The general impression among philosophers of science and physicists alike is that maths is simple.

According to this viewpoint, maths may be—nay, even  must be—beautiful. But for all its complexity, speaking in the cultured tones, it is condemned to stay simple. The subtle shades of the evanescent feelings and emotions, say as captured by a piece of poetry or a work of fine art, they say, is not accessible to the hard, cold, “objective,” world of even of science in general, let alone the “world” of mathematics.

And, yes, as a matter of a plain truth, blogs must still be written, for the most part, using plain languages, for instance, in English! Not in mathematics.

Now, as far as I am concerned, I do seem to have sometime in the past much appreciated what folks such as these mean by those words.

But a subtle change took a root in my mind over the course of the last, ummmm…, 6–7 days, whose final culmination is what this post is all going to be about.

I mean to say, over the course of the past week or so, I seemed to be steadily recovering from my RSI (duly reported earlier on this very blog; see my last post).

Yesterday, the situation was that I seemed to have “fully” recovered from it.

And yet, as I was at it—I mean: at my poor keyboard—once again, I developed, you know, … a feeling. A feeling, now, near the base of my right-hand thumb. A feeling of a bit of a pain.

Now, given the really, really smart person that I am, I exactly knew what to do next: I stopped doing work, and ordered for me, through official channels [if you must be ever so curious], a new, more ergonomic, and < Rs. 500 keyboard. And then, I rested upon my newfound hint of an oncoming pain. [“Prevention is better than cure.”]

Then, sometime this late afternoon, as I was toying with the idea of slipping myself out of this sense of a highly diluted but nevertheless all-pervading boredom, I noticed that I cannot express myself at all. I mean to say: in plain English.

The “real truth” of the matter is this:

I think I have recovered—at least with all of today’s (and past few days’) boredom.

The thing also is: I think I have not recovered—not at least with that slight-ish pain, now appearing at the basal region of my right thumb.

Now, see, this is a situation that is so well-captured by maths in the following manner [but before going over that, may I remind you, for the nth time, that the proper spelling of the proper short-form of “mathematics” does naturally carry an ‘s’ at its end]:

Let w be defined as the wellness index. Then, states of well-/ill-ness can be easily expressed according to the following scheme:

  • Illness \Leftrightarrow -1.0 \leq w \leq 0.0
  • Recovered \Leftrightarrow w = 1.0
  • Recovering \Leftrightarrow 0.0 < w < 1.0

Simple enough a scheme, right?

So, now, the only question is: what English phrase do you use for the case which is captured by the expression: 0.999\dots \leq w < 1.0? especially if it also includes a time-evolution? a progress with the passage of time?

If you try to put it in English, referring to the above-mentioned points, there is no word in the English language (or any other “natural” language) to express this thought, this aspect of the actual reality (i.e. the condition of my typing hands). After all, “Recovered” does mean 1.0 but this number is not acceptable because of the use of the strong “<” sign.

As to “Recovering,” the 0.0 < w < 1.0 range, in this case, turns out to be of a rather Very Large Scale. In fact, as compared to the expression: “0.999\dots \leq w < 1.0“, it actually refers to an infinitely large Scale.

So, how do you express yourself in English, as far as that quoted expression, viz., “0.999\dots \leq w < 1.0,” goes?

After taking into account the time-evolution part of it, you would very naturally say something like: “recovering-ed” or “recovered-ing”. … You choose between the two.

Precisely both precisely are kind of usages that the Wren and Martin of my childhood times wouldn’t permit me, or any other child. (It’s not that I took the pair very seriously even back then, but the point is: I’ve come to know what painful book to quote when.)

And yet, the title usage is amply justified. As so well illustrated by the already established correspondence of maths and English.

And so, as I once again get back to typing [a lot]—but not on this (or any other) blog—what do you do in the meanwhile?

You listen to this song which I like…

A Song I Like:

(Marathi) “naval vartale ge maaye, ujaLalaa prakaashu…”
Lyrics: G. D. Madgulkar [Yes, that’s right, the words didn’t come to you from “sant dnyaaneshwara.”  [Yes, you further are wrong, “dnyaaneshwara” is never pronounced as “dnyaaneshwaraa,” let alone a “dnyaaneshwaraaaaaa.”]]
Singer: Asha Bhosale
Music: C. Ramchandra

[PS: May be I will streamline this post just a bit later tomorrow or the day after or so… .]


25 thoughts on “Recovering-ed/Recovered-ing

  1. “Recovering” is a process, not a state and, so, implicit is the termporal element which you have not allowed for in your methematical description. Because your statement is, 0.0 < w < 1.0 equates to recovering, perhaps you need to really describe it as dw/dt rather than w, assuming here that w is the state of health, for this was implicit in the way you defined the terms; i.e.: illness -1.0 <= w < 0.0, etc. Since "illness" is not a process but, rather, is a state, as is "recovered", you have mixed state and state change terms, for "recovering" is a process (a changing of state), not a state.

    Then, 0.0 < w < 1.0 should be described as a state, not a process. What would we call it? "Wellness" comes to mind. I would also introduce another state: dead (or the equivalent of dead if referring to a subsystem of the body).

    Dead: w = -1.0
    Illness: -1.0 < w < 0.0
    Wellness: 0.0 < w 0.0
    Convalescing: dw/dt < 0.0
    No change: dw/dt = 0.0

    What to do about w = 0.0? Perhaps that is an artefact of the scale we used, creating the illusion of another well-defined inttermediate state, which we know there is not. So I will endeavour to redefine the terms:

    Dead (total system or subsystem collapse): w = 0.0
    Illness (deteriorating health): 0.0 < w < 1.0 AND dw/dt < 0.0
    Wellness (improving health): 0.0 < w 0.0
    Perfect health: w = 1.0
    Sick: dw/dt = 0.0 AND w = E(w).

    So, here I have combined both the state and the rate of change of state to determine a set of terms … of course it is far from perfect but may form the basis of a type 1 fuzzy logic approach to computational analysis of health. Yeah, yeah, I know it is crummy but, hey, it’s a start?

    Your thoughts?


  2. It did it again: I will try again:
    Wellness: 0.0 < w 0.0″
    Perhaps lowercase “and” and placing slashed term in quotes might pass the silly filter.

  3. Nope: it did not get through
    Wellness (getting better) 0.0 is less than w is less than 1.0 and dee-w over dee-t is greater than 0.0.
    Maybe using worded terms will work.

  4. Maybe, to talk more about meathematical terms, posts need to come through as written – seems something in your comments filter is stripping things like slashes and greater-than symnbols, etc. Is there a way to post comments with maths in them without having the filter bugger them up?

  5. Let me try from outside of the author’s dashboard.
    1. I will try “0.0 less than w less than 1.0” in plain text below:
    0.0 < w < 1.0
    2. I will try "0.0 less than or equal to w less than or equal to 1.0" below, now using latex:
    0.0 \leq w \leq 1.0

    • Hey, it works!

      (This current reply however is from within the Dashboard.)

      I will have to think deeply, very deeply, about the points you were trying to make, before I come back!


    • Apologies, Ajit, but I do not know what you mean by “author’s dashboard”, except, perhaps, the web page you access as the author where you edit your posts? Sorry but I am not overly familiar with some Internet phraseology. Is there a way I can post replies that safely ensures symbolic language integrity without resorting entirely to English phrases? Having read over my replies again, I have noticed further errors.

  6. I will just try a line with backslashes to escape the following characters. It is likely to fail because filters may detect that as an attempt to insert malicious script but, hey, if I don’t try then I will never know, so here goes:
    Wellness: 0.0 \< w \ 0.0

  7. Thanks, Ajit.
    OK, been over a decade since I last touched any LaTeX but let’s give it a go… sorry if this makes a mess. Don’t remember much of it … might have to read the manual.


  8. OK, so it goes something like this (hoping this works)…
    \mbox{Dead (total collapse, resuscitation may be possible): }w = 0.0
    \mbox{Dead (total collapse, resuscitation impossible): }w \equiv 0.0 AND \frac{dw}{dt} = 0.0 \forall t
    \mbox{Illness level (during deteriorating health): }0.0 < w < 1.0 AND \frac{dw}{dt} < 0.0
    \mbox{Wellness level (during improving health): }0.0  0.0
    \mbox{No change: }0.0 \leqslant w \leqslant 1.0 AND \frac{dw}{dt} = 0.0
    \mbox{Perfect health: }w = 1.0
    \mbox{Sick: }w < E(w) AND \frac{dw}{dt} \leqslant 0.0 \mbox{ where E() is the expectation operator}
    \mbox{Usual health and stable state: }w = E(w) AND \frac{dw}{dt} \approxeq 0.0
    et cetera.
    We could mess with this all day and introduce other variables such as environmental state because that also has a bearing on E(w).
    Anyway, just a bit of fun.

  9. I suspect that html is interpreting the greater-than sign as a delimiter BEFORE the latex parser gets the data, so it trashes the result. So, here I will try using backslash gt and see what happens…
    \mbox{Wellness level (during improving health): } 0.0 < w < 1.0 AND \frac{dw}{dt} \gt 0.0
    Again, sorry to litter your comments section, Ajit, but if we can sort this out here then future attempts will not be so full of problems. I am sure you have better things to do than deal with this stream of "stuff".

  10. Nope, didn’t work…. which is perhaps because there is no backslash gt in the mathematical symbol list for latex that I could find. One more go, delimiting the gt symbol itself with curly braces, and I will quit…
    \mbox{wellness... blah blah: } {0.0} {< w} { 0.0}

    • Sorry for running all your pending comments late. Was very busy, then was down a bit, and then again was too busy to check any comments/personal emails.


      Looks like you are succeeding in some places, at least. Good to note that.



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