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Intuitive explanation of currying.
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no.to...@gmail.com
Jul 15, 2012, 9:17:19 AM7/15/12
to
I was reading/reminded that 'lambda calculus is not easy'.
So I a got-out my copy of
http://en.wikipedia.org/wiki/Lambda_calculus
But I can't afford the effort to learn how to edit wikis.
So I'll put it here:- [my wiki contaminated by my 'comments']
> Currying may best grasped intuitively through the use of an
> example. Compare the function (x, y) | x*x + y*y with its curried
> form, x | (y | x*x + y*y). Given two arguments, we have:
> ((x, y) | x*x + y*y)(5, 2) = 5*5 + 2*2 = 29. <-- f(5, 2) = 29
> However, using currying, we have:
> ((x | (y | x*x + y*y))(5)) (2) <--- (functn) (arg)
>
> (<1 arg> maps-to <lambda1Funct> (5) ) (2)
>
> = (y | 5*5 + y*y) (2)
> = 5*5 + 2*2 = 29 <----------------- * !!
> and we see the uncurried and curried forms compute the same result.
>
So what? That's not an intuitive explanation.
Intuitive means related to concrete/familiar life.
Eg. take a 3D/volume: semi-sphere, rect-cube or a 'wedge' is
interesting; and place it on your x-y-coordinate 'pad'.
The task/function is to know the <heights above your x-y-pad>
of the top-surface. Like the heights of a mountain at a specific
longtitude, latitude.
For the wedge: if you know the x-value and the the y-value
is constant at THAT x-value, you've got the answer.
For the mountain: if you can only buy services of a flying-saucer
that gives the longtitude-to-terain-height-function for a FIXED
latitude, you've got the height, from you single parameter.
So the set of (x,y) tuples & f1 is collaped into an eqivalent:
[say] (x, y-cuts/slices/function) .
By induction, it extends to N-dimensions.
Here's a very intuitive example:
the fare for transport is quoted in a table, as being a function of
'route' and class. Where route means 'A to B' equals 'B to A'.
So 'Albany to Boston', class:2 costs $7,
and 'Boston to Albany', class:1 costs $9.
If you want to know the fare from 'Albany to Cooktown', class:3,
you don't need to provide both paramenters: 'route' and class.
You can just give the route, and ask for the singleton-function
[list of all prices for 'Albany to Cooktown' for all classes].
Thanks, I think I understand currying better now.
Do you?
== Chris Glur.
PS. explanations that I have of 'monads' are disasterous.
So I a got-out my copy of
http://en.wikipedia.org/wiki/Lambda_calculus
But I can't afford the effort to learn how to edit wikis.
So I'll put it here:- [my wiki contaminated by my 'comments']
> Currying may best grasped intuitively through the use of an
> example. Compare the function (x, y) | x*x + y*y with its curried
> form, x | (y | x*x + y*y). Given two arguments, we have:
> ((x, y) | x*x + y*y)(5, 2) = 5*5 + 2*2 = 29. <-- f(5, 2) = 29
> However, using currying, we have:
> ((x | (y | x*x + y*y))(5)) (2) <--- (functn) (arg)
>
> (<1 arg> maps-to <lambda1Funct> (5) ) (2)
>
> = (y | 5*5 + y*y) (2)
> = 5*5 + 2*2 = 29 <----------------- * !!
> and we see the uncurried and curried forms compute the same result.
>
So what? That's not an intuitive explanation.
Intuitive means related to concrete/familiar life.
Eg. take a 3D/volume: semi-sphere, rect-cube or a 'wedge' is
interesting; and place it on your x-y-coordinate 'pad'.
The task/function is to know the <heights above your x-y-pad>
of the top-surface. Like the heights of a mountain at a specific
longtitude, latitude.
For the wedge: if you know the x-value and the the y-value
is constant at THAT x-value, you've got the answer.
For the mountain: if you can only buy services of a flying-saucer
that gives the longtitude-to-terain-height-function for a FIXED
latitude, you've got the height, from you single parameter.
So the set of (x,y) tuples & f1 is collaped into an eqivalent:
[say] (x, y-cuts/slices/function) .
By induction, it extends to N-dimensions.
Here's a very intuitive example:
the fare for transport is quoted in a table, as being a function of
'route' and class. Where route means 'A to B' equals 'B to A'.
So 'Albany to Boston', class:2 costs $7,
and 'Boston to Albany', class:1 costs $9.
If you want to know the fare from 'Albany to Cooktown', class:3,
you don't need to provide both paramenters: 'route' and class.
You can just give the route, and ask for the singleton-function
[list of all prices for 'Albany to Cooktown' for all classes].
Thanks, I think I understand currying better now.
Do you?
== Chris Glur.
PS. explanations that I have of 'monads' are disasterous.
Василий Воронков
Jul 16, 2012, 10:12:25 AM7/16/12
to
Your explanation doesn't really explain currying. It actually explains the whole concept of partial application. Currying is in fact a very simple concept.
Imagine, that we have language where a function can be applied only to one argument - there are no multiple argument functions at all. What we can do in such situation to imitate multiple argument functions? We can write functions that return other functions.
For example, a function for two arguments is a function for one argument that take this argument and returns another function for one argument. Here is an example in JavaScript:
function sum(x) {
return (function(y) { return x+y });
}
Applying:
sum(2)(2)
Or in a sane language:
sum = \x -> \y -> x+y
Applying:
sum 2 2 --That's equivalent to '(sum 2) 2' because of application left associativity
Of course, for this trick to work our language should support closures (because the nested function capture a argument of its parent functon). But if you understand closures it shouldn't be a problem for you.
On Sunday, July 15, 2012 5:17:19 PM UTC+4, (unknown) wrote:
> I was reading/reminded that 'lambda calculus is not easy'.
> But I can't afford the effort to learn how to edit wikis.
> So I'll put it here:- [my wiki contaminated by my 'comments']
>
> > Currying may best grasped intuitively through the use of an
> > example. Compare the function (x, y) | x*x + y*y with its curried
> > form, x | (y | x*x + y*y). Given two arguments, we have:
> > ((x, y) | x*x + y*y)(5, 2) = 5*5 + 2*2 = 29. <-- f(5, 2) = 29
> > However, using currying, we have:
> > ((x | (y | x*x + y*y))(5)) (2) <--- (functn) (arg)
> >
> > (<1 arg> maps-to <lambda1Funct> (5) ) (2)
> >
> > = (y | 5*5 + y*y) (2)
> > = 5*5 + 2*2 = 29 <----------------- * !!
> > and we see the uncurried and curried forms compute the same result.
> >
> So what? That's not an intuitive explanation.
> interesting; and place it on your x-y-coordinate 'pad'.
>
> The task/function is to know the <heights above your x-y-pad>
>
> So the set of (x,y) tuples & f1 is collaped into an eqivalent:
> So 'Albany to Boston', class:2 costs $7,
> and 'Boston to Albany', class:1 costs $9.
>
> If you want to know the fare from 'Albany to Cooktown', class:3,
> you don't need to provide both paramenters: 'route' and class.
On Sunday, July 15, 2012 5:17:19 PM UTC+4, (unknown) wrote:
> I was reading/reminded that 'lambda calculus is not easy'.
> But I can't afford the effort to learn how to edit wikis.
> So I'll put it here:- [my wiki contaminated by my 'comments']
>
> > Currying may best grasped intuitively through the use of an
> > example. Compare the function (x, y) | x*x + y*y with its curried
> > form, x | (y | x*x + y*y). Given two arguments, we have:
> > ((x, y) | x*x + y*y)(5, 2) = 5*5 + 2*2 = 29. <-- f(5, 2) = 29
> > However, using currying, we have:
> > ((x | (y | x*x + y*y))(5)) (2) <--- (functn) (arg)
> >
> > (<1 arg> maps-to <lambda1Funct> (5) ) (2)
> >
> > = (y | 5*5 + y*y) (2)
> > = 5*5 + 2*2 = 29 <----------------- * !!
> > and we see the uncurried and curried forms compute the same result.
> >
> So what? That's not an intuitive explanation.
> interesting; and place it on your x-y-coordinate 'pad'.
>
> The task/function is to know the <heights above your x-y-pad>
>
> So the set of (x,y) tuples & f1 is collaped into an eqivalent:
> So 'Albany to Boston', class:2 costs $7,
> and 'Boston to Albany', class:1 costs $9.
>
> If you want to know the fare from 'Albany to Cooktown', class:3,
> you don't need to provide both paramenters: 'route' and class.
Imagine, that we have language where a function can be applied only to one argument - there are no multiple argument functions at all. What we can do in such situation to imitate multiple argument functions? We can write functions that return other functions.
For example, a function for two arguments is a function for one argument that take this argument and returns another function for one argument. Here is an example in JavaScript:
function sum(x) {
return (function(y) { return x+y });
}
Applying:
sum(2)(2)
Or in a sane language:
sum = \x -> \y -> x+y
Applying:
sum 2 2 --That's equivalent to '(sum 2) 2' because of application left associativity
Of course, for this trick to work our language should support closures (because the nested function capture a argument of its parent functon). But if you understand closures it shouldn't be a problem for you.
On Sunday, July 15, 2012 5:17:19 PM UTC+4, (unknown) wrote:
> I was reading/reminded that 'lambda calculus is not easy'.
> But I can't afford the effort to learn how to edit wikis.
> So I'll put it here:- [my wiki contaminated by my 'comments']
>
> > Currying may best grasped intuitively through the use of an
> > example. Compare the function (x, y) | x*x + y*y with its curried
> > form, x | (y | x*x + y*y). Given two arguments, we have:
> > ((x, y) | x*x + y*y)(5, 2) = 5*5 + 2*2 = 29. <-- f(5, 2) = 29
> > However, using currying, we have:
> > ((x | (y | x*x + y*y))(5)) (2) <--- (functn) (arg)
> >
> > (<1 arg> maps-to <lambda1Funct> (5) ) (2)
> >
> > = (y | 5*5 + y*y) (2)
> > = 5*5 + 2*2 = 29 <----------------- * !!
> > and we see the uncurried and curried forms compute the same result.
> >
> So what? That's not an intuitive explanation.
> Intuitive means related to concrete/familiar life.
>
> Eg. take a 3D/volume: semi-sphere, rect-cube or a 'wedge' is
>
> interesting; and place it on your x-y-coordinate 'pad'.
>
> The task/function is to know the <heights above your x-y-pad>
> of the top-surface. Like the heights of a mountain at a specific
> longtitude, latitude.
>
> For the wedge: if you know the x-value and the the y-value
> is constant at THAT x-value, you've got the answer.
> longtitude, latitude.
>
> For the wedge: if you know the x-value and the the y-value
>
> For the mountain: if you can only buy services of a flying-saucer
> that gives the longtitude-to-terain-height-function for a FIXED
> latitude, you've got the height, from you single parameter.
> For the mountain: if you can only buy services of a flying-saucer
> that gives the longtitude-to-terain-height-function for a FIXED
>
> So the set of (x,y) tuples & f1 is collaped into an eqivalent:
> [say] (x, y-cuts/slices/function) .
> By induction, it extends to N-dimensions.
>
> Here's a very intuitive example:
> By induction, it extends to N-dimensions.
>
> the fare for transport is quoted in a table, as being a function of
> 'route' and class. Where route means 'A to B' equals 'B to A'.
> So 'Albany to Boston', class:2 costs $7,
> and 'Boston to Albany', class:1 costs $9.
>
> If you want to know the fare from 'Albany to Cooktown', class:3,
> you don't need to provide both paramenters: 'route' and class.
> You can just give the route, and ask for the singleton-function
> [list of all prices for 'Albany to Cooktown' for all classes].
>
> Thanks, I think I understand currying better now.
> Do you?
>
> == Chris Glur.
>
> PS. explanations that I have of 'monads' are disasterous.
> Thanks, I think I understand currying better now.
> Do you?
>
> == Chris Glur.
>
On Sunday, July 15, 2012 5:17:19 PM UTC+4, (unknown) wrote:
> I was reading/reminded that 'lambda calculus is not easy'.
> But I can't afford the effort to learn how to edit wikis.
> So I'll put it here:- [my wiki contaminated by my 'comments']
>
> > Currying may best grasped intuitively through the use of an
> > example. Compare the function (x, y) | x*x + y*y with its curried
> > form, x | (y | x*x + y*y). Given two arguments, we have:
> > ((x, y) | x*x + y*y)(5, 2) = 5*5 + 2*2 = 29. <-- f(5, 2) = 29
> > However, using currying, we have:
> > ((x | (y | x*x + y*y))(5)) (2) <--- (functn) (arg)
> >
> > (<1 arg> maps-to <lambda1Funct> (5) ) (2)
> >
> > = (y | 5*5 + y*y) (2)
> > = 5*5 + 2*2 = 29 <----------------- * !!
> > and we see the uncurried and curried forms compute the same result.
> >
> So what? That's not an intuitive explanation.
> Intuitive means related to concrete/familiar life.
>
> Eg. take a 3D/volume: semi-sphere, rect-cube or a 'wedge' is
>
> interesting; and place it on your x-y-coordinate 'pad'.
>
> The task/function is to know the <heights above your x-y-pad>
> of the top-surface. Like the heights of a mountain at a specific
> longtitude, latitude.
>
> For the wedge: if you know the x-value and the the y-value
> is constant at THAT x-value, you've got the answer.
> longtitude, latitude.
>
> For the wedge: if you know the x-value and the the y-value
>
> For the mountain: if you can only buy services of a flying-saucer
> that gives the longtitude-to-terain-height-function for a FIXED
> latitude, you've got the height, from you single parameter.
> For the mountain: if you can only buy services of a flying-saucer
> that gives the longtitude-to-terain-height-function for a FIXED
>
> So the set of (x,y) tuples & f1 is collaped into an eqivalent:
> [say] (x, y-cuts/slices/function) .
> By induction, it extends to N-dimensions.
>
> Here's a very intuitive example:
> By induction, it extends to N-dimensions.
>
> the fare for transport is quoted in a table, as being a function of
> 'route' and class. Where route means 'A to B' equals 'B to A'.
> So 'Albany to Boston', class:2 costs $7,
> and 'Boston to Albany', class:1 costs $9.
>
> If you want to know the fare from 'Albany to Cooktown', class:3,
> you don't need to provide both paramenters: 'route' and class.
> You can just give the route, and ask for the singleton-function
> [list of all prices for 'Albany to Cooktown' for all classes].
>
> Thanks, I think I understand currying better now.
> Do you?
>
> == Chris Glur.
>
> PS. explanations that I have of 'monads' are disasterous.
> Thanks, I think I understand currying better now.
> Do you?
>
> == Chris Glur.
>
Aatu Koskensilta
Jul 16, 2012, 10:40:04 AM7/16/12
to
Василий Воронков <ba...@voronkov.name> writes:
> Imagine, that we have language where a function can be applied only to
> one argument - there are no multiple argument functions at all. What
> we can do in such situation to imitate multiple argument functions? We
> can write functions that return other functions.
Well, we can also write functions that take tuples as arguments. The
> Imagine, that we have language where a function can be applied only to
> one argument - there are no multiple argument functions at all. What
> we can do in such situation to imitate multiple argument functions? We
> can write functions that return other functions.
types A1 x A2 x ... x An --> C and A1 --> A2 --> ... --> An --> C are
(morally or literally, depending on the setting) isomorphic.
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Василий Воронков
Jul 16, 2012, 10:46:21 AM7/16/12
to
Yes, but in order to do that, we have to introduce another concept - a tuple. The solution with currying is the most "minimalistic" approach to simulation of multiple argument functions, which also allows us to partially apply functions.
On Monday, July 16, 2012 6:40:04 PM UTC+4, Aatu Koskensilta wrote:
> Василий Воронков writes:
>
> > Imagine, that we have language where a function can be applied only to
> > one argument - there are no multiple argument functions at all. What
> > we can do in such situation to imitate multiple argument functions? We
> > can write functions that return other functions.
On Monday, July 16, 2012 6:40:04 PM UTC+4, Aatu Koskensilta wrote:
> Василий Воронков writes:
>
> > Imagine, that we have language where a function can be applied only to
> > one argument - there are no multiple argument functions at all. What
> > we can do in such situation to imitate multiple argument functions? We
> > can write functions that return other functions.
>
> Well, we can also write functions that take tuples as arguments. The
> types A1 x A2 x ... x An --> C and A1 --> A2 --> ... --> An --> C are
> Well, we can also write functions that take tuples as arguments. The
> (morally or literally, depending on the setting) isomorphic.
>
> --
> Aatu Koskensilta (aatu.kos...@uta.fi)
>
> "Wovon man nicht sprechen kann, darüber muss man schweigen"
>
> --
> Aatu Koskensilta (aatu.kos...@uta.fi)
>
no.to...@gmail.com
Jul 20, 2012, 4:26:55 AM7/20/12
to
In article <ab2fa618-e841-48dc...@googlegroups.com>, =?KOI8-R?B?98HTyczJyiD3z9LPzsvP1w==?= <ba...@voronkov.name> wrote:
> Your explanation doesn't really explain currying. It actually explains the
> whole concept of partial application. Currying is in fact a very simple
> concept.
>
> Imagine, that we have language where a function can be applied only to one
> argument - there are no multiple argument functions at all. What we can do
> in such situation to imitate multiple argument functions? We can write
> functions that return other functions.
>
> For example, a function for two arguments is a function for one argument
> that take this argument and returns another function for one argument.
> Here is an example in JavaScript:
>
> function sum(x) {
> return (function(y) { return x+y });
> }
>
> Applying:
>
> sum(2)(2)
>
> Or in a sane language:
>
> sum =3D \x -> \y -> x+y
> Your explanation doesn't really explain currying. It actually explains the
> whole concept of partial application. Currying is in fact a very simple
> concept.
>
> Imagine, that we have language where a function can be applied only to one
> argument - there are no multiple argument functions at all. What we can do
> in such situation to imitate multiple argument functions? We can write
> functions that return other functions.
>
> For example, a function for two arguments is a function for one argument
> that take this argument and returns another function for one argument.
> Here is an example in JavaScript:
>
> function sum(x) {
> return (function(y) { return x+y });
> }
>
> Applying:
>
> sum(2)(2)
>
> Or in a sane language:
>
>
> Applying:
>
> sum 2 2 --That's equivalent to '(sum 2) 2' because of application
> left associativity
>
> Of course, for this trick to work our language should support closures
> (because the nested function capture a argument of its parent functon).
> But if you understand closures it shouldn't be a problem for you.
We are talking past each other.
> Applying:
>
> sum 2 2 --That's equivalent to '(sum 2) 2' because of application
> left associativity
>
> Of course, for this trick to work our language should support closures
> (because the nested function capture a argument of its parent functon).
> But if you understand closures it shouldn't be a problem for you.
My attempt to enlarge on the TITLE of my post, has failed.
There are several levels here.
One is what 'currying' IS: which I don't clain to know and
I just 'pasted' from the wikipedia.
Second is the INTUITIVE explanation / translation of what
I read in the wiki. Admittedly <intuitive> must be subjective;
but I believe that most writers don't even try to think what is
intuitive.
Lacking training in this field: psychology/cog-sci, I DO still
maintain that "II + II = IIII" is more intuitive than "2+2=4".
Don't you think the east-asians math superiority comes
from their use of 'pictogram writing', instead sound-based?
For me the important point of your post is [one of ] the
REASON for [what I'll call currying]: is if you've got an
automata which accepts only one arg and returns a singleton;
like *nix-piping, or forth.
IMO explanations from writers who resort to 'their'
language/s are the most unintuitive. Your examples added no
value for me.
== Chris Glur.
Aatu Koskensilta
Jul 20, 2012, 9:04:47 AM7/20/12
to
no.to...@gmail.com writes:
> Don't you think the east-asians math superiority comes from their use
> of 'pictogram writing', instead sound-based?
No.
> Don't you think the east-asians math superiority comes from their use
> of 'pictogram writing', instead sound-based?
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon man nicht sprechen kann, dar�ber muss man schweigen"
Barb Knox
Jul 21, 2012, 1:46:35 AM7/21/12
to
In article <87wr1y1...@uta.fi>,
rote memorisation. Does anyone her know of any published experimental
work regarding this?
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum videtur.
| BBB aa a r bbb |
-----------------------------
Aatu Koskensilta <aatu.kos...@uta.fi> wrote:
> no.to...@gmail.com writes:
>
> > Don't you think the east-asians math superiority comes from their use
> > of 'pictogram writing', instead sound-based?
>
> No.
But it plausibly does account for some of their apparent superiority in
> no.to...@gmail.com writes:
>
> > Don't you think the east-asians math superiority comes from their use
> > of 'pictogram writing', instead sound-based?
>
> No.
rote memorisation. Does anyone her know of any published experimental
work regarding this?
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum videtur.
| BBB aa a r bbb |
-----------------------------
Dirk Thierbach
Jul 21, 2012, 2:32:53 AM7/21/12
to
Barb Knox <s...@sig.below> wrote:
> In article <87wr1y1...@uta.fi>,
> Aatu Koskensilta <aatu.kos...@uta.fi> wrote:
>
>> no.to...@gmail.com writes:
>>
>> > Don't you think the east-asians math superiority comes from their use
>> > of 'pictogram writing', instead sound-based?
BTW, when I was a teaching assistant at university, I taught some
> In article <87wr1y1...@uta.fi>,
> Aatu Koskensilta <aatu.kos...@uta.fi> wrote:
>
>> no.to...@gmail.com writes:
>>
>> > Don't you think the east-asians math superiority comes from their use
>> > of 'pictogram writing', instead sound-based?
first year asian students in mathematics. Maube it was because they
had enough other problems at that time to deal with (another language,
culture shock, different level of education after finishing school),
but they were in no way superior in the abilities that really count
in maths, namely abstract thinking, careful reasoning and detecting
patterns.
>> No.
> But it plausibly does account for some of their apparent superiority in
> rote memorisation.
part of learning, no matter what subject, is just rote memorisation. If
you train something often enough, you become good at it.
Of course learning 2000 Kanji/Hanzi counts as part of the training. :-)
> Does anyone her know of any published experimental work regarding this?
one above.
- Dirk
no.to...@gmail.com
Jul 21, 2012, 2:42:45 PM7/21/12
to
In article <see-8E36F1.1...@news.eternal-september.org>, Barb Knox <s...@sig.below> wrote:
> In article <87wr1y1...@uta.fi>,
> Aatu Koskensilta <aatu.kos...@uta.fi> wrote:
>
> > no.to...@gmail.com writes:
> >
Co-ordinating *my* thead is like trying to herd cats ?
> In article <87wr1y1...@uta.fi>,
> Aatu Koskensilta <aatu.kos...@uta.fi> wrote:
>
> > no.to...@gmail.com writes:
> >
> > > Don't you think the east-asians math superiority comes from their use
> > > of 'pictogram writing', instead sound-based?
> >
> > No.
>
Let me try to fill-in-the-dots:
> > > of 'pictogram writing', instead sound-based?
> >
> > No.
>
anybody who's learned how to read schematic-diagrams or music,
knows the MASSIVE advantage of going directly from the <image> to
the <concept>, instead of going via the extra stage of the <sound
repesenting the word/s> to the concept.
> But it plausibly does account for some of their apparent superiority in
> rote memorisation.
authoritarian society stiffles creativety;
so simplistic method of learning i.e. rote memorisation is used.
I.e. brute-force-and-ignorance.
So, I was suggesting that since any 2-arg-function can be represented
by [is isomorphic to] a 3-dimensional-space, an intuitive way to
explain currying/partial-implemenataion is by getting a 2-dimensional
slice-out-of-the-3-dimensional-space.
And then I was fishing for a similarly intuitive explanation of
monads. But I got none -- yet.
But geometrical-thinking may NOT be intuitive to others, even if
the APL high-priest who's award winning ACM paper was entitled
<notation as an aid the thought> and he was VERY graphic.
== Chris Glur.
PS. <Babs> asked about literature on this.
'The stuff of thought' by Steven Pinker [from the library] was
brilliant. And a 4-part of <google:BBC+Reith+lecture> in the
last decade title < ? the mind ?> authored by a <Tamil-name>,
like 'Malaburi..' is a good easy read.
Steve Schafer
Jul 21, 2012, 3:21:15 PM7/21/12
to
On Sat, 21 Jul 2012 18:42:45 +0000 (UTC), no.to...@gmail.com wrote:
>anybody who's learned how to read schematic-diagrams or music,
>knows the MASSIVE advantage of going directly from the <image> to
>the <concept>, instead of going via the extra stage of the <sound
>repesenting the word/s> to the concept.
I can read schematic diagrams and music, as well as various other
>anybody who's learned how to read schematic-diagrams or music,
>knows the MASSIVE advantage of going directly from the <image> to
>the <concept>, instead of going via the extra stage of the <sound
>repesenting the word/s> to the concept.
graphical notations (Feynman diagrams, etc.). While I will agree that
those specialized notations do have substantial advantages in their
respective fields, that advantage arises primarily out of the brevity of
the notation rather than intuition. Thus, the disadvantage of those
notations is that you have to learn their rules before you can use them
effectively. There is little that is truly "intuitive" about the
notations; it's almost all learned.
An example: I was recently given a piece of clothing that was
manufactured in Italy. The care label sewn into the piece has no written
words; it is just a series of pictographic symbols that represent the
various things that you can and cannot do as far as caring for the piece
(e.g., machine wash, use medium iron, do not dry clean, etc.). Although
I am familiar with the concept of this "language," I don't know all of
the "words." So I had to go online to figure out what they meant. The
ironing symbol is partially intuitive in that it looks like an
old-fashioned clothes iron, but it has additional subsymbols (one ore
more dots inside) that alter the meaning in a way that is hardly
intuitive at all (more dots means hotter iron, but unless you know what
the scale is, it doesn't really help much). And the symbol for "do not
dry clean" (an X superimposed on a circle) is not intuitive at all. (The
"X" is well established as meaning "do not...," but even that is a
learned, not intuitive, interpretation. I have no idea why a circle
means "dry clean.")
So getting back to the written word... Written language is, essentially,
a general-purpose and extensible pictographic notation. For the most
part, the pictures have completely lost their original meanings, but
they're still pictures, just a different kind. I can't speak for others,
but when I'm reading text, there is no "extra stage of the <sound
repesenting the word/s>"; for familiar words, the _visual_ arrangement
of symbols in a word is, as far as I can tell, translated directly into
the concept in my brain.
-Steve Schafer
Mok-Kong Shen
Jul 21, 2012, 4:56:24 PM7/21/12
to
Am 21.07.2012 21:21, schrieb Steve Schafer:
[snip]
languages, I presume), for I thought till the present that that
applies only to a language like Chinese where the characters have
genuine pictographic origins.
M. K. Shen
[snip]
> So getting back to the written word... Written language is, essentially,
> a general-purpose and extensible pictographic notation. For the most
> part, the pictures have completely lost their original meanings, but
> they're still pictures, just a different kind. I can't speak for others,
> but when I'm reading text, there is no "extra stage of the <sound
> repesenting the word/s>"; for familiar words, the _visual_ arrangement
> of symbols in a word is, as far as I can tell, translated directly into
> the concept in my brain.
I find it very interesting that you wrote this (about European
> a general-purpose and extensible pictographic notation. For the most
> part, the pictures have completely lost their original meanings, but
> they're still pictures, just a different kind. I can't speak for others,
> but when I'm reading text, there is no "extra stage of the <sound
> repesenting the word/s>"; for familiar words, the _visual_ arrangement
> of symbols in a word is, as far as I can tell, translated directly into
> the concept in my brain.
languages, I presume), for I thought till the present that that
applies only to a language like Chinese where the characters have
genuine pictographic origins.
M. K. Shen
Steve Schafer
Jul 21, 2012, 6:17:04 PM7/21/12
to
On Sat, 21 Jul 2012 22:56:24 +0200, Mok-Kong Shen
<mok-ko...@t-online.de> wrote:
>I find it very interesting that you wrote this (about European
>languages, I presume), for I thought till the present that that
>applies only to a language like Chinese where the characters have
>genuine pictographic origins.
>
>M. K. Shen
The modern Latin alphabet can be traced back to Phoenecian, but from
<mok-ko...@t-online.de> wrote:
>I find it very interesting that you wrote this (about European
>languages, I presume), for I thought till the present that that
>applies only to a language like Chinese where the characters have
>genuine pictographic origins.
>
>M. K. Shen
that point on the trail runs cold. There is, however, evidence that many
of the letters can be traced directly to pictographic representations.
For example, the letter "A" is linked to the word for "ox," and it's
pretty clear from the Phoenecian rendering of that glyph that it started
out as a literal picture of an ox's head, complete with horns.
There was something that circulated around the Internet a few years
back:
--------8<--------
I cnduo't bvleiee taht I culod aulaclty uesdtannrd waht I was rdnaieg.
Unisg the icndeblire pweor of the hmuan mnid, aocdcrnig to rseecrah at
Cmabrigde Uinervtisy, it dseno't mttaer in waht oderr the lterets in a
wrod are, the olny irpoamtnt tihng is taht the frsit and lsat ltteer be
in the rhgit pclae. The rset can be a taotl mses and you can sitll raed
it whoutit a pboerlm. Tihs is bucseae the huamn mnid deos not raed ervey
ltteer by istlef, but the wrod as a wlohe. Aaznmig, huh? Yaeh and I
awlyas tghhuot slelinpg was ipmorantt! See if yuor fdreins can raed tihs
too.
-------->8--------
As it turns out, this was a bit of a hoax, in that the jumbled words
were in fact carefully crafted to remain legible. But the fact that an
English reader can read it at all tells us that there is something
complicated going on in our visual systems when we read. Here's a good
overview of what we know about word recognition (in European scripts, at
least):
http://www.microsoft.com/typography/ctfonts/WordRecognition.aspx
TL;DR version: It appears that our visual system processes and
recognizes groups of 5-10 letters in parallel. With shorter words, the
groups are large enough to encompass one or more entire words; in longer
words, we process them in chunks.
-Steve Schafer
Shmuel Metz
Jul 22, 2012, 11:14:07 PM7/22/12
to
In <qb9m089vmgt11447a...@4ax.com>, on 07/21/2012
by way of Aramaic.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
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at 06:17 PM, Steve Schafer <st...@fenestra.com> said:
>The modern Latin alphabet can be traced back to Phoenecian,
As can the Cyrillic and Greek alphabets, and various Semitic alphabets
>The modern Latin alphabet can be traced back to Phoenecian,
by way of Aramaic.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to spam...@library.lspace.org
Shmuel Metz
Jul 22, 2012, 10:56:28 PM7/22/12
to
In <r3vl08lgnisrr452s...@4ax.com>, on 07/21/2012
language.
at 03:21 PM, Steve Schafer <st...@fenestra.com> said:
>An example: I was recently given a piece of clothing that was
>manufactured in Italy. The care label sewn into the piece has no
>written words; it is just a series of pictographic symbols that
>represent the various things that you can and cannot do as far as
>caring for the piece (e.g., machine wash, use medium iron, do not dry
>clean, etc.).
I refer to those as icons that are equally unintelligible in any
>An example: I was recently given a piece of clothing that was
>manufactured in Italy. The care label sewn into the piece has no
>written words; it is just a series of pictographic symbols that
>represent the various things that you can and cannot do as far as
>caring for the piece (e.g., machine wash, use medium iron, do not dry
>clean, etc.).
language.
Aatu Koskensilta
Jul 24, 2012, 10:13:00 AM7/24/12
to
no.to...@gmail.com writes:
> Let me try to fill-in-the-dots:
> anybody who's learned how to read schematic-diagrams or music,
> knows the MASSIVE advantage of going directly from the <image> to
> the <concept>, instead of going via the extra stage of the <sound
> repesenting the word/s> to the concept.
This is an argument for specialized notation in mathematics. It has
> Let me try to fill-in-the-dots:
> anybody who's learned how to read schematic-diagrams or music,
> knows the MASSIVE advantage of going directly from the <image> to
> the <concept>, instead of going via the extra stage of the <sound
> repesenting the word/s> to the concept.
nothing to do with, say, the Chinese writing system. There's nothing
remotely like "going directly from the image to the concept" involved in
reading Chinese (or other similar scripts). You seem to be under the
mistaken idea that Chinese characters are pictograms. They're not --
indeed can not be; it's not Pictionary. A dog looks like something,
perhaps. But what does being slow look like, or a measurable cardinal,
communism, pining for the happy days of old, primitive recursion, being
directed at something, taking place in the future, being owned by
someone, not taking place?
> No, I suspect that's just cultural: authoritarian society stiffles
> creativety; so simplistic method of learning i.e. rote memorisation is
> used. I.e. brute-force-and-ignorance.
http://pinyin.info/readings/texts/moser.html/
for an informed rant about the horrors of the Chinese writing
system. There's nothing "intuitive" about it and rote memorization
simply can't be avoided when learning the system.
> And then I was fishing for a similarly intuitive explanation of
> monads. But I got none -- yet.
the most important thing to keep in mind is that whenever one gets
stuck, it's time to go back to the definition. Understanding and
intuition comes with practice, playing with examples, and so on. It's
unrealistic to expect any analogy or metaphor alone to be enough,
although they may of course be illuminating and helpful. It's also
unrealistic to expect any one "intuitive explanation" to be helpful to
everyone. What is intuitive depends on what one is familiar with. Case
in point, when reading physics texts I often have to apply the metaphors
and explanations backwards. They will explain that this or that bit of
mathematics is just like this bit of physics, if you squint your eyes
just so, hoping this will allow physics students to grasp the necessary
mathematical insight, idea, technique, concept. Since I know virtually
no physics, but do know a bit of mathematics, I will instead develop
some (vague and indefinite) intuition or understanding of the physics
involved, by relating it to mathematical arcana I feel at home with.
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