Barnette's Zeno's Coffeehouse
Challenge #61 Result
Coffeehouse patrons! This challenge prompted over 150 replies, which is
I have listed
below the original challenge, followed by several respondents' thoughts
on the matter. I
want to thank ALL respondents for their thoughtful time taken with
Zeno's Coffeehouse, and
to encourage your continued support, as critical thinking exercises are
mental growth and recreation. Minds need exercising with shared,
reflective thinking; this is enjoyable and enriching.
week, a patron asked a question at the Coffehouse which
pertained to the concept of God as an omnipotent being and what might
be the limits of possibility, if such a being could exist. Charles
thought about a challenge he once read about this topic, and decided to
share it with Zeno's Patrons. Take a look, and please share your
Presumably, there are countless tasks that an
omnipotent, all-powerful, being could perform, that we, non-omnipotent
creatures (strong as we may be), could not, if such a being could
exist. Moreover, given our standards of what we take to be logical
limits on what is possible and what is not, it might be argued that
among the tasks performable by an all-powerful being are included some
that we might judge to be seemingly impossible. Yet clarity demands
some notion of logical possibility as the limit, even for omnipotent
performances. What I would like to explore in this brief piece is the
concept of a supertask, which is to be understood
as a task that only an omnipotent being could perform.
The notion of a task is a helpful one, I submit,
since it connotes an activity with an achievement, or terminus---an
outcome or successful completion; in other words, a process of means to
an accomplished end. Further, a task lends itself to a procedural
explication popular in the terminology of logic and computational
theory; viz., a flow-chart, or a general set of
instructions which indicate, sequentially, just how the task can be
performed to completion. From start to finish, there is precision,
understanding, and theoretical description offered by a flow-chart,
which characterizes a program of calculation. Now consider the
following chart, which defines a particular task involving one's
listing of natural numbers in series: 1, 2, 3, 4, and so on. We can
then go on to discuss features of the task with regard to omnipotence,
aided by the flow-chart.
INSTRUCTIONAL FLOW-CHART FOR THE
LISTING OF ALL NATURAL NUMBERS
2 SECONDS OF THE START, WRITE DOWN THE NUMBER '1'
ONE-HALF THE TIME TAKEN TO PERFORM THE PREVIOUS TASK, WRITE DOWN THE
NEXT NUMBER IN THE SERIES OF NATURAL NUMBERS
THE PREVIOUS INSTRUCTION....then REPEAT, and REPEAT, and REPEAT, and so
AFTER FIVE SECONDS HAVE ELAPSED FROM START AND THE LAST TASK WAS
Is the above a possible program? That is, could any
possible being execute it? Think about what the task involves. You
might even try running it yourself, although I suspect that you won't
get too far before the five seconds runs out---maybe reach '5'? Maybe
even '6'? But this is to be expected, since you're not omnipotent,
after all. How would such a being fare, do you think? To '100'? Why not
more? After all, omnipotence is at stake. How
about '100,000', then? How about all the natural
numbers? Why not? Let's agree that if a being could
run the program (i.e., follow successfully all the instructions), and
thereby not omit a single number, then such a being would be indeed
omnipotent, and that such a task would be a supertask.
QUESTION: Is the above a possible
supertask? Or: Is it logically possible
for any being to successfully run the program described by the
flow-chart? Or: Is an omnipotent being possible?
Think about this....
Included below are responses from Mark Young, Eric
Pavlov and Bradley McGregor. Readers should appreciate their thoughtful
ideas, as they are most valued. Thanks to all of you!
From Mark Young in Wolfville, Canada:
comments: Well, you're asking about logical possibilities and
omnipotent beings, but I'm kinda interested in the supertask itself.
I've taken the liberty of rewriting your "instructional flow chart"
into a structured language:
constant integer END_OF_TIME = 0;
integer n = 1;
real t = 2.000;
// "add one to n"
2.0; // "divide t by two"
As far as I know, no language offers the "within TIME" construct or
anything like it. (The intention is that the task that
to be completed within the given amount of time or to be abandoned at
the end of the allotted period. There are ways to get that
of behaviour, so I don't feel too bad about introducing the
Beyond the implementation of the within construct, what would be
necessary to make the code execute as required?
1st) the ability to represent arbitrarily large integers
2nd) the ability to represent arbitrarily small Real numbers.
3rd) the ability to write an arbitrarily large integer in an
arbitrarily short period of time.
4th) the ability to do integer arithmetic (adding one) in an
arbitrarily short period of time.
5th) the ability to do real arithmetic (dividing by two) in an
arbitrarily short period of time.
So, what is the outlook for these conditions?
1st) Never gonna happen.
2nd) Never gonna happen.
3rd) Never gonna happen.
4th) Never gonna happen.
5th) Never gonna happen.
So, doesn't look good. Our (sadly) finite computer will
stop at some finite n > 0 because it no longer has time to
write/calculate the required numbers (possibly because the time has
become too small to represent, and so t has been set to zero), or it
will "wrap around" to a negative value or throw an integer overflow
exception (because of the limited range of integers
But for a being with no such limitations....
Consider the following definition: An infinite-task is a task
that requires either
(a) the representastion of arbitrarily large pieces of data
(b) the completion of finite tasks in arbitrarily short periods of
(Or both, of course.)
And a conjecture -- all super-tasks are infinite-tasks, and vice
(As a slogan: "only infinity is impossible.")
As for whether it is "logically possible" to run any super-task
successfully -- that'd depend on the logic. I reject the
that there is a single logic strong enuf to represent all possible
realities -- or even that there is a single *simplest* such
logic. Different ways of representing the world/universe will
result in different answers to questions of possibility.
But I will say this -- any logic that says that successful completion
of a super-task (or infinite-task) is possible, is a logic that defines
"possible" too broadly for any practical purposes (which are
From Eric Pavlov, in Portland, Oregon:
comments: I think the program is a logically possible program, in that
some infinite tasks are achievable in a finite time frame, given a
suitable model of external/internal timeframes in, for example, quantum
physics (paradoxically enough). Whether any system could ever execute
such a program is another matter, but I suppose that an omnipotent
being, if there is one, could run it, given that omnipotence generally
entails the ability to do all things possible.
Great problem, but way too technical!:)
We love Zeno's Coffeehouse in Portland!!!
From Bradley McGregor, in Glasgow, Scotland:
comments: I think that this is an impossible program, since running it
would entail accomplishing an infinite number of tasks in a finite
period of time--i.e. in 5 seconds! So, if an omnipotent being is to be
considered as one who could run the program, I would conclude that no
such being is possible. QED:) Great thought experiment, btw! Keep up
the good work.
Keep up the Zeno's Coffeehouse involvement, as it's good for