Thursday, February 11, 2010

On proof, models, theories, math and morons

As pointed out in 'The Atheist Dilemma' (Part 1, 2) the atheist must wage an incessant rearguard action against the armies of ignorance which now appear to outnumber the cognoscenti by 10 to one or more. As much as we try to impart critical knowledge about basic facts to do with the scientific or empirical process, there are dozens who actively seek to obscure it. Part of this ability to obscure is not due to any inherent substance they bring to the issue, but because computer and the internet now permit even the ignorant to search at will by googling and make it appear as if they know something - when they don't know squat.

Some of these deliberately confuse proof with evidence (just as I noted in my earlier blog piece how opinion is taken for evidence) and also models with theories, and mathematical techniques with empirical methods. All of this is done to browbeat even more ignorant followers into thinking their "guru" knows what he's talking about.

But let's look deeper, beginning with what we mean by "proof".

First, in the strict scientific sense, we don't mean using the same methods as mathematicians- say to prove the Pythagorean theorem! As anyone who does scientific research knows, it is quite impossible to "prove" a particular solution to a scientific problem to be "true" (that is, true for all times and conditions). Solutions of scientific problems are instead assessed for adequacy, that is, in respect to the extent to which the researcher's stated aims have been carried out.

Two categories of criteria are those related to argument and to the evidence presented. To judge adequacy then, we look for the strength and consistency of logical/mathematical arguments, and the goodness of fit of the data in a given context. By "goodness of fit" I mean that two different datasets on comparison are either strongly correlated or anti-correlated. As an example, the rate of growth of tree rings is strongly correlated to the level of activity of a particular sunspot cycle. There is agreement and an excellent "goodness of fit".

All such determinations of adequacy perform the same function for scientific research that quality control does for industry. Most importantly, no determination of adequacy can be rendered until and unless the research is published in a refereed journal. If I am asked to invest mental and emotional energy in some extraordinary (e.g. “supernatural”) claim or other, then what exactly are the rational criteria of adequacy by which I can judge that claim?

Can it be set against original and actual scientific hypotheses? Can it admit the basis of numerous empirical tests- and moreover- can it be susceptible to any form of prediction?

If the answer is ‘No’, then we cannot place it into any scientific context. It will then have to be admitted that “faith” be enjoined to embrace or accept it, since no scientific rationale will permit true scientific inquiry. Since there are no genuine objects of scientific inquiry.

Of course, different theories of science represent different levels of abstraction: quantum theory is at a higher level than general relativity, and general relativity is at a higher level than Newton's theory of gravitation. But-- and here is the key point-- the limits of validity for each theory are ultimately founded in measurements, specifically through careful experiments carried out to test predictions.

It is this testing of reality which provides a coherent basis for scientific claims, and which bestows on science a legitimacy founded in reality rather than wish fulfillment fantasies. This is a basis, moreover, for which theological claims have no counterpart, despite that fact that theologians have often tried to make their claims sound like proven theories.

Let's use an example to illustrate: Which theory, Brans-Dicke or Einstein's General theory - predicts the solar oblation better in order to decide the superior theory of gravity?

Each begins with a hypothesis (call it 'X'), that: "If the solar oblation is less than +/- (x) then Einstein's theory is the default." (Note the oblation is the ratio of the solar polar to equatorial diameter)

As I noted the process earlier:

You have preliminary information (say from earlier research efforts) that leads to some hypothesis 'X'. You then continue the process, gathering more data, and accessory information which leads to some predictive result which tests a particular hypothesis- call it:

X' = x (n+1) = x + P(x)

where x(n +1) denotes an improvement via iteration, with P(x) the predictive confirmation (of x(n +1) from x) that allows it. Later, more refined data become available, such that:

x(n + 2) = x(n + 1) + P'(x + 1)

and so on, and so on and so forth.

Here, P'(x + 1) denotes the most recent and enhanced measurement of the oblateness.

Now, what if at these stage of testing we have:

x(n + 2) = x(n + 1) + P'(x + 1) + E(x + 1)

where E(x + 1) is an ERROR term.

In this process of falsification either one of two things will be true:

E(x+ 1) > > P'(x + 1) (call this E(e'))

I.e. the magnitude of the error term is drastically larger than the prediction value.


E(x+ 1) < < P'(x + 1) (call this E(e"))

I.e. the magnitude of the error term is drastically smaller than the predicted value.

Brans-Dicke theory then only trumps Einstein's if the relative error magnitudes are such that:

[E(e') + E{e")]/2 < e[P' (x + 1)]

where e[P' (x + 1)] is the error associated with Einstein's prediction.

It is for reasons like this that we need mathematics to show what is going on. We do not require mathematics to "baffle" anyone or to "win arguments" since"all logical efforts etc. have failed" etc.. Hardly! All that's happened is that sundry people, pastors, fundies are too stupid to process them - when the arguments clearly follow a logical trajectory. These morons wouldn't get the arguments if they were signed, sealed and uniformly delivered in single syllables - never mind the math (which they are clearly too innumerate to grasp).

The other role of mathematics is to describe the theory or hypothesis behind a model so it can be quantified in ways that enable measurements. Words alone are inadequate to the task. For example, the hypothesis that certain solar flares are triggered by "double layers" opens itself to test (or falsification) if one realizes that a loss cone is typically associated with a double layer. We define what's called the “loss cone angle”:

sin (THETA)_L = ± [B_min/ B_max]^1/2

where B_min is the minimum magnetic field strength or induction at the apex, say, of a loop magnetic mirror system. Then B_max represents the maximum value, usually at the loop ends or "foot points" as they are called. A special condition obtains which applies to the angle - for which the electrons will be TRAPPED, provided:

THETA (min) > (THETA)_L

Thus, THETA (min) = (THETA)_L

is said to be the "loss cone" of the system or machine.Now, the criterion for the hydrodynamic loss cone instability requires that the particular condition for the ratio of untrapped to trapped particles:

n/ n_o > 2 OMEGA e / (pi) w_p = 0.1

where OMEGA_e is the electron cyclotron frequency, and w_p is the electron plasma frequency.If such a condition were to apply, say to a solar coronal loop, it could elicit an "inverse population" in the transverse velocities (e.g. v_perp) for electrons in the loop. If the loss cone instability specified by the preceding condition then occurs in electrostatic waves near the upper hybrid frequency, we can get an anisotropic distribution of the electrons in velocity space. This can give rise to an electron particle beam.More importantly, energy to support the beam - and perhaps trigger a flare.

Now, it is important to note that neither Einstein's general theory or Brans-Dicke's are MODELS. A model is not a theory, but (generally) a mathematically described translation of what a hypothesis ought to look like in the real world. For example, Figure 1 depicts the model for a sunspot in which dynamo action by a Hall electric field generated the rotary motion and outward current density.

At this stage NO predictions have been made based on the model! It is up to the model proposer to put it in a form which can allow test, say maybe by showing how the rotary velocity (around the periphery) can be measured and how large it must be to attain the objective, e.g. of a large current density (J) directed outwards.

Now, in terms of evolution, it is not a "model" but a full theory since it has already met a number of its predictions and passed them, as well as other tests for falsification. For example, the theory of evolution as it applies to the elements of common descent, predicts humans and chimpanzees ought to have very nearly the same cytochrome-c protein sequence. This has been found to be the case. It also predicts that the two ape chromosomes designated 2p and 2q ought to be fused in the human to be one: designated '2'.

The theory of evolution has also predicted the full evolutionary development of foraminfera and this is validated. Finally, it predicts that a species - say the German cockroach - subjected to a mutagen like deildrin, will acquire resistance and thereby increase its fitness to the level that it effectively becomes a new, resistant species. (See chart in Fig. 2 showing how the successive generations of fitness are tabulated)

We note here that two quantitative measures for success of natural selection are the fitness (w) and the selective value (s): These can be measured on either absolute or relative scales, but are related algebraically on the latter by:

w = 1 – s, or

s = 1 – w

In natural selection there is a genetic "favoritism", as it were, for certain species' traits or characteristics to be passed on or selected out of a group of competing traits in the gene pool. In more technical terms, preferential alleles[1] appear by virtue of their relative increase in gene frequency. In the case of this cockroach, the favored genotype is DD, the less favored are Dd, and dd. The table shows how DD outpaces dd and Dd in fitness and hence how natural selection works.

What natural selection does is to consolidate and direct particular random mutations into a more stable, adaptative adjustment. This is exactly what was illustrated above in the case of the hypothetical cockroach resistance to dieldrin. Without natural selection, very few living organisms could persist over time as recognizable species.

The exceptionally rapid development of the neocortex in Man is also an example of natural selection. By implication, human survival, in competition with large carnivores, was favored by the preferential development of the neocortex. This development permitted abstract conceptualization, enabling weapons to be fashioned as well as sophisticated language for communication and communal organization against larger predators.

As for "proving" or "disproving" God - no scientists in his right mind claims any such thing. The point eluding ardent fundies given to confusing their followers (more than enlightening them) is that science cannot possibly refute “divine existence” because it cannot hold it as a legitimate hypothesis in the first place.

Unless one can forge or articulate a working hypothesis, one can’t have “refutation”, now or ever. “Divine creation” can’t be a valid hypothesis since it is contingent on a putative non-physical agent - undetectable by any scientific means. Even the Big Bang’s relic radiation can be detected as the isotropic cosmic microwave background – but the same can’t be said for the “divine”.

So it's like trying to prove the existence of "XCMNMYTET".

This means that the Jewish concept of Yahweh (‘YHWH’) , the Muslim concept of Allah, the Hindu concept of Brahmin and the Christian concept of the Trinity all stand in the same conceptual relation. From an informational point of view, none can be selected as "true" to the exclusion of the others.

To put it another way, all god-concepts are ultimately relative *– depending entirely on which subjective tract or “sacred book” its adherents embrace.Is "God" based on the deist (“create it and leave it be”) model? The pantheist (“all is God”) model? The personal but "infinite" Christian model? The Christian Trinity? The Hindu impersonal model? Until this is resolved in a uniform, operational sense – skeptics and scientists are justified in taking any uses of the G-word with the proverbial grain of salt. Just like the subjective works of “revelation” (often re-translated, mistranslated and bowdlerized) that gave birth to them.

If religionists are going to spout on their blogs about science, and write about "models", "theories", proof, and mathematics - they at least owe it to their followers to get basic definitions correct. If they refuse to do that they only reveal themselves as non-serious clowns and morons. More invested in entertaining their minions than informing and educating them (never mind how well they copy and paste from Google!)

[1] By which I mean one of the more adaptive forms of a single gene, hence favored to multiply at greater rates in the gene pool.

* I do not include the Old Testament "creator" god (demiurgos) as a proper god-concept for reasons given in my comment following the blog 'Beyond Absolutism and Relativism'

1 comment:

Unknown said...

This is a terrific comprehensive piece on the differences pertaining to proof, evidence, models, theories and why math is needed to separate them all. However, if directed at your brother's idiocy it's likely a waste of time if you're trying to get him to see any of this.

He only sees what he wants to see, like the quotes he cherry picks from his Bible as well as how he interprets them.

If the Bible says Noah was swallowed by a whale, it was meant to be take absolutely literally. A real guy being swallowed by real whale.

But if his "6th commandment" says 'Thou shalt not kill" it really means 'Thou shalt not murder' so murder is separated from killing, meaning the state can kill criminals, and soldiers can kill other soldiers.

In other words, his elastic interpretation in this case enables him to escape being held accountable for his absolute morality since he has an escape hatch.

He's an idiot, and it's no use even trying to indirectly combat his foolishness. As Asimov once said, as I believe you once quoted him, you can never best an irrational ignoramus in debate because his wealth of irrationality will always exceed rational arguments (since logical limits are imposed on the last).

Ah well, if you saved even one vulnerable mind from his garbage I guess it was worth it.