Re: Need help in interpreting symbol 225e (measured by)

From: Philippe Verdy (
Date: Fri Mar 10 2006 - 11:06:16 CST

  • Next message: Kenneth Whistler: "Re: Need help in interpreting symbol 225e (measured by)"

    From: "philip chastney" <>
    > HAZARD WARNING: this is pure conjecture . . but the
    > description MEASURED BY suggests a specific metric

    If not even the UTC members know the exact meaning or usage of the symbol, but only acknowledge the existence of the symbol, mostly as a glyph, then the normative English or French names defined by ISO is also probably suggestive or conjectured regarding this usage.

    So why not defining a name that does not attempt to translate "measured by", but instead a name that is descriptive of its graphic aspect? (additionally, if one would want to translate "measured by", it could be a word that does not even contain any "m" letter, so using this symbol in a mathematic document written in another language than french or english wouldprobably be a bad choice for authors.)

    After all, mathematic symbols most often have various contextual usages and are often defined specifically by different authors. So why not translating instead by "equal with m"

    In fact the symbol looks more as if it actually meant "equals by measure to". I would say that mathematically, two entities can be different but still equal by measure, and "m" symbolizes the application of an implicit measurement (or projection on a measure axis, such as a norm, or an angular argument) on both sides of the equality. This suggests that items on both sides are comparable using a projection in some metric space, and that inequalities could complement this operator (so we would also have "lower by measure than", and so on...)

    This U+225E operator is then just another variant of another similar symbols of the same family, like:
    * U+2251 (geometrically equal to: equal by measure of geometric proportions, i.e. isometric)
    * U+2256 (ring in equal to: equal by measure through projection symbolized by this ring)
    * U+2257 (ring equal to: equal by measure through projection symbolized by this ring, ignoring infinitesimal differences)
    * U+2259 (estimates, corresponds to: equal by measure through projection in a cartesian space, ignoring infinitesimal or unmeasurable differences in this space such as probablistic variance)
    * U+225A (equiangular to: equal by measure of an angle)
    * U+225B (star equals: equal by measure through a projection or injection in some space symbolized by this star)
    * U+225C (delta equal to, equiangular, equal to by definition, see also U+225A: equal by measure of an angle or of measurable definition characteristics...)

    All those symbols use an equal sign completed by some diacritic that specifies or limits what is considered equal (they all look like ignoring some aspects of the two compared items, just focusing on some of their characteristics).

    Then, these symbols cannot be used without first defining separately what are those characteristics (which could also be non-numeric, or numeric in a multidimensional space like complex numbers, quaternions, or functional spaces, or infinitesimal spaces, or probabilistic distribution spaces like Dirac pulses, or wavelet function spaces)

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