User talk:Ancheta Wis/z

The expansion of scope of the new additions to the paragraph reflect a common viewpoint, which is that the facts involved are a matter of direct reflection or observation. This is OK, of course, when there is a recording method or other basis for the fact, such as a television camera, multiple witnesses, disinterested parties with a record of trained observation (such as a judge in a trial), journalist, etc. As Banno has pointed out, the solid grounding in facts has a philosophical limitation: the facts serve only to prove existence but do not suffice for the philosophical leap required for categorical statements like All X are Y or No W's are Z. Thus reproducibility is the unsung workhorse of the scientific method, involving definition as well as the observation of fact.

The definition of "scientific fact" in the intro therefore has some baggage. There has to be some theory behind it. When that fact is a detail in a larger mosaic, the fact, the underlying theory, the corroboration of some prediction, the error in the fact, the reputation of the scientist, the reliability of the experimental technology, the journal in which the fact was published, all come into play.

Later stances include physicist Lee Smolin's 2013 essay "There Is No Scientific Method"

While this schema outlines a typical hypothesis/testing method, many philosophers, historians, and sociologists of science, including Paul Feyerabend, claim that such descriptions of scientific method have little relation to the ways that science is actually practiced.

Constructive empiricism

phenomena and noumena https://askaphilosopher.org/2011/08/08/the-theory-of-phenomena-and-noumena/ :  Paul: Why do you think the problem of phenomena and noumena has baffled great philosophers up to today? Answer by Helier Robinson: The words phenomena and noumena are old fashioned words meaning the same as the modern theoretical and empirical. The empirical or phenomenal is known by the senses, and the theoretical or noumenal is known by the mind because it cannot be known through the senses, only evidence for it can be so known. The noumenal is invoked when trying to explain the phenomenal, by describing underlying causes. Explanation is causal: to describe causes is to explain their effects.

Testing
Tests of a hypothesis compare the expected values from the tests of that hypothesis with the actual results of those tests. Equivalently the difference between expected and the actual value (denoted the measured error in the hypothetical test) can be reported. Scientists (and other people) test their hypotheses by conducting experiments.

Brain–computer_interface

In the diagram, the System corresponds to the proposed explanation (the hypothetical explanation); the Controller corresponds to a published difference between the published prediction and the measured actual result — the adjunct infrastructure is the consumer of the published explanation; the Sensor corresponds to an instrument for the test; the Reference corresponds to the published prediction; the Measured output corresponds to the actual result of the test; the System input corresponds to the array of values which characterize the System.

Note that in the absence of error, the System is unperturbed, and operates in a stable way (negative feedback loop), as compared to a positive feedback system, which drives to the limiting values inherent in the System, and system operation can oscillate between limiting values. See Isaac Newton (1726) The System of the World    Symplectic integrator

The output of the system y(t) is fed back through a sensor measurement F to a comparison with the reference value r(t). The controller C then takes the error e (difference) between the reference and the output to change the inputs u to the system under control P. This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller.

This is called a single-input-single-output (SISO) control system; MIMO (i.e., Multi-Input-Multi-Output) systems, with more than one input/output, are common. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite-dimensional (typically functions).



If we assume the controller C, the plant P, and the sensor F are linear and time-invariant (i.e., elements of their transfer function C(s), P(s), and F(s) do not depend on time), the systems above can be analysed using the Laplace transform on the variables. This gives the following relations:


 * $$Y(s) = P(s) U(s)$$
 * $$U(s) = C(s) E(s)$$
 * $$E(s) = R(s) - F(s)Y(s).$$

Solving for Y(s) in terms of R(s) gives


 * $$Y(s) = \left( \frac{P(s)C(s)}{1 + P(s)C(s)F(s)} \right) R(s) = H(s)R(s).$$

The expression $$H(s) = \frac{P(s)C(s)}{1 + F(s)P(s)C(s)}$$ is referred to as the closed-loop transfer function of the system. The numerator is the forward (open-loop) gain from r to y, and the denominator is one plus the gain in going around the feedback loop, the so-called loop gain. If $$|P(s)C(s)| \gg 1$$, i.e., it has a large norm with each value of s, and if $$|F(s)| \approx 1$$, then Y(s) is approximately equal to R(s) and the output closely tracks the reference input.