A Quote by Ada Lovelace
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.
Related Quotes
One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations.
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 science, which they must do in studying the engine.
But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.
Seurat and Signac mixed paintings with the dry and abstract laws of science. This approach, in my opinion, usually strays from the purpose of art in general. Because it means that one cannot expect from an artifact, that is created with mathematical laws, to establish an improbable and irrational relationship between the work and the viewer.
The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.
Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.
The Analytical Engine might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine… Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.
A man's knowledge may be said to be mature, in other words, when it has reached the most complete state of perfection to which he, as an individual, is capable of bringing it, when an exact correspondence is established between the whole of his abstract ideas and the things he has actually perceived for himself. His will mean that each of his abstract ideas rests, directly or indirectly, upon a basis of observation, which alone endows it with any real value; and also that he is able to place every observation he makes under the right abstract idea which belongs to it.
The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value.
The master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher - in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light ofthe past for the purposes of the future
Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.
Art has to be incredibly layered. Symbols, signifiers... layers that relate. Combine signifiers with more abstract notions. Push! Vary lines.
... scientific research is compounded of ... empirical procedures, general speculative ideas, and mathematical or abstract reasoning.
To abstract is to draw out the essence of a matter. To abstract in art is to separate certain fundamentals from irrelevant material which surrounds them.
The history of art cannot be properly understood without some reference to the history of science. In both we are studying the symbols by which man affirms his mental scheme, and these symbols, be they pictorial or mathematical, a fable or formula, will reflect the same changes.
Men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite , which dislocate all mathematical operations.
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