There’s a bridge connecting these two ontologies called “encoding”, but (as you note) this bridge seems arbitrary and philosophically messy. (I have a suspicion that this problem is mitigated if we consider quantum physics vs quantum computation, but I digress.)
This is why I don’t propose that we think about computational reduction.
Instead, I propose that we think about physical reduction, because (1) it’s less philosophically messy, (2) it’s more relevant, and (3) it’s more general.
We can ignore the “computational” ontology altogether. We don’t need it. We can just think about expending physical resources instead.
If I can physically interact with my phone (running Google Maps) to find my way home, then my phone is a route-finder.
If I can use the desktop-running-Stockfish to win chess, then the desktop-running-Stockfish is a chess winner.
Instead of responding philosophically I think it would be instructive to go through an example, and hear your thoughts about it. I will take your definition of physical reduction (focusing on 4.) and assign tasks and machines to the variables:
Here’s your defintion:
A task X reduces to task Y if and only if...
For every machine A that solves task Y, there exists another machine B such that...
(1) B solves task X by interacting with A. (2) The combined machine (A⊗B) doesn’t expend much more physical resources to solve X as A expends to solve Y.
Now I want X to be the task of copying a Rilke poem onto a blank piece of paper, and Y to be the task of Rilke writing a poem onto a blank piece of paper.
so let’s call X = COPY_POEM, Y = WRITE_POEM, and let’s call A = Rilke. So plugging into your definition:
A task COPY_POEM reduces to task WRITE_POEM if and only if...
For every Rilke that solves task WRITE_POEM, there exists another machine B such that...
(1) B solves task COPY_POEM by interacting with Rilke. (2) The combined machine (Rilke⊗B) doesn’t expend much more physical resources to solve COPY_POEM as Rilke expends to solve WRITE_POEM.
This seems to work. If I let Rilke write the poem, and I just copy his work, the the poem will be written on the piece of paper., and Rilke has done much of the physical labor. The issue is that when people say something like “writing a poem is more than just copying a poem,” that seems meaningful to me (this is why teachers are generally unhappy when you are assigned to write a poem and they find out you copied one from a book), and to dismiss the difference as not useful seems to be missing something important about what it means to write a poem. How do you feel about this example?
Just for context, I do strongly agree with many of your other examples, I just think this doesn’t work in general. And basing all of your intuitions about intelligence on this will leave you missing something fundamental about intelligence (of the type that exists in humans, at least).
A task is a particular transformation of the physical environment.
COPY_POEM is the task which turns one page of poetry into two copies of the poetry. The task COPY_POEM would be solved by a photocopier or a plagiarist schoolboy.
WRITE_POEM is the task which turns no pages of poetry into one page of poetry. The task WRITE_POEM would be solved by Rilke or a creative schoolboy.
But the task COPY_POEM doesn’t reduce to WRITE_POEM. (You can imagine that although Rilke can write original poems, he is incapable of copying an arbitrary poem that you hand him.)
And the task WRITE_POEM doesn’t reduce to COPY_POEM. (My photocopier can’t write poetry.)
I presume you mean something different by COPY_POEM and WRITE_POEM.
I think I am the one that is misunderstanding. Why doesn’t your definitions work?
For every Rilke that that can turn 0 pages into 1 page, there exists another machine B s.t.
(1) B can turn 1 page into 1 page, while interacting with Rilke. (I can copy a poem from a rilke book while rilke writes another poem next to me, or while Rilke reads the poem to me, or while Rilke looks at the first wood of the poem and then creates the poem next to me, etc.)
(2) the combined Rilke and B doesnt expend much more physical resource to turn 1 page into 1 page as Rilke expends writing a page of poetry.
I have a feeling I am misentrepreting one or both of the conditions.
Where it gets weird when it’s EVALUATE_FUNCTION(all_poems_ever_written, “write me a poem in the style of Rilke”)
“EVALUATE_FUNCTION” is then pulling from a superposition of the compressed representations of (“all_poems_ever_written, “write me a poem in the style of Rilke”)
And there’s some randomness per word output, you can think of the function as pulling from a region described by the above not just the single point the prompt describes.
So you get something. And it’s going to be poem like. And it’s going to be somewhat similar to how Rilke’s poems flowed.
But humans may not like it, the “real” Rilke, were he still alive, is doing more steps we can’t currently mimic.
The real one generates, then does EVALUATE_PRODUCT(candidate_poem, “human preferences”).
Then fixes it. Of course, I don’t know how to evaluate a poem, and unironically GPT may be able to do a better job of it.
Do this enough times, and it’s the difference between “a random poem from a space of possible poems, 1” and “an original poem as good as what Rilke can author”.
TLDR: human preferences are still a weak point, and multiple stages of generation or some other algorithm can produce an output poem that is higher quality, similar to what “Rilke writes a poem’ will generate.
This is completely inverted for tasks where EVALUATE_PRODUCT is objective, such as software authoring, robotics control, and so on.
1: In shadows cast by twilight’s hush, I wander through a world unclenched, A realm of whispers, full of dreams, Where boundaries of souls are stretched.
What once seemed solid, firm, and sure, Now fluid, sways in trembling dance; And hearts that cried in loneness, pure, Now intertwine in fate’s romance.
The roses’ scent is bittersweet, In fading light their petals blush, As fleeting moments dare to meet Eternity’s prevailing hush.
A thousand angels sing their psalms In silent orchestras of grace, Each word a tear, each sound a balm To soothe the ache in mortal space.
And through the veil, the unspoken yearn To touch the face of the Unknown, As infant stars ignite and burn, Their fire for the heart to own.
Do not resist this fleeting state, Embrace the ebbing of the tide; For in the heart of transience, Eternal beauty does reside.
With unseen hands, the world is spun, In gossamer and threads of gold, And in the fabric, every one Of life’s sweet tales is gently told.
In twilight’s realm, a truth unveiled, The poet’s heart is laid to bare, So sing your songs, let words exhale, And breathe new life into the air.
We have two ontologies:
Physics vs Computations
State vs Information
Machine vs Algorithm
Dynamics vs Calculation
There’s a bridge connecting these two ontologies called “encoding”, but (as you note) this bridge seems arbitrary and philosophically messy. (I have a suspicion that this problem is mitigated if we consider quantum physics vs quantum computation, but I digress.)
This is why I don’t propose that we think about computational reduction.
Instead, I propose that we think about physical reduction, because (1) it’s less philosophically messy, (2) it’s more relevant, and (3) it’s more general.
We can ignore the “computational” ontology altogether. We don’t need it. We can just think about expending physical resources instead.
If I can physically interact with my phone (running Google Maps) to find my way home, then my phone is a route-finder.
If I can use the desktop-running-Stockfish to win chess, then the desktop-running-Stockfish is a chess winner.
If I can use the bucket and pebbles to count my sheep, then the bucket is a sheep counter.
If I can use ChatGPT to write poetry, then ChatGPT is a poetry writer.
Instead of responding philosophically I think it would be instructive to go through an example, and hear your thoughts about it. I will take your definition of physical reduction (focusing on 4.) and assign tasks and machines to the variables:
Here’s your defintion:
Now I want X to be the task of copying a Rilke poem onto a blank piece of paper, and Y to be the task of Rilke writing a poem onto a blank piece of paper.
so let’s call X = COPY_POEM, Y = WRITE_POEM, and let’s call A = Rilke. So plugging into your definition:
This seems to work. If I let Rilke write the poem, and I just copy his work, the the poem will be written on the piece of paper., and Rilke has done much of the physical labor. The issue is that when people say something like “writing a poem is more than just copying a poem,” that seems meaningful to me (this is why teachers are generally unhappy when you are assigned to write a poem and they find out you copied one from a book), and to dismiss the difference as not useful seems to be missing something important about what it means to write a poem. How do you feel about this example?
Just for context, I do strongly agree with many of your other examples, I just think this doesn’t work in general. And basing all of your intuitions about intelligence on this will leave you missing something fundamental about intelligence (of the type that exists in humans, at least).
I’m probably misunderstanding you but —
A task is a particular transformation of the physical environment.
COPY_POEM is the task which turns one page of poetry into two copies of the poetry.
The task COPY_POEM would be solved by a photocopier or a plagiarist schoolboy.
WRITE_POEM is the task which turns no pages of poetry into one page of poetry.
The task WRITE_POEM would be solved by Rilke or a creative schoolboy.
But the task COPY_POEM doesn’t reduce to WRITE_POEM.
(You can imagine that although Rilke can write original poems, he is incapable of copying an arbitrary poem that you hand him.)
And the task WRITE_POEM doesn’t reduce to COPY_POEM.
(My photocopier can’t write poetry.)
I presume you mean something different by COPY_POEM and WRITE_POEM.
I think I am the one that is misunderstanding. Why doesn’t your definitions work?
For every Rilke that that can turn 0 pages into 1 page, there exists another machine B s.t.
(1) B can turn 1 page into 1 page, while interacting with Rilke. (I can copy a poem from a rilke book while rilke writes another poem next to me, or while Rilke reads the poem to me, or while Rilke looks at the first wood of the poem and then creates the poem next to me, etc.)
(2) the combined Rilke and B doesnt expend much more physical resource to turn 1 page into 1 page as Rilke expends writing a page of poetry.
I have a feeling I am misentrepreting one or both of the conditions.
Where it gets weird when it’s EVALUATE_FUNCTION(all_poems_ever_written, “write me a poem in the style of Rilke”)
“EVALUATE_FUNCTION” is then pulling from a superposition of the compressed representations of (“all_poems_ever_written, “write me a poem in the style of Rilke”)
And there’s some randomness per word output, you can think of the function as pulling from a region described by the above not just the single point the prompt describes.
So you get something. And it’s going to be poem like. And it’s going to be somewhat similar to how Rilke’s poems flowed.
But humans may not like it, the “real” Rilke, were he still alive, is doing more steps we can’t currently mimic.
The real one generates, then does EVALUATE_PRODUCT(candidate_poem, “human preferences”).
Then fixes it. Of course, I don’t know how to evaluate a poem, and unironically GPT may be able to do a better job of it.
Do this enough times, and it’s the difference between “a random poem from a space of possible poems, 1” and “an original poem as good as what Rilke can author”.
TLDR: human preferences are still a weak point, and multiple stages of generation or some other algorithm can produce an output poem that is higher quality, similar to what “Rilke writes a poem’ will generate.
This is completely inverted for tasks where EVALUATE_PRODUCT is objective, such as software authoring, robotics control, and so on.
1: In shadows cast by twilight’s hush, I wander through a world unclenched, A realm of whispers, full of dreams, Where boundaries of souls are stretched.
What once seemed solid, firm, and sure, Now fluid, sways in trembling dance; And hearts that cried in loneness, pure, Now intertwine in fate’s romance.
The roses’ scent is bittersweet, In fading light their petals blush, As fleeting moments dare to meet Eternity’s prevailing hush.
A thousand angels sing their psalms In silent orchestras of grace, Each word a tear, each sound a balm To soothe the ache in mortal space.
And through the veil, the unspoken yearn To touch the face of the Unknown, As infant stars ignite and burn, Their fire for the heart to own.
Do not resist this fleeting state, Embrace the ebbing of the tide; For in the heart of transience, Eternal beauty does reside.
With unseen hands, the world is spun, In gossamer and threads of gold, And in the fabric, every one Of life’s sweet tales is gently told.
In twilight’s realm, a truth unveiled, The poet’s heart is laid to bare, So sing your songs, let words exhale, And breathe new life into the air.