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Author
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Topic: Teleological Algorithms
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warren_bergerson
Member
Member # 262
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posted 10. March 2004 09:25
Rigorous ‘hard’ science requires testable, mathematically predictive scientific theories. The centerpiece of any mathematically predictive theory is a predictive mathematical algorithm or function. A predictive algorithm is a mathematical function which given the values of the applicable input or causal variables will generate or calculate the value of the applicable output or effect variable.
The centerpiece of the goal directed or teleological predictive scientific hypotheses, I propose, is the goal directed or teleological algorithm. Goal directed algorithms have the general form ‘Select the response r from the set R of possible responses which has the greatest likelihood of achieving goal or purpose G’.
It should be reasonably obvious that the set or class of goal directed algorithms is very large and very diverse. The simplest algebraic type of goal directed algorithm occurs when the relationship between r and G is permanent. More complex, and more interesting goal directed algorithms arise when the member of R most likely to produce G changes with time and location.
It will be noted that human beings have a built in ability to calculate fairly complex goal directed algorithms. If you describe a goal and a set of possible responses or actions, a human being will in many instances be able to determine or calculate which response is most likely to produce the goal under a particular set of circumstances. Goal directed algorithms expressed in terms of formal mathematics can be quite complex. Except for the simplest types of goal directed algorithm where the relationship between r and G is permanent, goal directed algorithm will generally be expressed as computer programs.
It should also be reasonably obvious that goal directed or teleological algorithms can be quite effective at predicting both simple and complex behaviors generated by biological systems. It is reasonably well known that biological systems behave or generate responses compatible with the goal or purpose of survival. If you recognize the goal of survival, and if you know the responses or behaviors a biological system is capable of generating, you can produce reasonably reliable predictions of behavior using goal directed algorithms.
Predictive algorithms and reliable real world predictions are two of the key features or requirements predictive scientific theories. Goal directed or teleological hypotheses satisfy both these critical requirements. Whether goal directed hypotheses satisfy the other requirements for scientific theories is a subject of future discussion.
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Evan
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Member # 164
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posted 10. March 2004 16:43
Warren writes,
quote:
It will be noted that human beings have a built in ability to calculate fairly complex goal directed algorithms. If you describe a goal and a set of possible responses or actions, a human being will in many instances be able to determine or calculate which response is most likely to produce the goal under a particular set of circumstances.
Question: do you think that human beings do this by following “a predictive algorithm [which] is a mathematical function which given the values of the applicable input or causal variables will generate or calculate the value of the applicable output or effect variable?” That is, do you think human beings decide there goal-directed behavior on the basis of “built-in” mathematical procedures (algorithms.)?
Warren writes,
quote:
Goal directed algorithms expressed in terms of formal mathematics can be quite complex. Except for the simplest types of goal directed algorithm where the relationship between r and G is permanent, goal directed algorithm will generally be expressed as computer programs.
But this is not true of human beings. How are these algorithms expressed in real living things which are goal directed?
Warren writes,
quote:
It should also be reasonably obvious that goal directed or teleological algorithms can be quite effective at predicting both simple and complex behaviors generated by biological systems.
This is not obvious. As you said, “Goal directed algorithms expressed in terms of formal mathematics can be quite complex,” and as I am trying to point out, mapping those onto real biological systems is at the very least extremely difficult and at the worst it may be that such ideas modeled on mathematics and computers might not be at all how living things decide on their behaviors. So it is not obvious, and is in fact debatable, that “teleological algorithms can be quite effective at predicting both simple and complex behaviors generated by biological systems.”
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warren_bergerson
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Member # 262
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posted 10. March 2004 18:04
Evan,
Quote: But this is not true of human beings. How are these algorithms expressed in real living things which are goal directed?
Human beings with appropriate training perform arithmetic calculations and calculus calculations and the calculations associated with goal directed algorithms. Many organism perform complex calculations associated with anticipating where an rapidly moving object will be at some point in the future. Computers can also perform these calculations. The physical chemical processes associated with such calculations is not relevant to whether the calculations are being performed. The physical mechanisms associated with realizing calculations while it may be an interesting topic does not seem germane to the discussion here.
In the absence of unusual conditions, if you give someone a choice between $10,000 and $10 you can reasonably predict the person will choose the $10,000. IMO that prediction is reasonably reliable and fairly obvious. It should be obvious that there are many such examples.
The use of goal directed algorithms in predictive scientific theories involves a number of issues. The existence of this type of algorithm and the ability of these algorithms to generate reasonably reliable predictions, are not, IMO, issues of contention.
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RBH
Member
Member # 380
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posted 11. March 2004 00:13
warren_bergerson wrote quote:
Many organism perform complex calculations associated with anticipating where an rapidly moving object will be at some point in the future.
Many organisms behave as though they "perform complex calculations," but there is no evidence that they actually perform those calculations. To use an example I've used in other contexts: Was Jackie Robinson a better outfielder than I was because he knew more calculus? Should one really believe that an outfielder running to catch a ball is actually computing the equations of motion of a struck ball in a 1-G field, calculating its point of impact, while simultaneously calculating speed of running, adjusting it so as to arrive at the ball's predicted point of impact just as the ball does? The system behaves as though it performs all those calculations, but I strongly doubt that teaching the mathematics of ballistics will catch on as a baseball coaching tool.
There are systems that generate behavior that appears as though it is based on the performance of complex calculations, when in fact the behavior is due to a particular pattern of wiring in neural structures. For example, there are neural circuits in the human visual system that enhance edges by applying the equivalent of the Laplacian of the Gaussian filter, yet you'll find not a single symbol being manipulated in an equation there. Those circuits use hard-wired lateral inhibition and excitation to produce the effect of the LOG filter. One can represent that operation, or the differentiation performed by other neural circuits, in symbolic form and do calculations, but it does not follow that the neural structures themselves perform calculations in the same way. One must be wary of conflating a model with the reality it abstracts from and represents for analytic purposes.
RBH
[ 11. March 2004, 00:16: Message edited by: RBH ]
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warren_bergerson
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Member # 262
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posted 11. March 2004 07:24
RBH,
I am sure there are many ways of interpreting this issue, but in set theoretic mathematics a function is defined as a set of ordered pairs where each member of the set defines or identifies the value of the range (set of output values) associated with a specific value of the domain (set of input values). In terms of set theoretic concepts, the technique or process by which output values are calculated from input values is not relevant. Using set theoretic concepts, a system can be said to calculate a function if given specific input or domain values it can generate the appropriate output or range values.
Using this interpretation, Jackie Robinson did perform complex calculus calculations. As Evan points out, we do actually know what process your brain is actually using when you perform a calculus calculation.
The informal point here is that 1)we can at least informally define a general class of mathematical functions which we label goal directed or teleological functions, 2)we can write computer programs (formal mathematics) which perform or calculate values for some such functions, 3)humans can perform such calculations ‘in their heads’ and finally 4)in at least some settings, these algorithms can predict behavior with a degree of reliability.
One of the problems in the study of behavior is identifying predictive theories or laws governing behavior. If you are to develop a predictive theory of behavior, two of the criteria you need to satisfy are 1)identify a predictive algorithm and 2)generate reliable predictions. The purpose of this thread is to make the observation that goal directed algorithms appear to satisfy both these criteria.
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Evan
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Member # 164
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posted 11. March 2004 08:07
Warren writes, "As Evan points out, we do actually know what process your brain is actually using when you perform a calculus calculation."
I didn't say this at all. Did you mean to write that we "actually do not know what process ...", because that would be my position.
As RBH points out, the fact that we can model something mathematically does not at all imply that the object being modeled “knows” and employs that mathematics in its behavior. Diffusion across a cell membrane proceeds according to the saturation model formula y = y(0) (1 - e^rt) (which I just finished teaching in calculus class), but it would not be reasonable to assert that the molecules involved use calculus in order to decide how fast to diffuse.
There is an ambiguity about the concept of function that students must be explicitly taught. THis ambiguity can lead to confusion, as is illustrated by Warren when he writes,
quote:
In terms of set theoretic concepts, the technique or process by which output values are calculated from input values is not relevant. Using set theoretic concepts, a system can be said to calculate a function if given specific input or domain values it can generate the appropriate output or range values.
The confusion is this: the word “function” can refer to either the output value y corresponding to the input values x, or it can refer to the process that produces those values. In the latter case, the function can be a “black box” - the process by which the output value is produced can be totally unknown even though the functional output value is known.
For instance, when teaching trig, we start by drawing a whole bunch of right triangles with the same acute angle, measuring the sides, and then calculating the various ratios. From this, I demonstrate to the students that those ratios are constant for any angle.
Then I show them how to push buttons on their calculator - presto, the same numbers they reached experimentally by drawing pictures are produced by the calculator.
Now how does that work? What process (function in the second sense) does the calculator use to produce the proper value (function in the first sense)? I tell them that when they push buttons, a bunch of little bitty people in the calculator quickly draw a bunch of pictures, measure the sides in nanometers, and then report the average of their calculations, but the students don’t believe me.
So as far as the students are concerned, the calculator is a “black box” - the process by which the trig ratios are calculated are a completely mystery to them. Of course, later in calculus I teach them how this is really done mathematically via the series expansions for the trig functions, but even then the electronics responsible for those calculations are mysterious.
So, back to Warren’s statement, just because two processes produce the same output (functional value) doesn’t mean they used the same functional process to reach that value. Just because we can model a situation mathematically doesn’t mean that the situation in question used and employed that mathematics in manifesting its behavior.
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