Essays On Education And Kindred Subjects (Fiscle Part- 11) by Herbert Spencer (best mobile ebook reader TXT) 📖
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- Author: Herbert Spencer
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Beyond Ten--The Limit Of The Simple Finger Notation. The Fact That In So
Many Instances, Remote, And Seemingly Unrelated Nations, Have Adopted
_Ten_ As Their Basic Number; Together With The Fact That In The
Remaining Instances The Basic Number Is Either _Five_ (The Fingers Of
One Hand) Or _Twenty_ (The Fingers And Toes); Almost Of Themselves Show
That The Fingers Were The Original Units Of Numeration. The Still
Surviving Use Of The Word _Digit_, As The General Name For A Figure In
Arithmetic, Is Significant; And It Is Even Said That Our Word _Ten_
(Sax. _Tyn_; Dutch, _Tien_; German, _Zehn_) Means In Its Primitive
Expanded Form _Two Hands_. So That Originally, To Say There Were Ten
Things, Was To Say There Were Two Hands Of Them.
Part 2 Chapter 3 (On The Genesis Of Science) Pg 109
From All Which Evidence It Is Tolerably Clear That The Earliest Mode Of
Conveying The Idea Of Any Number Of Things, Was By Holding Up As Many
Fingers As There Were Things; That Is--Using A Symbol Which Was _Equal_,
In Respect Of Multiplicity, To The Group Symbolised. For Which Inference
There Is, Indeed, Strong Confirmation In The Recent Statement That Our
Own Soldiers Are Even Now Spontaneously Adopting This Device In Their
Dealings With The Turks. And Here It Should Be Remarked That In This
Recombination Of The Notion Of Equality With That Of Multiplicity, By
Which The First Steps In Numeration Are Effected, We May See One Of The
Earliest Of Those Inosculations Between The Diverging Branches Of
Science, Which Are Afterwards Of Perpetual Occurrence.
Indeed, As This Observation Suggests, It Will Be Well, Before Tracing
The Mode In Which Exact Science Finally Emerges From The Merely
Approximate Judgments Of The Senses, And Showing The Non-Serial
Evolution Of Its Divisions, To Note The Non-Serial Character Of Those
Preliminary Processes Of Which All After Development Is A Continuation.
On Reconsidering Them It Will Be Seen That Not Only Are They Divergent
Growths From A Common Root, Not Only Are They Simultaneous In Their
Progress; But That They Are Mutual Aids; And That None Can Advance
Without The Rest. That Completeness Of Classification For Which The
Unfolding Of The Perceptions Paves The Way, Is Impossible Without A
Corresponding Progress In Language, By Which Greater Varieties Of
Objects Are Thinkable And Expressible. On The One Hand It Is Impossible
To Carry Classification Far Without Names By Which To Designate The
Classes; And On The Other Hand It Is Impossible To Make Language Faster
Than Things Are Classified.
Again, The Multiplication Of Classes And The Consequent Narrowing Of
Each Class, Itself Involves A Greater Likeness Among The Things Classed
Together; And The Consequent Approach Towards The Notion Of Complete
Likeness Itself Allows Classification To Be Carried Higher. Moreover,
Classification Necessarily Advances _Pari Passu_ With Rationality--The
Classification Of _Things_ With The Classification Of _Relations_. For
Things That Belong To The Same Class Are, By Implication, Things Of
Which The Properties And Modes Of Behaviour--The Co-Existences And
Sequences--Are More Or Less The Same; And The Recognition Of This
Sameness Of Co-Existences And Sequences Is Reasoning. Whence It Follows
That The Advance Of Classification Is Necessarily Proportionate To The
Advance Of Generalisations. Yet Further, The Notion Of _Likeness_, Both
In Things And Relations, Simultaneously Evolves By One Process Of
Culture The Ideas Of _Equality_ Of Things And _Equality_ Of Relations;
Which Are The Respective Bases Of Exact Concrete Reasoning And Exact
Abstract Reasoning--Mathematics And Logic. And Once More, This Idea Of
Equality, In The Very Process Of Being Formed, Necessarily Gives Origin
To Two Series Of Relations--Those Of Magnitude And Those Of Number: From
Which Arise Geometry And The Calculus. Thus The Process Throughout Is
One Of Perpetual Subdivision And Perpetual Intercommunication Of The
Divisions. From The Very First There Has Been That _Consensus_ Of
Different Kinds Of Knowledge, Answering To The _Consensus_ Of The
Intellectual Faculties, Which, As Already Said, Must Exist Among The
Sciences.
Let Us Now Go On To Observe How, Out Of The Notions Of _Equality_ And
_Number_, As Arrived At In The Manner Described, There Gradually Arose
The Elements Of Quantitative Prevision.
Equality, Once Having Come To Be Definitely Conceived, Was Readily
Applicable To Other Phenomena Than Those Of Magnitude. Being Predicable
Of All Things Producing Indistinguishable Impressions, There Naturally
Grew Up Ideas Of Equality In Weights, Sounds, Colours, Etc.; And Indeed
It Can Scarcely Be Doubted That The Occasional Experience Of Equal
Weights, Sounds, And Colours, Had A Share In Developing The Abstract
Conception Of Equality--That The Ideas Of Equality In Size, Relations,
Forces, Resistances, And Sensible Properties In General, Were Evolved
During The Same Period. But However This May Be, It Is Clear That As
Fast As The Notion Of Equality Gained Definiteness, So Fast Did That
Lowest Kind Of Quantitative Prevision Which Is Achieved Without Any
Instrumental Aid, Become Possible.
The Ability To Estimate, However Roughly, The Amount Of A Foreseen
Result, Implies The Conception That It Will Be _Equal To_ A Certain
Imagined Quantity; And The Correctness Of The Estimate Will Manifestly
Depend Upon The Accuracy At Which The Perceptions Of Sensible Equality
Have Arrived. A Savage With A Piece Of Stone In His Hand, And Another
Piece Lying Before Him Of Greater Bulk Of The Same Kind (A Fact Which He
Infers From The _Equality_ Of The Two In Colour And Texture) Knows About
What Effort He Must Put Forth To Raise This Other Piece; And He Judges
Accurately In Proportion To The Accuracy With Which He Perceives That
The One Is Twice, Three Times, Four Times, Etc., As Large As The Other;
That Is--In Proportion To The Precision Of His Ideas Of Equality And
Number. And Here Let Us Not Omit To Notice That Even In These Vaguest Of
Quantitative Previsions, The Conception Of _Equality Of Relations_ Is
Also Involved. For It Is Only In Virtue Of An Undefined Perception That
The Relation Between Bulk And Weight In The One Stone Is _Equal_ To The
Relation Between Bulk And Weight In The Other, That Even The Roughest
Approximation Can Be Made.
But How Came The Transition From Those Uncertain Perceptions Of Equality
Which The Unaided Senses Give, To The Certain Ones With Which Science
Deals? It Came By Placing The Things Compared In Juxtaposition. Equality
Being Predicated Of Things Which Give Us Indistinguishable Impressions,
And No Accurate Comparison Of Impressions Being Possible Unless They
Occur In Immediate Succession, It Results That Exactness Of Equality Is
Ascertainable In Proportion To The Closeness Of The Compared Things.
Hence The Fact That When We Wish To Judge Of Two Shades Of Colour
Whether They Are Alike Or Not, We Place Them Side By Side; Hence The
Fact That We Cannot, With Any Precision, Say Which Of Two Allied Sounds
Is The Louder, Or The Higher In Pitch, Unless We Hear The One
Immediately After The Other; Hence The Fact That To Estimate The Ratio
Of Weights, We Take One In Each Hand, That We May Compare Their
Pressures By Rapidly Alternating In Thought From The One To The Other;
Hence The Fact, That In A Piece Of Music We Can Continue To Make Equal
Beats When The First Beat Has Been Given, But Cannot Ensure Commencing
With The Same Length Of Beat On A Future Occasion; And Hence, Lastly,
The Fact, That Of All Magnitudes, Those Of _Linear Extension_ Are Those
Of Which The Equality Is Most Accurately Ascertainable, And Those To
Which By Consequence All Others Have To Be Reduced. For It Is The
Peculiarity Of Linear Extension That It Alone Allows Its Magnitudes To
Part 2 Chapter 3 (On The Genesis Of Science) Pg 110Be Placed In _Absolute_ Juxtaposition, Or, Rather, In Coincident
Position; It Alone Can Test The Equality Of Two Magnitudes By Observing
Whether They Will Coalesce, As Two Equal Mathematical Lines Do, When
Placed Between The Same Points; It Alone Can Test _Equality_ By Trying
Whether It Will Become _Identity_. Hence, Then, The Fact, That All Exact
Science Is Reducible, By An Ultimate Analysis, To Results Measured In
Equal Units Of Linear Extension.
Still It Remains To Be Noticed In What Manner This Determination Of
Equality By Comparison Of Linear Magnitudes Originated. Once More May We
Perceive That Surrounding Natural Objects Supplied The Needful Lessons.
From The Beginning There Must Have Been A Constant Experience Of Like
Things Placed Side By Side--Men Standing And Walking Together; Animals
From The Same Herd; Fish From The Same Shoal. And The Ceaseless
Repetition Of These Experiences Could Not Fail To Suggest The
Observation, That The Nearer Together Any Objects Were, The More Visible
Became Any Inequality Between Them. Hence The Obvious Device Of Putting
In Apposition Things Of Which It Was Desired To Ascertain The Relative
Magnitudes. Hence The Idea Of _Measure_. And Here We Suddenly Come Upon
A Group Of Facts Which Afford A Solid Basis To The Remainder Of Our
Argument; While They Also Furnish Strong Evidence In Support Of The
Foregoing Speculations. Those Who Look Sceptically On This Attempted
Rehabilitation Of The Earliest Epochs Of Mental Development, And Who
More Especially Think That The Derivation Of So Many Primary Notions
From Organic Forms Is Somewhat Strained, Will Perhaps See More
Probability In The Several Hypotheses That Have Been Ventured, On
Discovering That All Measures Of _Extension_ And _Force_ Originated From
The Lengths And Weights Of Organic Bodies; And All Measures Of _Time_
From The Periodic Phenomena Of Either Organic Or Inorganic Bodies.
Thus, Among Linear Measures, The Cubit Of The Hebrews Was The _Length Of
The Forearm_ From The Elbow To The End Of The Middle Finger; And The
Smaller Scriptural Dimensions Are Expressed In _Hand-Breadths_ And
_Spans_. The Egyptian Cubit, Which Was Similarly Derived, Was Divided
Into Digits, Which Were _Finger-Breadths_; And Each Finger-Breadth Was
More Definitely Expressed As Being Equal To Four _Grains Of Barley_
Placed Breadthwise. Other Ancient Measures Were The Orgyia Or _Stretch
Of The Arms_, The _Pace_, And The _Palm_. So Persistent Has Been The Use
Of These Natural Units Of Length In The East, That Even Now Some Of The
Arabs Mete Out Cloth By The Forearm. So, Too, Is It With European
Measures. The _Foot_ Prevails As A Dimension Throughout Europe, And Has
Done Since The Time Of The Romans, By Whom, Also, It Was Used: Its
Lengths In Different Places Varying Not Much More Than Men's Feet Vary.
The Heights Of Horses Are Still Expressed In _Hands_. The Inch Is The
Length Of The Terminal Joint Of _The Thumb_; As Is Clearly Shown In
France, Where _Pouce_ Means Both Thumb And Inch. Then We Have The Inch
Divided Into Three _Barley-Corns_.
So Completely, Indeed, Have These Organic Dimensions Served As The
Substrata Of All Mensuration, That It Is Only By Means Of Them That We
Can Form Any Estimate Of Some Of The Ancient Distances. For Example, The
Length Of A Degree On The Earth's Surface, As Determined By The Arabian
Astronomers Shortly After The Death Of Haroun-Al-Raschid, Was Fifty-Six
Of Their Miles. We Know Nothing Of Their Mile Further Than That It Was
4000 Cubits; And Whether These Were Sacred Cubits Or Common Cubits,
Would Remain Doubtful, But That The Length Of The Cubit Is Given As
Twenty-Seven Inches, And Each Inch Defined As The Thickness Of Six
Barley-Grains. Thus One Of The Earliest Measurements Of A Degree Comes
Down To Us In Barley-Grains. Not Only Did Organic Lengths Furnish Those
Approximate Measures Which Satisfied Men's Needs In Ruder Ages, But
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