I guess I see what you guys mean. I just thought of tactics as being moves made for reasons beyond the move itself. It seems like under this loose definition pretty much any move could be considered a tactic.
Is this really a tactic?
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Nov 6, 2014
0
#23
iamdave220 wrote:
I guess I see what you guys mean. I just thought of tactics as being moves made for reasons beyond the move itself. It seems like under this loose definition pretty much any move could be considered a tactic.
Hopefully you make every move for reasons beyond the move itself.
Roughly: tactics = calculated forced move sequences leading to some kind of advantage. It doesn't matter if the sequence consists of just one move.
Can you have a sequence of one? I'm not sure you can.
Every definition seems to say that it's an ordered list.
You can't order one thing.
Zero isn't nothing. 101 isn't 11.
Therefore nothing isn't part of a sequence.
I don't believe that the uncertainty principle allows empty space, it must have certain quantum fluctuations.
(Off topic?)
Nov 6, 2014
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#28
Scottrf, you are probably not a mathematician. We have sequences of one, empty sequences, sets of one, empty sets.
Of course it's just a matter of definition, but it turned out that it's very inconvenient to define things in ways that exclude the degenerated cases - your theorems will get much more clumsy to formulate.
Nov 6, 2014
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#29
Scottrf wrote:
Every definition seems to say that it's an ordered list.
You can't order one thing.
Yes, I can. Ordering a list of one element is entirely trivial, as is ordering an empty list.
If you want to get the most out of your collections terminology, you have to keep it simple or you end up mumbling things like: we have this arbitrary number of elements, now let's put them into an ordered list - of course, only if there are more than one, let's look at the other cases later...
Maybe order means something different when translated to German but in English it's relative. You can't order one thing.
I would look at this like a developer. When as developer defines an array, is it really an array before there are multiple items in it? Yes. The key is that a container has been set up that allows an array of contents.
The array refers to the container of X potential elements, not to the elements themselves. When the array is empty, it is still a container.
Same in math. Is an empty set really a set? I would say yes. It's a conceptual container of potential elements, nothing more. If you have a set of two items and remove one, you can still refer to it as a set, because the idea of a set is fluid...it can contain any number of elements...including one or none. It does not drop it's "setness" in discussion, because it may expand to many elements again shortly.
A sequence is basically an ordered set. You can order one thing: you can say "this is the number 1, it is the first integer". You do not have to say anything about two or any other integer to know now that number 1 is first in the sequence of integers. Ordinality is just a property/characteristic that you attach to the number one (which would be an arbitrary number/symbol without ordinality and other properties ;)...).
The same with zero. Zero always represents something, and that something...is the concept of nothing. When you say "zero", you are not saying "nothing"...you are saying "prepare yourself; I am about to impart something to you that requires you to conceptualize the idea of nothing for the purposes of some discussion/point".
That's like calling a word a sentence because you could make it in to one. It isn't until it is.
Nov 6, 2014
0
#33
Scottrf wrote:
Maybe order means something different when translated to German but in English it's relative. You can't order one thing.
No, it means the same. You can order one thing if you define your notion of ordering correctly. Then an empty sequence and a sequence of one are always ordered automatically.
In math (and software development, as pointed out by btickler) you have the freedom to define your notions in the most sensible way. Now you might object that we are not talking math but common language, which is of course correct. But in common language it's totally unclear anyway - 50% will say that an empty list is ordered because it does't contain elements violating the ordering, the other 50% will insist that the notion of an ordered empty list is pointless.
But it's not pointless, it makes it much easier to talk about ordered lists.
Scottrf wrote:
That's like calling a word a sentence because you could make it in to one. It isn't until it is.
Interesting. <-- Sentence.
That's backward, though...the sequence in this scenario is playing the part of sentence, not word. So it would be like calling a sentence a word...is a one word sentence just a word? No, it's still a sentence. The period tells us so...it adds the property of sentence-ness to the word.
Think of the "empty container" of a set, seqeunce, array, etc. as an invisible punctuation mark ;). It's there in concept and holds place in the discussion/communication taking place.
Some can be. Not all. I was obviously referring to the words that can't be sentences by themselves. It's not backwards.
How can something be ordered if it can't be disordered?
A one element set can be either ordered or disordered. The ordinality is just an attached property. The ordered set/sequence is defined by the person imparting it. If someone doesn't impart ordinality, it can't be understood.
The conceptual number one has a worldwide agreed-upon ordinality, so let's set it aside. If I gave you the numbers:
3 13 313
...and did not say anything else, they would be a disordered set.
If I say "take a set of numbers starting with..." before I give you the numbers, then in your mind, you will create a sequence/container with implied additional numbers, and probably decide that 1313 belongs in the sequence. The phrase adds a characteristic that wasn't there when I just gave you the three numbers.
If you turn around and give those same three numbers to someone else without telling them it's a set/sequence, then it reverts to being disordered.
The order/disorder is a characteristic of the conceptual set/sequence, not a characteristic of the element itself. The element itself just goes into the conceptual container.
Someone can't impart order to a single entity because order by it's very nature is in relation to something else.
Scottrf wrote:
Someone can't impart order to a single entity because order by it's very nature is in relation to something else.
If you say that this single entity is part of a set, then the order is attached to the conceptual set, not the entity :). You have an ordered set, which contains one element.
If you remodel your kitchen and tell your contractor "I haven't picked all the colors yet, but the primary color will be yellow...", then you have created an ordered set with one element in it. Yellow is first in the order even though all the other elements are still undefined.
Na.
@justus - like I said, that knight wasn't in the puzzle when it first appeared, he added it later. Without the N, 1.Qe8+ mates 2 moves faster.