Essays On Education And Kindred Subjects (Fiscle Part- 11) - Herbert Spencer (if you give a mouse a cookie read aloud txt) 📗
- Author: Herbert Spencer
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Fixed, Could So Regular An Architecture Be Executed. In The Case Of The
Other Division Of Concrete Mathematics--Mechanics, We Have Definite
Evidence Of Progress. We Know That The Lever And The Inclined Plane Were
Employed During This Period: Implying That There Was A Qualitative
Prevision Of Their Effects, Though Not A Quantitative One. But We Know
More. We Read Of Weights In The Earliest Records; And We Find Weights In
Ruins Of The Highest Antiquity. Weights Imply Scales, Of Which We Have
Also Mention; And Scales Involve The Primary Theorem Of Mechanics In Its
Least Complicated Form--Involve Not A Qualitative But A Quantitative
Prevision Of Mechanical Effects. And Here We May Notice How Mechanics,
In Common With The Other Exact Sciences, Took Its Rise From The Simplest
Application Of The Idea Of _Equality_. For The Mechanical Proposition
Which The Scales Involve, Is, That If A Lever With _Equal_ Arms, Have
_Equal_ Weights Suspended From Them, The Weights Will Remain At _Equal_
Altitudes. And We May Further Notice How, In This First Step Of Rational
Mechanics, We See Illustrated That Truth Awhile Since Referred To, That
As Magnitudes Of Linear Extension Are The Only Ones Of Which The
Equality Is Exactly Ascertainable, The Equalities Of Other Magnitudes
Have At The Outset To Be Determined By Means Of Them. For The Equality
Of The Weights Which Balance Each Other In Scales, Wholly Depends Upon
The Equality Of The Arms: We Can Know That The Weights Are Equal Only By
Proving That The Arms Are Equal. And When By This Means We Have Obtained
A System Of Weights,--A Set Of Equal Units Of Force, Then Does A Science
Of Mechanics Become Possible. Whence, Indeed, It Follows, That Rational
Mechanics Could Not Possibly Have Any Other Starting-Point Than The
Scales.
Let Us Further Remember, That During This Same Period There Was A
Limited Knowledge Of Chemistry. The Many Arts Which We Know To Have Been
Carried On Must Have Been Impossible Without A Generalised Experience Of
The Modes In Which Certain Bodies Affect Each Other Under Special
Conditions. In Metallurgy, Which Was Extensively Practised, This Is
Abundantly Illustrated. And We Even Have Evidence That In Some Cases The
Knowledge Possessed Was, In A Sense, Quantitative. For, As We Find By
Analysis That The Hard Alloy Of Which The Egyptians Made Their Cutting
Tools, Was Composed Of Copper And Tin In Fixed Proportions, There Must
Have Been An Established Prevision That Such An Alloy Was To Be Obtained
Only By Mixing Them In These Proportions. It Is True, This Was But A
Simple Empirical Generalisation; But So Was The Generalisation
Respecting The Recurrence Of Eclipses; So Are The First Generalisations
Of Every Science.
Respecting The Simultaneous Advance Of The Sciences During This Early
Epoch, It Only Remains To Remark That Even The Most Complex Of Them
Must Have Made Some Progress--Perhaps Even A Greater Relative Progress
Than Any Of The Rest. For Under What Conditions Only Were The Foregoing
Developments Possible? There First Required An Established And Organised
Social System. A Long Continued Registry Of Eclipses; The Building Of
Palaces; The Use Of Scales; The Practice Of Metallurgy--Alike Imply A
Fixed And Populous Nation. The Existence Of Such A Nation Not Only
Presupposes Laws, And Some Administration Of Justice, Which We Know
Existed, But It Presupposes Successful Laws--Laws Conforming In Some
Degree To The Conditions Of Social Stability--Laws Enacted Because It
Was Seen That The Actions Forbidden By Them Were Dangerous To The State.
We Do Not By Any Means Say That All, Or Even The Greater Part, Of The
Laws Were Of This Nature; But We Do Say, That The Fundamental Ones Were.
It Cannot Be Denied That The Laws Affecting Life And Property Were Such.
It Cannot Be Denied That, However Little These Were Enforced Between
Class And Class, They Were To A Considerable Extent Enforced Between
Members Of The Same Class. It Can Scarcely Be Questioned, That The
Administration Of Them Between Members Of The Same Class Was Seen By
Rulers To Be Necessary For Keeping Their Subjects Together. And Knowing,
As We Do, That, Other Things Equal, Nations Prosper In Proportion To The
Justness Of Their Arrangements, We May Fairly Infer That The Very Cause
Of The Advance Of These Earliest Nations Out Of Aboriginal Barbarism Was
The Greater Recognition Among Them Of The Claims To Life And Property.
But Supposition Aside, It Is Clear That The Habitual Recognition Of
These Claims In Their Laws Implied Some Prevision Of Social Phenomena.
Even Thus Early There Was A Certain Amount Of Social Science. Nay, It
May Even Be Shown That There Was A Vague Recognition Of That Fundamental
Principle On Which All The True Social Science Is Based--The Equal
Rights Of All To The Free Exercise Of Their Faculties. That Same Idea Of
_Equality_ Which, As We Have Seen, Underlies All Other Science,
Underlies Also Morals And Sociology. The Conception Of Justice, Which Is
The Primary One In Morals; And The Administration Of Justice, Which Is
The Vital Condition Of Social Existence; Are Impossible Without The
Recognition Of A Certain Likeness In Men's Claims In Virtue Of Their
Common Humanity. _Equity_ Literally Means _Equalness_; And If It Be
Admitted That There Were Even The Vaguest Ideas Of Equity In These
Primitive Eras, It Must Be Admitted That There Was Some Appreciation Of
The Equalness Of Men's Liberties To Pursue The Objects Of Life--Some
Appreciation, Therefore, Of The Essential Principle Of National
Equilibrium.
Thus In This Initial Stage Of The Positive Sciences, Before Geometry Had
Yet Done More Than Evolve A Few Empirical Rules--Before Mechanics Had
Passed Beyond Its First Theorem--Before Astronomy Had Advanced From Its
Merely Chronological Phase Into The Geometrical; The Most Involved Of
The Sciences Had Reached A Certain Degree Of Development--A Development
Without Which No Progress In Other Sciences Was Possible.
Only Noting As We Pass, How, Thus Early, We May See That The Progress Of
Exact Science Was Not Only Towards An Increasing Number Of Previsions,
But Towards Previsions More Accurately Quantitative--How, In Astronomy,
The Recurring Period Of The Moon's Motions Was By And By More Correctly
Ascertained To Be Nineteen Years, Or Two Hundred And Thirty-Five
Lunations; How Callipus Further Corrected This Metonic Cycle, By Leaving
Part 2 Chapter 3 (On The Genesis Of Science) Pg 113Out A Day At The End Of Every Seventy-Six Years; And How These
Successive Advances Implied A Longer Continued Registry Of Observations,
And The Co-Ordination Of A Greater Number Of Facts--Let Us Go On To
Inquire How Geometrical Astronomy Took Its Rise.
The First Astronomical Instrument Was The Gnomon. This Was Not Only
Early In Use In The East, But It Was Found Also Among The Mexicans; The
Sole Astronomical Observations Of The Peruvians Were Made By It; And We
Read That 1100 B.C., The Chinese Found That, At A Certain Place, The
Length Of The Sun's Shadow, At The Summer Solstice, Was To The Height Of
The Gnomon As One And A Half To Eight. Here Again It Is Observable, Not
Only That The Instrument Is Found Ready Made, But That Nature Is
Perpetually Performing The Process Of Measurement. Any Fixed, Erect
Object--A Column, A Dead Palm, A Pole, The Angle Of A Building--Serves
For A Gnomon; And It Needs But To Notice The Changing Position Of The
Shadow It Daily Throws To Make The First Step In Geometrical Astronomy.
How Small This First Step Was, May Be Seen In The Fact That The Only
Things Ascertained At The Outset Were The Periods Of The Summer And
Winter Solstices, Which Corresponded With The Least And Greatest Lengths
Of The Mid-Shadow; And To Fix Which, It Was Needful Merely To Mark The
Point To Which Each Day's Shadow Reached.
And Now Let It Not Be Overlooked That In The Observing At What Time
During The Next Year This Extreme Limit Of The Shadow Was Again Reached,
And In The Inference That The Sun Had Then Arrived At The Same Turning
Point In His Annual Course, We Have One Of The Simplest Instances Of
That Combined Use Of _Equal Magnitudes_ And _Equal Relations_, By Which
All Exact Science, All Quantitative Prevision, Is Reached. For The
Relation Observed Was Between The Length Of The Sun's Shadow And His
Position In The Heavens; And The Inference Drawn Was That When, Next
Year, The Extremity Of His Shadow Came To The Same Point, He Occupied
The Same Place. That Is, The Ideas Involved Were, The Equality Of The
Shadows, And The Equality Of The Relations Between Shadow And Sun In
Successive Years. As In The Case Of The Scales, The Equality Of
Relations Here Recognised Is Of The Simplest Order. It Is Not As Those
Habitually Dealt With In The Higher Kinds Of Scientific Reasoning, Which
Answer To The General Type--The Relation Between Two And Three Equals
The Relation Between Six And Nine; But It Follows The Type--The Relation
Between Two And Three, Equals The Relation Between Two And Three; It Is
A Case Of Not Simply _Equal_ Relations, But _Coinciding_ Relations. And
Here, Indeed, We May See Beautifully Illustrated How The Idea Of Equal
Relations Takes Its Rise After The Same Manner That That Of Equal
Magnitude Does. As Already Shown, The Idea Of Equal Magnitudes Arose
From The Observed Coincidence Of Two Lengths Placed Together; And In
This Case We Have Not Only Two Coincident Lengths Of Shadows, But Two
Coincident Relations Between Sun And Shadows.
From The Use Of The Gnomon There Naturally Grew Up The Conception Of
Angular Measurements; And With The Advance Of Geometrical Conceptions
There Came The Hemisphere Of Berosus, The Equinoctial Armil, The
Solstitial Armil, And The Quadrant Of Ptolemy--All Of Them Employing
Shadows As Indices Of The Sun's Position, But In Combination With
Angular Divisions. It Is Obviously Out Of The Question For Us Here To
Trace These Details Of Progress. It Must Suffice To Remark That In All
Of Them We May See That Notion Of Equality Of Relations Of A More
Complex Kind, Which Is Best Illustrated In The Astrolabe, An Instrument
Which Consisted "Of Circular Rims, Movable One Within The Other, Or
About Poles, And Contained Circles Which Were To Be Brought Into The
Position Of The Ecliptic, And Of A Plane Passing Through The Sun And The
Poles Of The Ecliptic"--An Instrument, Therefore, Which Represented, As
By A Model, The Relative Positions Of Certain Imaginary Lines And Planes
In The Heavens; Which Was Adjusted By Putting These Representative Lines
And Planes Into Parallelism And Coincidence With The Celestial Ones; And
Which Depended For Its Use Upon The Perception That The Relations
Between These Representative Lines And Planes Were _Equal_ To The
Relations Between Those Represented.
Were There Space, We Might Go On To Point Out How The Conception Of The
Heavens As A Revolving Hollow Sphere, The Discovery Of The Globular Form
Of The Earth, The Explanation Of The Moon's Phases, And Indeed All The
Successive Steps Taken, Involved This Same Mental Process. But We Must
Content Ourselves With Referring To The Theory Of Eccentrics And
Epicycles, As A Further Marked Illustration Of It. As First Suggested,
And As Proved By Hipparchus To Afford An Explanation Of The Leading
Irregularities In The Celestial Motions, This Theory Involved The
Perception That The Progressions, Retrogressions, And Variations Of
Velocity Seen In The Heavenly Bodies, Might Be Reconciled With Their
Assumed Uniform Movement In Circles, By Supposing That The Earth Was Not
In The Centre Of Their Orbits; Or By Supposing That They Revolved In
Circles Whose Centres Revolved Round The Earth; Or By Both. The
Discovery That This Would Account For The Appearances, Was The Discovery
That In Certain Geometrical Diagrams The Relations Were Such, That The
Uniform Motion Of A Point Would, When Looked At From A Particular
Position, Present Analogous Irregularities; And The Calculations Of
Hipparchus Involved The Belief That The Relations Subsisting Among These
Geometrical Curves Were _Equal_ To The Relations Subsisting Among The
Celestial Orbits.
Leaving Here These Details Of Astronomical Progress, And The Philosophy
Of It, Let Us Observe How The Relatively Concrete Science Of Geometrical
Astronomy, Having Been Thus Far Helped Forward By The Development Of
Geometry In General, Reacted Upon Geometry, Caused It Also To Advance,
And Was Again Assisted By It. Hipparchus, Before Making His Solar And
Lunar Tables, Had To Discover
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