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A good day

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superpig

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I spent much of the day being hugged by pretty girls.

I've also discovered the history of the terms "Escape sequence" and "Escape characters." It's very simple - an 'escape sequence' was ESCAPE (0x1B) followed by any other character, and indicated some particular action that was not what that other character would usually produce. An escape character is thus any character used in an escape sequence.

Now, a question for you: Is there any solvable problem which has a finite number of distinct solutions?

I mean, consider the problem "What is the value of 1+1 ?". The 'normal' solution is just "1+1 = 2", but you could also have "1+1 = 2*1 = 2" or "1+1 = 1.0 + 1.0 = 2.0". Or even just "1+1 = 1+1+0+0+0+...+0 = 2," where the ellipses omit any number of "+0" terms.

Each of these solutions give the same end result, but differ in their characteristics. The number of stages, and the number of terms at each stage, differ; the nature of the terms themselves differ. Simple things like the length in characters of the solution differ. Thus, the solutions are distinct from one another. Note that by "solution," I'm not just talking about the end result - I'm talking about the process used to derive it.

I submit that any problem that has at least one solution must have an infinite number of distinct solutions. Can you prove me wrong?
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Quote:
Original post by superpig
I spent much of the day being hugged by pretty girls.


I can't believe no one commented on this yet [wow].

Details please ...

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Quote:
Original post by superpig
I spent much of the day being hugged by pretty girls.


I suspect he means in some MMORPG game, where a lot of the pretty girls are neither pretty or even girls :-)

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it seems like you're mostly playing with semantics, you're using a very odd definition of 'distinct solutions'. Is 1 really different from 1.0, mathematically? is 1+0 different from 1? I'd say that two solutions are distinct if you cannot simplify one into the other (that might not be rigorous, I haven't thought it through much).

edit: rereading your post I see you're talking about the process rather than the answer, which is different. It's confusing to say an infinite number of distinct solutions. Perhaps an infinite number of distinct methods? And even so, what about this counter example:

How many apples are there here?

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Quote:
Original post by baldurk
it seems like you're mostly playing with semantics, you're using a very odd definition of 'distinct solutions'. Is 1 really different from 1.0, mathematically? is 1+0 different from 1? I'd say that two solutions are distinct if you cannot simplify one into the other (that might not be rigorous, I haven't thought it through much).
Mathematically, no, they're the same. But I'm talking about much more than maths. "1.0," "1+0", and "1*1" are all 'correct' responses to "2-1 =", as indeed is "2-1" itself. But the point is that they have different attributes. The first uses floating point, the second addition, the third multiplication, the fourth subtraction... the first has only one term, the rest all have two. The key property we're interested in is evaluated value, for which all produce the same result; but their other properties differ. When all their properties are not the same, they are distinct.

We don't usually care about that, we usually only consider whether the key properties are distinct, but it remains that if we suddenly find ourselves in a situation where we care about whether or not floating point is being employed, e.g. on a system with no floating point processor - "uses floating point" becomes a key property. And suddenly, "1" and "1.0" become distinct for our purposes.

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Quote:
Original post by baldurk
it seems like you're mostly playing with semantics, you're using a very odd definition of 'distinct solutions'. Is 1 really different from 1.0, mathematically? is 1+0 different from 1? I'd say that two solutions are distinct if you cannot simplify one into the other (that might not be rigorous, I haven't thought it through much).

edit: rereading your post I see you're talking about the process rather than the answer, which is different. It's confusing to say an infinite number of distinct solutions. Perhaps an infinite number of distinct methods? And even so, what about this counter example:

How many apples are there here?


As a mathematician, I would say that "There is at lease on apple!"[lol]

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Quote:
Original post by superpigMathematically, no, they're the same. But I'm talking about much more than maths. "1.0," "1+0", and "1*1" are all 'correct' responses to "2-1 =", as indeed is "2-1" itself. But the point is that they have different attributes. The first uses floating point, the second addition, the third multiplication, the fourth subtraction... the first has only one term, the rest all have two. The key property we're interested in is evaluated value, for which all produce the same result; but their other properties differ. When all their properties are not the same, they are distinct.

We don't usually care about that, we usually only consider whether the key properties are distinct, but it remains that if we suddenly find ourselves in a situation where we care about whether or not floating point is being employed, e.g. on a system with no floating point processor - "uses floating point" becomes a key property. And suddenly, "1" and "1.0" become distinct for our purposes.


I see where you're coming from then. I imagine it's possibly true (I'm not sure how you'd go about proving it), but I'm not sure exactly what value it has practically. Obviously we know that there are several ways to do most things, and mostly there are better and worse ways - or at least pros and cons to the ways - but where does knowing there are an infinite number of methods get you?

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Original post by baldurk
Obviously we know that there are several ways to do most things, and mostly there are better and worse ways - or at least pros and cons to the ways - but where does knowing there are an infinite number of methods get you?
It's just an important realisation as many people don't realise that there are pros and cons in play. That's why we see people asking what the "best" language to use is, or the "best" way to do something - it makes no sense without knowledge of which properties are key properties.

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Do these count as seperate solutions?


  • I sit down. I add "1 + 1" to get the value "2". I write this down.
  • I stand up. I add "1 + 1" to get the value "2". I finish my jug of wine and throw a book at my girlfriend.

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For each solution I find I move half the distance of the room. Ah but an infinite series can have a finite sum :-) I can now solve any equation with a total number of methods that move me across the length of my room. I'll call this the solution distance. Now I will arbitarily set the solution distance at 1. Also I can say there are a given number of solutions in a distance, or solutions per distance.

Using this simple maths I get:
1 solution metres
------------------ = 1 Solution
metres

Q.E.D. T.I.C. (Tongue In Cheek)


Of course if it's a quadratic then you move twice each time, end up covering 2 solution metres and end up with 2 Solutions :D Not sure on the S.I. units here though!

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