robert@hpfclq.UUCP (06/09/84)
I think a human or computer presented this problem may end up asking for clarification provided more context (not supplied) were not available. For the problem given I would suspect perhaps not an inconsistancy but rather that I was being asked to setup a mapping from one "world" to another. A similar problem is: If 32 is 0 and 212 is 100 what is 65? This is of course a fahrenheit to celsius conversion problem. Read out of context it sure sounds strange. This kind of mapping problem is very common and might be done correctly by a computer without blinking a led. :-) -Robert (animal) Heckendorn ..!hplabs!hpfcla!robert
Laws@SRI-AI.ARPA (06/15/84)
From: Ken Laws <Laws@SRI-AI.ARPA>
I'm not sure whether the following probes our commonsense reasoning
ability or simply demonstrates a quirk of natural language:
"The Monday class will meet on Tuesday next week. The Wednesday
class will thus be the day after the Monday class. (We may
decide to hold the Friday class on Wednesday and the Wednesday
class on Friday if everyone can make it then.)"
Another example along the same line is:
If 3 were half of 5, what would a third of 10 be?
Although it's easy enough to finesse the problem by claiming that
this is nonsense, most people would find the answer 4 to be quite
reasonable. The answer is derived by following the chain 3:5/2
as 6:5 as 12:10 as 4:10/3, where ":" represents some unspecified
transformation that is assumed to be linear. I consider this similar
to the nonlinear Monday:Tuesday reasoning above.
-- Ken Lawsbrianp@shark.UUCP (06/20/84)
About "if 3 is half of 5, what is a third of 10?" It is interesting to note the assumptions that might be made here. One could assume that all numbers retain their good-old standard meaning, except 3, when compared to 5. Then the chain of relationships (3:5/2, 6:5, 12:10, 4:10/3) can be made. What I first thought was "so what's a '10'? " I.e, let's toss out all the definitions of the numbers along with 3. 'Half' could be redefined, but that says nothing about what to do with 'third'. One could redefine 'is', in effect, making it mean the ':' relation of the previous article. Anybody have hypotheses on which assumptions or definitions one would tend to drop first, when solving a puzzle of this sort? Brian Peterson ...!ucbvax!tektronix!shark!brianp
davep@tekecs.UUCP (06/20/84)
[!] > From: brianp@shark.UUCP (Brian Peterson) > > About "if 3 is half of 5, what is a third of 10?" > > It is interesting to note the assumptions that might be made here. > One could assume that all numbers retain their good-old standard meaning, > except 3, when compared to 5. Then the chain of relationships > (3:5/2, 6:5, 12:10, 4:10/3) can be made. If one redefines "3, when compared to 5", shouldn't the 3 be redefined in all instances of the "chain of relationships"? If so, one could conclude that one-"third" of 10 is 24/5 : 3:5/2, 6:5, 12:10, 12/(5/2):10/3, 24/5:10/3. David Patterson Tektronix, Inc. Wilsonville Industrial Park P.O. Box 1000 Wilsonville, Oregon 97070 (503) 685-2568 {ucb or dec}vax!tektronix!tekecs!davep uucp address davep@tektronix csnet address davep.tektronix@rand-relay arpa address
swart@rayna.DEC (Mark W Swartwout) (06/21/84)
I am reminded of an old children's riddle:
Q. If you call a tail a leg, how many legs does a horse have?
A. Four. Calling a tail a leg doesn't make it so.
Mark Swartwout
UUCP {allegra,decvax,ihnp4,ucbvax}!decwrl!rhea!rayna!swart
ARPA MSWART@DEC-MARLBOROkeller@uicsl.UUCP (06/21/84)
#R:sri-arpa:-95300:uicsl:12300001:000:119 uicsl!keller Jun 21 11:45:00 1984 1/2 * 5 = 2.5 round up to 3 1/3 * 10 = 3.333... round down to 3 Just another possible interpretation. -Shaun Keller
slag@charm.UUCP (Peter Rosenthal) (06/21/84)
Pay no attention to that man behind the curtain. In solving a puzzle like: If 3 is half of 5, what is a third of ten? One might try a series of solutions like the ones suggested, but I would consider them incorrect if they were logically inconsistant. The meaning of the problem would be undermined if one redefined three but not two, five, ten, half or third. One approach I would take would be to explore alternate bases. For instance, in base nine, three is a third of ten. This approach does not solve the above problem though so it must be marked as wrong, and thrown out. At what point should a problem like that be given up on as illogical?
brianp@shark.UUCP (06/24/84)
When presented with a problem like the 'if 3 is half of 5' one, how many dive right in and try to solve something, and how many start by checking for inconsistencies? Solving problems that are 'inconsistent' sounds like it goes in the same pile as working with insufficient data. (problems with problems :-) Brian Peterson ...ucbvax!tektronix!shark!brianp
Laws@SRI-AI.ARPA (06/25/84)
From: Ken Laws <Laws@SRI-AI.ARPA>
1/2 * 5 = 2.5 round up to 3
1/3 * 10 = 3.333... round down to 3
-Shaun Keller
Shaun's solution is the same as Richard Treitel's solution in the
previous issue, derived independently. I like it better than my
own solution except for the fact that it makes the problem less
metaphysical.
Roger Hale's solution of (temporarily) subtracting one from each
number was essentially a solution to "If 3-X were half of 5-X, what
would X plus a third of 10-X be?" It seems as valid as my own
solution to "If 3 were half of 5X, what would a third of 10X be?"
I am surprised that such good alternatives to my explanation were found,
especially after I had exposed everyone to my own way of thinking.
For 18 years I've thought I had >>the<< answer.
-- Ken Lawsbrianp@shark.UUCP (06/30/84)
the computer could do the temperature conversion without blinking an led, if it knows that this here's a mapping, (not a monkey and banana to simulate), and its one of those easy linear jobs, and if it knows how to read and can figure out the question. (no fair writing a temperature conversion (or any give-it-some-numbers interpolation/extrapolation) program. you have to write a run of the mill common sense reasoning program, and send it through elementary school. or hire a tutor. little kids can tease new types of people real bad. wouldn't want our program to have emotional problems, would we? :-) Brian Peterson ...!ucbvax!tektronix!shark!brianp