> Sounds like there could be quite a few takes on inversion + quite a lot of > hidden value in this theoretical level.
I believe that there's enormous suppressed commercial demand for an "Excel" which will backfit changes to the value of a formula cell to its inputs. Even if this "backfit" is chosen on a fairly arbitrary basis. If it alters inputs you don't want altered (or not to that extent) you can "hold" those inputs and progressively steer the backfit to an acceptable result. Theoreticians will snigger at this: there's enormous suppressed demand for a process which spins straw into gold, they'll say (which no doubt accounts for the banter on this thread about "come-from".) They will tell you that the problem of inverting a given "mapping" (generalisation of "function") embraces the whole of modern mathematics, especially analysis and point-set topology, at least what could be termed the Bourbaki approach to mathematics. Furthermore, restricting yourself to mappings that can be expressed as Excel formulas nevertheless has embedded in it the Wortschatzproblem for semigroups, proved (Chaitin, nineteen-sixty-something) to be Turing-uncomputable. Ergo a general solution is impossible, ergo it's a holy grail, ergo it's not worth looking for. George Kunzle wasn't a mathematician, so nobody told him it was impossible, so he chewed off a commercially valuable subset of the problem domain. And by "commercially valuable" I mean millions of $, which is what Adaytum sold for eventually. You can argue that selling a function inverter is like selling snake-oil, but that's not true in practice. Adaytum's break-back algorithm (let me stress it's basically different from the TABULA approach, so there isn't just one algorithm in existence) satisfied 95% of what their planning clientele could throw at it, and the remaining 5% succumbed to simple heuristics which could be offered to the affected customer as an add-on, or thrown into the mix (let's not call it an "algorithm"). The same holds true for TABULA. For example, TABULA doesn't make a good job of formulae of the form z=x+(k/y) in the neighbourhood of z=0 because that's the rectangular hyperbola (xy=k) and TABULA can easily find itself backfitting up the wrong arm. Now any hacker worth his salt can think of a dozen heuristics to nail that problem, but that's not intellectually satisfying for a mathematician and a reviewer would sneer if you tried to publish a paper on the topic. Yes, there was a lot of interest in the 1960s in a related area called hill-climbing but AFAICT it's all gone off the boil. Or perhaps it's me that's got out of touch. > Sometimes I wish the smaller players could somehow stay indigeneous... I do agree. And somehow I wish algorithm theorists would take the problem seriously and publish more about it, even if it's just a collection of hacks. Because right now the state-of-art is such (IMHO) that the bundle of heuristics which have come back exclusively into IBM's hands is so secret, effective and commercially valuable as to be a patentable process, which will have serious implications for the small guy in some potentially innovative areas. Such as... eco-modelling for the rest of us (my main area of interest in developing TABULA). On Sun, Feb 27, 2011 at 3:56 PM, Steven Taylor <[email protected]> wrote: > Hi Ian, > > (just catching up on email) > > thanks for the back-story on inversion. Sometimes I wish the smaller > players could somehow stay indigeneous... > > I knew about Cognos, but not that IBM now owns them as well. > > Sounds like there could be quite a few takes on inversion + quite a lot of > hidden value in this theoretical level. > > Could the inversion algorithim also be useful outside of planning circles? > I'll be checking out Tabula. Thanks for making this public. > > "Each item has a *label*, a numeric *value* and *units (of measurement)*." > > neat. > > cheers, > -Steven > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
