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1SSPDSSPD
Models & Paradigms
Another look at systems modelling
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2SSPD
Paradigm Shift
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3SSPD
Not Just Jackson• There is growing awareness of the need
for change in the software process• Large studies indicate that software
process is a feedback loop• Estimated that in every system there is
one implicit assumption for every 10 LOC
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4SSPD
Modelling Reality• The system and the domain in which it
is to reside form an infinite universe.• Our understanding of these must be
finite• The finished system must also be finite we must construct a model of the
infinity.
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5SSPD
Modelling Problems• But to reduce infinity to the finite requires
abstraction and thus omission of detail• It is here that our assumptions come in• e.g., let’s assume that all dates can be
represented in this system by two digits.• Or, we know that this system will not be
used fifteen years from now
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6SSPD
Dynamic Environment• We said previously that dynamic
environment creates problems…• …it can also cause our domain to
change...• …thus rendering our model (and hence
our system) invalid.
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7SSPD
What to Do?• Much effort is being spent on
understanding & improving the software process
• But attention has not been focused on system design methods and methodology
• Hence: a certain difficulty
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8SSPD
Difficulty?• Now recognised that software process is
not linear (as assumed by waterfall model)
• But that later stages inform earlier ones…
• …that is, as more is learnt, earlier assumptions are challenged and understanding is refined.
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9SSPD
So What?• Well, traditional methods hinder this
process…• …because the system architecture is
built upon foundations…• ...resulting from very large assumptions
about the system and its domain…• when we understand them the least.
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10SSPD
Feedback = Problem• But feedback from later stages causes
us to challenge our earlier assumptions…
• …which might make our entire system design sub-optimal, a bit flaky or even untenable
• Hence: plan to throw one away.
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11SSPD
Towards a Solution?• Get rid of the pointy-haired boss and his
dysfunctional decomposition
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12SSPD
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13SSPD
So how do we model?• Is there a way to construct a model that
reduces the scope for errors caused by our assumptions and finite understanding?
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14SSPD
Some Jargon• Model• Reality• Abstraction• Simulation• Real world
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15SSPD
What is a System• The system to be developed is nothing more
than a finite state machine which simulates the workings of a given real-world domain.
• Because it is finite & static it necessarily omits detail and is founded on abstractions & assumptions
• There is an uncertainty principle involved here
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16SSPD
Nature of a Model• A model is a representation of a real-
world.• It is this model which is realised to bring
about the working system• Hence, if the model is wrong, so is the
resultant system
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17SSPD
Nature of the Model• A model is necessarily an abstraction
because…• …it is only possible to make an exact
representation of a reality with a model that is exactly as complex and detailed as the original…
• …i.e, we replace the real-world with a carbon copy. Back to square one.
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18SSPD
Conundrum• So, there is a dichotomy.• Leaving out information can lead to loss
of quality• But we must leave out something else
we can’t produce a model.
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19SSPD
Compact Disc Analogy• Consider the compact disc.• Uses digital sampling to approximate a
sound wave.• By sampling at a rate of 44.1Khz at a
resolution of 16 bits we get• A recording with a dynamic range of
approx 96dB and a maximum frequency of 22050Hz.
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20SSPD
Consequences• Dynamic range of human ear is about
120db (which requires 20bit resolution)• Lose sounds above 22.05KHz even
though experiments show an effect on the human auditory system by sounds greater than this (old analogue tapes could typically reproduce 25Khz)
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21SSPD
Good Enough?• But CD deemed to be ‘good enough’• What about compression?• 1 second of CD audio requires:• 44100 x 16bits x 2(stereo channels) =
172.27Kbytes• = 10.09Mbytes per minute
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22SSPD
Mini Disc & MPEG-3• How do mini-discs get the ‘same’ sound
into such a small space? • How does MPEG-3 compress audio to
about 10% of its size without us noticing the difference?
• We make assumptions and abstractions
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23SSPD
Compression Model• These audio compression techniques
utilise psychoacoustic phenomena to delete information which our auditory system does not ‘hear’.
• But these are based on sound empirical observations and mathematical techniques
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24SSPD
Systems Modelling?
• So how do we model a system accurately without losing information?
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25SSPD
We Don’t Know
• Anyone fancy doing a PhD?
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26SSPD
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27SSPD
The Jackson Approach• In my opinion, Jackson’s approach is a
major step towards an accurate model.• Consider the following:
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28SSPD
“If you want to understand some aspect of the Universe, it helps if you simplify it as much as possible, and include only those properties and characteristics that are essential to understanding. If you want to determine how an object drops, you don’t concern yourself with whether it is new or old, is red or green, has an odour or not. You eliminate those things and thus do not needlessly complicate matters.”
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29SSPD
“Now, as you wish to know more and more about any phenomenon, or as a phenomenon becomes more complex, you need more and more elaborate equations, more and more detailed programming, and you end up with a computerized simulation that is harder and harder to grasp.”
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30SSPD
“Can’t you form a simulation of the simulation?” asked Hummin. “You would go down another degree.”
“In that case, you would have to eliminate some characteristic of the phenomenon which you want to include and your system becomes useless. The LPS - that is ‘the least possible simulation’ - gains in complexity faster than the object being simulated does and, eventually, the simulation catches up with the phenomenon.”
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31SSPD
“Thus, it was established thousands of years ago that the Universe as a whole, in its full complexity, cannot be represented by any simulation smaller than itself.”“In other words, you can’t get any picture of the Universe as a whole except by studying all the Universe.”
Hari Seldon talking to Hummin,from Prelude to Foundation,
by Isaac Asimov.
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32SSPD
Macbeth!• Aaarrghhh! What can we do?
Tomorrow, and tomorrow, and tomorrow, creeps in this petty pace from day to day to the last syllable of recorded time, and all our yesterdays have lighted fools the way to dusty death. Out, out, brief candle! Life's but a walking shadow, a poor player that struts and frets his hour upon the stage and then is heard no more: it is a tale told by an idiot, full of sound and fury, signifying nothing.
Macbeth, V:v
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33SSPD