Networks .. and those who made them possible

The history of communication on Earth is extensive. Every living thing has means of communication. Trees, insects, molluscs, the entirety of the plant and animal kingdoms all communicating between and within individuals and communities of organisms, as they, and the cells which compose them, organise to feed, reproduce and defend themselves.

While some communication in nature involves transfer of matter, some involves heat transfer, and some optical and auditory events, a lot of communication is chemically based (genetic codes; hormonal codes; pheromone codes) and electro-chemically based (brain, nerves, sensory organs and muscle). Humans distinguish themselves by having developed telecommunication systems, from simple messages in the form of smoke signals, ambulatory verbal messages and message sticks, semaphores and written messages, to modern electronic systems such as telegraph, telephone, radio, radar, sonar, television, facsimile, and now, the internet.

Our capacity to utilise electronic networks for communication commences in Europe, at Kӧnigsberg, in the 18th century.

There is much barely-penetrable mathematical network theory, based around the foundations of network analysis as embodied in the Seven Bridges of Kӧnigsberg problem, solved by Leonhard Euler in 1735 (Euler Circuits and Walks).

Euler Paths and Cycles are concerned with crossing every edge in a “graph” exactly once without repeating. The vertices may be crossed more than once.

In the following, a Hamilton Path is concerned with crossing every vertex in a “graph” exactly once without repeating. The edges may be crossed more than once.

In an Euler Cycle, the Path ends where the Path began. In a Hamilton Cycle, the Path, likewise, ends where it began, such that the initial and final vertices are identical (the only allowable repeated vertices in a Hamilton Cycle or Path)

Notice that in Euler Paths we are looking at crossing (following) edges. In Hamilton Paths it’s vertices we are looking at.
leonhardeuler williamhamilton

Related to the Bridges of Kӧnigsberg problem in network theory, and often attributed to William Rowan Hamilton: Hamiltonian paths and cycles are named after the man who invented the icosian game, now also known as Hamilton’s puzzle, which involves finding a Hamiltonian cycle in the edge graph of the dodecahedron. Hamilton solved this problem using the icosian calculus, an algebraic structure based on roots of unity with many similarities to the quaternions (also invented by Hamilton). This solution does not generalize to arbitrary graphs.

Despite being named after Hamilton, Hamiltonian cycles in polyhedra had also been studied a year earlier by Thomas Kirkman, who, in particular, gave an example of a polyhedron without Hamiltonian cycles.[1] Even earlier, Hamiltonian cycles and paths in the knight’s graph of the chessboard, the knight’s tour, had been studied in the 9th century in Indian mathematics by Rudrata, and around the same time in Islamic mathematics by al-Adli ar-Rumi [fr]. In 18th century Europe, knight’s tours were published by Abraham de Moivre and Leonhard Euler.[2] (See Hamilton Cycles and Paths)
Much detailed logical thought goes into proving sufficient conditions for various types of network problems, however no global statement of necessary and sufficient conditions for the existence of Hamilton Paths in a general network exists.
Nevertheless, all communication involves the sharing of coded messages (for example conversing in the Korean language). Modern networks have developed from point to point connections which run “bitstreams”, to current “packet-switching” networks which convey packets of signals, in coded forms, according to a protocol which is expected or “understood” by all nodes through which the packet passes to find its own destination, and such that the packet can be assembled in the correct order (with other asynchronously arriving packets in the full transmission) and the contents of the transmission can be decoded and “read”, displayed or understood at the receiving end.
It is obviously a far cry from an analysis of “walks” in a city, divided by a river and with two islands in the river (Kӧnigsberg), to a worldwide web of optoelectronic, electronic and wireless networks, interlinked to successfully support the modern “hypertext”-based html browsers, and so much more.
A history of Computers as Machines needs to be considered alongside the history of Electrical and Electronic Networks themselves.
Some of the key people (Morse, Bell, Maxwell, Hertz, Marconi, Wiener and Shannon) involved in the development of electical communications are mentioned here: Electrical Communication Networks. For those who followed the Maxwell link, it may be interesting to know that when you involve an understanding of Einstein’s theory of Special Relativity (1905) in an analysis of an oscillating electron (such as you get in a vertical “rod” antenna driven by a radio transmitter, for example), Maxwell’s equations may be deduced but with the revelation of a specific relation between electricity and magnetism. This relationship means it is only necessary to specify the behaviour of an Electric Field (E) to completely determine the behaviour of what Maxwell had to call a separate Force – Magnetism – (though related by Maxwell’s Equations). The related Magnetic Field is often referred to a as H, but also called B. That’s correct – Electricity and Magnetism are both parts of a single physical phenomenon. Paul Dirac later went further, unifying the Electromagnetic Forces and the Weak Nuclear Force – in the so called ‘Electro-Weak Force’. Your editor is unsure of history after that.
Note that Einstein’s authority, scientifically, for bringing the transformation metric of this new non-Euclidean space, (which is the foundation of Relativity) into his theory of physical reality, came only after Hertz’s confirmation of the existence of the radio waves,  predicted originally by Maxwell himself.  It also required the putting to rest of the concept of an Ether as the medium which transmits light in the universe.  Einstein was able to confidently assume that light (electromagnetic radiation) is conveyed directly along rays embedded (as it were) in space-time itself.  There is no medium besides.  This was conclusively demonstrated in the Michelson- Morley Experiment
Light Waves, Radio Waves, Photons, Black Bodies, Planck’s Experiment, Einstein’s ‘thought experiments’, Electrons, Mass, Energy, Bosons and Gravitation
All of this opened the door to new non-Euclidean spaces, previously mathematical curiosities only, when the discrepancies between Newton’s Euclidean foundations and scientific reality began appearing, at first here in electromagnetism (but also in Cosmology and Astronomy).  Ever since the early 1900’s there were no “right angles” and the parallel lines (that never crossed according to Euclid’s Fifth Axiom of Geometry) now crossed, more like meridians of longitude on the earth’s surface, than the parallels of latitude, except immersed in the cosmos rather than confined to the earth’s surface.  By the way, Einstein simply needed to apply two traditional conservation principles (although with a relativistic flavour) to a situation in a thought experiment where a single photon collides with a mass at rest (zero acceleration). By equating the energy before (with mass considered at rest, thus all kinetic energy is photon’s) to the system energy after the collision, and requiring the mass to be a perfect Black Body, thus absorbing the photon entirely), but also utilising the relativistic conservation of momentum principle, he is able to easily demonstrate that E= mc2. The result sort of ‘drops out’ of the relativistic conservation principles. The same principles (Conservation of Momentum and Energy) are applied in modern particle colliders. In Newton’s Mechanics there is an ancestral set of Principles. The main point is to remark at the way Relativity has unified Electricity and Magnetism (and the Weak Nuclear Force, with Paul Dirac’s assistance), as well as unifying our concepts of Mass and Energy.  Euclid’s Fifth had to fall to make way for this new knowledge.
E & H are examples of  dependent “Vector Fields”. At every point in a vector field there exists a force on a body with magnitude and direction ie a vector. Fields of temperature, mass or energy values are examples, on the other hand, of scalar fields. Multi-dimensional Tensor fields exist in physics (eg Mechanical Stress in solids and viscous fluids, and space-time curvature Tensors in General Relativity). 

.. Just for clarity, Special Relativity (1905) is concerned with reconciling physics to the space-time transformation ‘metric’ revealed in Hertz’s Experiment’s verification of the existence of radio waves, but predictable from Maxwell’s equations before him. A ‘metric’ here refers to finding a formulaic way we may consistently model relative velocities, and other physical properties, between 2 observers traveling separately in space-time, in “light” of the fact that there is really nowhere to be taken as a zero velocity point and that we may only consistently measure velocities relative to the local velocity of light (radio waves equally). Einstein discovered the metric inherent in Maxwell’s equations, relating to electromagnetism, and argued that there can be only one metric in this universe, and that therefore Newton, a man who apparently walked out of his first opera, was wrong (in 1687) to assume a Euclidean ‘orthogonal’ space for physical reality, which naturally seemed to separate time from space. The metric of Maxwell’s equations revealed skewed axes in 4 dimensions where the upper limit to universal velocities is the speed of light. By progressing from this point, Einstein was able to unite our concepts of Electricity and Magnetism as well as uniting Energy and Mass.  Our concepts of Energy and Mass were unified by Einstein applying the Conservation of Energy Principle followed by the Conservation of Momentum Principle (in special relativistic formats) to a collision (in a thought-experiment) where a so-called Black Body absorbs a colliding photon fully. By equating the total Energy and Momentum prior to the collision with the total Energy and Momentum after, and utilising the Planck Relation for Energy of a photon E = hf, Albert was able to show with simple algebra and calculus that the total Energy of that system post collision E = mc2, where m is the mass of the black body (the photon has zero mass itself) and c is the velocity of light.

Planck’s experiment some few years after Hertz’s experiment, revealed to Einstein an interpretation of results stating light (and thus radio waves) is actually composed of light “particles” or quanta called photons. Albert deduced this publicly in a paper in 1904, giving birth to a field of research still continuing today, called quantum mechanics. Due to the incompatibility of the Classical Wave based theory of light with a particle based theory at the time, the effort to find the linking equations between quantum mechanics and the classical theory (adequate until Planck’s Experiment) led scientists to a probabilistic theory which Einstein always disowned. Incidentally Erwin Schrödinger also believed that there exists a deterministic underlying continuous theory possible in physics. The possibility that many events could happen simultaneously is required for the theory to work.

The answer in any case seems to lie in the success Schrӧdinger had in 1926, (and Werner Heisenberg at the same time), with an approach that replaced the value for total field Energy (E) with hf in a single frequency (laser) light field’s theoretical “Work Function”. The basic experimental relation E = hf (Energy of a photon = its frequency f multiplied by Plank’s constant h) is reliable and verifiable by anyone who wants to repeat Planck’s Experiment. The result of Schrӧdinger’s substitution in the field equation had to be integrated to uncover the general “Quantum Mechanical” version of the Wave Equation, which as required, approaches the behaviour of the Classical Wave Equation, as the value of Planck’s Constant is made to approach zero. This requirement is a way of mimicking the idea that Energy in a light field be taken as independent of frequency, in the classical limit. The Classical Wave Equation also applies to Sound waves in the limit, and thus there exist “Phonons” or stress/pressure particles, since the Quantum Mechanical Wave Equation also applies more accurately to sound/pressure/stress waves, including both types of seismic wave the shear waveform or aftershock, and the direct wave or primary shock, in similarity with the sonic boom and aftershock with supersonic objects (the shear wave arrives last). These waves are all carried in the final result by phonons in rays spreading out from the source(s).

The theoretical Schrӧdinger and Heisenberg treatments also matched predictions from practical absorption spectra experiments with Hydrogen, in a model of the Hydrogen Atom, with its single electron as a wave-particle, obeying the new Wave Equation, absorbing energy in stable quantum stages as predicted. The wavelike nature of electron beams themselves was experimentally established when Electron diffraction, in fact, was observed (1927) by C.J. Davisson and L.H. Germer in New York and by G.P. Thomson in Aberdeen, Scot. , thus supporting an underlying principle of quantum mechanics, “Wave Particle Duality”.

The Theory of General Relativity (1915) went further than Einstein’s Special Theory, as Special Relativity still rested upon a ‘flat’ space-time cosmology, whereas the General Theory concerned itself with further revelations, now about Gravitation; specifically, that it is caused by the local magnitude and direction of curvature of space-time in a “hyper-volume” (possibly a multiverse) of a larger number of dimensions (larger than 4, but otherwise unspecified).  This actual curvature of space-time is caused by the presence of matter (such as the earth or the sun or a pencil), and Einstein gave equations which accurately predict the behaviour of our solar system as well as real galaxies, contrary to Newton’s inconsistent predictions.  (Although, Einstein was never good with pencils .. they never weigh enough and they move too slowly – moreover it was Newton’s Mechanics that enabled the development of the fundamental Impulse/Momentum Equation of Rocketry and the Finite Element Method of Stress and Strain analysis, for the Apollo rocketships, that took men to the moon successfully, and any navigator since well before Newton would have been happy to plot the course – as it was done in Euclidean space).

However, much has happened in physics since publication of the General Theory of Relativity in 1915 ..  starting with quantum mechanics, Schrӧdinger, Heisenberg, Dirac and Stephen Hawking’s life devoted to reaching past Einstein into Black Holes .. go search .. and remember that although God may not play dice, people may be required to, in physics, because the human intellect needs a way to comprehend wave-particle duality, and many other probabilistic phenomena, such as the question of how is the particle, the Higgs boson, which confers “mass” on some objects (although not all), related to the universal curvature-of-space-time tensor in a generally-relativistic quantum mechanics, or, how would a Higgs boson be related to Gravitons, as emitted by pulsars?

(Please refer to History Of Computer Communication Networks (wiki).)
The following link is also a wikipedia article. History Of The Internet. (wiki)
timberners-lee
Tim Berners-Lee,
inventor of the World Wide Web
It should be known that it is in the nature of Internet Operations that data packets, in their journeys, may be “sniffed” by any interested hackers, operators or authorities, and that modern JavaScript allows the collection of certain types of network-behavioural information on people in the form of “cookies”. Despite the use of secure protocols such as the Secure Socket Layer (SSL a.k.a. “https://”), and a multitude of other practices to defend us, such as Anti-Virus and Anti-Malware Software, and firewalls and “tripwires”, the modern World Wide Web remains a very wild and dangerous place, brimming with schemes, strategies and tactics to take advantage of unsuspecting users, including “Ip-Spoofing”, where the fact that the source address in the Header section of any data packet may be altered, can be used to mount Denial of Service Attacks as well as allowing Device Masquerading .. see Security.
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