex systems it is often difficult to know where to start. Simulation and modeling can help in advancing in a principled way. | |
| | When real-world experiments are not possible | In scientific fields such as psychology and astrophysics, many types of experiments are not possible. | | | When real-world experiments are not possible | In scientific fields such as psychology and astrophysics, many types of experiments are not possible. | |
| | As augmentation to real-world experiments | It is not only when experiments are not possible that simulations can be a powerful aid. | | | As augmentation to real-world experiments | It is not only when experiments are not possible that simulations can be a powerful aid. | |
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| | [[http://cadia.ru.is/wiki/public:e-217-prog-2010-1:thorisson-simulation-2|Thórisson Lecture 2 ->]] |
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