“Synergetics” is our name for a novel understanding of the nature of computation and how mathematics is manifested in reality. Computers can be designed using the principles of Synergetics to obtain intrinsic performance and capability many orders of magnitude beyond that of current technology.
Much of modern technology is based upon computers. Microprocessors are now employed with vast swathes of software for even the most trivial of applications. Requirements for “next generation” products are extrapolated upwards from the current generation. A vicious circle ensues, and complexity proliferates.
This costs the world billions of dollars a year in R&D. The underlying technology is a wheel overdue for reinvention.
It is routinely said that technology advances with ever-increasing pace. But does it? Complexity certainly does, but what about function, efficiency, usefulness? We believe that a kind of technological “Dark Age” began in the 1990s. Since then, integrated circuits have become smaller, faster and cheaper, and so too have the computing devices based upon them. The principles by which they operate, however, have not changed; progress is being made through brute force and expensively pushing the boundaries of physics.
We suggest that a better approach is to, instead, remove the barriers. In doing so, that brute force will not be needed and the pressure will be removed from physics. Greater technological development can be achieved through simpler underlying design principles. Why spend billions clambering over obstacles when it would be considerably easier and cheaper to take a route which avoids those obstacles?
The rise of Synergetics
At the turn of the century, in conjunction with our sister company ADR Ltd., we began developing a new computational theory, which we call “Synergetics”. The first prototype was demonstrated by ADR in 2000 using Xilinx Virtex FPGAs, and is still under active research.
The theory considers what is meant for data to even exist. The operational principles that arose almost trivialise the design of computational systems even on cosmological scales, while also being eminently suitable at miniature scales.
It is not a computer architecture – it can be applied to anything involving information, even physics and chemistry – but when applied to technology its obvious application is in computation.
Arbitrarily high computing power can be obtained with very low design complexity and cost because many small, simple units (simpler than a modern smartphone), can assimilate each other even over vast distance and act as a single unit of combined power and resources – a universal computational aether which can be tapped on demand – without any hardware or software coordination. An analogy that we use for this is water: trillions of raindrops add to the expanse of an ocean, yet the ocean is not composed of raindrops, it is always a single body of water. Today’s concepts, such as the cloud, mobile phones, and even the internet itself, could all be rendered obsolete.
When seen through Synergetic principles, many computational and technological problems disappear. It is found that many of the most serious problems facing current technological developments are self-inflicted and caused primarily through our perceptions of the problems — in essence, the wrong questions are asked because the problems are misinterpreted. It appears that the problems perpetuate because of a reluctance to let go of received wisdom.
Small answers to big questions
Interestingly, theoretical Synergetics gives a solution to the Halting Problem for all programs and inputs. To be more precise, it shows that the Halting Problem is incorrectly formulated, which in turn leads to the simple answer “yes“ — everything will halt within finite time. The question which should really be asked is not whether the program will halt, but rather what its output will be; a typically difficult example being Grandi’s series. However, even here if an ideal Synergetic computer were given the task of solving this through simple eternal summation of the infinite series then it would, within finite time, yield a superposition of 0 and 1 as its output.
A computer built on Synergetic principles is not programmed in the conventional sense, and similarly nor does it contain processors and memories. Instead, the work for it to perform is simply arranged within the system and the work will resolve itself to completion. An analogy to this is a chemical reaction — no program is required to tell two molecules how and when to interact, it is instead a natural process which occurs simply by their introduction to each other. Synergetic computers can thus be well suited to simulations such as protein folding, climate modelling, and n-body problems.
However, all work for a Synergetic computer can still be expressed using any pre-existing programming language, so there is no great learning curve or lead-time for use.
Synergetic principles allows systems to be built with significant security, such as being impervious to viruses, worms, and ‘hacking’. It is possible to ensure that eavesdroppers cannot access information without detection.
A particular problem for conventional multiprocessing computers is that of caching data that is shared between processors. If one processor changes its local cached copy of the data then the other processors need to see the change too, so as to not be working with out-of-date information. This requires the implementation of “cache coherency”. Typically this is either implemented with expensive and complex hardware, or with slow and complex software (aided by extra complexity in compilers, libraries, and operating systems).
Through the application of Synergetic computational principles, our Coherence-Free Cache eliminates all of this. It is a transparent self-contained black-box which can be inserted on a whim anywhere in a system, involves no communication of changes (can even be totally isolated), and its presence or absence requires no consideration on the part of any hardware, software, compiler, or programmer. It is undetectable in all but its reducing effect on up-stream latencies and down-stream traffic.
In essence, it divines global behaviour on any scale, even of that in the future, using only instantaneous local observational knowledge and with no external guidance or communication. To a casual outside observer of the cache as a black-box, it appears to exhibit the popular quantum-mechanical concepts of entanglement, action-at-a-distance, and even reversal of cause-and-effect. For example, cache X can determine that a copy of its data in cache Y will be modified in the future, and act accordingly in advance – without even knowing that cache Y exists.
With Synergetics and Coherence-Free Caches, data can be easily shared between computational systems of any size and across any distance, with every remote copy of the data always being correct without any part having to notify or observe any changes anywhere else. This can bring about a staggering increase in simplicity.
Of course, we do not break any laws of physics – such a cache can be implemented using nothing more than ordinary boolean logic circuits. The behaviour is easily understood and obvious once explained, but these apparently outrageous claims serve to illustrate the difference in understanding that Synergetics can bring to the mathematical philosophy and design of computational systems.