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
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.  The main point is to remark at the way Relativity has unified Electricity and Magnetism, 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 the first opera he attended, 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. 

The Theory of General Relativity (1915) went further, 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 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, Schroedinger, Heisenberg and Dirac .. go search ..

(Please refer to History Of Computer Communication Networks (wiki).)
The following link is also a wikipedia article. History Of The Internet. (wiki)
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 or authorities at any time, 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 .. see Security.