Ambiguous Quotes (13 quotes)
A chess problem is genuine mathematics, but it is in some way “trivial” mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful—“important” if you like, but the word is very ambiguous, and “serious” expresses what I mean much better.
Given any domain of thought in which the fundamental objective is a knowledge that transcends mere induction or mere empiricism, it seems quite inevitable that its processes should be made to conform closely to the pattern of a system free of ambiguous terms, symbols, operations, deductions; a system whose implications and assumptions are unique and consistent; a system whose logic confounds not the necessary with the sufficient where these are distinct; a system whose materials are abstract elements interpretable as reality or unreality in any forms whatsoever provided only that these forms mirror a thought that is pure. To such a system is universally given the name MATHEMATICS.
I think people get it upside down when they say the unambiguous is the reality and the ambiguous is merely uncertainty about what is really unambiguous. Let’s turn it around the other way: the ambiguous is the reality and the unambiguous is merely a special case of it, where we finally manage to pin down some very special aspect.
Journalists do not like to report on uncertainties. They would almost rather be wrong than ambiguous.
Keep in mind that new ideas are commonplace, and almost always wrong. Most flashes of insight lead nowhere; statistically, they have a half-life of hours or maybe days. Most experiments to follow up the surviving insights are tedious and consume large amounts of time, only to yield negative or (worse!) ambiguous results.
Man … begins life as an ambiguous speck of matter which can in no way be distinguished from the original form of the lowest animal or plant. He next becomes a cell; his life is precisely that of the animalcule. Cells cluster round this primordial cell, and the man is so far advanced that he might be mistaken for an undeveloped oyster; he grows still more, and it is clear that he might even be a fish; he then passes into a stage which is common to all quadrupeds, and next assumes a form which can only belong to quadrupeds of the higher type. At last the hour of birth approaches; coiled within the dark womb he sits, the image of an ape; a caricature of the man that is to be. He is born, and for some time he walks only on all fours; he utters only inarticulate sounds; and even in his boyhood his fondness for climbing trees would seem to be a relic of the old arboreal life.
Most classifications, whether of inanimate objects or of organisms, are hierarchical. There are “higher” and “lower” categories, there are higher and lower ranks. What is usually overlooked is that the use of the term “hierarchy” is ambiguous, and that two fundamentally different kinds of arrangements have been designated as hierarchical. A hierarchy can be either exclusive or inclusive. Military ranks from private, corporal, sergeant, lieutenant, captain, up to general are a typical example of an exclusive hierarchy. A lower rank is not a subdivision of a higher rank; thus, lieutenants are not a subdivision of captains. The scala naturae, which so strongly dominated thinking from the sixteenth to the eighteenth century, is another good illustration of an exclusive hierarchy. Each level of perfection was considered an advance (or degradation) from the next lower (or higher) level in the hierarchy, but did not include it.
No hypothesis concerning the nature of this 'something' shall be advanced thereby or based thereon. Therefore it appears as most simple to use the last syllable 'gen' taken from Darwin's well-known word pangene since it alone is of interest to use, in order thereby to replace the poor, more ambiguous word, 'Anlage'. Thus, we will say for 'das pangene' and 'die pangene' simply 'Das Gen' and 'Die Gene,' The word Gen is fully free from every hypothesis; it expresses only the safely proved fact that in any case many properties of organisms are conditioned by separable and hence independent 'Zustiinde,' 'Grundlagen,' 'Anlagen'—in short what we will call 'just genes'—which occur specifically in the gametes.
On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Science now finds itself in paradoxical strife with society: admired but mistrusted; offering hope for the future but creating ambiguous choice; richly supported yet unable to fulfill all its promise; boasting remarkable advances but criticized for not serving more directly the goals of society.
The marriage of reason and nightmare which has dominated the 20th century has given birth to an ever more ambiguous world. Across the communications landscape move the specters of sinister technologies and the dreams that money can buy. Thermonuclear weapons systems and soft drink commercials coexist in an overlit realm ruled by advertising and pseudoevents, science and pornography. Over our lives preside the great twin leitmotifs of the 20th century—sex and paranoia.
There are still psychologists who, in a basic misunderstanding, think that gestalt theory tends to underestimate the role of past experience. Gestalt theory tries to differentiate between and-summative aggregates, on the one hand, and gestalten, structures, on the other, both in sub-wholes and in the total field, and to develop appropriate scientific tools for investigating the latter. It opposes the dogmatic application to all cases of what is adequate only for piecemeal aggregates. The question is whether an approach in piecemeal terms, through blind connections, is or is not adequate to interpret actual thought processes and the role of the past experience as well. Past experience has to be considered thoroughly, but it is ambiguous in itself; so long as it is taken in piecemeal, blind terms it is not the magic key to solve all problems.
We live in an essential and unresolvable tension between our unity with nature and our dangerous uniqueness. Systems that attempt to place and make sense of us by focusing exclusively either on the uniqueness or the unity are doomed to failure. But we must not stop asking and questing because the answers are complex and ambiguous.