“When /I/ use a word,” Humpty Dumpty said, in rather a scornful
tone, “it means just what I choose it to mean—neither more nor less.”
“The question is,” said Alice, “whether you /can/ make words mean
so many different things.”
“The question is,” said Humpty Dumpty, “which is to be masterthat’s
all.”
Alice was too much puzzled to say anything, so after a minute
Humpty Dumpty began again. “They’ve a temper, some of them—particularly
verbs, they’re the proudest—adjectives you can do anything with, but not
verbs—however, /I/ can manage the whole lot! Impenetrability! That’s
what /I/ say!
--- Lewis Carroll, "Through the Looking Glass." It is evident that Lewis
Carroll was a mathematician.
On 10/20/2011 09:45 PM, Ric Sherlock wrote:
> I'm very happy thinking of a scalar as a zero rank array. I.e. scalars
> aren't distinct from arrays, they are just a type of array.
>
> Distinguishing a scalar from a single-element list can be confusing,
> but the same issue applies to lists and single-row tables etc. It is
> not confined to scalars vs arrays.
>
> On Fri, Oct 21, 2011 at 5:28 PM, Alan Stebbens<[email protected]> wrote:
>> On Oct 20, 2011, at 8:24 PM, Roger Hui wrote:
>>
>>> You have to use a different word than "noun". It's already taken and
>>> it means "array".
>> Roger,
>>
>> I have to agree with Rich.
>>
>> With all due respect (and that is not a trite phrase -- I really _do_
>> respect the tremendous work and thought that you have put into APL and J),
>> it seems incorrect to me to say that the word "noun" means "array".
>>
>> The object on which verbs operate, that is, a noun, can be either an array,
>> or a scalar.
>>
>> The J Primer says that
>>
>>> In the following sentence the numbers 2 and 5 are both nouns.
>>>
>>> 2 + 5
>> In the example, both 2 and 5 are scalars. So, a noun, by definition, is at
>> least a scalar.
>>
>> But, from other examples, we know that a noun can also be an array.
>>
>> So a noun is either a scalar or an array.
>>
>> This can be demonstrated in J itself:
>>
>>> f =: 3 : 0
>>> (('Rank';$$y),:('Shape';$y)),'Tally';#y
>>> )
>>> f '' NB. strings are arrays, even empty strings
>>> ┌─────┬─┐
>>> │Rank │1│
>>> ├─────┼─┤
>>> │Shape│0│
>>> ├─────┼─┤
>>> │Tally│0│
>>> └─────┴─┘
>>> f 1 NB. pass a scalar (no rank)
>>> ┌─────┬─┐
>>> │Rank │0│
>>> ├─────┼─┤
>>> │Shape│ │
>>> ├─────┼─┤
>>> │Tally│1│
>>> └─────┴─┘
>>> f ,1 NB. pass an array of one scalar
>>> ┌─────┬─┐
>>> │Rank │1│
>>> ├─────┼─┤
>>> │Shape│1│
>>> ├─────┼─┤
>>> │Tally│1│
>>> └─────┴─┘
>>> f 1 2 NB. pass an array of two scalars
>>> ┌─────┬─┐
>>> │Rank │1│
>>> ├─────┼─┤
>>> │Shape│2│
>>> ├─────┼─┤
>>> │Tally│2│
>>> └─────┴─┘
>>> f 0$1 NB. pass an empty array (zero shape)
>>> ┌─────┬─┐
>>> │Rank │1│
>>> ├─────┼─┤
>>> │Shape│0│
>>> ├─────┼─┤
>>> │Tally│0│
>>> └─────┴─┘
>>> f ''$1 NB. pass a null rank object (scalar)
>>> ┌─────┬─┐
>>> │Rank │0│
>>> ├─────┼─┤
>>> │Shape│ │
>>> ├─────┼─┤
>>> │Tally│1│
>>> └─────┴─┘
>> Alan
>>
>>
>> ----------------------------------------------------------------------
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> ----------------------------------------------------------------------
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