If you haven’t done so already, you may want to start by reading the Preface to Knowledge Engineering & Emerging Technologies.
January 31st, 2024 (4th ed)
When designing a system, what should you optimize? If it is a user-interface or process, you should be minimizing clicks, or process steps. But for hardware-software systems, the answer is not obvious, and a common mistake is to fail to consider the end-to-end problem. This article explores what is involved in optimizing end-to-end in hardware-software systems. The goal here is to minimize the overall complexity of the system, i.e. of the triple hardware-software-user combination. The following remarks set the stage for our discussion:
- “Any [one] can make things bigger, more complex. It takes a touch of genius, and a lot of courage, to move in the opposite direction.” – Ernst F. Schumacher, 1973, from “Small is Beautiful: A Study of Economics As If People Mattered”.
- “The goal [is] simple: to minimize the complexity of the hardware-software combination. [Apart from] some lip service perhaps, no-one is trying to minimize the complexity of anything and that is of great concern to me.” – Chuck Moore, [Moore, 1999] (For a succinct introduction to Chuck Moore’s minimalism, see Less is Moore by Sam Gentle, [Gentle, 2015]
- “We are reaching the stage of development [in computer science] where each new generation of participants is unaware both of their overall technological ancestry and the history of the development of their speciality, and have no past to build upon.” – J.A.N. Lee, [Lee, 1996, p.54].
- “The arc of change is long, but it bends towards simplicity”, paraphrasing Martin Luther King.
 Between complexity and simplicity, progress, and new layers of abstraction. Continue reading this article…
This is Part 2 in the Ancient Mathematics series. (Part 1: The Prehistoric Origins of Mathematics, Part 3: Exploring Cuneiform Culture 8500-2500 BCE)
Summary The written mathematics of ancient Iraq and Iran (Mesopotamia, Khuzistan) developed out of an administrative/bureaucratic program to control the surplus raw and manufactured goods of the settled societies of the late neolithic/early bronze age: grains & grain products, sheep & other herded animals, jugs of dairy fats & beer, rope & textiles. It evolved through a sequence of literary and mathematical innovations, each making more efficient the ability to record quantitative/metrological information and use it for planning and control. Initially, impressed tokens and pictographs were used whose meaning was clear by association. Subsequently, this repertoire was written signs was expanded in a consious effort to provide a standard, all-encompassing collection of signs/symbols (ideographs/logograms) that could represent all aspects of importance in early thought (professions, animals, foods, containers, textiles, etc.). The standard sign lists were spread through scribal schools to produce the scribes that administered the temple economies of the early city-states.
Uruk was the hegemonic centre of this innovation in mathematics and writing, starting from 3500 BCE. The increased administrative control generated economic efficiencies accelerating Uruk’s growth and which supported greater military effectiveness and the ability to dominate neighboring polities and support longer distance trading missions [Adams/2005], [Algaze/2013]. The success of Uruk’s structures had the effect of radiating the new inventions outward throughout the Greater Mesopotamian region (evidence in Aratta/Susa adoption of writing/adminstrative control), even reaching Anatolia (Turkey) in the far north (Uruk expansion phenomenon).
The gains in economic power and increased resilience to subsistence unpredictability conferred by the new planning and control capabilities, set in motion the development of a bureaucratic administrative culture in the southern Mesopotamian city states that, over the next 1000 years would reach its hypertrophic apex in the ambitious Ur III program under King Shulgi to plan, manage, and control all economic/productive assets in his vast empire through mathematics (c.2050 BCE). This required an army of scribes which in turn led to the standardization and systematization of the scribal school institution responsible for producing them.
Two examples of mathematical innovation are from the cattle redistribution center Puzrish-Dagan outside Nippur during the Ur III empire. One shows perfection of the form of tabular accounting (world’s earliest normalized two-dimensional table with rows and columns and sums in both dimensions) [Robson/2003]. The other shows the population growth modeling of a cattle-herd over 10 years with projected economic yields in dairy and cheese, solving, in modern terms, population difference equations in table form (see illustrated explanation of cuneiform tablet TCL 2, no.5499, [Nissen/1993: 97-102])
In this paper, we will look in more detail at mathematical development during the archaic period of writing (3500-3000 BCE) which gave rise to a new literate and quantitative layer in society in the main urban centres of Mesopotamia. Our thesis (which we have seen play out already in Part 1) is that technology (in this case mathematics/writing) and culture (in this case the impulse to plan/control) are inextricably linked. Their development influences the trajectory of the surrounding societies.
 Ur III mathematical model projecting annual dairy/cheese yields from a herd of 4 cows and a bull with assumptions on calving rates Download article (PDF)
Continue reading this article…
By Assad Ebrahim, on May 21st, 2014 (7,606 views) |
Topic: Maths--General Interest
Duelling with pistols. If you were the one issuing the challenge, your dilemma was that custom dictated that your adversary be allowed to shoot first. Only then, if you were still able to shoot, would you be permitted to seek “satisfaction”.
How much of an advantage does the first shooter really have? In this article, we build a simple probability model, and implement a numerical model in a few lines of R code.
 Two gentleman face off in the snow. Convention dictates the challenged shoots first. Continue reading this article…
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