Sequence Quotes (68 quotes)
… 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.
…The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein’s special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein’s amazing revelations have likewise sunk into the commonplaces of educated thought.
[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.
[Defining Life] The definite combination of heterogeneous changes, both simultaneous and successive, in correspondence with external co-existences and sequences.
[The object of education is] to train the mind to ascertain the sequence of a particular conclusion from certain premises, to detect a fallacy, to correct undue generalisation, to prevent the growth of mistakes in reasoning. Everything in these must depend on the spirit and the manner in which the instruction itself is conveyed and honoured. If you teach scientific knowledge without honouring scientific knowledge as it is applied, you do more harm than good. I do think that the study of natural science is so glorious a school for the mind, that with the laws impressed on all these things by the Creator, and the wonderful unity and stability of matter, and the forces of matter, there cannot be a better school for the education of the mind.
I believe in logic, the sequence of cause and effect, and in science its only begotten son our law, which was conceived by the ancient Greeks, thrived under Isaac Newton, suffered under Albert Einstein…
That fragment of a 'creed for materialism' which a friend in college had once shown him rose through Donald's confused mind.
That fragment of a 'creed for materialism' which a friend in college had once shown him rose through Donald's confused mind.
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.
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.
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]
[Paper co-author]
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.
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.
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.
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.
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.
Among the multitude of animals which scamper, fly, burrow and swim around us, man is the only one who is not locked into his environment. His imagination, his reason, his emotional subtlety and toughness, make it possible for him not to accept the environment, but to change it. And that series of inventions, by which man from age to age has remade his environment, is a different kind of evolution—not biological, but cultural evolution. I call that brilliant sequence of cultural peaks The Ascent of Man. I use the word ascent with a precise meaning. Man is distinguished from other animals by his imaginative gifts. He makes plans, inventions, new discoveries, by putting different talents together; and his discoveries become more subtle and penetrating, as he learns to combine his talents in more complex and intimate ways. So the great discoveries of different ages and different cultures, in technique, in science, in the arts, express in their progression a richer and more intricate conjunction of human faculties, an ascending trellis of his gifts.
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.
As for me ... I would much rather be a perfected ape than a degraded Adam. Yes, if it is shown to me that my humble ancestors were quadrupedal animals, arboreal herbivores, brothers or cousins of those who were also the ancestors of monkeys and apes, far from blushing in shame for my species because of its genealogy and parentage, I will be proud of all that evolution has accomplished, of the continuous improvement which takes us up to the highest order, of the successive triumphs that have made us superior to all of the other species ... the splendid work of progress.
I will conclude in saying: the fixity of species is almost impossible, it contradicts the mode of succession and of the distribution of species in the sequence of extant and extinct creatures. It is therefore extremely likely that species are variable and are subject to evolution. But the causes, the mechanisms of this evolution are still unknown.
I will conclude in saying: the fixity of species is almost impossible, it contradicts the mode of succession and of the distribution of species in the sequence of extant and extinct creatures. It is therefore extremely likely that species are variable and are subject to evolution. But the causes, the mechanisms of this evolution are still unknown.
As was predicted at the beginning of the Human Genome Project, getting the sequence will be the easy part as only technical issues are involved. The hard part will be finding out what it means, because this poses intellectual problems of how to understand the participation of the genes in the functions of living cells.
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.
Finally one should add that in spite of the great complexity of protein synthesis and in spite of the considerable technical difficulties in synthesizing polynucleotides with defined sequences it is not unreasonable to hope that all these points will be clarified in the near future, and that the genetic code will be completely established on a sound experimental basis within a few years.
For any one who is pervaded with the sense of causal law in all that happens, who accepts in real earnest the assumption of causality, the idea of a Being who interferes with the sequence of events in the world is absolutely impossible! Neither the religion of fear nor the social-moral religion can have, any hold on him. A God who rewards and punishes is for him unthinkable, because man acts in accordance with an inner and outer necessity, and would, in the eyes of God, be as little responsible as an inanimate object is for the movements which it makes. Science, in consequence, has been accused of undermining morals—but wrongly. The ethical behavior of man is better based on sympathy, education and social relationships, and requires no support from religion. Man’s plight would, indeed, be sad if he had to be kept in order through fear of punishment and hope of rewards after death.
For more than ten years, my theory was in limbo. Then, finally, in the late 1980s, physicists at Princeton said, “There’s nothing wrong with this theory. It’s the only one that works, and we have to open out minds to hyperspace.” We weren’t destined to discover this theory for another 100 years because it’s so bizarre, so different from everything we’d been doing. We didn’t use the normal sequence of discoveries to get to it.
Describing reaction to his superstring theory of hyperspace which mathematically relates the universe’s basic forces.
Describing reaction to his superstring theory of hyperspace which mathematically relates the universe’s basic forces.
For the philosopher, order is the entirety of repetitions manifested, in the form of types or of laws, by perceived objects. Order is an intelligible relation. For the biologist, order is a sequence in space and time. However, according to Plato, all things arise out of their opposites. Order was born of the original disorder, and the long evolution responsible for the present biological order necessarily had to engender disorder.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.
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.
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!
Historical chronology, human or geological, depends... upon comparable impersonal principles. If one scribes with a stylus on a plate of wet clay two marks, the second crossing the first, another person on examining these marks can tell unambiguously which was made first and which second, because the latter event irreversibly disturbs its predecessor. In virtue of the fact that most of the rocks of the earth contain imprints of a succession of such irreversible events, an unambiguous working out of the chronological sequence of these events becomes possible.
History tells us that [leading minds] can’t do it alone. From landing on the moon, to sequencing the human genome, to inventing the Internet, America has been the first to cross that new frontier because we had leaders who paved the way: leaders like President Kennedy, who inspired us to push the boundaries of the known world and achieve the impossible; leaders who not only invested in our scientists, but who respected the integrity of the scientific process.
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.
I think it [the World Series] should be called the World Sequence.
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.
If new species arise very rapidly in small, peripherally isolated local populations, then the great expectation of insensibly graded fossil sequences is a chimera. A new species does not evolve in the area of its ancestors; it does not arise from the slow transformation of all its forbears.
co-author with Niles Eldridge (palaeontologist, 1943- )
co-author with Niles Eldridge (palaeontologist, 1943- )
If the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force—and every other representation remains indefinite and therefore useless—it follows that, in the great dice game of existence, it must pass through calculable number of combinations. In infinite time, every possible combination would at some time or another be realized; more: it would be realized an infinite number of times. And since between every combination and its next recurrence all other possible combinations would have to take place, and each of these combination conditions of the entire sequence of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated: the world as a circular movement that has already repeated itself infinitely often and plays its game in infinitum. This conception is not simply a mechanistic conception; for if it were that, it would not condition an infinite recurrence of identical cases, but a final state. Because the world has not reached this, mechanistic theory must be considered an imperfect and merely provisional hypothesis.
In describing a protein it is now common to distinguish the primary, secondary and tertiary structures. The primary structure is simply the order, or sequence, of the amino-acid residues along the polypeptide chains. This was first determined by Sanger using chemical techniques for the protein insulin, and has since been elucidated for a number of peptides and, in part, for one or two other small proteins. The secondary structure is the type of folding, coiling or puckering adopted by the polypeptide chain: the a-helix structure and the pleated sheet are examples. Secondary structure has been assigned in broad outline to a number of librous proteins such as silk, keratin and collagen; but we are ignorant of the nature of the secondary structure of any globular protein. True, there is suggestive evidence, though as yet no proof, that a-helices occur in globular proteins, to an extent which is difficult to gauge quantitatively in any particular case. The tertiary structure is the way in which the folded or coiled polypeptide chains are disposed to form the protein molecule as a three-dimensional object, in space. The chemical and physical properties of a protein cannot be fully interpreted until all three levels of structure are understood, for these properties depend on the spatial relationships between the amino-acids, and these in turn depend on the tertiary and secondary structures as much as on the primary. Only X-ray diffraction methods seem capable, even in principle, of unravelling the tertiary and secondary structures.
Co-author with G. Bodo, H. M. Dintzis, R. G. Parrish, H. Wyckoff, and D. C. Phillips
Co-author with G. Bodo, H. M. Dintzis, R. G. Parrish, H. Wyckoff, and D. C. Phillips
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.”
It is impossible to disassociate language from science or science from language, because every natural science always involves three things: the sequence of phenomena on which the science is based; the abstract concepts which call these phenomena to mind; and the words in which the concepts are expressed. To call forth a concept a word is needed; to portray a phenomenon a concept is needed. All three mirror one and the same reality.
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.
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.
Melvin [Calvin]’s marvellous technique for delivering a scientific lecture was unique. His mind must have roamed constantly, especially in planning lectures. His remarkable memory enabled him to formulate a lecture or manuscript with no breaks in the sequence of his thoughts. His lectures usually began hesitatingly, as if he had little idea of how to begin or what to say. This completely disarmed his audiences, who would try to guess what he might have to say. Soon enough, however, his ideas would coalesce, to be delivered like an approaching freight train, reaching a crescendo of information at breakneck speed and leaving his rapt audience nearly overwhelmed.
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.
My own thinking (and that of many of my colleagues) is based on two general principles, which I shall call the Sequence Hypothesis and the Central Dogma. The direct evidence for both of them is negligible, but I have found them to be of great help in getting to grips with these very complex problems. I present them here in the hope that others can make similar use of them. Their speculative nature is emphasized by their names. It is an instructive exercise to attempt to build a useful theory without using them. One generally ends in the wilderness.
The Sequence Hypothesis
This has already been referred to a number of times. In its simplest form it assumes that the specificity of a piece of nucleic acid is expressed solely by the sequence of its bases, and that this sequence is a (simple) code for the amino acid sequence of a particular protein...
The Central Dogma
This states that once 'information' has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein. This is by no means universally held—Sir Macfarlane Burnet, for example, does not subscribe to it—but many workers now think along these lines. As far as I know it has not been explicitly stated before.
The Sequence Hypothesis
This has already been referred to a number of times. In its simplest form it assumes that the specificity of a piece of nucleic acid is expressed solely by the sequence of its bases, and that this sequence is a (simple) code for the amino acid sequence of a particular protein...
The Central Dogma
This states that once 'information' has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein. This is by no means universally held—Sir Macfarlane Burnet, for example, does not subscribe to it—but many workers now think along these lines. As far as I know it has not been explicitly stated before.
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.
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.
Our natural way of thinking about these coarser emotions is that the mental perception of some fact excites the mental affection called the emotion, and that this latter state of mind gives rise to the bodily expression. My theory, on the contrary, is that the bodily changes follow directly the perception of the exciting fact, and that our feeling of the same changes as they occur IS the emotion. Common-sense says, we lose our fortune, are sorry and weep; we meet a bear, are frightened and run; we are insulted by a rival, are angry and strike. The hypothesis here to be defended says that this order of sequence is incorrect, that the one mental state is not immediately induced by the other, that the bodily manifestations must first be interposed between, and that the more rational statement is that we feel sorry because we cry, angry because we strike, afraid because we tremble, and not that we cry, strike, or tremble, because we are sorry, angry, or fearful, as the case may be. Without the bodily states following on the perception, the latter would be purely cognitive in form, pale, colorless, destitute of emotional warmth. We might then see the bear, and judge it best to run, receive the insult and deem it right to strike, but we should not actually feel afraid or angry.
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.
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.
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.”
The automatic computing engine now being designed at N.P.L. [National Physics Laboratory] is atypical large scale electronic digital computing machine. In a single lecture it will not be possible to give much technical detail of this machine, and most of what I shall say will apply equally to any other machine of this type now being planned. From the point of view of the mathematician the property of being digital should be of greater interest than that of being electronic. That it is electronic is certainly important because these machines owe their high speed to this, and without the speed it is doubtful if financial support for their construction would be forthcoming. But this is virtually all that there is to be said on that subject. That the machine is digital however has more subtle significance. It means firstly that numbers are represented by sequences of digits which can be as long as one wishes. One can therefore work to any desired degree of accuracy. This accuracy is not obtained by more careful machining of parts, control of temperature variations, and such means, but by a slight increase in the amount of equipment in the machine.
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.
The cosmogonist has finished his task when he has described to the best of his ability the inevitable sequence of changes which constitute the history of the material universe. But the picture which he draws opens questions of the widest interest not only to science, but also to humanity. What is the significance of the vast processes it portrays? What is the meaning, if any there be which is intelligible to us, of the vast accumulations of matter which appear, on our present interpretations of space and time, to have been created only in order that they may destroy themselves.
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.
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.
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.
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 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.
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.
Then if the first argument remains secure (for nobody will produce a neater one, than the length of the periodic time is a measure of the size of the spheres), the order of the orbits follows this sequence, beginning from the highest: The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth’s motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon’s attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention. All these phenomena proceed from the same course, which lies in the motion of the Earth. But the fact that none of these phenomena appears in the fixed stars shows their immense elevation, which makes even the circle of their annual motion, or apparent motion, vanish from our eyes.
There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.
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.
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.
To him [Faraday], as to all true philosophers, the main value of a fact was its position and suggestiveness in the general sequence of scientific truth.
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.
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.
We share half our genes with the banana. [After the announcement Jun 2000 that a working draft of the genetic sequence of humans had been completed by the Human Genome Project.]
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.
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.
Whatever Nature undertakes, she can only accomplish it in a sequence. She never makes a leap. For example she could not produce a horse if it were not preceded by all the other animals on which she ascends to the horse’s structure as if on the rungs of a ladder. Thus every one thing exists for the sake of all things and all for the sake of one; for the one is of course the all as well. Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in any part of that whole, the rest must serve as a basis for that particular manifestation, and the latter must have a relationship to the rest of the system.
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'.
Zenophobia: the irrational fear of converging sequences.
Pun on the name of the Greek philosopher, Zeno, famous for his challenging paradoxes concerning converging sequences.
Pun on the name of the Greek philosopher, Zeno, famous for his challenging paradoxes concerning converging sequences.