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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index S > Category: Sequence

Sequence Quotes (41 quotes)

The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiassed by personal feeling is characteristic of what may be termed the scientific frame of mind.
From The Grammar of Science (1892), 8.
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A comparison between the triplets tentatively deduced by these methods with the changes in amino acid sequence produced by mutation shows a fair measure of agreement.
In Nobel Lecture (11 Dec 1962). Collected in Nobel Lectures, Physiology or Medicine 1942-1962 (1964).
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A DNA sequence for the genome of bacteriophage ΦX174 of approximately 5,375 nucleotides has been determined using the rapid and simple “plus and minus” method. The sequence identifies many of the features responsible for the production of the proteins of the nine known genes of the organism, including initiation and termination sites for the proteins and RNAs. Two pairs of genes are coded by the same region of DNA using different reading frames.
[Paper co-author]
Frederick Sanger, et al., 'Nucleotide Sequence of Bacteriophage ΦX174 DNA', Nature (1977), 265, 687.
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A final proof of our ideas can only be obtained by detailed studies on the alterations produced in the amino acid sequence of a protein by mutations of the type discussed here.
In Nobel Lecture (11 Dec 1962). Collected in Nobel Lectures, Physiology or Medicine 1942-1962 (1964).
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A noteworthy and often-remarked similarity exists between the facts and methods of geology and those of linguistic study. The science of language is, as it were, the geology of the most modern period, the Age of the Man, having for its task to construct the history of development of the earth and its inhabitants from the time when the proper geological record remains silent … The remains of ancient speech are like strata deposited in bygone ages, telling of the forms of life then existing, and of the circumstances which determined or affected them; while words are as rolled pebbles, relics of yet more ancient formations, or as fossils, whose grade indicates the progress of organic life, and whose resemblances and relations show the correspondence or sequence of the different strata; while, everywhere, extensive denudation has marred the completeness of the record, and rendered impossible a detailed exhibition of the whole course of development.
In Language and the Study of Language (1867), 47.
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A science cannot be played with. If an hypothesis is advanced that obviously brings into direct sequence of cause and effect all the phenomena of human history, we must accept it, and if we accept it, we must teach it.
In The Degradation of the Democratic Dogma (1919), 131.
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All revolutionary advances in science may consist less of sudden and dramatic revelations than a series of transformations, of which the revolutionary significance may not be seen (except afterwards, by historians) until the last great step. In many cases the full potentiality and force of a most radical step in such a sequence of transformations may not even be manifest to its author.
The Newtonian Revolution (1980), 162.
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An honest man, armed with all the knowledge available to us now, could only state that in some sense, the origin of life appears at the moment to be almost a miracle, so many are the conditions which would have had to have been satisfied to get it going. But this should not be taken to imply that there are good reasons to believe that it could not have started on the earth by a perfectly reasonable sequence of fairly ordinary chemical reactions. The plain fact is that the time available was too long, the many microenvironments on the earth's surface too diverse, the various chemical possibilities too numerous and our own knowledge and imagination too feeble to allow us to be able to unravel exactly how it might or might not have happened such a long time ago, especially as we have no experimental evidence from that era to check our ideas against.
In Life Itself: Its Origin and Nature (1981), 88.
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Earlier this week … scientists announced the completion of a task that once seemed unimaginable; and that is, the deciphering of the entire DNA sequence of the human genetic code. This amazing accomplishment is likely to affect the 21st century as profoundly as the invention of the computer or the splitting of the atom affected the 20th century. I believe that the 21st century will be the century of life sciences, and nothing makes that point more clearly than this momentous discovery. It will revolutionize medicine as we know it today.
Senate Session, Congressional Record (29 Jun 2000) Vol. 146, No 85, S6050.
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Gates is the ultimate programming machine. He believes everything can be defined, examined, reduced to essentials, and rearranged into a logical sequence that will achieve a particular goal.
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Gel’fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel’fand found hedgehogs lurking in the rows of his spectral sequences!
In '1991 Ruth Lyttle Satter Prize', Notices of the American Mathematical Society (Mar 1991), 38, No. 3, 186. This is from her acceptance of the 1991 Ruth Lyttle Satter Prize.
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However, the small probability of a similar encounter [of the earth with a comet], can become very great in adding up over a huge sequence of centuries. It is easy to picture to oneself the effects of this impact upon the Earth. The axis and the motion of rotation changed; the seas abandoning their old position to throw themselves toward the new equator; a large part of men and animals drowned in this universal deluge, or destroyed by the violent tremor imparted to the terrestrial globe.
Exposition du Système du Monde, 2nd edition (1799), 208, trans. Ivor Grattan-Guinness.
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I think it [the World Series] should be called the World Sequence.
As given in essay, Ronald Coifman and Robert S. Strichartz, 'The School of Antoni Zygmund', collected in Peter Duren (ed.), A Century of Mathematics in America (1989), 348. The essay states Zygmund was “walking past a lounge in the University of Chicago that was filled with a loud crowd watching TV, he asked one of his students what was going on. The student told him that the crowd was watching the World Series and explained to him some of the features of this baseball phenomenon. Zygmund thought about it all for a few minutes and commented” with the subject quote above. The authors acknowledge students of Zygmund provided personal recollections to them for the essay in general. Webmaster speculates the quote is from a student recollection, and not necessarily verbatim.
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I want to argue that the ‘sudden’ appearance of species in the fossil record and our failure to note subsequent evolutionary change within them is the proper prediction of evolutionary theory as we understand it ... Evolutionary ‘sequences’ are not rungs on a ladder, but our retrospective reconstruction of a circuitous path running like a labyrinth, branch to branch, from the base of the bush to a lineage now surviving at its top.
…...
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In gaining knowledge you must accustom yourself to the strictest sequence. You must be familiar with the very groundwork of science before you try to climb the heights. Never start on the “next” before you have mastered the “previous.”
Translation of a note, 'Bequest of Pavlov to the Academic Youth of his Country', written a few days before his death for a student magazine, The Generation of the Victors. As published in 'Pavlov and the Spirit of Science', Nature (4 Apr 1936), 137, 572.
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It will be possible, through the detailed determination of amino-acid sequences of hemoglobin molecules and of other molecules too, to obtain much information about the course of the evolutionary process, and to illuminate the question of the origin of species.
'Molecular Disease and Evolution'. Typescript of the Rudolph Virchow Lecture (5 Nov 1962). Quoted in T. Hager, Force of Nature: The Life of Linus Pauling (1997), 541.
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Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
As quoted in G. Simmons Calculus Gems (1992).
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My original decision to devote myself to science was a direct result of the discovery which has never ceased to fill me with enthusiasm since my early youth—the comprehension of the far from obvious fact that the laws of human reasoning coincide with the laws governing the sequences of the impressions we receive from the world about us; that, therefore, pure reasoning can enable man to gain an insight into the mechanism of the latter. In this connection, it is of paramount importance that the outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life.
'A Scientific Autobiography' (1948), in Scientific Autobiography and Other Papers, trans. Frank Gaynor (1950), 13.
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Not only do the various components of the cells form a living system, in which the capacity to live, react, and reproduce is dependent on the interactions of all the members of the system; but this living system is identical with the genetic system. The form of life is determined not only by the specific nature of the hereditary units but also by the structure and arrangement of the system. The whole system is more than the sum of its parts, and the effect of each of the components depends on and is influenced by all previous reactions, whose sequence is in turn determined by the whole idiotype.
'Cytoplasmic Inheritance in Epilobium and Its Theoretical Significance', Advances in Genetics (1954), 6, 320.
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Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
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Placed as the fossils are in their several tiers of burial-places the one over the other; we have in them true witnesses of successive existences, whilst the historian of man is constantly at fault as to dates and even the sequence of events, to say nothing of the contradicting statements which he is forced to reconcile.
Siluria (1872), 476.
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Science quickens and cultivates directly the faculty of observation, which in very many persons lies almost dormant through life, the power of accurate and rapid generalizations, and the mental habit of method and arrangement; it accustoms young persons to trace the sequence of cause and effect; it familiarizes then with a kind of reasoning which interests them, and which they can promptly comprehend; and it is perhaps the best corrective for that indolence which is the vice of half-awakened minds, and which shrinks from any exertion that is not, like an effort of memory, merely mechanical.
Anonymous
Report of the Royal Commission on Education (1861), Parliamentary Papers (1864), Vol 20, 32-33, as cited in Paul White, Thomas Huxley: Making the "Man of Science" (2003), 77, footnote. Also quoted in John Lubbock, The Pleasures of Life (1887, 2007), 63.
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The body of science is not, as it is sometimes thought, a huge coherent mass of facts, neatly arranged in sequence, each one attached to the next by a logical string. In truth, whenever we discover a new fact it involves the elimination of old ones. We are always, as it turns out, fundamentally in error.
In 'On Science and Certainty', Discover Magazine (Oct 1980)
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The man who classifies facts of any kind whatever, who sees their mutual relation and describes their sequence, is applying the scientific method and is a man of science.
From The Grammar of Science (1892), 15.
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The nation that prepares for war will sooner or later have war. We get just anything we prepare for, and we get nothing else. Everything that happens is a sequence: this happened today because you did that yesterday.
Aphorism in The Philistine (Apr 1905), 20, No. 5, 160.
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The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics “knows nothing of causation” could only be taken to express the whole truth, if by the term “causation” is understood “efficient causation.” The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
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The resolution of revolutions is selection by conflict within the scientific community of the fittest way to practice future science. The net result of a sequence of such revolutionary selections, separated by periods of normal research, is the wonderfully adapted set of instruments we call modern scientific knowledge.
The Structure of Scientific Revolutions (1962), 171.
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The sequence of theorist, experimenter, and discovery has occasionally been compared to the sequence of farmer, pig, truffle. The farmer leads the pig to an area where there might be truffles. The pig searches diligently for the truffles. Finally, he locates one, and just as he is about to devour it, the farmer snatches it away.
In Leon Lederman and Dick Teresi, The God Particle: If the Universe is the Answer, What is the Question (1993, 2006), 16.
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The theory of punctuated equilibrium, proposed by Niles Eldredge and myself, is not, as so often misunderstood, a radical claim for truly sudden change, but a recognition that ordinary processes of speciation, properly conceived as glacially slow by the standard of our own life-span, do not resolve into geological time as long sequences of insensibly graded intermediates (the traditional, or gradualistic, view), but as geologically ‘sudden’ origins at single bedding planes.
…...
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The … publicity is always the same; only the blanks need to be filled in: “It was announced today by scientists at [Harvard, Vanderbilt, Stanford] Medical School that a gene responsible for [some, many, a common form of] [schizophrenia, Alzheimer’s, arterio-sclerosis, prostate cancer] has been located and its DNA sequence determined. This exciting research, say scientists, is the first step in what may eventually turn out to be a possible cure for this disease.”
From review, 'Billions and Billions of Demons', of the book, The Demon-Haunted World: Science as a Candle in the Dark, by Carl Sagan, in New York Review of Books (9 Jan 1997).
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Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.
In Arithmetic in Public Education (1909), 13. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 68.
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Time’s arrow of ‘just history’ marks each moment of time with a distinctive brand. But we cannot, in our quest to understand history, be satisfied only with a mark to recognize each moment and a guide to order events in temporal sequence. Uniqueness is the essence of history, but we also crave some underlying generality, some principles of order transcending the distinction of moments–lest we be driven mad by Borges’s vision of a new picture every two thousand pages in a book without end. We also need, in short, the immanence of time’s cycle.
…...
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We inhabit a complex world. Some boundaries are sharp and permit clean and definite distinctions. But nature also includes continua that cannot be neatly parceled into two piles of unambiguous yeses and noes. Biologists have rejected, as fatally flawed in principle, all attempts by antiabortionists to define an unambiguous ‘beginning of life,’ because we know so well that the sequence from ovulation or spermatogenesis to birth is an unbreakable continuum–and surely no one will define masturbation as murder.
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We receive it as a fact, that some minds are so constituted as absolutely to require for their nurture the severe logic of the abstract sciences; that rigorous sequence of ideas which leads from the premises to the conclusion, by a path, arduous and narrow, it may be, and which the youthful reason may find it hard to mount, but where it cannot stray; and on which, if it move at all, it must move onward and upward… . Even for intellects of a different character, whose natural aptitude is for moral evidence and those relations of ideas which are perceived and appreciated by taste, the study of the exact sciences may be recommended as the best protection against the errors into which they are most likely to fall. Although the study of language is in many respects no mean exercise in logic, yet it must be admitted that an eminently practical mind is hardly to be formed without mathematical training.
In Orations and Speeches (1870), Vol. 8, 510.
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We should first look at the evidence that DNA itself is not the direct template that orders amino acid sequences. Instead, the genetic information of DNA is transferred to another class of molecules which then serve as the protein templates. These intermediate templates are molecules of ribonucleic acid (RNA), large polymeric molecules chemically very similar to DNA. Their relation to DNA and protein is usually summarized by the central dogma, a How scheme for genetic information first proposed some twenty years ago.
In Molecular Biology of the Gene (1965), 281-282.
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What attracted me to immunology was that the whole thing seemed to revolve around a very simple experiment: take two different antibody molecules and compare their primary sequences. The secret of antibody diversity would emerge from that. Fortunately at the time I was sufficiently ignorant of the subject not to realise how naive I was being.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 248.
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With the nervous system intact the reactions of the various parts of that system, the 'simple reflexes', are ever combined into great unitary harmonies, actions which in their sequence one upon another constitute in their continuity what may be termed the 'behaviour'.
The Integrative Action of the Nervous System (1906), 237.
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Zenophobia: the irrational fear of converging sequences.
Pun on the name of the Greek philosopher, Zeno, famous for his challenging paradoxes concerning converging sequences.
Anonymous
In Wieslaw Krawcewicz, Bindhyachal Rai, Calculus with Maple Labs (2003), 407.
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[Decoding the human genome sequence] is the most significant undertaking that we have mounted so far in an organized way in all of science. I believe that reading our blueprints, cataloguing our own instruction book, will be judged by history as more significant than even splitting the atom or going to the moon.
Interview (23 May 1998), 'Cracking the Code to Life', Academy of Achievement web site.
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[Defining Life] The definite combination of heterogeneous changes, both simultaneous and successive, in correspondence with external co-existences and sequences.
Herbert Spencer, "Principles of Psychology" 1835, p. 354. Compare "Physiology of Common Life" 1860, ii., 426. In The British Controversialist and Literary Magazine (1865), 234.
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… the reasoning process [employed in mathematics] is not different from that of any other branch of knowledge, … but there is required, and in a great degree, that attention of mind which is in some part necessary for the acquisition of all knowledge, and in this branch is indispensably necessary. This must be given in its fullest intensity; … the other elements especially characteristic of a mathematical mind are quickness in perceiving logical sequence, love of order, methodical arrangement and harmony, distinctness of conception.
In Treatise on Infinitesimal Calculus (1868), Vol. 8, 6.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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