Gamogenesis

“ Hence, as functional deviation must ever be inducing structural deviation, each individual throughout the area occupied tends to become fitted for the particular habits which its particular conditions necessitate; and in so far, unfitted for the average habits proper to the species. But these undue specializations are continually checked by gamogenesis. ”

“ At the outset, we will turn our attention wholly to the antagonism displayed between the integrative process which results in individual evolution and the disintegrative process which results in multiplication of individuals; and this we will consider first as we see it under the several forms of agamogenesis, and then as we see it under the several forms of gamogenesis. We will next look at the antagonism between propagation and that evolution which is shown by increased complexity. ”

“ Just as, in each organism, incident forces constantly produce divergences from the mean state in various directions, which are constantly balanced by opposite divergences indirectly produced by other incident forces; and just as the combination of rhythmical functions thus maintained, constitutes the life of the organism; so, in a species, there is, through gamogenesis, a perpetual neutralization of those contrary deviations from the mean state which are caused in its different parts by different sets of incident forces ”

“ A polype, feeding on minute annelids and crustaceans which, flitting through the water, come in contact with its tentacles, and limited to that quantity of prey which chance brings within its grasp, buds out young polypes which, either as a colony or as dispersed individuals, spread their tentacles through a larger space of water than the parent alone can; and by producing them, the parent better insures the continuance of its species than it would do if it went on slowly growing until its nutrition was nearly balanced by its waste, and then multiplied by gamogenesis. ”

“ Thus, one of the main hardware functions of the brain is to make models of the external reality and to predict, by simulation on the model, the possible evolution of the associated external reality.
We already defined the reality as all the information which is or could be generated by a model. This means that we understand the external reality by the reality, which is generated by a model, which is associated with the external reality.
Example: For a given external reality, any person makes an associated model. Any person has his/her own model associated to the same external reality. ”

“ The cards receive the impress of these conceptions, and transmit to the various trains of mechanism composing the engine the orders necessary for their action. When once the engine shall have been constructed, the difficulty will be reduced to the making out of the cards; but as these are merely the translation of algebraical formulæ, it will, by means of some simple notations, be easy to consign the execution of them to a workman. Thus the whole intellectual labour will be limited to the preparation of the formulæ, which must be adapted for calculation by the engine. ”

“ This putative pattern R is empirically adequate as a theory of how this sequence of numbers behaves; it fits all the data we have been given. How do we know if this is indeed a genuine pattern, though? Here’s an answer that should occur to us immediately: we can continue to watch how the sequence of numbers behaves, and see if our predictions bear out. If we’ve succeeded in identifying the pattern underlying the generation of these numbers, then we’ll be able to predict what we should see next: we should see a ‘zero’ followed by a 'one,’ and then another ‘zero,’ and so on. ”

“ Some few of these remaining two millions devoted themselves to the adventure of discovery and exploration of places unseen, of other worlds and other planets. But fewer still devoted themselves to the highest adventure, the unseen places of the mind. Machines—with their irrefutable logic, their cold preciseness of figures, their tireless, utterly exact observation, their absolute knowledge of mathematics—they could elaborate any idea, however simple its beginning, and reach the conclusion. ”

“ It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the [Pg 28] science, which they must do in studying the engine. ”

“ Purely by chance, a man of the Dawn Civilization discovered a talisman—a small nonmechanical engine controlled by thought—giving him the power of traveling in time, and across time, and into the regions beyond time. There it led him to seven other talismans, and to a similar but larger engine of even greater power, which he named the Probability Engine. He took in with him seven accomplices, I being one, and together we used the Probability Engine to split time and make actual all possible worlds, preserving only the best of them, and—so we thought—destroying the rest. ”

“ Nothing lures a man to destruction quicker than a system that can be mathematically demonstrated. It gives an air of business to gambling which is soothing to the conscience of a person brought up on statistics. The system generally works beautifully at first; then a cog slips and you are mangled in the machinery before you know where you are. As young Forme left the table he felt a hand on his shoulder, and looking around, met the impassive gaze of Pony Rowell. ”

“ Again, who can foresee the consequences of such an invention? In truth, how many precious observations remain practically barren for the progress of the sciences, because there are not powers sufficient for computing the results! And what discouragement does the perspective of a long and arid computation cast into the mind of a man of genius, who demands time exclusively for meditation, and who beholds it snatched from him by the material routine of operations! Yet it is by the laborious route of analysis that he must reach truth ”

“ The bounds of arithmetic were however outstepped the moment the idea of applying the cards had occurred; and the Analytical Engine does not occupy common ground with mere "calculating machines." It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together general symbols, in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science. ”

“ The Analytical Engine, on the contrary, is not merely adapted for tabulating the results of one particular function and of no other, but for developing and tabulating any function whatever. In fact the engine may be described as being the material expression of any indefinite function of any degree of generality and complexity, such as for instance, which is, it will be observed, a function of all other possible functions of any number of quantities. ”

“ Therefore that engine can only produce results depending on data which have been arrived at by the explicit and actual working out of processes that are in their nature different from any that come within the sphere of its own powers. In other words, an analysing process must have been gone through by a human mind in order to obtain the data upon which the engine then synthetically builds its results. The Difference Engine is in its character exclusively synthetical, while the Analytical Engine is equally capable of analysis or of synthesis. ”

“ One such component which has evolved from bionics research is the Artron, or artificial neuron. Inside the Artron are logic gates and inhibit 137gates. By means of reward or punishment, the Artron learns to operate a “statistical switch” and send impulses to other Artrons or to a readout. There are two interesting parallels here besides the operation of a simulated neural net. One is the statistical approach to decisions and learning. The late John von Neumann theorized that the brain’s actions might be statistical, or based on probability. ”

“ We shall add some considerations about the speed of action on external reality. So, when we walk on a plane surface, for each step there is at least one simulation before the step is done. Due to a large number of internal and external factors, any step is unique. Thus, if we walk on a raw surface (a stony trail in the mountains, for instance) not only every step in based on a simulation but even during the execution of a step, it is possible to make a new simulation based on new data and so a step in execution can be modified at all time to meet the goal as ZAM requires. ”

“ Babbage’s engine is called a calculating machine only in a metaphorical sense, seeing that it does not evolve its results by any process at all resembling, or in any way analogous to, those of a human mind. It would be an absurd misstatement to say that a machine either reasons or predicates, only because it “marks in some way the existence, the co-existence, the succession, and the likeness and unlikeness of things.” ”

“ Progress in understanding and emulating human thinking shows a progression from a literacy-based model to a model rooted in the new pragmatic framework. Rule- based, pattern-matching systems generalize predicate calculus; neural networking is devoted to mimicking the way minds work, in a synthetic neuron-plex array; fuzzy logic addresses the limitations of Boolean calculus and the nondeterminism of neural networks, and concentrates on modeling imprecision, ambiguity, and undecidability as these are embodied in new human practical experiences. ”

“ Babbage, renouncing his original essays, conceived the plan of another system of mechanism whose operations should themselves possess all the generality of algebraical notation, and which, on this account, he denominates the Analytical Engine.
Having now explained the state of the question, it is time for me to develope the principle on which is based the construction of this latter machine. When analysis is employed for the solution of any problem, there are usually two classes of operations to execute: firstly, the numerical calculation of the various coefficients ”

“ Thirdly, economy of intelligence: a simple arithmetical computation requires to be performed by a person possessing some capacity; and when we pass to more complicated calculations, and wish to use algebraical formulæ in particular cases, knowledge must be possessed which pre-supposes preliminary mathematical studies of some extent. Now the engine, from its capability of performing by itself all these purely material operations, spares intellectual labour, which may be more profitably employed. ”

“ Thus it appears that the whole of the conditions which enable a finite machine to make calculations of unlimited extent are fulfilled in the Analytical Engine. The means I have adopted are uniform. I have converted the infinity of space, which was required by the conditions of the problem, into the infinity of time. The means I have employed are in daily use in the art of weaving patterns. It is accomplished by systems of cards punched with various holes strung together to any extent which may be demanded. ”

“ Then all worked, and gradually, in the great dome-case, there were stacked the memory-units of the new type, and into these fed all the sensation-ideas of all the science-machines, till nearly a tenth of them were used. Countless billions of different factors on which to work, countless trillions of facts to combine and recombine in the extrapolation that is imagination.
Then—a widely different type of thought-combine, and a greater sense-receptor. It was a new brain-machine. ”

“ The world at large had heard vaguely of Professor Van Dusen as The Thinking Machine. It was a newspaper catch-phrase applied to him at the time of a remarkable exhibition at chess; he had demonstrated then that a stranger to the game might, by the force of inevitable logic, defeat a champion who had devoted a lifetime to its study. The Thinking Machine! ”

“ As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise—By what course of calculation can these results be arrived at by the machine in the shortest time?
In the drawings I have prepared I proposed to have a thousand variables, upon each of which any number not having more than fifty figures can be placed. This machine would multiply 50 figures by other 50, and print the product of 100 figures. ”

“ But it would be a mistake to suppose that because its results are given in the notation of a more restricted science, its processes are therefore restricted to those of that science. The object of the engine is in fact to give the utmost practical efficiency to the resources of numerical interpretations of the higher science of analysis, while it uses the processes and combinations of this latter. ”

“ The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. ”