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The Errors Which Arise From The Absence Of Facts Are Far More Numerous And More Durable Than Those Which Result From Unsound Reasoning Respecting True Data.

-Charles Babbage

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The Errors Which Arise

Charles Babbage

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The Errors Which Arise From The Absence Of Facts Are Far More Numerous And More Durable Than Those Which Result From Unsound Reasoning Respecting True Data.

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You Will Be Able To Appreciate The Influence Of Such An Engine On The Future Progress Of Science. I Live In A Country Which Is Incapable Of Estimating It.

To Those Who Have Chosen The Profession Of Medicine, A Knowledge Of Chemistry, And Of Some Branches Of Natural History, And, Indeed, Of Several Other Departments Of Science, Affords Useful Assistance.

On Two Occasions I Have Been Asked, 'pray, Mr. Babbage, If You Put Into The Machine Wrong Figures, Will The Right Answers Come Out?' I Am Not Able Rightly To Apprehend The Kind Of Confusion Of Ideas That Could Provoke Such A Question.

A Tool Is Usually More Simple Than A Machine; It Is Generally Used With The Hand, Whilst A Machine Is Frequently Moved By Animal Or Steam Power.

What Is There In A Name? It Is Merely An Empty Basket, Until You Put Something Into It.

The Quantity Of Meaning Compressed Into Small Space By Algebraic Signs, Is Another Circumstance That Facilitates The Reasonings We Are Accustomed To Carry On By Their Aid.

Another Mode Of Accumulating Power Arises From Lifting A Weight And Then Allowing It To Fall.

That Science Has Long Been Neglected And Declining In England, Is Not An Opinion Originating With Me, But Is Shared By Many, And Has Been Expressed By Higher Authority Than Mine.

Remember That Accumulated Knowledge, Like Accumulated Capital, Increases At Compound Interest: But It Differs From The Accumulation Of Capital In This; That The Increase Of Knowledge Produces A More Rapid Rate Of Progress, Whilst The Accumulation Of Capital Leads To A Lower Rate Of Interest. Capital Thus Checks It Own Accumulation: Knowledge Thus Accelerates Its Own Advance. Each Generation, Therefore, To Deserve Comparison With Its Predecessor, Is Bound To Add Much More Largely To The Common Stock Than That Which It Immediately Succeeds.

The Half Minute Which We Daily Devote To The Winding-up Of Our Watches Is An Exertion Of Labour Almost Insensible; Yet, By The Aid Of A Few Wheels, Its Effect Is Spread Over The Whole Twenty-four Hours.

An Object Is Frequently Not Seen, From Not Knowing How To See It, Rather Than From Any Defect Of The Organ Of Vision.

At Each Increase Of Knowledge, As Well As On The Contrivance Of Every New Tool, Human Labour Becomes Abridged.

The Accumulation Of Skill And Science Which Has Been Directed To Diminish The Difficulty Of Producing Manufactured Goods, Has Not Been Beneficial To That Country Alone In Which It Is Concentrated Distant Kingdoms Have Participated In Its Advantages.

In Mathematical Science, More Than In All Others, It Happens That Truths Which Are At One Period The Most Abstract, And Apparently The Most Remote From All Useful Application, Become In The Next Age The Bases Of Profound Physical Inquiries, And In The Succeeding One, Perhaps, By Proper Simplification And Reduction To Tables, Furnish Their Ready And Daily Aid To The Artist And The Sailor.

In Mathematics We Have Long Since Drawn The Rein, And Given Over A Hopeless Race.

There Is Nothing In The Nature Of A Miracle That Should Render It Incredible:;: Its Credibility Depends Upon The Nature Of The Evidence By Which It Is Supported. An Event Of Extreme Probability Will Not Necessarily Command Our Belief Unless Upon A Sufficiency Of Proof; And So An Event Which We May Regard As Highly Improbable May Command Our Belief If It Is Sustained By Sufficient Evidence. So That The Credibility Or Incredibility Of An Event Does Not Rest Upon The Nature Of The Event Itself, But Depends Upon The Nature And Sufficiency Of The Proof Which Sustains It.

As Soon As An Analytical Engine Exists, It Will Neccessarily Guide The Future Course Of Science.

Long Intervals Frequently Elapse Between The Discovery Of New Principles In Science And Their Practical Application... Those Intellectual Qualifications, Which Give Birth To New Principles Or To New Methods, Are Of Quite A Different Order From Those Which Are Necessary For Their Practical Application.

The Council Of The Royal Society Is A Collection Of Men Who Elect Each Other To Office And Then Dine Together At The Expense Of This Society To Praise Each Other Over Wine And Give Each Other Medals.

A Young Man Passes From Our Public Schools To The Universities, Ignorant Almost Of The Elements Of Every Branch Of Useful Knowledge.

Surely, If Knowledge Is Valuable, It Can Never Be Good Policy In A Country Far Wealthier Than Tuscany, To Allow A Genius Like Mr. Dalton's, To Be Employed In The Drudgery Of Elementary Instruction.

There Is, However, Another Purpose To Which Academies Contribute. When They Consist Of A Limited Number Of Persons, Eminent For Their Knowledge, It Becomes An Object Of Ambition To Be Admitted On Their List.

Mechanical Notation ... I Look Upon It As One Of The Most Important Additions I Have Made To Human Knowledge. It Has Placed The Construction Of Machinery In The Rank Of A Demonstrative Science. The Day Will Arrive When No School Of Mechanical Drawing Will Be Thought Complete Without Teaching It.

No Person Will Deny That The Highest Degree Of Attainable Accuracy Is An Object To Be Desired, And It Is Generally Found That The Last Advances Towards Precision Require A Greater Devotion Of Time, Labour, And Expense, Than Those Which Precede Them.

The Successful Construction Of All Machinery Depends On The Perfection Of The Tools Employed; And Whoever Is A Master In The Arts Of Tool-making Possesses The Key To The Construction Of All Machines... The Contrivance And Construction Of Tools Must Therefore Ever Stand At The Head Of The Industrial Arts.

Precedents Are Treated By Powerful Minds As Fetters With Which To Bind Down The Weak, As Reasons With Which To Mistify The Moderately Informed, And As Reeds Which They Themselves Fearlessly Break Through Whenever New Combinations And Difficult Emergencies Demand Their Highest Efforts.

That A Country, [england], Eminently Distinguished For Its Mechanical And Manufacturing Ingenuity, Should Be Indifferent To The Progress Of Inquiries Which Form The Highest Departments Of That Knowledge On Whose More Elementary Truths Its Wealth And Rank Depend, Is A Fact Which Is Well Deserving The Attention Of Those Who Shall Inquire Into The Causes That Influence The Progress Of Nations.

If We Look At The Fact, We Shall Find That The Great Inventions Of The Age Are Not, With Us At Least, Always Produced In Universities.

Great Inventions

The Errors Which Arise From The Absence Of Facts Are Far More Numerous And More Durable Than Those Which Result From Unsound Reasoning Respecting True Data.

Unless There Exist Peculiar Institutions For The Support Of Such Inquirers, Or Unless The Government Directly Interfere, The Contriver Of A Thaumatrope May Derive Profit From His Ingenuity, Whilst He Who Unravels The Laws Of Light And Vision, On Which Multitudes Of Phenomena Depend, Shall Descend Unrewarded To The Tomb.

Whenever A Man Can Get Hold Of Numbers, They Are Invaluable: If Correct, They Assist In Informing His Own Mind, But They Are Still More Useful In Deluding The Minds Of Others. Numbers Are The Masters Of The Weak, But The Slaves Of The Strong.

The Tastes And Pursuits Of Manhood Will Bear On Them The Traces Of The Earlier Impressions Of Our Education. It Is Therefore Not Unreasonable To Suppose That Some Portion Of The Neglect Of Science In England, May Be Attributed To The System Of Education We Pursue.

A Powerful Attraction Exists, Therefore, To The Promotion Of A Study And Of Duties Of All Others Engrossing The Time Most Completely, And Which Is Less Benefited Than Most Others By Any Acquaintance With Science.

In Turning From The Smaller Instruments In Frequent Use To The Larger And More Important Machines, The Economy Arising From The Increase Of Velocity Becomes More Striking.

Propose To An Englishman Any Principle, Or Any Instrument, However Admirable, And You Will Observe That The Whole Effort Of The English Mind Is Directed To Find A Difficulty, A Defect, Or An Impossibility In It. If You Speak To Him Of A Machine For Peeling A Potato, He Will Pronounce It Impossible: If You Peel A Potato With It Before His Eyes, He Will Declare It Useless, Because It Will Not Slice A Pineapple.

It Will Be Readily Admitted, That A Degree Conferred By An University, Ought To Be A Pledge To The Public That He Who Holds It Possesses A Certain Quantity Of Knowledge.

I Have No Desire To Write My Own Biography, As Long As I Have Strength And Means To Do Better Work.

For One Person Who Is Blessed With The Power Of Invention, Many Will Always Be Found Who Have The Capacity Of Applying Principles.

It Is Difficult To Estimate The Misery Inflicted Upon Thousands Of Persons, And The Absolute Pecuniary Penalty Imposed Upon Multitudes Of Intellectual Workers By The Loss Of Their Time, Destroyed By Organ-grinders And Other Similar Nuisances.

There Are Few Circumstances Which So Strongly Distinguish The Philosopher, As The Calmness With Which He Can Reply To Criticisms He May Think Undeservedly Severe.

That The State Of Knowledge In Any Country Will Exert A Directive Influence On The General System Of Instruction Adopted In It, Is A Principle Too Obvious To Require Investigation.

Trimming Consists Of Clipping Off Little Bits Here And There From Those Observations Which Differ Most In Excess From The Mean, And In Sticking Them Onto Those Which Are Too Small; A Species Of 'equitable Adjustment,' As A Radical Would Term It, Which Cannot Be Admitted In Science.

The Fatigue Produced On The Muscles Of The Human Frame Does Not Altogether Depend On The Actual Force Employed In Each Effort, But Partly On The Frequency With Which It Is Exerted.

The Difference Between A Tool And A Machine Is Not Capable Of Very Precise Distinction; Nor Is It Necessary, In A Popular Explanation Of Those Terms, To Limit Very Strictly Their Acceptation.

Perhaps The Most Important Principle On Which The Economy Of A Manufacture Depends, Is The Division Of Labour Amongst The Persons Who Perform The Work.

I Am Inclined To Attach Some Importance To The New System Of Manufacturing; And Venture To Throw It Out With The Hope Of Its Receiving A Full Discussion Among Those Who Are Most Interestedin The Subject.

The Influence Of Electricity In Producing Decompositions, Although Of Inestimable Value As An Instrument Of Discovery In Chemical Inquiries, Can Hardly Be Said To Have Been Applied To The Practical Purposes Of Life, Until The Same Powerful Genius [davy] Which Detected The Principle, Applied It, By A Singular Felicity Of Reasoning, To Arrest The Corrosion Of The Copper-sheathing Of Vessels. ... This Was Regarded As By Laplace As The Greatest Of Sir Humphry's Discoveries.

Perhaps It Would Be Better For Science, That All Criticism Should Be Avowed.

The Possessors Of Wealth Can Scarcely Be Indifferent To Processes Which, Nearly Or Remotely Have Been The Fertile Source Of Their Possessions.

The Proportion Between The Velocity With Which Men Or Animals Move, And The Weights They Carry, Is A Matter Of Considerable Importance, Particularly In Military Affairs.

Those From Whose Pocket The Salary Is Drawn, And By Whose Appointment The Officer Was Made, Have Always A Right To Discuss The Merits Of Their Officers, And Their Modes Of Exercising The Duties They Are Paid To Perform.

The True Value Of The Christian Religion Rests, Not Upon Speculative Views Of The Creator, Which Must Necessarily Be Different In Each Individual, According To The Extent Of The Knowledge Of The Finite Being, Who Employs His Own Feeble Powers In Contemplating The Infinite: But It Rests Upon Those Doctrines Of Kindness And Benevolence Which That Religion Claims And Enforces, Not Merely In Favour Of Man Himself But Of Every Creature Susceptible Of Pain Or Of Happiness.

[in Response To Alfred Tennyson's Poem "vision Of Sin," Which Included The Line "every Moment Dies A Man, Every Moment One Is Born."] If This Were True, The Population Of The World Would Be At A Stand-still. In Truth, The Rate Of Birth Is Slightly In Excess Of Death. I Would Suggest That The Next Edition Of Your Poem Should Read: "every Moment Dies A Man, Every Moment 1 [and] 1/16 Is Born." Strictly Speaking, The Actual Figure Is So Long I Cannot Get It Into A Line, But I Believe The Figure 1 [and] 1/16 Will Be Sufficiently Accurate For Poetry.

Whenever The Work Is Itself Light, It Becomes Necessary, In Order To Economize Time, To Increase The Velocity.

Forging Differs From Hoaxing, Inasmuch As In The Later The Deceit Is Intended To Last For A Time, And Then Be Discovered, To The Ridicule Of Those Who Have Credited It; Whereas The Forger Is One Who, Wishing To Acquire A Reputation For Science, Records Observations Which He Has Never Made.

Some Kinds Of Nails, Such As Those Used For Defending The Soles Of Coarse Shoes, Called Hobnails, Require A Particular Form Of The Head, Which Is Made By The Stroke Of A Die.

As Soon As An Analytical Engine Exists, It Will Necessarily Guide The Future Course Of The Science. Whenever Any Result Is Sought By Its Aid, The Question Will Then Arise — By What Course Of Calculation Can These Results Be Arrived At By The Machine In The Shortest Time?

Telegraphs Are Machines For Conveying Information Over Extensive Lines With Great Rapidity.

The Public Character Of Every Public Servant Is Legitimate Subject Of Discussion, And His Fitness Or Unfitness For Office May Be Fairly Canvassed By Any Person.

Mr. Herschel... Brought With Him The Calculations Of The Computers, And We Commenced The Tedious Process Of Verification. After A Time Many Discrepancies Occurred, And At One Point These Discordances Were So Numerous That I Exclaimed, "i Wish To God These Calculations Had Been Executed By Steam," To Which Herschel Replied, "it Is Quite Possible."

Science In England Is Not A Profession: Its Cultivators Are Scarcely Recognised Even As A Class. Our Language Itself Contains No Single Term By Which Their Occupation Can Be Expressed. We Borrow A Foreign Word [savant] From Another Country Whose High Ambition It Is To Advance Science, And Whose Deeper Policy, In Accord With More Generous Feelings, Gives To The Intellectual Labourer Reward And Honour, In Return For Services Which Crown The Nation With Imperishable Renown, And Ultimately Enrich The Human Race.

The Triumph Of The Industrial Arts Will Advance The Cause Of Civilization More Rapidly Than Its Warmest Advocates Could Have Hoped, And Contribute To The Permanent Prosperity And Strength Of The Country Far More Than The Most Splendid Victories Of Successful War.

It Can Happen To But Few Philosophers, And But At Distant Intervals, To Snatch A Science, Like Dalton, From The Chaos Of Indefinite Combination, And Binding It In The Chains Of Number, To Exalt It To Rank Amongst The Exact. Triumphs Like These Are Necessarily 'few And Far Between.'

The Economy Of Human Time Is The Next Advantage Of Machinery In Manufactures.

If We Define A Miracle As An Effect Of Which The Cause Is Unknown To Us, Then We Make Our Ignorance The Source Of Miracles! And The Universe Itself Would Be A Standing Miracle. A Miracle Might Be Perhaps Defined More Exactly As An Effect Which Is Not The Consequence Or Effect Of Any Known Laws Of Nature.

The Whole Of The Developments And Operations Of Analysis Are Now Capable Of Being Executed By Machinery ... As Soon As An Analytical Engine Exists, It Will Necessarily Guide The Future Course Of Science.

Miracles May Be, For Anything We Know To The Contrary, Phenomena Of A Higher Order Of God's Laws, Superior To, And, Under Certain Conditions, Controlling The Inferior Order Known To Us As The Ordinary Laws Of Nature.

He Will Also Find That The High And Independent Spirit, Which Usually Dwells In The Breast Of Those Who Are Deeply Versed In Scientific Pursuits, Is Ill Adapted For Administrative Appointments; And That Even If Successful, He Must Hear Many Things He Disapproves, And Raise No Voice Against Them.

Of Cooking. This Is An Art Of Various Forms, The Object Of Which Is To Give Ordinary Observations The Appearance And Character Of Those Of The Highest Degree Of Accuracy. One Of Its Numerous Processes Is To Make Multitudes Of Observations, And Out Of These To Select Only Those Which Agree, Or Very Nearly Agree. If A Hundred Observations Are Made, The Cook Must Be Very Unhappy If He Cannot Pick Out Fifteen Or Twenty Which Will Do For Serving Up.

In England, The Profession Of The Law Is That Which Seems To Hold Out The Strongest Attraction To Talent, From The Circumstance, That In It Ability, Coupled With Exertion, Even Though Unaided By Patronage, Cannot Fail Of Obtaining Reward.

The First Steps In The Path Of Discovery, And The First Approximate Measures, Are Those Which Add Most To The Existing Knowledge Of Mankind.

Errors Using Inadequate Data Are Much Less Than Those Using No Data At All.

Mathematical Logic

I Wish To God These Calculations Had Been Executed By Steam.

Scientific Knowledge Scarcely Exists Amongst The Higher Classes Of Society. The Discussion In The Houses Of Lords Or Of Commons, Which Arise On The Occurrence Of Any Subjects Connected With Science, Sufficiently Prove This Fact.

The Church Has Been Reproached With Endeavouring To Appropriate To Itself All Those Professorships In Our Universities Which Are Connected With Science: It Is However Certain That The Larger Portion Of These Ill-remunerated Offices Have Been Filled By Clergymen.

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