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If the input signal is a sine wave, the steady state system response will be a sine wave at the same frequency, but with a change in phase. A system is linear if the response to a sum of input signals is the sum of the responses that would result from the individual input signals. Linear and Non-linear: The distinction between linear and non-linear dynamic systems is fundamental. The distinction is useful because somewhat different mathematical techniques are used for discrete and continuous modelling. For example: the size of a population of animals is an integer number, but if it is large it can be treated as a continuous variable time is continuous but provided we sample sufficiently quickly we can model it as a sequence of discrete steps. The mathematical models needed for research programmes are more complicated but the sequence of:ĭiscrete and continuous variables: Although we perceive time and space to be continuous, and variables that vary over space or time (often referred to as field or state variables) as discrete or continuous, we do not have to model variables in the same way. However, it would not be adequate for working out suitable sizes and positions for central heating radiators. Your rectangles will not correspond to the three dimensional shape of the room, and will not include details such as light switches, but the simple model is quite suitable for calculating the number of rolls of wallpaper you should buy. A more typical example is provided by the answer to the question: How much wallpaper do you need to redecorate your living room? You could probably model the area to be papered by rectangles, work out their areas, add them up, and make some allowance for matching edges of rolls and so on. The numbers represent the physical currency, or perhaps electronic credits, but the example is exceptional because no approximation need be involved. The most common example is arithmetic, which we use for calculating monetary transactions, amongst other things. We all use simple mathematical models in our everyday lives. It is called this because it leads to a predictive model that has the form of a weighted sum (a linear combination) of the predictor variables. This model leads to what is known as linear discriminant analysis. There are many ways in which the distributions might be modelled, but the most common assumes a particular class of forms for the distributions. In particular, we will have a sample of people who have known predictor variable values (such as age) and whom we have followed up so we know their outcome. Again, we shall build a model to do this, and again we will base our model on a sample of people. We would like to predict the future outcome, say recovery or not, on the basis of some of these variables. It will depend on many factors, including age, response to stimulation, and change in neurological function over the first 24 hours after the injury. In my experience, to be creative means to think from the impossible through the improbable to the probable.ĭiscriminant analysis: Prognosis means determining the likely future outcome, and is important for people who have suffered a head injury. An alternative approach for generating an 'impossible' or 'inventive' problem can be found in the ideal solution method in the Theory of Inventive Problem Solving, which has the Russian acronym 'TRIZ'. The versatile checklist could facilitate the generation of 'impossible' situations, tasks and problems. For best use of the versatile map, I recommend that you convert given issues to 'impossible' situations, tasks and problems. In the questions, the word 'object' may refer to a situation, task, activity, problem, opportunity, objective or project. Based on ideas in the template theory and PAO Thinking, a checklist of generic questions that can be used with the versatile map. When mindstorming, I usually play the role of a 'paoist', whose maxim is: 'every object in the universe is connected.' The ideas on a versatile map can therefore be generated intuitively, randomly and systematically with the view that everything will eventually be connected. Such intermediate prompters might later generate strategies or solutions that can then be included in the solutions-space. If an answer does not appear worthwhile, it can be categorised under the branch of (intermediate) idea prompters. In mindstorming, there is no right or wrong answer. On the versatile map, mindstorming is used to populate and enrich with ideas, the problem-definition, methods and solutions-spaces. Mindstorming simply means suspending judgement. It is a cross between mind mapping and brainstorming. When using the versatile map, words, sentences, paragraphs, drawings and/or tables are added to the existing branches of the template.