Response to a Remark

Subject:Re: Simple vs. Compound leaves
Date:Fri, 09 Jun 2000 17:56:16 -0400
From:Alexander Bogomolny

Francisco Moore wrote:

> I thought that you might like to know that your web page commentary
> on inaccuracy of words might be a little bit confusing to some people.
> For instance you use a text book derived example that relates to
> technical botanical language. You show a portion of a page of that text.
> On that diagram there are 3 compound leaves, and 1 simple leaf. The
> compound leaves contain from 7 to 132 leaflets per leaf (each appearing
> to be a leaf blade). In the simple leaf there is but one blade which has
> little, if any, more complexity than the leaflets of the compound
> leaves. I would conclude that the botanical terms 'Compound and Simple
> leaf' are in excellent congruence with the general use of compound and
> simple.

I've nothing against this usage. In so far as biologists agree on it, and have sufficient reasons for the nomenclature (e.g., as you explained above), I have no objections. The opposite is true. I am all for fixing terminology in any field of study. All I wanted to say was that a simple leaf may possess quite a complicated structure. If you look at the Hersh's letter, you'll see how mathematicians often deride their own terminology however justifiable and entrenched it is. I think this is wrong. Biologists call a leaf simple if it has a single blade - very legitimate, for all I care. Mathematicians call a curve simple if it has no self-intersections - no less legitimate a definition. Why should one be defensive about calling a curve that appears as a tangle but yet has no self-intersections simple this is what I can't understand.

> It is also an excellent point that the two terms are relative.
> As a population biologist (theoretical and empirical) I can't comment on
> the general congruence of botanical terms with common usage.

I hope I made this clear. For all I care, it does not matter. The common usage itself is not adequately defined, and the same word may even have contradictory meanings.

Every science has its own language and has a right to such a language. It may be an advantage, but also may lead to a confusion, to incorporate into that language common words. I do not mind that either. In short, my intention was to say that in mathematics, as in any other science, one should not assume that words that were borrowed from the common language inherit their common meaning - whatever that may be. One simply has to study that language first if there's a desire to advance in the related field.

> I am
> competent to assess some of the other definitions you mention. I would
> say that the definitions of energy and adaptation are simply (not in the
> botanical sense!) inaccurate.

I would not call my examples a definition. They are just a particular usage. There could not possibly be anything inaccurate about them.

> Having worked in theoretical biology I appreciate the points that you
> are making about the power of a consistent (mathematical) language.
> Interestingly, in math as any other language concise Description is
> predicated on the rigor of initial definition.

> In any case I am having fun at your web site.
> thanks,

Thank you for the kind words and the note. Would you mind if I append it to my page? The note and my response may better clarify my intention.

All the best,
Alexander Bogomolny

Language of Mathematics, Language of Science and Plain Language

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