Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index N > Category: Necessarily

Necessarily Quotes (30 quotes)

Access to more information isn’t enough—the information needs to be correct, timely, and presented in a manner that enables the reader to learn from it. The current network is full of inaccurate, misleading, and biased information that often crowds out the valid information. People have not learned that “popular” or “available” information is not necessarily valid.
Response to the Pew Research Center survey question, “Is Google making us stupid?” Posted 19 Feb 2010 on page 'Future of the Internet IV' at pewinternet.org website.
Science quotes on:  |  Access (16)  |  Available (25)  |  Bias (16)  |  Correct (83)  |  Current (54)  |  Enable (44)  |  Full (63)  |  Google (4)  |  Inaccurate (4)  |  Information (121)  |  Learn (281)  |  Manner (57)  |  Misleading (15)  |  Need (283)  |  Network (13)  |  People (388)  |  Popular (29)  |  Present (174)  |  Reader (38)  |  Timely (3)  |  Valid (11)

Hyper-selectionism has been with us for a long time in various guises; for it represents the late nineteenth century’s scientific version of the myth of natural harmony–all is for the best in the best of all possible worlds (all structures well designed for a definite purpose in this case). It is, indeed, the vision of foolish Dr. Pangloss, so vividly satirized by Voltaire in Candide–the world is not necessarily good, but it is the best we could possibly have.
…...
Science quotes on:  |  Best (172)  |  Case (98)  |  Definite (42)  |  Design (113)  |  Foolish (21)  |  Good (345)  |  Guise (5)  |  Harmony (70)  |  Late (52)  |  Long (172)  |  Myth (48)  |  Natural (167)  |  Nineteenth (6)  |  Possible (155)  |  Possibly (19)  |  Purpose (193)  |  Represent (41)  |  Scientific (232)  |  Structure (221)  |  Time (594)  |  Various (46)  |  Version (7)  |  Vision (94)  |  Vividly (4)  |  Francois Marie Arouet Voltaire (38)  |  World (892)

I am willing to believe that my unobtainable sixty seconds within a sponge or a flatworm might not reveal any mental acuity that I would care to ca ll consciousness. But I am also confident ... that vultures and sloths, as close evolutionary relatives with the same basic set of organs, lie on our side of any meaningful (and necessarily fuzzy) border–and that we are therefore not mistaken when we look them in the eye and see a glimmer of emotional and conceptual affinity.
…...
Science quotes on:  |  Acuity (2)  |  Affinity (14)  |  Basic (66)  |  Belief (503)  |  Border (9)  |  Care (95)  |  Close (66)  |  Conceptual (10)  |  Confident (9)  |  Consciousness (82)  |  Emotional (17)  |  Evolutionary (23)  |  Eye (218)  |  Fuzzy (3)  |  Glimmer (4)  |  Lie (115)  |  Meaningful (16)  |  Mental (78)  |  Mistake (131)  |  Organ (64)  |  Relative (39)  |  Reveal (50)  |  Same (155)  |  Second (59)  |  See (369)  |  Set (97)  |  Side (51)  |  Sixty (6)  |  Sloth (3)  |  Sponge (9)  |  Vulture (5)

I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
In The Conduct of the Understanding, Sect. 7.
Science quotes on:  |  Argument (81)  |  Bottom (33)  |  Bring (90)  |  Closely (12)  |  Coherence (10)  |  Connection (107)  |  Deep (121)  |  Demonstration (81)  |  Dependence (37)  |  Follow (123)  |  Habit (107)  |  Idea (577)  |  Knowledge (1293)  |  Manage (15)  |  Mathematician (364)  |  Mathematics (1149)  |  Mention (23)  |  Mind (743)  |  Necessary (147)  |  Observe (75)  |  Occasion (23)  |  Part (220)  |  Reason (454)  |  Settle (18)  |  Single (119)  |  Sort (49)  |  Source (90)  |  Study (461)  |  Think (341)  |  Train (45)  |  Transfer (12)  |  Value Of Mathematics (55)

If physical science is dangerous, as I have said, it is dangerous because it necessarily ignores the idea of moral evil; but literature is open to the more grievous imputation of recognizing and understanding it too well.
In 'Duties of the Church Towards Knowledge', The Idea of a University Defined and Illustrated (1852, 1873), Discourse 9, 229.
Science quotes on:  |  Dangerous (60)  |  Evil (78)  |  Grievous (3)  |  Idea (577)  |  Ignore (30)  |  Literature (79)  |  Moral (123)  |  Physical Science (65)  |  Recognize (66)  |  Understand (326)

If, then, there must be something eternal, let us see what sort of Being it must be. And to that it is very obvious to Reason, that it must necessarily be a cogitative Being. For it is as impossible to conceive that ever bare incogitative Matter should produce a thinking intelligent Being, as that nothing should of itself produce Matter...
In Essay Concerning Human Understanding (1690, 1801), Book 4, Chap. 10, Sec. 10, 114.
Science quotes on:  |  Bare (11)  |  Conceive (36)  |  Eternal (67)  |  Impossible (108)  |  Intelligent (47)  |  Matter (340)  |  Nothing (385)  |  Obvious (79)  |  Produce (100)  |  Reason (454)  |  Thinking (231)

It is for such inquiries the modern naturalist collects his materials; it is for this that he still wants to add to the apparently boundless treasures of our national museums, and will never rest satisfied as long as the native country, the geographical distribution, and the amount of variation of any living thing remains imperfectly known. He looks upon every species of animal and plant now living as the individual letters which go to make up one of the volumes of our earth’s history; and, as a few lost letters may make a sentence unintelligible, so the extinction of the numerous forms of life which the progress of cultivation invariably entails will necessarily render obscure this invaluable record of the past. It is, therefore, an important object, which governments and scientific institutions should immediately take steps to secure, that in all tropical countries colonised by Europeans the most perfect collections possible in every branch of natural history should be made and deposited in national museums, where they may be available for study and interpretation. If this is not done, future ages will certainly look back upon us as a people so immersed in the pursuit of wealth as to be blind to higher considerations. They will charge us with having culpably allowed the destruction of some of those records of Creation which we had it in our power to preserve; and while professing to regard every living thing as the direct handiwork and best evidence of a Creator, yet, with a strange inconsistency, seeing many of them perish irrecoverably from the face of the earth, uncared for and unknown.
In 'On the Physical Geography of the Malay Archipelago', Journal of the Royal Geographical Society (1863), 33, 234.
Science quotes on:  |  Add (40)  |  Age (174)  |  Allowed (3)  |  Amount (30)  |  Animal (356)  |  Apparently (19)  |  Available (25)  |  Back (104)  |  Best (172)  |  Blind (47)  |  Boundless (13)  |  Branch (102)  |  Certainly (31)  |  Charge (34)  |  Collect (16)  |  Collection (44)  |  Consideration (85)  |  Country (144)  |  Creation (239)  |  Creator (52)  |  Cultivation (27)  |  Destruction (85)  |  Direct (82)  |  Distribution (29)  |  Earth (635)  |  Entail (4)  |  European (5)  |  Evidence (181)  |  Extinction (66)  |  Face (108)  |  Form (308)  |  Future (284)  |  Geographical (6)  |  Government (93)  |  Handiwork (6)  |  Higher (36)  |  History (368)  |  Immediately (21)  |  Imperfectly (2)  |  Important (202)  |  Inconsistency (4)  |  Individual (215)  |  Inquiry (40)  |  Institution (39)  |  Interpretation (69)  |  Invaluable (7)  |  Invariably (9)  |  Known (16)  |  Letter (50)  |  Life (1124)  |  Living (56)  |  Long (172)  |  Look (52)  |  Lost (32)  |  Made (14)  |  Material (154)  |  Modern (159)  |  Museum (24)  |  National (25)  |  Native (15)  |  Natural (167)  |  Naturalist (54)  |  Numerous (29)  |  Object (169)  |  Obscure (31)  |  Past (150)  |  Perfect (83)  |  Perish (29)  |  Person (153)  |  Plant (199)  |  Possible (155)  |  Power (358)  |  Preserve (51)  |  Professing (2)  |  Progress (362)  |  Pursuit (76)  |  Record (67)  |  Regard (93)  |  Remain (111)  |  Render (30)  |  Rest (92)  |  Satisfied (23)  |  Scientific (232)  |  Secure (20)  |  Seeing (47)  |  Sentence (28)  |  Species (220)  |  Step (109)  |  Strange (94)  |  Study (461)  |  Treasure (45)  |  Tropical (8)  |  Unintelligible (9)  |  Unknown (105)  |  Variation (61)  |  Volume (19)  |  Want (175)  |  Wealth (66)

It usually develops that after much laborious and frustrating effort the investigator of environmental physiology succeeds in proving that the animal in question can actually exist where it lives. It is always somewhat discouraging for an investigator to realize that his efforts can be made to appear so trite, but this statement does not belittle the ecological physiologist. If his data assist the understanding of the ways in which an animal manages to live where it does, he makes an important contribution to the study of distribution, for the present is necessarily a key to the past.”
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
Science quotes on:  |  Actually (27)  |  Animal (356)  |  Appear (115)  |  Assist (9)  |  Belittle (2)  |  Contribution (60)  |  Data (120)  |  Develop (103)  |  Discourage (9)  |  Distribution (29)  |  Ecological (7)  |  Effort (143)  |  Environment (180)  |  Exist (147)  |  Frustrate (4)  |  Important (202)  |  Investigator (35)  |  Key (50)  |  Laborious (6)  |  Live (269)  |  Manage (15)  |  Past (150)  |  Physiologist (17)  |  Physiology (83)  |  Present (174)  |  Prove (108)  |  Question (404)  |  Realize (90)  |  Statement (72)  |  Study (461)  |  Succeed (26)  |  Trite (4)  |  Understand (326)  |  Usually (31)

It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule.* This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
[* This sentence has been reworded for the purpose of this quotation.]
In Leibnitz (1884), 44-45.
Science quotes on:  |  Acquire (38)  |  Algebraic (5)  |  Applicable (11)  |  Arithmetic (115)  |  Arrangement (58)  |  Attain (42)  |  Attitude (59)  |  Bridge (30)  |  Bring (90)  |  Calculation (98)  |  Certainty (129)  |  Characteristic (94)  |  Clear (97)  |  Clearness (9)  |  Combination (91)  |  Common (118)  |  Compound (58)  |  Continuity (30)  |  Contrast (28)  |  Conviction (71)  |  Corporeal (5)  |  Deal (49)  |  Degree (81)  |  Depend (87)  |  Destroy (80)  |  Discussion (47)  |  Early (61)  |  Elaborate (20)  |  Element (162)  |  Exist (147)  |  Express (63)  |  Favorable (11)  |  Form (308)  |  Formal (29)  |  Gain (67)  |  Gap (23)  |  General (156)  |  Geometry (215)  |  Grow (98)  |  Habit (107)  |  Harmony (70)  |  Highly (16)  |  Idea (577)  |  Import (5)  |  Increase (145)  |  Inestimable (4)  |  Infinite (128)  |  Infinity (72)  |  Introduce (41)  |  Investigation (175)  |  Language (217)  |  Lecture (67)  |  Legal (8)  |  Gottfried Wilhelm Leibniz (49)  |  Letter (50)  |  Logical (54)  |  Love (221)  |  Mathematicians and Anecdotes (123)  |  Mathematics (1149)  |  Mental (78)  |  Method (230)  |  Mind (743)  |  Model (80)  |  Motion (158)  |  Multitude (20)  |  Nature (1211)  |  Nothing (385)  |  Notion (57)  |  Number (276)  |  Occupation (40)  |  Opinion (176)  |  Order (239)  |  Orderly (13)  |  Original (57)  |  Philosophical (23)  |  Philosophy (257)  |  Precision (50)  |  Probable (20)  |  Process (261)  |  Progress (362)  |  Prove (108)  |  Purpose (193)  |  Quality (93)  |  Quantity (64)  |  Question (404)  |  Quotation (8)  |  Real World (13)  |  Reason (454)  |  Reduce (53)  |  Rule (173)  |  See (369)  |  Sentence (28)  |  Serve (57)  |  Simplicity (146)  |  Small (161)  |  Space (257)  |  Special (74)  |  Special Interest (2)  |  Step (109)  |  Strength (79)  |  Success (248)  |  Symbol (65)  |  System (191)  |  Tendency (54)  |  Term (120)  |  Theory (690)  |  Thought (536)  |  Try (141)  |  Type (51)  |  Understand (326)  |  Universal (100)  |  Variety (69)  |  Year (299)

Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
Science quotes on:  |  Accord (36)  |  Add (40)  |  Admit (44)  |  Alone (101)  |  Amount (30)  |  Ask (157)  |  Attentive (3)  |  Bear (66)  |  Case (98)  |  Certain (125)  |  Certainty (129)  |  Chain (50)  |  Clear (97)  |  Comprehend (39)  |  Conceive (36)  |  Conception (88)  |  Consequence (110)  |  Continuous (38)  |  Declare (27)  |  Deduce (22)  |  Deduction (68)  |  Deductive (10)  |  Derive (33)  |  Distinct (46)  |  Distinguish (61)  |  Doubt (159)  |  Draw (55)  |  Error (275)  |  Evident (26)  |  Extravagant (4)  |  Eye (218)  |  Fear (141)  |  Fellow (37)  |  First (313)  |  Follow (123)  |  Former (25)  |  Glance (19)  |  Great (524)  |  Hold (92)  |  Imagination (268)  |  Immediately (21)  |  Inasmuch (5)  |  Incontestable (2)  |  Intermediate (20)  |  Intuition (57)  |  Join (25)  |  Judgment (98)  |  Know (547)  |  Knowledge (1293)  |  Latter (21)  |  Let (61)  |  Light (345)  |  Link (41)  |  Long (172)  |  Mark (42)  |  Mean (101)  |  Means (171)  |  Mind (743)  |  Mode (40)  |  Movement (82)  |  Naturally (10)  |  Nature Of Mathematics (77)  |  Obliged (6)  |  Primary (39)  |  Principle (285)  |  Process (261)  |  Progress (362)  |  Proposition (80)  |  Provide (68)  |  Reason (454)  |  Recall (10)  |  Regard (93)  |  Remain (111)  |  Remote (39)  |  Rise (70)  |  Run (57)  |  Same (155)  |  Say (228)  |  Second (59)  |  Sense (315)  |  Simple (172)  |  Sound (88)  |  Spring (70)  |  Step (109)  |  Succession (43)  |  Testimony (13)  |  Therefrom (2)  |  Thought (536)  |  True (201)  |  Understand (326)  |  Uninterrupted (3)  |  Vary (25)  |  View (171)  |  Whereby (2)

Mathematics will not be properly esteemed in wider circles until more than the a b c of it is taught in the schools, and until the unfortunate impression is gotten rid of that mathematics serves no other purpose in instruction than the formal training of the mind. The aim of mathematics is its content, its form is a secondary consideration and need not necessarily be that historic form which is due to the circumstance that mathematics took permanent shape under the influence of Greek logic.
In Die Entivickelung der Mathematik in den letzten Jahrhunderten (1884), 6.
Science quotes on:  |  Aim (88)  |  Circle (55)  |  Circumstance (66)  |  Consideration (85)  |  Content (66)  |  Due (20)  |  Esteem (15)  |  Form (308)  |  Formal (29)  |  Greek (71)  |  Historic (7)  |  Impression (69)  |  Influence (137)  |  Instruction (72)  |  Logic (247)  |  Mathematics (1149)  |  Mind (743)  |  Need (283)  |  Permanent (28)  |  Properly (20)  |  Purpose (193)  |  Rid (13)  |  School (117)  |  Secondary (14)  |  Serve (57)  |  Shape (69)  |  Teach (179)  |  Teaching of Mathematics (31)  |  Training (64)  |  Unfortunate (14)  |  Wide (27)

Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
Science quotes on:  |  A Priori (22)  |  Accord (36)  |  Accordance (10)  |  Alone (101)  |  Ascribe (17)  |  Attribute (38)  |  Author (61)  |  Belief (503)  |  Beyond (104)  |  Celebrate (14)  |  Certainty (129)  |  Change (363)  |  Chiefly (12)  |  Concept (143)  |  Concern (108)  |  Construction (83)  |  Contrary (34)  |  Demonstrate (50)  |  Distant (32)  |  Early (61)  |  Easy (98)  |  Egyptian (4)  |  Experiment (600)  |  Far (154)  |  Figure (68)  |  Find (405)  |  First (313)  |  Flash (34)  |  Follow (123)  |  Fortunate (10)  |  Greek (71)  |  Happy (46)  |  History (368)  |  Human (548)  |  Important (202)  |  Intellectual (120)  |  Investigate (65)  |  Isosceles Triangle (3)  |  Know (547)  |  Learn (281)  |  Light (345)  |  Logic (247)  |  Long (172)  |  Mathematics (1149)  |  Mere (78)  |  Name (165)  |  Nature Of Mathematics (77)  |  New (483)  |  Open (66)  |  Order (239)  |  Passage (20)  |  Path (84)  |  People (388)  |  Period (64)  |  Place (174)  |  Point (122)  |  Preserve (51)  |  Produce (100)  |  Property (123)  |  Reach (119)  |  Reason (454)  |  Represent (41)  |  Revolution (69)  |  Round (26)  |  Royal Road (3)  |  Safe (27)  |  Science (2043)  |  See (369)  |  Single (119)  |  Suppose (49)  |  Tentative (8)  |  Thales (9)  |  Thought (536)  |  Time (594)  |  Trace (51)  |  Unmistakably (2)  |  Wonderful (59)  |  Work (626)

Only reason can convince us of those three fundamental truths without a recognition of which there can be no effective liberty: that what we believe is not necessarily true; that what we like is not necessarily good; and that all questions are open.
In Civilization: An Essay (1928), 125.
Science quotes on:  |  Belief (503)  |  Convince (23)  |  Effective (29)  |  Fundamental (158)  |  Good (345)  |  Liberty (25)  |  Open (66)  |  Question (404)  |  Reason (454)  |  Recognition (70)  |  True (201)  |  Truth (914)

Our knowledge can only be finite, while our ignorance must necessarily be infinite.
Essy, 'On the Sources of Knowledge and of Ignorance', in Conjectures and Refutations: The Growth of Scientific Knowledge (1962), 28.
Science quotes on:  |  Finite (31)  |  Ignorance (213)  |  Infinite (128)  |  Knowledge (1293)

Reason is always a kind of brute force; those who appeal to the head rather than the heart, however pallid and polite, are necessarily men of violence. We speak of “touching” a man’s heart, but we can do nothing to his head but hit it.
From 'Charles II', Twelve Types (1906), 98.
Science quotes on:  |  Appeal (45)  |  Brute (15)  |  Brute Force (2)  |  Force (249)  |  Head (80)  |  Heart (139)  |  Hit (20)  |  Kind (138)  |  Man (373)  |  Nothing (385)  |  Polite (8)  |  Reason (454)  |  Speak (90)  |  Touching (4)  |  Violence (23)

Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science.
In Science and Hypothesis.
Science quotes on:  |  Collection (44)  |  Fact (725)  |  House (43)  |  Pile (12)  |  Science (2043)  |  Stone (76)

Scientific subjects do not progress necessarily on the lines of direct usefulness. Very many applications of the theories of pure mathematics have come many years, sometimes centuries, after the actual discoveries themselves. The weapons were at hand, but the men were not able to use them.
In Perry, Teaching of Mathematics (1902), 35.
Science quotes on:  |  Application (166)  |  At Hand (4)  |  Century (130)  |  Discovery (676)  |  Progress (362)  |  Pure Mathematics (63)  |  Scientific (232)  |  Study And Research In Mathematics (59)  |  Subject (235)  |  Theory (690)  |  Usefulness (77)  |  Weapon (66)  |  Year (299)

The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.
In Perry, Teaching of Mathematics (1902), 59-61.
Science quotes on:  |  Anticipation (14)  |  Author (61)  |  Average (41)  |  Bare (11)  |  Bargain (4)  |  Book (257)  |  Contention (10)  |  Contract (11)  |  Deal (49)  |  Difficult (116)  |  Difficulty (144)  |  Effective (29)  |  English (34)  |  Fact (725)  |  Forth (13)  |  Fulfill (19)  |  Great (524)  |  Helpful (15)  |  Humour (103)  |  Impression (69)  |  Instance (32)  |  Intelligent (47)  |  Leave (127)  |  Logical (54)  |  Mathematics (1149)  |  James Clerk Maxwell (82)  |  Mistake (131)  |  Naturally (10)  |  Nothing (385)  |  Notice (34)  |  Objection (18)  |  Occur (43)  |  Often (106)  |  Order (239)  |  Part (220)  |  Perfect (83)  |  Physics (346)  |  Possible (155)  |  Priceless (5)  |  Probable (20)  |  Propriety (4)  |  Pure Mathematics (63)  |  Raise (34)  |  Reader (38)  |  Recitation (2)  |  Recognition (70)  |  Require (79)  |  Salmon (6)  |  Seem (143)  |  Seldom (28)  |  Set (97)  |  Statement (72)  |  Strange (94)  |  Student (201)  |  Subject (235)  |  Teach (179)  |  Teaching of Mathematics (31)  |  Text (14)  |  Theory (690)  |  Touch (76)  |  Truth (914)  |  Unearth (2)  |  Value (240)  |  View (171)  |  Work (626)

The book [Future of an Illusion] testifies to the fact that the genius of experimental science is not necessarily joined with the genius of logic or generalizing power.
…...
Science quotes on:  |  Book (257)  |  Experimental (20)  |  Fact (725)  |  Future (284)  |  Generalize (14)  |  Genius (243)  |  Illusion (43)  |  Join (25)  |  Logic (247)  |  Power (358)  |  Science (2043)  |  Testify (5)

The child asks, “What is the moon, and why does it shine?” “What is this water and where does it run?” “What is this wind?” “What makes the waves of the sea?” “Where does this animal live, and what is the use of this plant?” And if not snubbed and stunted by being told not to ask foolish questions, there is no limit to the intellectual craving of a young child; nor any bounds to the slow, but solid, accretion of knowledge and development of the thinking faculty in this way. To all such questions, answers which are necessarily incomplete, though true as far as they go, may be given by any teacher whose ideas represent real knowledge and not mere book learning; and a panoramic view of Nature, accompanied by a strong infusion of the scientific habit of mind, may thus be placed within the reach of every child of nine or ten.
In 'Scientific Education', Lay Sermons, Addresses, and Reviews (1870), 71. https://books.google.com/books?id=13cJAAAAIAAJ Thomas Henry Huxley - 1870
Science quotes on:  |  Accompany (21)  |  Accretion (5)  |  Animal (356)  |  Answer (249)  |  Ask (157)  |  Book (257)  |  Child (245)  |  Crave (9)  |  Development (276)  |  Faculty (65)  |  Foolish (21)  |  Habit (107)  |  Idea (577)  |  Incomplete (15)  |  Infusion (4)  |  Intellectual (120)  |  Knowledge (1293)  |  Learning (177)  |  Limit (123)  |  Live (269)  |  Mere (78)  |  Mind (743)  |  Moon (199)  |  Nature (1211)  |  Plant (199)  |  Question (404)  |  Reach (119)  |  Real (148)  |  Represent (41)  |  Scientific (232)  |  Sea (187)  |  Shine (43)  |  Slow (55)  |  Solid (50)  |  Strong (72)  |  Stunt (3)  |  Teacher (119)  |  Tell (110)  |  Thinking (231)  |  True (201)  |  View (171)  |  Water (292)  |  Wave (67)  |  Wind (80)  |  Young (98)

The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
Science quotes on:  |  Adapt (27)  |  Ancestor (40)  |  Avoid (52)  |  Back (104)  |  Begin (106)  |  Change (363)  |  Compensate (3)  |  Contribution (60)  |  Data (120)  |  Distribution (29)  |  Environment (180)  |  Essentially (14)  |  Extend (41)  |  Historical (14)  |  Immensity (21)  |  Inferential (2)  |  Instantaneous (2)  |  Invariably (9)  |  Knowledge (1293)  |  Life On Earth (9)  |  Line (89)  |  Obtain (45)  |  Organism (150)  |  Phenomenon (276)  |  Physiological (17)  |  Physiology (83)  |  Student (201)  |  Time (594)  |  Understand (326)

The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet been formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe. In the last analysis magic, religion, and science are nothing but theories of thought.
In The Golden Bough: A Study in Magic and Religion (1890, 1900), Vol. 3, 460.
Science quotes on:  |  Analysis (159)  |  Best (172)  |  Common (118)  |  Complete (84)  |  Conclude (16)  |  Devise (14)  |  Dignify (2)  |  Explain (105)  |  Final (49)  |  Formulate (15)  |  Generalization (41)  |  History (368)  |  Hypothesis (249)  |  Law Of Nature (64)  |  Magic (77)  |  Mere (78)  |  Name (165)  |  Nothing (385)  |  Parlance (2)  |  Phantasmagoria (3)  |  Religion (239)  |  Remember (81)  |  Science (2043)  |  Scientific Theory (24)  |  Shifting (5)  |  Theory (690)  |  Thought (536)  |  Universe (683)  |  Warn (5)  |  World (892)

The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
Science quotes on:  |  Abstract (79)  |  Add (40)  |  Adopt (18)  |  Applicable (11)  |  Application (166)  |  Apply (76)  |  Arise (49)  |  Become (172)  |  Both (81)  |  Bring (90)  |  Case (98)  |  Cause (283)  |  Class (83)  |  Condition (160)  |  Confine (24)  |  Consistent (17)  |  Deem (6)  |  Department (47)  |  Discovery (676)  |  Distinct (46)  |  Effect (165)  |  Employ (35)  |  Entirely (33)  |  Entitle (3)  |  Especially (30)  |  Exist (147)  |  Expert (50)  |  Extension (30)  |  Finally (26)  |  Find (405)  |  First (313)  |  Form (308)  |  Generality (34)  |  Generally (15)  |  Gradually (21)  |  Great (524)  |  Group (72)  |  History (368)  |  Improvement (73)  |  Increase (145)  |  Insoluble (15)  |  Introduce (41)  |  Investigation (175)  |  Know (547)  |  Large (130)  |  Light (345)  |  Limit (123)  |  Machinery (32)  |  Mathematics (1149)  |  Merely (82)  |  Method (230)  |  Modification (35)  |  Nature (1211)  |  Necessary (147)  |  New (483)  |  Nomenclature (138)  |  Notation (19)  |  Occasion (23)  |  Old (147)  |  Ordinary (71)  |  Origin (86)  |  Original (57)  |  Particular (75)  |  Performance (33)  |  Physical (129)  |  Piece (38)  |  Powerful (66)  |  Principle (285)  |  Problem (490)  |  Process (261)  |  Produce (100)  |  Propose (23)  |  Question (404)  |  Rank (32)  |  Receive (59)  |  Recognize (66)  |  Reduction (41)  |  Require (79)  |  Result (376)  |  Same (155)  |  Science (2043)  |  Seek (104)  |  Several (31)  |  Similar (35)  |  Simple (172)  |  Solution (211)  |  Solve (76)  |  Soon (34)  |  State (136)  |  Study And Research In Mathematics (59)  |  Sufficiently (9)  |  System (191)  |  Systematic (32)  |  Thought (536)  |  Time (594)  |  Together (77)  |  Tool (87)  |  Treatise (32)  |  True (201)  |  Uniform (17)  |  Usually (31)  |  Work (626)  |  Workman (13)

The other line of argument, which leads to the opposite conclusion, arises from looking at artificial automata. Everyone knows that a machine tool is more complicated than the elements which can be made with it, and that, generally speaking, an automaton A, which can make an automaton B, must contain a complete description of B, and also rules on how to behave while effecting the synthesis. So, one gets a very strong impression that complication, or productive potentiality in an organization, is degenerative, that an organization which synthesizes something is necessarily more complicated, of a higher order, than the organization it synthesizes. This conclusion, arrived at by considering artificial automaton, is clearly opposite to our early conclusion, arrived at by considering living organisms.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
Science quotes on:  |  Artificial (32)  |  Automaton (10)  |  Complete (84)  |  Complicated (61)  |  Conclusion (157)  |  Contain (67)  |  Degenerative (2)  |  Description (84)  |  Living (56)  |  Organism (150)  |  Organization (84)  |  Potentiality (7)  |  Productive (12)  |  Synthesis (43)

The peculiar character of mathematical truth is, that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths, and a familiarity with their form and character.
This lesson is not only lost, but read backward, if the student is taught that there is no such difference, and that mathematical truths themselves are learned by experience.
In Thoughts on the Study of Mathematics. Principles of English University Education (1838).
Science quotes on:  |  Backward (9)  |  Character (115)  |  Difference (246)  |  Experience (338)  |  Familiarity (16)  |  Form (308)  |  Important (202)  |  Inevitably (6)  |  Knowledge (1293)  |  Learn (281)  |  Lesson (41)  |  Lose (93)  |  Mathematics (1149)  |  Nature Of Mathematics (77)  |  Peculiar (43)  |  Read (144)  |  Student (201)  |  Study (461)  |  Teach (179)  |  True (201)  |  Truth (914)

There are pessimists who hold that such a state of affairs is necessarily inherent in human nature; it is those who propound such views that are the enemies of true religion, for they imply thereby that religious teachings are utopian ideals and unsuited to afford guidance in human affairs. The study of the social patterns in certain so-called primitive cultures, however, seems to have made it sufficiently evident that such a defeatist view is wholly unwarranted.
…...
Science quotes on:  |  Afford (16)  |  Certain (125)  |  Culture (102)  |  Enemy (63)  |  Evident (26)  |  Guidance (20)  |  Hold (92)  |  Human Affairs (5)  |  Human Nature (60)  |  Ideal (69)  |  Imply (15)  |  Inherent (30)  |  Pattern (79)  |  Pessimist (7)  |  Primitive (41)  |  Propound (2)  |  Religion (239)  |  Religious (49)  |  Seem (143)  |  So-Called (21)  |  Social (108)  |  State Of affairs (5)  |  Study (461)  |  Sufficiently (9)  |  Teachings (3)  |  Thereby (5)  |  True (201)  |  Unwarranted (2)  |  Utopian (3)  |  View (171)  |  Wholly (12)

There is no need to worry about mere size. We do not necessarily respect a fat man more than a thin man. Sir Isaac Newton was very much smaller than a hippopotamus, but we do not on that account value him less.
…...
Science quotes on:  |  Account (67)  |  Fat (11)  |  Hippopotamus (2)  |  Less (102)  |  Mere (78)  |  Need (283)  |  Sir Isaac Newton (327)  |  Respect (86)  |  Size (60)  |  Small (161)  |  Thin (16)  |  Value (240)  |  Worry (33)

Those who are finer and nobler are always alone — and necessarily so — and that because of this they can enjoy the purity of their own atmosphere.
Letter (5 Apr 1933). As quoted in Jamie Sayen, Einstein in America: The Scientist’s Conscience in the Age of Hitler and Hiroshima (1985), 12. This is part of Einstein’s reply to a letter from a troubled, unemployed musician, presumably living in Munich.
Science quotes on:  |  Alone (101)  |  Atmosphere (79)  |  Enjoy (38)  |  Fine (33)  |  Noble (51)  |  Purity (14)

We cannot but think there is something like a fallacy in Mr. Buckle’s theory that the advance of mankind is necessarily in the direction of science, and not in that of morals.
…...
Science quotes on:  |  Advance (162)  |  Buckle (4)  |  Direction (74)  |  Fallacy (25)  |  Mankind (241)  |  Moral (123)  |  Science (2043)  |  Theory (690)  |  Think (341)

When I am violently beset with temptations, or cannot rid myself of evil thoughts, [I resolve] to do some Arithmetic, or Geometry, or some other study, which necessarily engages all my thoughts, and unavoidably keeps them from wandering.
In T. Mallon A Book of One’s Own: People and Their Diaries (1984), 107.
Science quotes on:  |  Arithmetic (115)  |  Beset (2)  |  Engage (25)  |  Evil (78)  |  Geometry (215)  |  Keep (100)  |  Myself (36)  |  Resolve (19)  |  Rid (13)  |  Study (461)  |  Temptation (11)  |  Thought (536)  |  Violently (3)  |  Wander (20)


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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.