* “Compulsory pass/fail” means that you must do this to continue on to the next assigned Pn, and your instructor will continue to provide feedback until you have satisfied its requirements.
|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.
|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.” 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.”
|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|
|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 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.|| To count as “scientific” a theory must be disprovable. There must be some measures that are possible to do whose results could 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.
|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.)
|… yet methodology varies significantly by field||For example:
- Illegal to make experiments on living human brains
- Difficult to make comparative studies in sociology or space science.
|Computer Science|| Direct testing of applications and programs.
Models and simulations.
Logical and mathematical proofs.
|Model||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 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 science, engineering and mathematics.
Direct testing of applications and programs; user studies
Models and simulations.
Logical and mathematical proofs.