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HOW DEMOCRACY WORKS (OR WHY PERFECT ELECTIONS SHOULD ALL END IN TIES)

Conversation : CULTURE


HOW DEMOCRACY WORKS (OR WHY PERFECT ELECTIONS SHOULD ALL END IN TIES)

By W. Daniel Hillis [11.19.00]

Danny Hillis, physicist and computer scientist, brings together, in full circle,
many of the ideas circulating among third culture thinkers: Marvin Minsky's
society of mind; Christopher G. Langton's artificial life; Richard Dawkins'
gene's-eye view; the plectics practiced at Santa Fe. Hillis developed the
algorithms that made possible the massively parallel computer. He began in
physics and then went into computer science — where he revolutionized the field
— and he brought his algorithms to bear on the study of evolution. He sees the
autocatalytic effect of fast computers, which lets us design better and faster
computers faster, as analogous to the evolution of intelligence. At MIT in the
late seventies, Hillis built his "connection machine," a computer that makes use
of integrated circuits and, in its parallel operations, closely reflects the
workings of the human mind. In 1983, he spun off a computer company called
Thinking Machines, which set out to build the world's fastest supercomputer by
utilizing parallel architecture.

The massively parallel computational model is critical to an understanding of
today's revolution in human communication. Hillis's computers, which are fast
enough to simulate the process of evolution itself, have shown that programs of
random instructions can, by competing, produce new generations of programs — an
approach that may well lead to the first machine that truly "thinks." Hillis's
work demonstrates that when systems are not engineered but instead allowed to
evolve — to build themselves — then the resultant whole is greater than the sum
of its parts. Simple entities working together produce some complex thing that
transcends them; the implications for biology, engineering, and physics are
enormous.

--------------------------------------------------------------------------------

 

Here is a simple, successful election. The graph shows how many voters are at
each point on the political spectrum. It also shows the positions of the
candidates. The Good candidate is the one whose opinions are closest to the will
of the voters.  Voters choose the candidate that is closest to their own
position, so the Good candidate wins.



The dividing line shows where the vote splits. Voters to the left of the line
will vote for the Good candidate, voters to the right of the line will vote for
the Bad candidate.

 

Of course I don't mean that Left is Good and Right is Bad.  The picture works
the same way if we flip it around.



Either way, the Good candidate wins, and the election is successful. Some voters
are unhappy, but even more voters would have been unhappy if the Bad candidate
had won.

In some cases most of the voters may be unhappy with the results. This depends
on the shape of the opinion curve. Here is one type of unpleasant outcomes:



In this case the voters' opinions are highly polarized, and the candidates are
uncompromising. Almost half the population will be extremely unhappy with the
result.

 

Here is a less unhappy variation:



In this case voters' opinions are highly polarized, but the candidates'
positions represent a compromise. Almost all of the voters are relatively
unhappy. As unpleasant as these outcomes may seem, they still represent
successes of the democratic process. No other choice of leader would have led to
a better result.

If we add a third candidate, the democratic process does not even necessarily
produce the best result.



In this case the Spoiler candidate takes away enough votes from the Good
candidate to allow the Bad candidate to win. This is very likely to happen if
there are three parties.

 

In a many-party system, the voters are more likely to be happy with the choice
of candidates, because they can find a candidate that is close to their own
position. Unfortunately, the voters are less likely to be happy with the result
of the election, because it will not necessarily choose the Best candidate. This
situation is even worse when there are many viable candidates.



In a multiple party vote, each voter will be able to choose a candidate with
opinions close to his or her own, but the candidate who gets elected will be the
one that has the broadest constituency, not the one who best represents the will
of the all the voters. Because the worst candidates pick up the outliers, it is
relatively easy for a very bad candidate to win.

Let's go back to the case of only two parties.



If the candidates are willing to be flexible, then either candidate can gain
votes by moving toward the Best Position. The Best Position is where an equal
number of voters are to the left and to the right. A candidate in the Best
Position is unbeatable. A candidate in the Best Position also does the best job
of making the voters happy, or at least making them less unhappy than they would
be otherwise.

 



If the candidates have some flexibility in their opinions and good information
about what the voters want, they will move their own positions towards the Best
Position, because it increases their chances of being elected. The closer one
candidate moves towards the Best Position, the closer the other candidate will
have to move to remain electable. With good pre-election polling, both
candidates will be able to determine very accurately how much they need to move.
If they are both willing to adjust their positions near the Best Position the
outcome of the race will depend on the accuracy of the polling. If the polling
is perfect, all elections will end in near ties.

This process of adjusting position in response to polling may seem to compromise
the integrity of the candidate, but it does produce candidates whose opinion is
very close to the Best Position. This may be regarded as a successful outcome,
because a candidate in the Best Position also does the best job of making the
voters happy.

Actually, a winner in the Best Position doesn't necessarily make many voters
happy; it just makes them less unhappy than they would be with a different
winner. In the previous illustrations, the best position was also the most
popular position. This is not always the case.



In this final example, the voters are polarized and the Best Position is highly
unpopular. Still, it represents the most electable position, and also the
position that makes the fewest people very unhappy. This is the best result that
any system can produce.

So in the end, two-party democracy is not necessarily good at giving voters a
chance to elect a candidate that they like. If the polls are very accurate and
the candidates are flexible, a successful election is likely to produce two
candidates whom the voter will regard as equally imperfect. The election results
will be very close.

For all its problems, the two-party democracy does a good job of producing and
selecting candidates that represent an acceptable compromise between a wide
spectrum of opinions. If the process is working well, then by the time of the
election many voters may feel that they have very little real choice.  This may
seem like a failure, but actually it is a sign of success. It means that the
system has produced candidates that represent the most acceptable compromise of
the conflicting opinions of the voters. If this process has worked perfectly,
the results of the election will be a tie.  Judging from the recent results of
the American presidential election, democracy is working well.

 * 
 * 

--------------------------------------------------------------------------------


REALITY CLUB DISCUSSION

Bernardo Huberman
HP Fellow and Director of the Systems Research Center at Hewlett Packard
Laboratories

Concerning Danny Hillis' arguments on "How Democracy Works (Or Why Perfect
Elections Should All End In Ties) " I'd like to point out that they are well
known in political science. As a matter of fact, there is even a theorem (can
you imagine, a theorem in political science?) that states it all rigorously.
This so called median-voter theorem states that if two parties are trying to
maximize their share of the votes, the only Nash equilibrium (each party making
a best response to the other candidate's choice) is where both candidates chose
the platform of the median voter's ideal policy.

While the assumptions underlying this theorem, originally proved by Hotelling in
the context of consumer preferences in 1929, are rather stark — but not
different from Danny's example — (it is assumed that voters have single-peaked
preferences over a left to right one-dimensional issue space, and that everyone
turns out and votes for the candidate whose platform they prefer), it turns out
that the theorem's conclusion is robust in many respects. That is, modest
departures from most of the canonical assumptions lead to only small changes in
the candidates' behavior.

The present presidential platforms, while far from fitting the classical
assumptions exactly, seem to indicate that the median voter theorem applies to
even more general cases.

Jaron Lanier
Computer Scientist; Musician; Author, Who Owns The Future?

Danny's analysis is exactly right for sincere players. When the players are
insincere, the story gets more complicated.

My sense of the 2000 presidential election is that some right-leaning Bush
supporters believed their candidate was being insincere on the campaign trail,
but with a welcome wink. For instance, opponents of gun control believed that
once in office Bush would become an active ally, even though he was able to
remain remarkably soft spoken, almost to the point of inaudibility, on gun
control during the campaign. The same dynamic played out in reverse for Gore,
however. Gore's most left-leaning potential supporters doubted his resolve or
sincerity on issues such as protection of the environment.

Thus the perception of sincerity became the deciding factor in an election where
both candidates sought the center. In some cases an appearance of selective
insincerity actually helped a candidate (as in Bush's courting of the pro-gun
vote).Speaking technically, Grover's algorithm show quantum search is only
polynomially faster than classical search. Part of my research is solving
continuous problems on a quantum computer and here there are problems which can
be solved exponentially faster on a quantum computer.

To state the obvious, actual sincerity is quite a different thing from the
appearance of sincerity. I know Gore a bit and find him to be utterly sincere in
person, but sadly artificial on television. I'll turn to Phil's remarks. He says
"Why does the quantum computer do new things? Why is complexity theory such a
poor quide to the real world of problems?"

Childhood play is often concerned with the management of the appearance of
sincerity. Children learn to present and detect poker faces, for example.

The most successful politicians not only excel at such skills, but even master
elaborations, like sincerely displaying to one set of people one's insincerity
to another, even if one has to be insincere to do so, and thus cementing an
alliance.

The fact that the votes in a surprising number of diverse states came out almost
perfectly tied demands further analysis. Maybe the arts and sciences of
demographic-driven campaigning have become perfected to the point that there is
almost no noise left in the system. I am reminded of the flat wall that can form
between two soap bubbles.

George Dyson
Science Historian; Author, Analogia

In the digital universe, every bit makes a difference. In a democracy, every
vote counts. Punched card ballots are where these two universes coincide. On
November 4, 1997, in Ferndale, Washington, the difference between two candidates
for city council came down to one bit of difference on one card.

"There's not much case law on this," argues Frank J. Chmelik. "The
responsibility of the canvassing board is to certify that universe of ballots
that make up the count. A recount is to re-count the ballots. It doesn't make
any sense to expand the universe of ballots. It would frustrate the purpose of
the law to allow the recounting of an infinite set of ballots. It may have been
in a sealed envelope but it was in a white envelope, not a pink envelope." It is
December 19, 1997 and I am in Whatcom County Superior Court, listening to
arguments before Judge Michael Moynihan in the matter of Yvonne Goldsmith vs.
the Whatcom County Canvassing Board. Yvonne Goldsmith came in one vote ahead of
Lloyd Zimmerman in the race for Ferndale City Council on election night. After a
mandatory manual recount and the discovery of a lost ballot, she is now one vote
behind. Her lawyers have appealed for a second recount, this time by machine.
Said machine to be a Documation card reader, one of the models now built by
Cardamation of Phoenixville, Pennsylvania — if the appeal is upheld. Right now
the lawyers are arguing over whether to include an absentee ballot — discovered
in a sealed envelope at the time of the first recount — whose validity depends
in part on whether the envelope it turned up in was white or pink.

"It doesn't make any sense for a subsequent computer recount to supersede the
manual recount," argues Karen Frakes on behalf of Whatcom County Auditor Sheila
Forslof, returning to the issue of human beings vs. machines. "We have no reason
to believe the computer recount will be any different."

Chmelik, however, cites chapter and verse of a statute (RCW 29.64.010) which
"allows for second recount upon application by the candidate, who may specify
such recount be done manually or by (electronic) vote tally machine. Goldsmith
has a right to an electronic recount that will control."

Judge Moynihan, who is reading the fine print, refers to a clause (RCW
29.62.050) which "stipulates `a recount by machine shall use separate and
distinct programming.' Can you explain?" Chmelik explains how the vote counting
software will be freshly installed (under Windows 95) from a copy delivered from
the State Capitol under official seal.

After some deliberation the judge decides: "They have to count that ballot. As
to whether or not the candidate is entitled to an electronic or manual recount —
she's entitled to make that choice. If there's a discrepancy, well, it will
probably have to be decided by another court."

The recount (by machine) is scheduled for Tuesday, December 23, at 9:00 a.m. I
arrive at the Whatcom County Courthouse at the appointed time and am
ceremoniously signed into the room. No one, as far as I can tell, has ever heard
of Wired magazine. The Bellingham Herald, a few blocks away, hasn't bothered to
send a reporter but is awaiting the results by phone. The card reader sits
facing the end of a long boardroom table, with various officials arrayed on
either side. The reader is hooked up to an IBM 300GL PC, with the "separate and
distinct programming" occupying an external Iomega Zip Drive. The software,
produced by Computer Elections of Benicia, CA, is up and running under Windows
95.

Pete Griffin, elections supervisor, is fiddling with the card reader. He's proud
of how much the machine cost and that it's recently been factory rebuilt. A
number of minor dignitaries are present, as well as representatives for the two
candidates and two official scrutineers. Lots of sealing and unsealing of metal
boxes containing the ballots, with forms signed and witnessed in triplicate
every time a deck of punched cards makes a move. The card reader is fired up. It
runs through a series of "Logic and Accuracy" test decks from the Secretary of
State. The results are compared with the results from election night, when the
Logic and Accuracy decks were placed under the seals we just removed. It's a
cryptic process, and we all just take the word of Peter Griffin that the string
of characters generated on the monitor means everything's OK. The reader
flutters smoothly through the piles of cards without missing a single beat — far
smoother than the readers I saw at Cardamation, being tested against cards that
had been stored for many years.

Finally, it's time to count the ballots. It doesn't take long, a few minutes at
most. We all hold our breath. The manual recount was repeated three times, under
strict supervision, and all three counts showed Zimmerman one vote ahead. Is
this the moment of truth? I'm watching the floor under the machine, to see how
many bits of "chad" — the card stock that is punched out to make a hole — fall
out when running through the decks. Occasionally, in running through the
vacuum-fed reader at high speed, a bit will be dislodged from a ballot. This is
a problem with partially pre perforated ballots — and human beings who sometimes
start to punch out one location and then change their mind. As Larry Olsen, the
Republican observer, whispers to me when he senses what I'm thinking, "If chad
falls out there's no way to put it back."

I count nine bits of chad on the carpet after all the ballots are run. The chad
may just have fallen innocently out of the innards of the machine, it may have
fallen out of any number of punch positions which had nothing to do with the
city council race, or one or more bits might have fallen out of the
Zimmerman-Goldsmith positions. Who knows? The seconds tick by, and I am acutely
conscious at this instant that language and reality sometimes coincide: in the
punched card universe a "bit" really is a bit, and Gregory Bateson's definition
of information as "any difference that makes a difference" is true indeed, as we
await the count of how many bits of difference between card and not-card have
just passed through the Cardamation machine. Pete Griffin sits down at the PC,
enters some commands, navigates through some dialog boxes, and a Hewlett-Packard
laser printer begins to hum. It's a tie: 954 to 954. The statistics show one
"overvote" — a ballot where both candidates have received a vote. Someone asks
Goldsmith's representative if she would like to run the cards again. No.

The auditor consults the Laws of the State of Washington and announces that the
election will now be decided by flipping a coin. The candidate who filed first —
Goldsmith — gets to call it heads or tails. Three days later, Judge Moynihan
tosses a 1921 silver dollar in the air. Goldsmith calls it tails — and wins.
Goldsmith gets the seat on City Council, while the Judge awards Zimmerman the
coin. The "Logic and Accuracy" decks go back, under seal, to the Secretary of
State. We live in a binary universe — and what isn't governed by logic is
governed by chance.

Al Seckel
Cognitive neuroscientist; Author, Optical Illusions: The Science of Visual
Perception

I thought this new visual illusion was symbolic of the recount in Florida. Hope
you enjoy it.

© Al Seckel, 2000



W. Daniel Hillis
Physicist, Computer Scientist, Co-Founder, Applied Invention.; Author, The
Pattern on the Stone

Response to Luyen Chou

Luyen Chou is correct is pointing out that the model I used to explain ties is
very much simpler that reality. However, I do not believe that the factors he
describes interfere with feedback mechanisms described in the essay. It is
certainly true that voter preference is determined by many factors, and that
many of these factors are not under control of the candidates. This means that
the candidate must use the variables that are under their control to achieve
electablilty. If the candidates have many such issues to choose from, they may
very well adopt different stances on particular issues to achieve the same net
effect. Thus, both candidates may be in the optimally electable position in
spite of holding very different positions on a particular issue, and spite of
other voter preference factors that are beyond their control.

Maryam Mohit
Vice-President of Site Development at amazon.com

A quite enjoyable issue. By the way, here's a little joke I cooked up with some
friends at work [amazon.com]. I thought you might enjoy it. Click here. 

Luyen Chou
Senior Vice President, Product Strategy, Pearson

Danny's argument for the statistical merits of two-party democracy seems to me
to be completely sound when considered in an idealized political setting. But it
ignores the reality of the contemporary American political landscape in which
elections are invariably decided by much less rational considerations than
Danny's article would have one believe.

To be more specific, the argument relies on a fundamentally unrealistic
assumption: namely, that voters vote based on an analysis of the candidates'
positions with respect to specific, definable issues — and the proximity of
these positions to their own.

In fact, one has only to read the opinion polls or listen to interviews with
voters to know that, overwhelmingly, voters cite much more qualitative reasons
for choosing one candidate over another. So, Gore is "arrogant", "overbearing",
"smart", or "well-informed"; Bush is "inexperienced", "immature",
"compassionate", or "good-natured" (these were adjectives used to describe the
candidates in actual interviews with voters conducted byThe New York
Times during the course of the election). In fact, it is probably safe to say
that a large percentage of voters aren't even aware of what the candidates'
positions are on the issues. Of course, one cannot simply blame an uninformed
electorate for this phemonemon. In many cases, the candidates purposely
obfuscate their position on popular issues to improve their chances of getting
elected. For instance, during the final 2000 presidential debate in East
Lansing, Michigan, George W. Bush refused to say that he was against affirmative
action, despite repeated questioning, choosing instead to say that he
was for "affirmative access" — whatever that means. And then there is the
fondness among politicians for stating their position on issues at such a level
of abstraction as to become virtually meaningless. Hence, we have Republicans
who claim to be "pro-family values", which leads one to the absurd conclusion
that Democrats are "anti-family values". Conversely Democrats often claim to be
"pro-environment" as if to say that Republicans are categorically
"anti-environment".

Danny's argument would also have you believe that the ideal candidate should
conduct polls on every important political issue, and simply adopt the more
popular position. But, as we all know, campaigns aren't run this way. One reason
for this is the fact that being perceived as wishy-washy and unprincipled may be
more damaging to the candidate than supporting the "wrong" side of an issue. In
other words, candidates are widely perceived to be more than the sum of their
positions. Instead, we look to them to be principled leaders and steadfast in
their convictions.

Two other reasons for candidates to ignore the polls are the influence of
special interest groups in election politics, and in the case of presidential
politics, the quirky nature of our (now infamous) electoral college system.
While the majority of Americans clearly support tighter gun control laws, Al
Gore rarely mentioned his support for such laws on the stump. Why? Because he
knew the importance of winning the swing votes of Rust-Belt (Reagan) Democrats,
many of whom happen to be gun owners. In the case of special interests,
candidates are forced to downplay or obfuscate their true positions on issues
(positions that may be supported by the majority of the electorate) because of
the political influence that these special interests wield (again, one has to
look no further than the NRA to find an organization that can be, at once, so
out of touch with America's electoral majority, yet strike such fear in the
hearts of politicians).

I think American Democracy is both better and worse than the idealized
description Danny provides. On the one hand, I am, like many others, often
dismayed by the influence of special interests in American electoral politics; I
am frustrated by the sometimes superficial and haphazard manner in which the
American electorate comparison shops for candidates; and I am frankly puzzled by
the need to maintain our seemingly antiquated electoral college system. But I am
also moved by the humanity of the American electoral process. Americans bring
all sorts of rationales with them to the polls -- some sound, some misinformed.
But on one day in November, they have an opportunity to pull a switch one way or
the other, and God help those who try to predict the outcome. If this weren't
the case, we might as well let one of Danny's supercomputers do the voting for
us.

Marvin Minsky
Mathematician; computer scientist; Professor of Media Arts and Sciences, MIT;
cofounder, MIT's Artificial Intelligence Laboratory; author, The Emotion Machine

The Election Selection

There is a popular view that says, "In the 2000 election, the popular vote seems
so close to chance that it almost seems due to random chance — as though each
voter was flipping a coin." A statistician might even suggest that "the
difference has no significance."

Now, the theory of probability tells us that if 100 million votes were to come
from flipping an "unbiased coin," we would expect the numbers of heads and tails
to differ by only a few thousands. There will be only about one chance in a
thousand that this will lead to a difference of more than 10,000 thousand votes.
A difference of a million or more would be inconceivably unlikely.

However, in the previous century, the popular votes for the two major parties
usually differed by several millions (except in '60 and '68). So, those people
are not flipping unbiased coin, but show strong 'biases' that comes from many
complex causes.

What could it mean, if anything, that in Florida, the popular vote differed by
only a few hundred?ï The likely explanation for this is that the biases were
biased themselves toward equality!

In other words, the more bias in the bias, the less chance to see for a close
tie in the popular vote. A deeper analysis suggests that what happened in
Florida was indeed an extremely unlikely event. For example, assume that the
"will" of the 6 million Floridians might range uniformly from say 2 million to 4
million for each party. Then there would be only one chance in a thousand for
this to lie within a thousand of votes of the center. If this is what happened,
it asks for an explanation

I suspect that two new phenomena have entered the scene that has cause these
numbers to come so close.

• The amounts of money for political campaigns have hugely increased.
• The technical tools for making good polls have also improved.

So now, campaigners can better predict where spending their money will be most
effective. They can pinpoint the critical districts in which voters will respond
to particular issues, and then target them with more personalized persuasion
techniques. (In other words, lie.) So, in effect, the budget for 'buying votes'
has gone up, while the cost per such vote has gone down. This pushes the vote
toward the center.

The Electoral College exacerbates this, because the campaigns can save money by
not spending it in districts where the differences are too large to reverse.
Consequently, huge amounts of money get focused at regions where they can be
effective. (One formerly almost unknown new senator is said to have done this by
spending what is estimated to be about 1000 dollars per vote.) And as soon as
the difference changes its sign, the funding gets focused somewhere else.

One approach to a remedy is political:

• Reduce the magnitude of campaign spending.
• Abolish the Electoral College, which amplifies the effectiveness of targeted
campaigns.ï

But neither of these seems feasible, because they'll be strongly opposed by
incumbents.ï

Another approach is social:

• Educate the voters to refuse to cooperate with polls.
• Point out that it's in their interest to lie when they are being polled!

Yes, lying is reprehensible — although in this realm, it's traditional. The
point is that if you're inclined toward Candidate X — but tell them that you
favor Y — this induces your opposition to spend less in your district.

James J. O'Donnell
Classics Scholar, University Librarian, ASU; Author, Pagans

The problem isn't with the closeness of the election (which is a perfectly
reasonable outcome, politically and statistically) or with the difficulties of
the count (wherever this ends up, the margin of victory will be within any
reasonable estimate of the margin of error), but with the disincentives to
candidates of greater substance than these. The presidency is an office that is
now open only to lifelong hypocrites of limited imagination, willing to
surrender privacy and personal life in order to achieve limited power, the
undivided attentions of potential assassins, and remarkably paltry financial
reward. 

Jeremy Bernstein
Professor Emeritus, Stevens Institute of Technology; Former Staff Writer, The
New Yorker

The situation with the Florida election vote is quite clear. There is no system
of counting votes that is accurate enough to determine a winner when six million
votes are cast and the difference is less than a thousand. Within any sensible
margin of error you have a tie. Therefore what is needed is a system to deal
with ties. Obviously this is a run off. I am quite certain that if the same
people who voted the first time were to vote to break a tie it would have
happened and how these votes were counted — by machine or human — would have
been irrelevant. The matter would long ago have been settled and we could all
get on with it.

Freeman Dyson
Physicist, Institute of Advanced Study; Author, Disturbing the Universe; Maker
of Patterns

For your entertainment, here is a piece by George Dyson. It shows the way to
deal equitably with the situation in Florida. It was written three years ago and
it is being published this week in the Bellingham Herald and in the Frankfurter
Algemeine Zeitung. You might consider it an addendum to Danny Hillis's piece in
the news-letter about "How Democracy Works". It describes a real case verifying
Hillis's theory of democracy. Implications for biology, engineering, and physics
are enormous.


WHAT'S RELATED


PEOPLE

W. Daniel Hillis
Physicist, Computer Scientist, Co-Founder, Applied...


CONTRIBUTORS

W. Daniel Hillis
Physicist, Computer Scientist, Co-Founder,... [ Read ]
Jeremy Bernstein
Professor Emeritus, Stevens Institute of... [ Read ]
Al Seckel
Cognitive neuroscientist; Author, Optical... [ Read ]
James J. O'Donnell
Classics Scholar, University Librarian, ASU;... [ Read ]
George Dyson
Science Historian; Author, Analogia [ Read ]
Marvin Minsky
Mathematician; computer scientist; Professor of... [ Read ]
Jaron Lanier
Computer Scientist; Musician; Author, Who Owns... [ Read ]
Luyen Chou
Senior Vice President, Product Strategy, Pearson [ Read ]
Bernardo Huberman
HP Fellow and Director of the Systems Research... [ Read ]
Maryam Mohit
Vice-President of Site Development at amazon.com [ Read ]
Freeman Dyson
Physicist, Institute of Advanced Study; Author,... [ Read ]


BEYOND EDGE

Applied Minds


BOOKS

The Pattern on the Stone (Science Masters)
By W. Daniel Hillis Paperback

Masters of Deception: Escher, Dalí & the...
By Al Seckel Paperback


EVENTS

Edge Master Class 2010: W. DANIEL HILLIS ON "CANCERING"
Master Classes [ 12.27.10 ]
Edge-Serpentine Gallery-MAPS FOR THE 21ST CENTURY
Special Events [ 10.16.10 ]
Edge Master Class 2009: GEORGE CHURCH & J. CRAIG VENTER: A SHORT COURSE ON
SYNTHETIC GENOMICS
Master Classes [ 7.24.09 ]
THE EDGE "BILLIONAIRES' DINNER" 2009
Edge Dinners [ 2.5.09 ]
Edge Master Class 2008: Richard Thaler, Sendhil Mullainathan, Daniel Kahneman -
A Short Course in Behavioral Economics
Master Classes [ 7.25.08 ]
Edge Master Class 2007 DANIEL KAHNEMAN: "A SHORT COURSE IN THINKING ABOUT
THINKING"
Master Classes [ 7.19.07 ]
THE EDGE "BILLIONAIRES' DINNER" 2007
Edge Dinners [ 3.6.07 ]
THE EDGE "BILLIONAIRES' DINNER" 2006
Edge Dinners [ 2.27.06 ]
THE EDGE "BILLIONAIRES' DINNER" 2005
Edge Dinners [ 2.22.05 ]
THE EDGE SCIENCE DINNER 2003
Edge Dinners [ 2.27.03 ]
THE EDGE "BILLIONAIRES' DINNER" 2002
Edge Dinners [ 2.21.02 ]
THE "BILLIONAIRES' DINNER" 2000
Edge Dinners [ 2.23.00 ]
THE EDGE "BILLIONAIRES' DINNER" 1999
Edge Dinners [ 2.16.99 ]




TAGS

democracy


CONVERSATIONS AT EDGE

Emergences
[9.4.19]
WHO GETS TO KEEP SECRETS? Hillis's Question: An EdgeSpecial Event!
Mentioned
Jonathan Haidt, Simone Schnall
[12.5.10]
THE HILLIS KNOWLEDGE WEB
Mentioned
Andy Clark, Alison Gopnik, Andrew Lih, Alvy Ray Smith
[7.18.10]
ADDENDUM TO ARISTOTLE: (THE KNOWLEDGE WEB)
[3.12.07]
"ARISTOTLE" (THE KNOWLEDGE WEB)
[5.6.04]
SPECIAL RELATIVITY: WHY CAN'T YOU GO FASTER THAN LIGHT?
Introduction by
John Brockman
[1.24.99]
Digerati - Chapter 13
[10.1.96]
SOMETHING THAT GOES BEYOND OURSELVES
[5.7.96]
Part Five SOMETHING THAT GOES BEYOND OURSELVES
[5.1.96]

John Brockman, Editor and Publisher

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