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# Buridan's Principle

Talk at Papers We Love NYC on Leslie Lamport's Buridan's Principle. ## Tom Santero

November 19, 2015

## Transcript

1. Buridan’s Principle
Tom Santero
Papers We Love
Nov 19, 2015

2. “I’m interested in the intersection
of philosophy and Computer
Science”
-- Michael R. Bernstein

3. Philosophy
Science!!!

Buridan’s Ass
Part I

5. Ἀριστοτέλης
384 – 322 BC
...a man, being just as
hungry as thirsty, and
placed in between food
and drink, must
necessarily remain where
he is and starve to death.
-- On The Heavens

6. Jean Buridan
1295 – 1363
Should two courses be
judged equal, then the
will cannot break the
deadlock; all it can do is
suspend judgement until
the circumstances
change, and the right
course of action is clear.

7. "Mr. Speaker, we have all heard of the
animal standing in doubt between
two stacks of hay, and starving to
death. The like would never happen to
General Cass; place the stacks a
thousand miles apart, he would stand
stock still midway between them, and
eat them both at once, and the green
grass along the line would be apt to
suffer some too at the same time."
-- insulting Democratic presidential candidate,
Lewis Cass, in 1848
Abraham Lincoln
1809 – 1865

8. Part II

9. Given:
an Ass, two equal bails of hay
Proposition:
If placed equidistant between each bail of
hay, there exists some finite starting positions for
which an Ass could possibly starve to death.

10. 1. Let x represent the starting position of our ass at time t = 0, such that x
falls along the line joining two equal bails of hay at positions 0 and 1,
where 0 < x < 1 [given]
2. Let A
t
(x) denotes the position of the ass at time t, as a function of time over x
3. t ≥ 0: A
t
(0) = 0;
A
t
(1) = 1;
{x ∈ ℝ | 0 < x < 1} [continuity]
4. Since A
t
(0) = 0 and A
t
(1) = 1 there must be a finite range of values of x for
which 0 < A
t
(x) < 1
Q.E.D

11. x
0 1

12. 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.

13. 1. Let x represent the starting position of our ass at time t = 0, such that x
falls along the line joining two equal bails of hay at positions 0 and 1,
where 0 < x < 1 [given]
2. Let A
t
(x) denotes the position of the ass at time t, as a function of time over x
3. t ≥ 0: A
t
(0) = 0;
A
t
(1) = 1;
{x ∈ ℝ | 0 < x < 1} [continuity]
4. Since A
t
(0) = 0 and A
t
(1) = 1 there must be a finite range of values of x for
which 0 < A
t
(x) < 1
Q.E.D

14. Lamport’s
Asses
Part III

15. Choo Choooo!
(hi Caitie, Kyle, Ryan and Jared)

16. Protip: pay attention to the direction of the arrows

17. You’re gonna get run over,
you ass!

18. Continuity
Part IV

19. Buridan’s Principle does not rely
upon any assumption about how the
decision is made; it rests only on the
assumption of continuity.

20. A continuous mechanism must
either forgo discreteness,
permitting a continuous range of
decisions, or must allow an
unbounded length of time to make
the decision.

21. Should we trust Lamport
?

22. Reasons to trust Lamport:
- Manufacture d’horlogerie
- taught us how to properly order pastries at a bakery
- warned us about dangers of participating in Greek
politics
- the Art of War in Byzantium

23. It has been shown by Vosbury  and by Palais and Lamport  that the
glitch phenomenon is inherent in arbiter circuits. These proofs are based on a
continuous model of asynchronous circuits. In fact, Palais and Lamport state
that a proof of this result must be based on a continuous model. We show
otherwise; that is, we give a proof of the unavoidability of the glitch
phenomenon that is based on a discrete circuit model.

24. The impossibility of building a bounded-time arbiter
seems to be a fundamental law of physics, not a
mathematical theorem. For example, Anderson and
Gouda  proved that a bounded-time arbiter cannot be
constructed from certain kinds of components, but their
proof offers no insight into why the quantum-
mechanical arbiter described in  doesn’t work. We
take the nonexistence of a bounded-time arbiter as an
axiom.

25. Buridan’s Law of Measurement:
If x < y < z, then any measurement performed in a
bounded length of time that has a nonzero probability of
yielding a value in a neighborhood of x and a nonzero
probability of yielding a value in a neighborhood of z
must also have a nonzero probability of yielding a value
in a neighborhood of y

26. Other
Asses
Part V

27. decisions may sometimes
take longer than we expect

28. indecision considered harmful

29. there are certain
circumstances where we
cannot prolong choice

30. Entropy ain’t what it used to be
Randomness can make it impossible deliberately to starve the ass

31. asynchronous message passing as a
continuous function of our initial state
over time

32. Buridan’s Reliable Failure Detector:
A process cannot make a discrete decision about the state of
another process based upon an input having a continuous
range of values within a bounded length of time.

33. Byzantine faults as
accidental starvation

34. Computability (P v NP)
Topologies and Category Theory

35. Thanks!