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Re: Language design, orthogonality, paternalism, bad rules,and

• From: Michael Kay <mike@saxonica.com>
• To: Dave Pawson <dave.pawson@gmail.com>
• Date: Wed, 2 Mar 2022 15:20:08 +0000

If three properties of an object (say colour, weight, and cost) are completely independent of each other, so none of them is a function of the others, then the object exists in a three-dimensional space whose axes/dimensions are colour, weight, and cost, and these axes/dimensions are "at right angles" to each other in this three-dimensional space.

So two properties of an object are orthogonal if, in effect, all combinations of the values of the two properties are possible.

So we can say, for most modern programming languages, that the names of variables are orthogonal to their type - there's no dependence of one property on the other.

For XPath nodes, node name and node kind are NOT orthogonal properties; the node kind constrains what the name of the node can be. 

I suspect that corresponds to the "inner product equal to zero" meaning, but it's 50 years since I did any vector algebra...

Michael Kay
Saxonica

> On 2 Mar 2022, at 14:59, Dave Pawson <dave.pawson@gmail.com> wrote:
> 
> On Wed, 2 Mar 2022 at 14:39, Roger L Costello <costello@mitre.org> wrote:
> 
>> The answer is orthogonality. Michael Kay explains:
>> 
>> “Orthogonality (or, "no needless restrictions")
> adjective
> Mathematics.
> 
> Also orthographic. pertaining to or involving right angles or
> perpendiculars:an orthogonal projection.
> (of a system of real functions) defined so that the integral of the
> product of any two different functions is zero.
> (of a system of complex functions) defined so that the integral of the
> product of a function times the complex conjugate of any other
> function equals zero.
> (of two vectors) having an inner product equal to zero.
> (of a linear transformation) defined so that the length of a vector
> under the transformation equals the length of the original vector.
> (of a square matrix) defined so that its product with its transpose
> results in the identity matrix.
> 
> Mike?
> 
> -- 
> Dave Pawson
> XSLT XSL-FO FAQ.
> Docbook FAQ.
> 
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• References:
  • Language design, orthogonality, paternalism, bad rules, and elephanttraps
    • From: Roger L Costello <costello@mitre.org>
  • Re: Language design, orthogonality, paternalism, bad rules,and elephant traps
    • From: Dave Pawson <dave.pawson@gmail.com>