**Ron
Barnette's Zeno's Coffeehouse
Challenge #61 Result**

Thanks, Zeno's Coffeehouse patrons! This challenge prompted over 150 replies, which is most appreciated!

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 explored for mental growth and recreation. Minds need exercising with shared, reflective thinking; this is enjoyable and enriching.

Thanks!...Ron Barnette

Last 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 thoughts:

**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.
**

Is the above a

**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!

.....Ron Barnette

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;

within Seconds(5.000)

repeat

within Seconds(t)

{

write(n);

n++; // "add one to n"

t /= 2.0; // "divide t by two"

}

until END_OF_TIME;

-----

As far as I know, no language offers the "within TIME" construct or anything like it. (The intention is that the task that follows is 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 kind of behaviour, so I don't feel too bad about introducing the syntax.

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 either 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 available).

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

or

(b) the completion of finite tasks in arbitrarily short periods of time.

(Or both, of course.)

And a conjecture -- all super-tasks are infinite-tasks, and vice versa.

(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 notion 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 necessarily finite).

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.

Slainte va!

Keep up the Zeno's Coffeehouse involvement, as it's good for the mind!