
Buridan's Principle (1984) [pdf] - waterhouse
https://www.microsoft.com/en-us/research/publication/buridans-principle/?from=http%3A%2F%2Fresearch.microsoft.com%2Fen-us%2Fum%2Fpeople%2Flamport%2Fpubs%2Fburidan.pdf
======
EGreg
This thing drove me wild for like 2 weeks, I was not sure it could be true.
Until I realized that the composition of continuous functions is continuous.

But that makes me wonder ... how can we then have unstable problems in the
real world? Google "unstable problem definition". If everything is continuous,
then small enough changes in input always result in small changes in output.
And yet, unstable problems are the opposite. If a pencil is released when
standing on its point, it can fall to one side or another side, rather far
away.

To me, this has to do also with comparing timestamps across distributed
systems, like Spanner's database timestamping synchronization. When I started
architecting distributed systems, and quorums, I had to deal with this.

I remember emailing Leslie Lamport a few times and arguing with him about this
:)

Some people don't even believe Leslie Lamport's Buridan's Principle:

[https://www.youtube.com/watch?v=dVkSJ0QWzXA](https://www.youtube.com/watch?v=dVkSJ0QWzXA)

~~~
ffhhj
Even the video got 3 likes and 3 unlikes... so paradoxical!

------
dooglius
Note: I believe the commentary here is copied from the Lamport's website,
[http://lamport.azurewebsites.net/pubs/pubs.html#buridan](http://lamport.azurewebsites.net/pubs/pubs.html#buridan)
which has similar commentary alongside each of his papers.

This makes perfect sense classically, but the quantum argument I'm not sure
about; as he admits, he only finds fault with a particular apparatus using
quantum behavior. But it seems that any implementation of a quantum bit that
is eventually "measured" would violate the principle--is there something I'm
missing, or is the problem just smoothed over by the probabilistic error
already assumed in quantum circuits?

------
yters
"Buridan's ass" was a philosophical intuition pump to argue for the reality of
free will. If we were really ultimately determined by our appetites, as the
Neoplatonic determinists would have it, then we can construct a scenario where
the perfectly determined ass would end up starving to death when surrounded by
the foods it most craved.

Since there are not dead asses all over the place, the philosophers took this
as evidence that free will exists, even in asses.

~~~
mannykannot
> Since there are not dead asses all over the place, the philosophers took
> this as evidence that free will exists, even in asses.

That falls apart as soon as you consider how frequently the precise scenario
is expected to occur. I hope no philosopher made an ass of himself by
vigorously defending this particular form of the argument.

That response is similar to the point made by one reviewer of an early version
of the paper discussed here, that if this were a problem (in practice), it
would have come to everyone's attention by now.

The Dining Philosophers problem is similar to Buridan's Ass, in that you have
hyper-rational actors at risk of starvation in the presence of food, but the
critical difference that makes this a model of something that could happen in
practice is that it involves each actor having to make _two_ temporally-
separated decisions, thus avoiding a singularity in time (though such
singularities appear when you apply a locking solution.)

~~~
yters
I don't think the scholastic philosophers were thinking the precise balance
would happen in reality, but rather the very concept seemed absurd. That's the
nature of intuition pumps. Not exactly a cut and dry deductive argument, but
they show certain conclusions are most compatible with what seems to be common
sense. And a general principle in philosophy is to try disrupting common sense
conservatively, that on balance if one worldview is much more at odds with
common sense than another worldview, the latter is preferred.

------
MaysonL
"Another amusing example occurred in an article by Charles Seif titled Not
Every Vote Counts that appeared on the op-ed page of the New York Times on 4
December 2008. Seif proposed that elections be decided by a coin toss if the
voting is very close, thereby avoiding litiginous disputes over the exact vote
count."

Interestingly enough, A.A. does this, where "very close" is deemed to be "less
than a 2/3 majority". (Although rather than a coin flip, a name is drawn at
random, usually from a hat).

~~~
dredmorbius
Election by lot is a thing.

[https://web.archive.org/web/20160320090358/https://aeon.co/e...](https://web.archive.org/web/20160320090358/https://aeon.co/essays/if-
you-can-t-choose-wisely-choose-randomly)

~~~
earthboundkid
A jury is essentially election by lot. We should use juries for more
oversight-type things.

------
hpoe
So can someone help me with my understanding I read the paper and feel I have
a grasp of it but there is still one thing I don't understand he says

>Buridan’s Principle. A discrete decision based upon an input having a
continuous range of values cannot be made within a bounded length of time.

Shouldn't it instead read

> Buridan’s Principle. For a discrete decision based upon an input having a
> continuous range of values, there exists some values such that a discrete
> decision cannot be made within a bounded length of time.

Because clearly there are many instances that a discrete decision is made in a
bounded length of time, as shown by the car does stop or goes for many values
of x even though there is a bounded length of time; however there is certain
values of x that result in the train running over the car, but not all.

Ergo, only some values of x will result in a decision being made impossible in
a bounded period of time.

Can someone help me understand the flaws in my thinking or understanding?

~~~
teraflop
The only difference between your phrasing and the paper's is terminology.

By definition, a "bound" is a limit, i.e. a range that the outcome falls into.
Saying that the time to make a decision is bounded simply means that you can
always rely on it to happen within that limit.

~~~
hpoe
Okay so what I am to understand by the phrase

> cannot be made within a bounded length of time.

Is not that it will not happen within a certain time period but rather I
cannot with certainty fix an upper or lower bound on the amount of time it
will take to reach a decision for all possible values of the input X.

Thank you for your reply I had to noodle on it a bit but think I get it now.

~~~
mikorym
Not bounded means that if you give me a number _x_ then there is some _y_ that
is bigger than _x_.

So, in the context of the paper, if you thought that your computer always made
a decision after a week, then there is some situation whereby the computer
takes longer than a week.

For the record, I think the mathematics is sounder than the computer science
which in turn is sounder than the social science. As the author admits when he
mentions Kepler, we can't really prove Buridan's Principle. But I think it
goes further than this in the social aspect: We don't know whether indecision
at traffic lights is even accurately modeled by Buridan's Principle. Then the
question becomes not whether it's true, but whether it is a good model. And
these kind of models are always dangerous ground in the social sciences.

Edit: The reason why I say the mathematics is sound is because he rephrases
the usual notion of compactness:
[https://en.wikipedia.org/wiki/Compact_space](https://en.wikipedia.org/wiki/Compact_space).

------
glitchc
“ One reviewer made a marvelous comment in rejecting one of the early papers,
saying that if this problem really existed it would be so important that
everybody knowledgeable in the field would have to know about it, and “I’m an
expert and I don’t know about it, so therefore it must not exist.” “

That’s gold. The hubris!

~~~
aj7
I’ve made similar arguments. I have a term for them, “economic reasoning.” The
argument is basically that economic forces, from greed and survival to the
basic underlying technical capabilities available would have ALREADY caused a
proposition to succeed or fail. This is a powerful principle, and in my
experience, does not mediate against innovation. That reviewer was using his
version of it. Secondarily, Buridan’s principle fails. An important lesson in
growing up is, sometimes you just have to choose, and if you waste enough
time, the urgency of choice exceeds the urgency to be right. In technology,
binary switches have an avalanche mechanism, and if properly designed, have
built in hysteresis. Noise then makes the decision, and the hysteresis
prevents “waffling” by turning off the ability to redecide. Read (older) data
sheets on comparators. That a person could write a scholarly paper and not
mention that indecision has been thought about, and workarounds have been
assiduously developed IS probably cause for rejection.

~~~
shakezula
[https://www.microsoft.com/en-
us/research/uploads/prod/2016/1...](https://www.microsoft.com/en-
us/research/uploads/prod/2016/12/On-the-Glitch-Phenomenon.pdf)

The author specifically addressed “noise” in another paper. In this paper, the
predecessor to the one linked, the author shows that noise doesn’t fix the
problem, rather it makes it impossible to determine which inputs would make it
hang for an arbitrary amount of time.

~~~
mannykannot
Are you referring to this passage?

 _2\. Introducing noise to drive the device out of its metastable state.The
noise can be considered to be just an unpredictable input.The introduction of
noise cannot eliminate the possibility of the device hanging up for an
arbitrarily long time, but can make it impossible to predict which inputs will
cause it to do so._

While I do not disagree, introducing noise changes the issue from being stuck
forever on a single decision, to being a series of decision points (each time
the noise signal changes), with the chain being broken as soon as one results
in a definite outcome. In practice, this allows us to engineer the risk of
being stuck, for longer than some specified period, to an arbitrarily small
probability - at the cost of a small loss of precision, and possibly much
greater complexity in modeling the device.

~~~
senderista
Coincidentally, this is reminiscent of the usual solution to Paxos liveness
violations: introduce randomness into the timing of the competing proposals.

~~~
shakezula
True! Wouldn’t be surprised if that’s why Lamport was originally thinking
about the problem.

------
js8
"I find myself unable to decide for a fraction of a second whether to stop for
a traffic light that just turned yellow or to go through"

I had a similar problem, and I resolved it by training myself to remind myself
of a point of no return, that is, a distance from the light at which I will go
no matter what. So every time I see a traffic light, I decide where is the
point of no return.

I think establishing point of no return is the standard method of dealing with
this. For example, parachute jumpers have a certain altitude at which they
have to make the decision whether to land on the main parachute or backup
parachute if something goes wrong with the main one.

~~~
phab
The paper points out that this doesn't resolve the problem in the discussion
about the crossing gate; all this approach does is move the decision from "do
I jump" to "have I met the point of no return yet", which is still a discrete
decision over a continuous input.

~~~
317070
However, the further it goes, the more clear the second one gets. I.e. "am I
already at the point of no return, I guess not, it's unclear. Oh wait, now I
am, let's trigger."

So, Buridan’s Principle is correct for time-invariant systems. But as far as I
can see you can totally build a time-dependent system which simply picks
option 1 after being undecisive for time T.

~~~
phab
I think the principle would state that by always picking option 1 you are no
longer making a decision based on the input.

This is discussed in the paper under section 3: "Other Asses", in the
paragraph starting "One way to circumvent Buridan’s Principle is to eliminate
the decision".

------
mikorym
I can see why the author had difficulty publishing the article. If I didn't
realise that he was talking about compactness I would have thought that he
wasn't making sense.

The target audience is a nontrivial subset of people and it's difficult to
optimise for everyone in the target audience. In any case I think that the
real interesting thing here is not what lead to his observation.
(Mathematicians have a tradition of not telling people what lead to their
observations, for better or worse.) Rather, I think the mathematics behind
this should be taken much further.

I guess it's off to the references.

------
coldtea
> _Buridan’s ass starves because it cannot make the discrete decision of which
> pile of hay to eat, a decision based upon an initial position having a
> continuous range of values, within the bounded length of time before it
> starves_

I don't see how that follows. Seems like a sibling problem rather than a
generalization.

The ass would starve even if the decision was among two same otherwise
discrete options with no continuous range of values in between (e.g. state -1
(left hay), 0, and 1 (right hay)), since there still wouldn't be a reason to
prefer -1 to 1.

~~~
ahelwer
The point is the underlying domain (physical space, in the donkey parable) is
continuous, and it needs to be partitioned into discrete values. The paper is
about the impossibility of constructing a device which does this within a
bounded amount of time.

The problem gets more difficult because you also have to worry about
measurement resolution. Anyway, rest assured this problem is very resistant to
any "what if you just..." solutions you can come up with.

~~~
coldtea
> _The point is the underlying domain (physical space, in the donkey parable)
> is continuous, and it needs to be partitioned into discrete values._

I don't think that was part of Buridan's concept. The concept was simply the
impossibility of choice between two same options -- the continuity of the
domain didn't play any role (in fact the description focuses on the discreet
binary choice alone).

> _Anyway, rest assured this problem is very resistant to any "what if you
> just..." solutions you can come up with._

I'm sure, I don't propose a solution - just say that the problem is not about
discreet/continuous.

~~~
ahelwer
Buridan's original problem is used here as an analogy for the problem, not
really the basis.

------
ffhhj
Nice paradox, searching about it found another proposed solution:

[http://steve-patterson.com/paradox-resolved-buridans-ass/](http://steve-
patterson.com/paradox-resolved-buridans-ass/)

It says: "there’s no such thing as “identical options”. More specifically,
there are no two separate things which are identical in every way. So when
talking about choice, having “alternative” possibilities implies having
“different” possibilities. We can not evaluate two things as both “identical
and different”, as this would be a contradiction in terms. Therefore, any
formulation of Buridan’s paradox which implies this contradiction runs into a
basic framing error."

Seems wrong, in a lottery all options are “identical and different”. Identical
since they have the same probability, different because only one has the
price. The paradox undecidability is produced by the perfect balance of
unknowns, the equilibrium must be broken to have a decision.

Buridan's can be combined with Xeno's as a 2D continous space/time paradox. So
cool!

I'm working on a solution for Xeno's, that's why I find it interesting.

~~~
coldtea
> _It says: "there’s no such thing as “identical options”. More specifically,
> there are no two separate things which are identical in every way._

Doesn't have to be "identical in every way".

Just "identical in every way that matters (regarding the decision)" e.g.
making the subject equally hesitant or equally willing to chose one or the
other...

E.g. two potential love interests might be very different but equally
tempting, and people have had that problem of choice (or regret when they
chose) hit them very heavily...

------
Sniffnoy
Link with extra junk shaved off: [https://www.microsoft.com/en-
us/research/publication/buridan...](https://www.microsoft.com/en-
us/research/publication/buridans-principle/)

------
Supermancho
> In the early 70s, computer designers rediscovered that it’s impossible to
> build an arbiter that is guaranteed to reach a decision in a bounded length
> of time. (This had been realized in the 50s but had been forgotten.)

> a device for making a binary decision based on inputs that may be changing

So it's the result of the halting problem, applied to a continuous function in
hardware?

~~~
dooglius
No, the halting problem says that one cannot determine whether an _arbitrary_
program halts, while this says that one cannot build a _particular_ physical
device that is guaranteed to output in bounded time.

------
fuzzybear3965
Flipping a coin if the vote is close seems to solve the voting dilemma... What
am I missing?

~~~
shakezula
The original paper specifically addresses “noise” as not a sufficient solution
to the problem. I’d call a coin toss “noise” in the context of this paper.

~~~
ffhhj
Correct!

> Another often-suggested escape from Buridan’s Principle is noise—the
> introduction of randomness into the system. In theory, one can balance a
> ball on a knife edge; in practice, this is impossible because tiny random 2
> vibrations will cause the ball to fall, despite our best efforts to balance
> it. Moreover, balancing the ball on a knife edge requires fixing very
> precisely both the position and the momentum of the ball, which is forbidden
> by Heisenberg’s Uncertainty Principle. A four-legged or human ass must also
> have random noise and be subject to the Uncertainty Principle, so it cannot
> be put into a situation where it will hang forever on a knife edge of
> indecision.

------
carapace
Interesting that this is the meta-story of Buridan’s Principle, not the thing
itself.

~~~
dooglius
Click "View Publication", the text on the page is just some commentary by the
author

~~~
carapace
I know. The commentary is the subject of the HN post, not the paper itself.

The meta-story is IMO just as fascinating if not more so than the principle
itself.

> A little research revealed that psychologists are totally unaware of the
> phenomenon.

> The singularity at zero was never mentioned in the paper.

> Philosophers have discussed Buridan’s ass for centuries, but it apparently
> never occurred to any of them that the planet is not littered with dead
> asses only because the probability of the ass being in just the right spot
> is infinitesimal.

> I submitted it first to Science. The four reviews ranged from “This well-
> written paper is of major philosophical importance” to “This may be an
> elaborate joke.” One of the other reviews was more mildly positive, and the
> fourth said simply “My feeling is that it is rather superficial.” The paper
> was rejected.

> Throughout this exchange, I wasn’t sure if he was taking the matter
> seriously or if he thought I was some sort of crank.

> My problems in trying to publish this paper and [22] are part of a long
> tradition.

WTF is going on here? This thing on our lawn is a dragon, why do some many
people think it's a cloud?

------
earthboundkid
Fascinating.

