Nerd Word of the Day: Idempotent

idempotentIdempotent: adj. f. L.  idem same +  potent-em powerful:  Of a quantity or element a: having the property that a × a = a, where × represents multiplication or some other (specified) binary operation. Also applied to an operator or set… enough of this mumble jumble!  English please!

OK! An idempotent operation in math is one that has the same effect whether you apply it once, or more than once. For example: 1 x 1 = 1 or 1 x 1 x 1 = 1.

The STOP button on a VCR remote is idempotent, push it once and the tape stops, push it more than once and the tape remains stopped.  The Pause button, on the other hand, is not idempotent.. push it twice and it starts to play again.

Now, if they just had a cure for idempotence, oh wait.. wrong word!

Can you think of any other examples of idempotence?

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69 Responses to Nerd Word of the Day: Idempotent

  1. Kyle Joiner says:

    Talking about mathematical definitions from an attractive woman like you Marina, here are a whole heap more attractive women and a whole heap of math lessons and tutorials –

  2. iluv2cutfarts says:

    I would have to say that a girl’s fun-button is definitely not an “idempotent” button!


    Sorry Marina – still fantasizing over your Guess The Word Origin game on the Sirius stations from a couple of years ago when you were describing the origins of Cunnilingus.

    I got it right, btw… :mrgreen:

  3. tonyb says:

    “I deduced in undergrad in college that the “nth” derivitive of an “nth order polynomial”was “n!” or “n-factorial” My insane mind!!

  4. HotForWords says:

    Wow.. figuring out a way to integrate twitter into my comments.. and it’s working! Yeah!

    • Greatest Potential says:

      plz integrate some my way

    • Greatest Potential says:

      A Twitoaster would be of no use if there was no tweetbread to slide into it. Perhaps it’s like a rotating toaster, those are funny actually, the thing spins around and pops toast down into a tray and you get whatever toast you can before someone else snags on it. Had that at this restaurant I worked at when I played waiter.

    • Greatest Potential says:

      Some cheated and took the toast off the racks before the bread was completely toasted. I would look for the tale tale signs then confront the guilty parties “You’ve got rack mark burns on your fingers!”

  5. Evan Owen says:

    Aye, damn potent! :mrgreen:

  6. Hs4Mm says:

    I think most sentences entered here end up being idempotent (reach equilibrium). If I remeber correctly, start of Gettysburg address isn’t idempotent.

  7. Rambler Che says:

    I rather be important than impotent.

    [Halycon] please do it, do it for me, do it, do it, do it…………..

    { pressing button but it wont stop }

    • beevee14 says:

      “Honey, why you got a suit on.”
      “Well, I went to the doctor today and he said I was impotent. And if you is impotent, you has to dress impotent!” ;-) :arrow: :mrgreen:

  8. HotForNumbers says:

    Broadly speaking normalization operations are often idempotent unitary operations.

    When the normalization of the elements in a given set S consists in assigning another element in S to it (or in transforming the first into the second) we can represent this normalization process by a function F in S. In this way, any given element x in S is assigned a normalized element y in S given by the rule y = F(x) and the normalization of y would be the same y.

    F: S—>S
    y = F(x) and F(F(x)) = F(x)

    Normalized elements are like fixed points: they remain the same when normalized. F(y) = y for all normalized y in S.

    All this amount to the same as saying that a such normalizations can be represented by a map F in S that maps all elements in S to fixed points.

    1. Sorting a list of words
    2. Ordering things: putting disordered things into their place when they belong to a unique place.
    3. The convex hull of a set of points.
    4. Statlistical standard normalization: transforming a set of data so that its mean = 0and its variance =1.
    5. Compactification of subsets in a topological space.
    6. the modulo m operation (the remainder in the division of an integer number by a given integer m).
    7. Matrix diagonalizations and canonicalizations
    8. Universally covering spaces.
    9. The closure of subsets of a topological space
    10. Adding a given set of colours to a palette.

    • pat haskett says:

      I don’t know why but I think I understand this. Thanks

    • neuroway says:

      Idempotent latin squares are also quite mathematically interesting, as a partial idempotent x*x latin square can be embedded into a bigger y*y one, for every x >= 2y+1.

      It is way more difficult to achieve than embedding a partial commutative latin square though. But you don’t want to see the proof. Believe me. It deals with hellishly fancy maths and will fiercely rock you in the head unless you can run through a math demonstration like you run through a hip-hop song.

      • neuroway says:

        Oooooops… Just rereading myself and I realize that what I wrote makes no freaking sense at all.

        ^ x >= 2y+1 ^ x < 2y+1 ^. Now. Looks much better. Obviously you can't embed the bigger into the smaller, but yes, you can embed the small into the big. No proof needed here I think. Every object must follow this basic law of the visible universe, idempotent latin squares or not. The law is the law.

        Sorry for the confusion HotForNumbers.

    • Anonymous says:

      Okay Marina, what mathematician did you get this from? Your list contains some graduate level stuff. I am very suspicious!

  9. pat haskett says:

    A button on my microwave, the #1, only does one minute. Press it again and it doesn’t change the time. I think this is what we’re talking about. Math hurts my head.

  10. michael duckett says:

    Elevator call button…

  11. Bob says:

    I have two examples of idempotence:-
    Women can be idempotent.
    Give them some money and they’ll spend it on clothes and shoes
    Give them more money and … guess what.
    Ask them ,”What’s wrong?” and they say, “Nothing”.
    Ask them again and … guess what.

    The maths explanations of idempotence here are idempotent.
    Tell me once and they go right over my head.
    Tell me again and … guess what.


  12. edgarjensen says:

    6(6 / 1) or 6 * 6 / 6 * 6 / 6 ….ect

  13. jmcargal says:

    I’ve spent more than a little time working with idempotent operations within algebraic groups and rings due to my own obsessions in algebra, but “idempotent” has never struck me as one of those math words that easily extrapolates outside of mathematics. Ordinarily I would use the word as here: In the integers under multiplication modulo 6 the number 3 is idempotent because 3×3 = 3. In some of the other discussions people seem to be associating the term with identity mappings, but I think that is not a proper usage. In general, if we have a function that is not the identity such that f(x) = x is a non-trivial case, then we would say that x is a [fixed point] of f.

    • Richard says:

      I’ve always seen “idempotent” applying to operators. The canonical example is a projection operator, P, for which P(P(x)) = P(x). For example, suppose P_x is a projection operator that projects a vector in a two-dimensional Euclidean space onto a chosen x-axis in the obvious way. Then the projection P_x(P_x(v)) of the projection P_x(v) of an arbitrary vector v is the same as P_x(v) itself.

  14. leonard says:

    Soul this marks the global UNITING………—…..the continent civil thing and can I request a nerd word :smile: [][Vegetable][]….plEAsE and thAnks :P [fruit] too…juicy tree…vegeTable tree :?:

    • beevee14 says:

      Hey leoNard, are you of the school that thinks Syd Barret was a musical genius? Or was he a guy that took some bad acid? or both? I’ve watched a few documentarys on him and I just don’t know. David Gilmour is underrated. I do know that. ;-)

  15. damienro says:

    when you turn the keys in your vehicles ignition. If the engine turns over and starts; turning the key again won’t shut off the engine. but you might kill the starting motor, and that is why kids shouldn’t drive drunk :cool:

    • neuroway says:

      Hmm… This would be a very special case of mechanical idempotence, as the starter would be dead after a few experiments of this sort. So idempotence would be applied to the engine, and death to the starter. I am not sure this concept has been invented yet, damienro. You may want to consider trademarking it.

      • damienro says:

        :mrgreen: Thanks Nueroway your compliment means a lot to me:-)
        Marina should do some words for us motor-heads, what do you think? I’m sure that I could google it but watching her and getting to hear that Russian accent all the way over here in Iraq is priceless.
        Marina could you perhaps dig deep and pop the origin on the word [clutch] I have just recently been thinking about it a lot because I’m going to remove my automatic transmission in my 1999 BMW 323IC and put in a standard from a ’97 325. As soon as I get home that is :idea:

        • neuroway says:

          Heck, why not?

          She could put on one of these intelligent bikinis of hers and show us the difference between power wheelies and clutch wheelies while we’re at it.

  16. leonard says:

    :oops: Can not think!!!imPotent!!! :idea: :grin: :cool:

  17. neuroway says:

    From the latin idem (same) and potent (having power). A fully computerized tic tac toe game is a simple idempotent binary operation, as the X always win. Similarly, in theory, a fully computerized chess game is a complex idempotent operation, provided no heuristic is used in the solution, as the white always win. Something which has never happened so far.

    If the brain is childishly regarded as a mere computer, then true knowledge is idempotent, and the only cure for it would be true feeling, which is what differentiates machines and living organisms.

    • neuroway says:

      “Win” should be replaced by “draw” in the post above, as these two games are obviously not races, and the first to finish is not the winner. It was written too fast. X and Os and blacks and whites may be of different shapes and colours, but in a perfect play, their value is idempotent, no matter who starts or finishes first, there will be no winner. :smile:

    • Pseudonym says:

      No, that’s not a good example of idempotence (even with the correction). Idempotence is an operation which you must be able to perform multiple times.

      Another example is rounding a fraction to the nearest whole number. If you perform that operation twice, in the second step you’re rounding a whole number to the nearest whole number, which does nothing. So performing this operation twice gives the same result as performing it once, hence it’s idempotent.

      WARNING: Maths nerding follows.

      One way to get idempotent operations is to use retractions and sections. Suppose that you have two functions:

      r : A -> B
      s : B -> A

      such that:

      r o s = 1

      That is, r(s(x)) = x. (Here, 1 is the identity function.)

      r and s could be any functions, so long as r o s = 1. So in the above example, taking Z as the integers and R as the reals:

      s : Z -> R
      where s(x) = x

      r : R -> Z
      where r(x) = round(x)

      So s injects integers into the reals, and r rounds a real to the nearest integer. It should be clear that r o s = 1.

      But what about this function?

      i = s o r

      The function i is not necessarily the identity function, however consider i o i:

      i o i = (s o r) o (s o r) = s o (r o s) o r = s o 1 o r = s o r = i

      So no matter what functions r and s r, if r o s = 1, then s o r is idempotent.

      • neuroway says:

        That is mathematical idempotence. But what about computing idempotence?

        I think computing idempotence is a method or subroutine that can be called multiple times and always leads to the same result. Looking for a record in a database, for instance. What about a perfect play? Doesn’t a perfect computerized play always leads to the same result (a draw), no matter how many times you play? Wouldn’t this be a good example of computing idempotence?

        Erm… Anyways. Thanks for the maths, Pseudonym. I guess I got a little too inspired here and I just quickly raised the whole concept of idempotence to scientifically unacceptable levels, without too much of a thinking.

        • Pseudonym says:

          An idempotent operation is any operation where performing it twice does the same thing as performing it only once. Tic-tac-toe doesn’t work because you can’t play tic-tac-toe on an already completed game board.

          An algorithm can be idempotent, in the sense that a function that maps a data structure to a data structure can do the “same thing” if you apply it twice compared to if you apply it once. For example, if deleting an element from a dictionary-like data structure (e.g. a hash table) does nothing if there is no element is not there, then deleting the same element twice does the same thing as deleting the element once. Hence, it’s an idempotent operation.

          Idempotent operations are important in computer science, especially in resource-intensive computing such as operating systems and databases, because you can use them to construct operations that are interruptable and restartable.

          Imagine an operation that does A, waits for some event to happen, then does B. For example, if you are reading data from disk, you could issue the read, and then wait for the disk to return your data.

          That wait could take a large amount of time, and if the operation has acquired system resources, it could starve other operations from using those resources for an unbounded amount of time.

          However, if you ensure that A is idempotent (in our example, this means that issuing a read from the disk twice does the same thing as issuing the read once), then if there is a risk of resource starvation during the wait phase, you can simply kill the whole operation and start it again. This works because applying A twice does the same thing as applying it once.

          Did that make sense?

          • neuroway says:

            Makes a lot of sense indeed.

            But what if a reset of the tic-tac-toe game is included in an operation A, then B plays the perfect game and displays the result. Or C displays the result to make it simpler. You could simply kill A or B or even C whenever you want at anytime in the routine, and restart at A. B would be dependant on the successful completion of A, and C on B. I agree it would be totally useless to come up with such a routine, unless someone really enjoys programming and the concept of an idempotent game, for the pure intellectual sake of it. Then, it becomes merely a fun thing for the person who plays with it. The result C of the perfect game always being a draw, wouldn’t consequently A and the ABC combo be idempotent also?

        • Pseudonym says:

          Sorry, neuroway, this is in reply to your other comment, but we seem to have hit a limit on how deeply you can nest comments. I’m posting it here so that you get the notification.

          An idempotent operation has to be a pure function, possibly on the “state of the world”. If operation A outputs something, then applying operation A twice outputs that thing twice. This has a different effect on the world as only outputting something once (e.g. if it’s outputting to a printer, it uses twice as much paper). Therefore an operation like this can’t be idempotent.

  18. Capman911 says:

    This is definitely a nerd word. I Googled this word and my mouse’s batteries died trying to figure out some of the formulas for this word. Trying to cram to much knowledge in this ole country boy. Good Nerd word though. ;-)

    • leonard says:

      COUNTRY BOYS ARE BORN CRAMED fUll Of knOwlEdgE..,,..boards of KeYeD :razz: :???: Referential transparency and referential opaqueness are properties of parts of computer programs. An expression is said to be referentially transparent if it can be replaced with its value without changing the program (in other words, yielding a program that has the same effects and output on the same input). The opposite term is referentially opaque.
      [][form :grin: ][]

    • originalistrick says:

      Yeah, this is giving me a headache. Let’s go huntin’! Or fishin’. Or skiin’. ANYTHING that isn’t math-related.

  19. billyinc1 says:

    Loving You Babe You are the Best Marina. ;-)

  20. beevee14 says:

    The alphabet buttons on your keyboard are indempotent while the numeral and puncuation keys are not.

    Is that correct? :???: And no, I’m not kidding…. :arrow: :cool:

  21. Richard says:

    Projection operators?

  22. Greatest Potential says:

    samplers loop a sound constant “tweek n’ tweeze” soft buttons can enhance and emulate a tape’s “wow and flutter” gristlizer boxes do something amazing Ping Pong (stereo delays which feed each other) reset the atari

    digital loop carrier (DLC)

    Long loops, such as those terminating at more than 18,000 feet from the central office, pose electrical challenges. When the subscriber goes off-hook, a cable pair behaves like a single loop inductance coil with a -48 V dc potential and an Electric current of between 20-50 mA dc. Electrical current values vary with cable length and gauge. A minimum current of around 20 mA dc is required to convey terminal signaling information to the network. There is also a minimum power level required to provide adequate volume for the voice signal. A variety of schemes were implemented before DLC technology to offset the impedance long loops offered to signaling and volume levels.

    source: internet

  23. wetsuit5 says:

    Death and taxes.

    Being taught a lesson you already got.
    OK the horse is dead, you don’t need to kill it anymore.

    Is “inevitable” and “makes no difference” the theme?

  24. Lennie says:

    When you hang up the telephone, you do it ones and the conversation will end. Do it again, it will not start again.

  25. Greatest Potential says:

    :razz: apples and oranges

  26. pedanticKarl says:

    Cure for idempotence?
    Conjugation with bijection involution
    complementing the reciprocals might do the trick.

    I keep on clicking on the Idempotent image up above
    and I am getting the same results.
    I must be a Idempotent.

    Did the planet just didn’t flip on its axis, did it?
    I’m starting to see things. :lol:

  27. Greatest Potential says:

    tho i hear there is a push to go with tote bags instead of plastic & paper bags at the grocery stores.

    won’t be the same, i think many folks will miss hearing that question; “paper or plastic?”

  28. Greatest Potential says:

    Can you think of any other examples of idempotence?

    my interests reside more in the business of potency

  29. Greatest Potential says:

    :o English Please :!:

  30. roberhor says:

    you mean like, no matter what I do women never find me attractive?

    • beevee14 says:

      Of course not :!: There are women out there who will find you attractive, no problem; for a nominal fee of course :arrow: :???: ;-)


      Both Hourly And Daily Rates
      3 hour minimum
      Cash…up front


  31. Hs4Mm says:

    Hey! This is a legit math word from Algebra. Algebra also has nilpotent (or two worded “null potent”). Computer science has nullipotent.

  32. pedanticKarl says:

    First, that was wayyyy toooo many button pushes.
    Now, where was I.
    Oh, yeah.
    Push the button and the PC is ON.
    Push the button again and the PC is OFF.

    How about a ball point pen.
    Push the same clicker and the pen retracts and extends.

    • pedanticKarl says:

      Bad examples as the outcome changes, when they are operating normally for the pen and PC example.

      But, have you ever pushed the same button and clicker to get a different result and continue to get the same results? That’s
      when things are abnormally Idempotent. Who would have thought.

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