A Quote by Ada Lovelace
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.
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Secondly, figures, the symbols of numerical magnitude, are frequently also the symbols of operations, as when they are the indices of powers. Wherever terms have a shifting meaning, independent sets of considerations are liable to become complicated together, and reasoning and results are frequently falsified.
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.
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.
Many persons who are not conversant with mathematical studies imagine that because the business of [Babbage’s Analytical Engine] is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly.
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.
I end with a word on the new symbols which I have employed. Most writers on logic strongly object to all symbols. ... I should advise the reader not to make up his mind on this point until he has well weighed two facts which nobody disputes, both separately and in connexion. First, logic is the only science which has made no progress since the revival of letters; secondly, logic is the only science which has produced no growth of symbols.
In fact a man in love or one consumed with hatred creates symbols for himself, as a superstitious man does, from a passion of conferring uniqueness on things or persons. A man who knows nothing of symbols is one of Dante's sluggards. This is why art mirrors itself in primitive rites or strong passions, seeking for symbols, revolving round the primitive taste for savagery, for what is irrational (blood and sex).
In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.
The twentieth-century artist who uses symbols is alienated because the system of symbols is a private one. After you have dealt with the symbols you are still private, you are still lonely, because you are not sure anyone will understand it except yourself. The ransom of privacy is that you are alone.
Language, after all, is only the use of symbols, and Art also can only affect us through symbols.
Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
The chief difficulty of modern theoretical physics resides not in the fact that it expresses itself almost exclusively in mathematical symbols, but in the psychological difficulty of supposing that complete nonsense can be seriously promulgated and transmitted by persons who have sufficient intelligence of some kind to perform operations in differential and integral calculus.
That’s what the human brain is there for—to turn the chaos of given experience into a set of manageable symbols. Sometimes the symbols correspond fairly closely to some of the aspects of the external reality behind our experience; then you have science and common sense. Sometimes, on the contrary, the symbols have almost no connection with external reality; then you have paranoia and delirium. More often there’s a mixture, part realistic and part fantastic; that’s religion.
I flee from symbols. I think those who don't want to solve problems go to the symbols. I'm looking for content.
The key to meditation is focusing on specific symbols. The symbols are the chakras.
It isn't up to the painter to define the symbols. Otherwise it would be better if he wrote them out in so many words! The public who look at the picture must interpret the symbols as they understand them.
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