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Function vs. Task Empty Function vs. Task

Mon Jan 11, 2021 10:40 am
Example: A teacher gives a student the task to compute sqrt(5)*3. The student uses a calculator which provides a square root function and a multiplication function. In this example, the task is specific, because it specifies the input (the numbers) and the goal (what should happen to the input). The functions provided by the calculator on the other side are generic, because they can be applied to many different numbers to serve many different goals. On some numbers, the functions cannot be applied and for some goals, it is not useful to use the functions. Depending on the specific input, a function provides a different output.

Analogously, a manipulation funnel is a mechanical function. It is generic, because it can be applied to many different inputs (the object). On some objects, the funnel cannot be applied and for some goals (what should happen to the object), the funnel is not useful. Depending on the specific input, the funnel provides a different output (hand-object configuration).

The square root function of the calculator is defined by programming instructions. These instructions operate on the specific number that the function is applied to. On the level of bits and bytes, the execution of the function will look completely different for different numbers. However, the programming instructions implement the same algorithm independently of the number. It is the abstraction level of the algorithm that leads to useful insights, not the level of specific bits and bites.

Analogously, the manipulation funnel is defined by a dynamic arrangement of compliant, actuated constraints that interact with an object. These constraints are affected by the specific object that the funnel is applied to. On the level of deformations, the morphologies of the compliant constraints will look completely different for different objects. However, the actuated compliant constraints implement the same prescriptive synergy independently of the object. It is the abstraction level of the prescriptive synergy that leads to useful insights, not the level of specific deformation of morphology.

(In a sense, a computer function is a funnel. Its funnel opening is the function parameter, its funnel exit is the return value and its funnel walls are the programming instructions. Together, this defines the function funnel.)

Example: An object resting on the palm of an open hand should be rotated by 90 degrees around the z-axis (orthogonal to the palm) and end up in a precision grasp.
The hand could first perform a funnel that rotates the object while it maintains contact with the palm and second, perform a funnel that brings the object in a precision grasp. Alternatively, the hand could first perform a funnel that brings the object in a precision grasp and second, perform a rotation funnel that rotates the object within the precision grasp. Here, each funnel is a mechanical function that can be applied to many different objects in many different initial configurations. The funnels are independent of the task. There is no unique solution to a task, because different sequences of funnels achieve the same task.

Because a task can be achieved by different sequences of funnels and the same funnel can be used for achieving many different tasks, the funnel is independent of the task.
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:06 am
[Adity@google-doc] So I guess the notion of "task" is not crucial to ascribe "funnel"ness, but certainly to ascribe utility to an already identified funnel.
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:07 am
[Oliver@google-doc] It's like the discussion about "computation". Once everything is a computation, the term is not useful. Without a task, it is not even possible to define uncertainty. So I think there needs to be a taslk.
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:12 am
@Oliver:
Nobody wants to say that everything is a computation or everything is a funnel. That seems to be a straw man argument. On the contrary, we want to identify the aspects that let us clearly and precisely define a funnel.
Uncertainty can be defined without a task, for example by defining it as uncertainty in hand-object configuration.
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:13 am
[Adrian @ google-doc]
Nevertheless, the desgin of the screw-driver is motivated by the size of the srews it is build for. The screw-driver constitues the funnel-walls that is changed by actuation of a hand holding the screw-driver. This generates the forces screwing the screw. Therefore, the funnel is defined by the constraints provided by the screw-driver, the actuation of the hand, all the screws it can screw and the dimension reduction it achives (Frame attached relative to the object the screw is screwed with z-axis pointing towards the screw - Then the funnel reduces the z-dimension of the screw).

In general, the screw-driver/RBO-Hand provides the mechanical aspect that have certain properties that can be leveraged - If leveraged they are part of a funnel if they reduce uncertainty of one aspect of the world - This constitutes a function/task.
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:19 am
@ Adrian

"Nevertheless, the desgin of the screw-driver is motivated by the size of the srews it is build for.
The screw-driver constitues the funnel-walls that is changed by actuation of a hand holding the screw-driver."

Yes, I agree

"Therefore, the funnel is defined by the constraints provided by i) the screw-driver, ii) the actuation of the hand, iii) all the screws it can screw and iv) the dimension reduction it achives (Frame attached relative to the object the screw is screwed with z-axis pointing towards the screw - Then the funnel reduces the z-dimension of the screw)."

Here, I disagree with iii) and iv).

iii) I would argue that the set of screws is implicitly defined by the morphology of the screwdriver. Just as the morphology of a common funnel implicitly defines the objects it can be applied to. The description of the funnel (not to confuse with the definition) could indicate the set of possible screws.
iv) same argument
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:35 am
[Adrian @ Google-Doc]

A funnel is only useful for some objects and to reduces uncertainty in some dimension. Those two properties define a set of tasks the funnel can be used for.
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Function vs. Task Empty Re: Function vs. Task

Mon Jan 11, 2021 11:40 am
@ Adrian

Yes, a funnel is only useful for some objects. But they do not define the funnel.
Let's say, we would try to define the set of objects that a funnel can be applied to. You could try to do that by shape or weight, etc. You will find out that your definition of this set of objects needs to take the funnel itself into account. In fact, it IS the funnel that defines this set.
So that is why I would argue that the set of possible objects follows from the definition of the funnel and not vice versa.
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Function vs. Task Empty Re: Function vs. Task

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