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Fig. – First Difference Engine. This impression from a woodcut was printed in 1853 showing a portion of the Difference Engine that was built in 1833 by Charles Babbage, an English mathematician, philosopher, inventor, and mechanical engineer who originated the concept of a programmable computer.

If all you have is a hammer, everything looks like to you as a nail” ~ Abraham Maslow, in “The Psychology of Science“, 1966.

Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible: if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple. […] Impart the same principle or show the same machine to an American or to one of our Colonists, and you will observe that the whole effort of his mind is to find some new application of the principle, some new use for the instrument“. ~ Charles Babbage quoted in Richard H. Babbage (1948), “The Work of Charles Babbage“, Annals of the Computation Laboratory of Harvard University, vol. 16.

At the beginning of the 1820’s, Babbage worked on a prototype of his first difference engine. Some parts of this prototype still survive in the Museum of the history of science in Oxford. This prototype evolved into the “first difference engine.” It remained unfinished and the completed fragment is located at the Museum of Science in London. This first difference engine would have been composed of around 25.000 parts, weighed around fourteen tons (13.600 kg), being 2.4 meters tall. Although it was never completed. He later designed an improved version, “Difference Engine No. 2”, which was not constructed until 1989–91, using Babbage‘s plans and 19th century manufacturing tolerances. It performed its first calculation at the London Science Museum returning results to 31 digits, far more than the average modern pocket calculator. (check Charles Babbage Wikipedia entry for more).

 

Soon after the attempt at making the difference engine crumbled, Babbage started designing a different, more complex machine called the Analytical Engine (fig. above). The engine is not a single physical machine but a succession of designs that he tinkered with until his death in 1871. The main difference between the two engines is that the Analytical Engine could be programmed using punched cards. He realized that programs could be put on these cards so the person had only to create the program initially, and then put the cards in the machine and let it run. It wasn’t until 100 years later that computers came into existence, with Babbage‘s work lying mostly ignored. In the late 1930s and 1940s, starting with Alan Turing‘s 1936 paper “On Computable Numbers, with an Application to the Entscheidungsproblem” (image below) teams in the US and UK began to build workable computers by, essentially, rediscovering what Babbage had seen a century before. Babbage had anticipated the impact of his Engine when he wrote in his memoirs: “As soon as an Analytical Engine exists, it will necessarily guide the future course of science.

Figure – Subcritical Turing bifurcation: formation of a hexagonal pattern from noisy initial conditions in the two-component reaction-diffusion system of Fitzhugh-Nagumo type. From left to rigth:a) Noisy initial conditions at t = 0. b) State of the system at t = 10. c) Almost converged state at t = 100. (source link)

Figure – Other patterns found in the above two-component reaction-diffusion system of Fitzhugh-Nagumo type. From left to rigth: a) Rotating spiral.b) Target pattern. c) Stationary localized pulse (dissipative soliton). (source link)

When an activator-inhibitor system undergoes a change of parameters, one may pass from conditions under which a homogeneous ground state is stable to conditions under which it is linearly unstable. The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number k=0 or a Turing bifurcation to a globally patterned state with a dominant finite wave number. The latter in two spatial dimensions typically leads to stripe or hexagonal patterns. [p.s. – a related lovely beach bay!.. state-phase diagram; Reaction-Diffusion by the Gray-Scott model: Pearson’s Parameterization (link) ]

Video – “BIG BANG BIG BOOM”: an unscientific point of view on the beginning and evolution of life … and how it could probably end. Direction and animation by BLU blublu.org / production and distribution by ARTSH.it / sountrack by Andrea Martignoni.

[…] It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically, unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading. […], A. M. Turing, “The Chemical Basis of Morphogenesis“, in Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Vol. 237, No. 641. (Aug. 14, 1952), pp. 37-72. (link)

“Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand. It turns out that chaos theory answers a question that mankind has asked for millennia – how did we get here?

Over this 2010 BBC 4 documentary “The Secret Life of Chaos“, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science – how does a universe that starts off as dust end up with intelligent life? How does order emerge from disorder? It’s a mind bending, counter-intuitive and for many people a deeply troubling idea. But Professor Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics. Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern. The natural world is full of awe-inspiring examples of the way nature transforms simplicity into complexity. From trees to clouds to humans – after watching this film you’ll never be able to look at the world in the same way again.” (description at YouTube).

[1 hour documentary in 6 parts: Part I (above), Part II, Part III, Part IV, Part V and Part VI. Even if you have no time, do not miss part 6. I mean, do really not miss it. Enjoy!]

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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