Note: Folks who prefer equations are referred to the (LaTeX'd) seminar notes for 2013, from which the following application-centric narrative is distilled.
Some Number-Ideas That Help Us To Better Understand
Computers That Work A Different Way
And Many Other Good Things Too
Motivation: The "Book You Would Like To Write" surveys the debate "Are Quantum Computers Feasible?", in which Aram Harrow postulated the affirmative, and Gil Kalai postulated the negative. In particular, Aram Harrow's question "Is there any place this is written up?" helped to inspire this essay.
Inspiration: This book's ultra-simple language was inspired by Scott Aaronson's (wonderful!) essay My Quantum Computing Research Explained, Using Only The 1000 Most Common English Words. In particular, the imagined preface (below) "Why Write This Book?" strictly respects the XKCD Up-Goer V text editor's 1000-word vocabulary list.
Notation The remaining text of this new-edition "Book You Would Like To Write" is now explained entirely in "XKCD Up-Goer V" non-technical language. The following proper names appear: Al, Aram, David, Dick, Emmy, Gil, Jean, Johnny, Norbert, Scott, and Si.
Why Write This Book? The ideas of Gil and Aram and Scott --- about "Computers that work a different way, and why maybe we can't build them" --- are beautiful thoughts, and so we can hope that the team of all three of them is right, and that much good comes of their fine ideas. This book hopes to give some short, simple thoughts of how their good ideas might be made more nearly real for everyone, so that we arrive at good places by ways that are more fast and sure.
Al's Happy Thoughts The way that we tell this story begins with a well-known number-teacher named Al (who still lives today). Al loves simple ideas, and what he writes reminds us of something that all of us already know from our own lives:
"New number-pictures in our brains can make hard problems seem soft and easy! Each new picture is like a little wave of water, that slowly lifts our minds above even our most-hard problems, until even little children can see how to fix them easily."
Al kept busy during every hour of the first half his of life to build these beautiful new number-pictures and share them.
Al's More Serious (and Sad) Thoughts Then during the second half of his life, Al began to think very hard about a more serious set of problems.
"Our world will soon have one hundred-hundred-hundred-hundred-hundred people living on it. The people of this huge number need safe homes and good jobs, so that they have chances to smile and hug and marry each other, and make more happy families, and do good works for each other. But instead, people hate and fight each other --- and even entire states hate and fight each other --- so that many people are killed, and very many more are hurt."
Mean-while, the world it-self has become slowly more sick, year-by-year from the huge crowds of people who live on it.
The Heavy Hearts Of Young People These hard facts give a heavy heart to everyone who lives today. Young people (especially) are right to wonder, "Will we ever be happy, and find hope, and even find a nice man/woman to love and start our own family? And when will it happen --- if ever --- that people and states leave behind hate and fear and hurt and killing?"
Al thought very hard about these heavy problems for many tens of years, but yet in his long struggle he found no good answers, and so (slowly) he has become old and sad --- even crazy, some say --- and so now-a-days Al hides himself and talks to no-one (not even his old friends, when they come to look for him).
Ideas Full of Hope However! During these same tens of years, more-and-more people are coming to understand that the beautiful number-ideas and number-pictures that came from the first half of Al's life can help practically to fix the hard problems that have filled the rest of Al's life. The way this works is as follows:
To begin, it is especially nice that the problem that Gil and Aram and Scott all love to think about --- "computers that would work in a different way" (as Scott says) even if we have to "draw a different picture [which] is hard and takes a lot of time" (as Gil says) --- gives people a beautiful (and fun!) way to quickly bring many of Al's number-ideas to life and especially, find practical answers to the hard questions that made him so sad.
The Too-Big Block of Books Everyone knows that building "computers that would work in a different way" isn't easy. To carefully read through a two-foot block of hard books --- having to understand more than ten-hundred-hundred single number-facts along the way! --- would be barely enough for a young person to even begin to think about how to build a practical one.
Al's Work Gives Us Hope We can take heart from Al's work, though. His number-pictures and number-ideas let us pack the key ideas of the whole two-foot block of "different computer" books into just seven short "Green Pieces" (together with a short end-story about what the number-pictures mean to doctors and hospitals, and a few other pictures too). This helps young people (especially) see that the big block of books need not be read as hundreds of hard-to-understand and hard-to-even-remember stories, but rather can be read as one easy-to-understand story that surprises us by being rather short-and-simple. This is a reason for every-one to say "Thank you!" to Al (and friends like Emmy who help Al to think-up and share these beautiful, practical ideas).
Al's Work Makes Gil's Ideas Real A beautiful thing about Al's ideas is that they help make Gil's deep ideas both stronger and more real. Here the short, simple story is this: once Gil starts us with a set of key number-truths, then Al's number-ideas immediately help us draw a number-picture of a world in which Gil's set of number-truths becomes real. This amazes us! Because as our number-thoughts begin to run along this new "Al-to-Gil" number-trail, we find over-and-over that looking into "Al's spaces" in search of "Gil's truths" shows us more number-surprises even than looking into "David's spaces" to build the "different computers" Aram and Scott like so much.
"Different Computers" Are Good for NOTHING -- And That's Great! Next, we notice a nice fact about Scott's "different computer" --- these computers are not (at present) good for any practical work what-so-ever. And so, when we have good number-ideas (along the lines of Al and Gil), then there is no reason at all to hide those number-ideas ... instead, it's definitely a good idea to share those ideas fast. Here there is no reason to whisper, and every reason to shout!
Let's Look Ahead To Better Times When we look more far-ahead in time, we see yet another good reason to share these number-ideas for free ... a reason that some people with well-known names (like Si and Johnny and Norbert and Dick) were the first to state:
"We say to our doctor friends: You should use more-and-better number-pictures (like the story of Al and Gil and Aram and Scott makes us want to learn). Especially, to help doctors learn faster, you should find out how to make the look-at-tiny-matter bit-box focus better. Then it will become very easy to learn how sick people can be helped to become well: we can just look at their living matter-bits! Once our doctors can focus their look-at-tiny-matter bit-box one hundred times stronger, then the hard problems of helping sick people to become whole-and-well will be made very much easier."
When Bad News is Good News As we learn new number-reasons why "different computers" are hard to make, those same new number-reasons help us to find new and better ways to make the focus of our look-at-tiny-matter bit-box one hundred times stronger. As Dick reminds us (and Si and Norbert and Johnny too): "That will be GREAT!"
So Let's Go Fast! Helping sick people is a very strong reason to share new number-ideas fast, for a reason that everyone knows, but makes us sad when we speak it out loud. For too many tens-of-years, from too-many states all around the world, mothers and fathers have sent their young sons and daughters away to fight, and many of these young people have come back not to home, but to a hospital. Perhaps a pretty good start at fixing Al's heavy problem-set can be made, by using Al's own number-ideas to find faster, better ways to make whole-and-well all those people who were sent to fight.
It's Hard At First, But Then It Gets Easy Many people find Al's number-ideas and number-pictures are hard to understand, but everyone understands that these ideas and pictures can help sick people become whole-and-well. And more: everyone wants the better jobs and new business start-ups that grow-up all around us, as we work together to help sick people to become whole-and-well. That is how everyone share, with a good heart, in this great world-wide work.
This big picture gives each of us good reasons to want to put in the long hours, and walk the long trails, and do the hard jobs, and beat the many doubts, that we need to realize the many practical uses of Al's number-ideas!
True Words from the Old Days That is why the true words that a number-person named Jean said almost two-hundred years ago, still sound good to our minds and hearts today:
"Let's move forward! We'll come to believe."
(Allez en avant, et la foi vous viendra.)
Reason For Hope This biggest of all, most beautiful of all, most hope-full work of all --- a great work in which we all share, that helps make people whole-and-well, so they can leave hospitals and return to normal lives --- can join both the hearts and the business interests of every state, as a world-wide job that (especially) lifts-up the hopes of those mothers and fathers and family, who sent their young people to fight in causes that so often seem good in the beginning.
This is how (already!) we all began to live a story that --- as the world hopes --- will have a best-ever and nicest-ever real-world ending.
A Huge "Thank You" Thank you Gil and Aram and Scott, for your free sharing of your many fun, beautiful, important ideas with all the world!