#Tale of big brain dreams of machine that think

#Bug demon in number table

Long time ago, men do math by hand. Math slow. Math wrong a lot.

Men on big boat need number to know where boat is. Number wrong, boat hit rock, boat man go to ancient spirit. Same with fire-tube that throw rock far. Same with lights in night sky. Same with water that come and go. Same with pile of shiny rocks for king (king always want bigger pile of shiny rock, need more number).

Number come from human person at desk all day doing sum. This person called computer. Word mean person, not machine, until much later. Bug demon wait for computer get tired. Then sneak in. Mistake written in book. Mistake copied to other book, then other book, then other book. Soon many ship hit rock, man go to ancient spirit. Bug demon have good time.

This is table problem. Many big brain stare at it and think same thought: how to fight bug demon in number table?

#Schickard build clock that count

First big brain with idea is Wilhelm Schickard. Year 1623, Tübingen, Germany. Schickard want to build machine that crunch number.

Schickard friend of Kepler, also big brain. Kepler stare at lights in night sky for many year, work out that big rocks up there move on stretched circle called ellipse, not regular circle like everyone think. Kepler do this with mammoth pile of math. Kepler tired of math. Schickard want to help friend.

Schickard build small wooden machine. Six digit, plus and minus. Bell ring when number get too big. Schickard call it Rechenuhr, “calculating clock”. First machine for crunching number ever.

Then disaster. First fire eat workshop and machine. Then invisible demon called plague club Schickard and his family and sent them to ancient spirit. Year 1635. Time demon eat the idea, chew on it for many many moon. Will see happen again and again.

Then in 1957, big brain named Franz Hammer find letter of Schickard in cave for old papers. Time demon spit out idea. World learn at last about first calculating machine.

#Pascal hate counting shiny rocks

Next is big brain Blaise Pascal. Year 1642. Rouen, in France. Pascal has seen only nineteen winter.

Pascal father collect shiny rocks for king. Pascal father bend over books all day, doing sum, doing sum, doing sum, counting how many shiny rocks each man owe king. Pascal watch father get older fast. Pascal feel sad. Pascal build machine for father.

Machine is brass box with wheels on top. Spin wheel, number show in window. Easy part is plus. Hard part is carry: when column go past nine, next column must add one. Pascal solve carry with falling weight he call sautoir, “the jumper”. Sautoir lift, drop, push next wheel exactly one tooth. Done.

Pascal try to sell Pascaline. Pascaline cost many shiny rocks. Men with big pile of shiny rock not want number box when sleepy human computer cost much less. Pascaline fail in market.

But Pascaline prove machine can do carry. This matter more than Pascal know.

#Leibniz dream of arguing machine

Third big brain is Gottfried Leibniz. Born 1646. Leibniz everywhere at once. Leibniz invent calculus (other big brain Newton invent same calculus, both club each other for many moon over who think it first). Leibniz also discover binary numbers, where every number written using only zero and one. Binary turn out very important. Hold this thought.

Leibniz see Pascaline, say: nice, but only plus and minus. Times is just plus done many time. Why machine not do that?

So Leibniz build Stepped Reckoner. Heart is special drum with teeth that get longer along its length. Roll drum past gear, drum push gear different number of teeth depending where gear sit. This is Leibniz wheel. Machine do all four operation: add, subtract, multiply, divide. Leibniz wheel show up in calculator till computer no longer human.

But math spirit big in Leibniz. Leibniz have shaman vision: two big brain club each other, everyone hurt, no one win, this stupid. He want math for reasoning so that clubbing can be settled by crunching number. Two men club each other, NO, they sit at machine, they say to each other: calculemus. “Let us calculate.”

Leibniz call this vision calculus ratiocinator. But stay vision. Vision too big for one big brain in one life. Leibniz go to ancient spirits in 1716. Time demon eat idea, chew on it for many many moon.

The tale grug tell here is all about Leibniz vision.

#Babbage hate the table

Then come big brain Charles Babbage from big island called Britain. Year now 1820s. Babbage possessed by anger demon. Babbage angry at organ grinder, angry at hat fashion, angry at people who clap wrong time. But mostly angry at number table.

Babbage strange man, like to look at number table of logarithms, always finding mistake. Old story go: one time Babbage pray to big spirit and wish the table had been done by steam engine instead. Story from long ago so maybe not true, but could be.

But big brain Babbage know trick from math spirit called method of finite differences. Trick let machine compute polynomial using only addition. Many useful table can be approximated by polynomial. So machine that just add can make many table.

Babbage call machine Difference Engine. British king’s men give Babbage big pile of shiny rocks. Many moon later, machine still not finish. Never will. Babbage club with engineer Joseph Clement. Shiny rocks run out. Difference Engine sit half-built in building cave.

In 1991, big brain at big building in London called Science Museum actually build Difference Engine No. 2 from Babbage drawings. Machine work. Babbage right. Babbage just born too early. Babbage gone to ancient spirits in 1871, never see it.

#Babbage dream bigger

While Difference Engine not finished, Babbage have new even bigger vision. Analytical Engine.

Analytical Engine have part Babbage call mill (where number get crunched) and part he call store (where number live). Mill and store separate. Mill take number from store, do thing, put answer back. This is architecture of every computer ever made. Babbage have it in 1837.

How tell mill what to do? Babbage borrow from weaving. Joseph Marie Jacquard make loom that weave fancy pattern using punched cards. Hole or no hole tell loom which thread to lift. Jacquard even use loom to weave picture of own face in silk cloth, from cards alone. Babbage own this woven face. Babbage realise: card can carry program.

Card tell mill what number to fetch, what to do, where to put answer. Card can also say: if number negative, skip three card. This is conditional. Card can say: go back twenty card. This is loop. With conditional and loop, machine can do almost anything.

Analytical Engine never built. Too big. Too many shiny rocks needed. King’s men already burned by Difference Engine, no more shiny rocks for Babbage. Babbage go to ancient spirits angry. Drawings go in box.

But before world forget, world get one note from one person who understand machine even better than Babbage.

#Lovelace see further

Ada Lovelace daughter of Lord Byron. Byron is word-maker, mad as bag of cat. Byron leave when Ada baby. Mother teach Ada math hard, on purpose, so Ada not turn out like father.

Ada meet Babbage in 1833. Ada seventeen. Ada fall in love with idea of machine.

Years later, Luigi Menabrea write paper about Analytical Engine in tongue of France. Lovelace turn paper into tongue of Britain, add notes. Notes three times longer than paper itself.

In Note G, Lovelace write step-by-step plan for machine to compute Bernoulli numbers. Plan use loop, use conditional, use intermediate values. This is first algorithm for general-purpose computer. Computer not exist yet. Will not exist for many many moon.

But shaman vision Lovelace see is not Bernoulli plan. Vision is this: Analytical Engine not just for number. Machine for any thing made of symbol and rule. She write machine could even make music, if music could be written as pattern.

Babbage see calculator. Big calculator. Lovelace see computer.

Lovelace also write that machine has no pretensions to originate anything. Machine only do what we tell it. Idea called Lady Lovelace’s Objection. Come back many many moon later when big brain Turing decide if machine can think.

Lovelace haunted by another invisible demon, this one eat her from inside, called cancer. Went to ancient spirits only after 36 winters, year 1852. Too young. And time demon go to work again.

#time demon eat all visions

All big brain went to ancient spirits without tribe to tell story after. So time demon have feast. Took sixty winter before anyone pick up thread again.

Pattern go like this: big brain have big vision. Time demon eat. World forget. Smaller brain rediscover later, from scratch, slow. This always make grug a bit sad.

#what grug learn

Machine can replace tired computer. Schickard, Pascal, Leibniz, Babbage all show this with gear and lever, no tame lightning, two hundred year before anyone need a wire.

But Lovelace see further. Machine that follow rule on symbol can do anything that can be written as symbol and rule. Number is symbol. Music is symbol. Logic is symbol. Any precise thing is symbol.

So machine that follow rule on symbol can do almost anything we know how to describe.

This is whole book in one sentence.

#what grug worry about next

Leibniz dream of language for reasoning. Lovelace see machine could follow rule. But what rule? Where is precise language for thinking, where every step is clear, where nothing ambiguous?

Leibniz want it. Babbage need it. Lovelace see machine could use it. None of them have it.

Two hundred year of dreaming about machine that reason. Nobody yet have algebra of reasoning.

Then in 1847, son of shoemaker who teach himself math from library books read about boring fight between two logicians, and he have an idea.

Grug come to him next.