(Left) Mammillaria elongata, or golden star cactus, displays a helical morphology. (Right) A magnetic cactus of dipole magnets on stacked bearings assumes phyllotactic spirals, similar to the biological cactus. With the magnetic cactus, physicists have investigated the dynamics of phyllotaxis.
One of humanity’s earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus appear with an intriguing regularity, providing a simple demonstration of mathematically complex patterns.
In a recent study, researchers have experimentally demonstrated for the first time a celebrated model of “phyllotaxis,” the study of mathematical regularities in plants. In 1991, S.L. Levitov proposed a model of phyllotaxis suggesting that the appearance of the Fibonacci sequence and golden mean in the pattern of spines on a cactus can be replicated for cylindrically constrained, repulsive objects. Now, researchers have constructed a “magnetic cactus” with 50 outward-pointing magnets acting as spines, which are mounted on bearings and free to rotate on a vertical axis acting as the plant stem. With this setup, the researchers, from Los Alamos National Laboratory in New Mexico; Cornell University in Ithaca, New York; and The Pennsylvania State University (PSU), have verified Levitov’s model, and their study has been published in a recent issue of Physical Review Letters.
Blavatsky’s masterwork on theosophy, covering cosmic, planetary, and human evolution, as well as science, religion, and mythology. Based on the Stanzas of Dzyan, with corroborating testimony from over 1,200 sources.
PROEM.
PAGES FROM A PRE-HISTORIC PERIOD.
An Archaic Manuscript — a collection of palm leaves made impermeable to water, fire, and air, by some specific unknown process — is before the writer’s eye. On the first page is an immaculate white disk within a dull black ground. On the following page, the same disk, but with a central point. The first, the student knows to represent Kosmos in Eternity, before the re-awakening of still slumbering Energy, the emanation of the Word in later systems. The point in the hitherto immaculate Disk, Space and Eternity in Pralaya, denotes the dawn of differentiation. It is the Point in the Mundane Egg (see Part II., “The Mundane Egg”), the germ within the latter which will become the Universe, the all, the boundless, periodical Kosmos, this germ being latent and active, periodically and by turns. The one circle is divine Unity, from which all proceeds, whither all returns. Its circumference — a forcibly limited symbol, in view of the limitation of the human mind — indicates the abstract, ever incognisablepresence, and its plane, the Universal Soul, although the two are one. Only the face of the Disk being white and the ground all around black, shows clearly that its plane is the only knowledge, dim and hazy though it still is, that is attainable by man. It is on this plane that the Manvantaric manifestations begin; for it is in this soul that slumbers, during the Pralaya, the Divine Thought,* wherein lies concealed the plan of every future Cosmogony and Theogony.
There has been a dramatic recent shift in sentiment in relation to the most appropriate model for developing software systems. The shift has marked a change from the tradition of preparing a detailed requirements specification as the first phase in the development cycle, to a less rigid adaptive evolutionary approach.
The ongoing goal of software engineering is to ensure that a system meets its primary aims in terms of the quality criteria of functionality, performance, reliability and efficiency. Achieving rigorous standards of reliability and efficiency has never been the major problem for developers; rather it has been the potential for basing the system’s requirements specification on obsolete or inadeqaute premises, which on completion delivers sub-optimal outcomes.
This is similar to the mathematical problem of using excellent deductive logic to draw conclusions from a set of axioms, but reaching a wrong conclusion because the axioms themselves are incorrect or incomplete.
Time and again this Archilles heel of software development emerges- particularly when a project is large, complex and operates within a dynamic environment. Systemic failure is more often the norm and the litany of collapsed projects keeps growing; particularly in the government and multinational business domains of procurement, supply, logistics, human resources, health, education, customer services etc.
European researchers have created a new software abstraction called Autonomic Communication Elements (ACEs) which will enable ecosystems for service networks, and make the future ‘internet of things’ a reality, now.
The internet is evolving in front of our eyes: Web 2.0 is beginning to reach it is potential as a ‘platform’, a computing and service delivery system in its own right.
At the same time, we are already seeing the emergence of Telco 2.0: telecommunications providers are seeking to create the same sort of open environment for user-generated content and services potential that the web is now renowned for.
Services like mash-ups, combining applications such as Google maps and real estate listings to provide powerful new services from currently available tools and data. For example, Telco 2.0 will allow users to combine mapped property information with voicemail, SMS and other telecommunications enablers.
And this is just a prelude to other, perhaps more sophisticated, technologies like Web 3.0, the so-called ‘semantic web’. Add to this the ‘future internet’ and the proposed ‘internet of things’ linking people, devices, telecoms and data networks into one, vast network of networks.
It is an ambitious vision, but it all invites increasing complexity; complexity that could kill innovation before it gains traction.
Economic law of increase of Kolmogorov complexity. Transition from financial crisis 2008 to the zero-order phase transition (social explosion)
V.P.Maslov:In Maslov (2003), a two level model of the occurrence of financial pyramid (bubbles) has been considered. We also considered the mathematical analogy of this model to Bose condensation. In the present paper, we explain why Ponzi schemes and bubbles result in a crisis in real economics. In Maslov (2005), the law of increase of entropy in financial systems, and consequently increase of Kolmogorov complexity, is formulated. If this law is broken, the financial system makes a phase transition to a different state. In Maslov (2005) the author considered a two level model of the zeroth-order phase transition which was interpreted in Maslov (2006) as an analog of social catastrophe. In the present paper we also examine this model.
(Left) Mammillaria elongata, or golden star cactus, displays a helical morphology. (Right) A magnetic cactus of dipole magnets on stacked bearings assumes phyllotactic spirals, similar to the biological cactus. With the magnetic cactus, physicists have investigated the dynamics of phyllotaxis.
