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      CommentAuthorAngus
    • CommentTimeOct 9th 2015
     
    In that case, my interpretation would be wrong, but the sentence is certainly unclear. To say ALL X IS NOT Y is a pretty cumbersome version of NO X IS Y.
  1.  
    And there are 22n ways of mapping n binary inputs to n binary outputs
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015
     
    So there are four ways of mapping the input of a wire to the output?
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    Yes indeed there are.
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015
     
    Only if it has a gate in it. You didn't specify what was between the inputs and outputs.
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    Mapping is mapping. Your attempted pedantry is of no avail.
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015
     
    In mathematics, the term mapping, usually shortened to map, refers to eitherA function, often with some sort of special structure, orA morphism in category theory, which generalizes the idea of a function.


    You must specify the mapping else I can say that a wire is a valid mapping of a binary i put to a binary output with two states.

    Do not unterestimste the power of moletrap pedantry.
  4.  
    What you have just described is but one of the four possible mappings.

    I expect you to lose, Mister Bond.
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015 edited
     
    Oh all right.

    Well...not really. I accept your statement that there are 22n mappings of n binary inputs to n binary outputs. But I laid a trap for you when I got you to say that there are four binary mappings of the input to the output of a wire. There aren't if it's just a wire.

    The pedantically correct response would have been to say that there are POTENTIALLY four binary mappings depending on the gate that might be between the ends of the wire.

    So there.
  5.  
    Since I can use special wire, and since I did not specify the type of wire I had in mind when formulating my answer, I accept your defeat with grace and glee.
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015 edited
     
    I refuse your claim of gloatworthiness in a dignified and diplomatic manner such as is rarely seen on the 'trap. The word "wire" is well defined to mean a thin strand of metal with two ends. The binary function that can be implemented with such a device is very simple and has only two states. You may not redefine it to suit your whim.

    I will accept your abject submission with grace and compassion.
  6.  
    You will have to wait a goodly while before receiving such a boon. That is because a wire may be cut, and any manner of transformations performed between the two pieces, and I claim the freedom to have specified that, or not to have.

    I also wonder whether you have fully appreciated the full diversity of the mapping of a single input to a single output, aka "a wire", based on you saying
    Posted By: AngusThe binary function that can be implemented with such a device is very simple and has only two states.
    On the contrary, there is only one binary function here, not two.

    It looks like I will have to claim a double win.
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015 edited
     
    [sarcasm][irony][withering][bitter]
    It is with considerable regret that I must consider the possibility of reporting your post to the Boolean Competence board as well as the Commission on English as a Basic Mode of Communication.

    A wire, when cut into two pieces becomes two wires. This is generally appreciated by children who have developed to the point of having a Theory of Mind, around one year of age according to Baron-Cohen. It doesn't matter into how many pieces you cut the wire, you must discard all but one to fit the parameters of this discourse.

    When I say
    The binary function that can be implemented with such a device is very simple and has only two states.
    I am referring to one function. This is clear to speakers of English from the use of the singular article "The" at the beginning of the sentence. While in certain other languages that lack articles, such as Russian or Latin, more clarification may be necessary, such is not the case with English.

    Therefore the statement means that the single function that can be implemented by a single (piece of, if you must) wire has only two states. A true statement. To make it more easily grasped I can put it in a more familiar context. A two input gate can have sixteen states.

    For completeness, I should point out that a NOT gate, which resembles a piece of wire in having only one input, has two states. Together with the piece of wire the NOT gate provides the four states possible in a one-input gate. If you like, you can say that a piece of wire by itself is a gate with n=0 ports and then your formula works. This would be consistent with EM theory which says that there can be no electric field in a conductor, implying that both ends of the wire are the same port but going in opposite directions so they cancel. Or something.

    [/bitter][/withering][/irony][/sarcasm]

    Edited for clarity
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      CommentAuthorAngus
    • CommentTimeOct 9th 2015 edited
     
    beaver dam trombone sausage

    A piece of wire is topologically equivalent to a sphere, which has no identifiable features that could be considered ports. It therefore makes sense that a piece of wire has no ports.

    And I'm claiming the double of your double win.
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      CommentAuthorAngus
    • CommentTimeOct 10th 2015 edited
     
    ++crickets++
    The ++crickets++ are insisting that I double the double double (Canadian reference there) because the win is uncontested.
    • CommentAuthorAsterix
    • CommentTimeOct 10th 2015
     
    Grace Hopper (if the name's not familiar, look it up) used to distribute pieces of 1 foot long wire in her classes. Basically a light-foot or approximately 1 nanosecond. Seymour Cray would hold his hands about a foot apart at various press events and intone "this is a nanosecond". That meant a lot when you had computer backplanes that looked like this:

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      CommentAuthorAngus
    • CommentTimeOct 10th 2015 edited
     
    I remember. The meme 30 cm to the light nanosecond is second nature to us optical guys. Except in fibre it is 20 cm to the light nanosecond.

    If you think about it you realize how difficult it is to do experiments in the femtosecond range, which depend on the intersection of optical or X-ray pulses, where the timing of the intersection depends on locating it in space to within less than one micron.

    Oh yeah - I also know who Grace Hopper was. The military version of Lady King.
  7.  
    Wire-wrapped, too.
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      CommentAuthorAngus
    • CommentTimeOct 10th 2015
     
    Tough looking babe, but I doubt that.
    • CommentAuthorAsterix
    • CommentTimeOct 10th 2015
     
    Posted By: alsetalokinWire-wrapped, too.


    That's a Cray I--wasn't that a taper-pin setup, rather than wire-wrap?