MATHEMATICS AND BRAINS AS MAPPERS (PATTERNERS)

Before explaining the title, I propose a WIN-WIN hypothesis about another "mapper": COGNITIVE PSYCHOLOGY (CP) OFFERS THE BEST CURRENT MODEL OF "BRAIN EVENTS".

The CP model (to date) shows considerable explanatory power, which is an internal property; but, primarily, I value the CP model for two external properties:

  1. THE COGNITIVE THESIS ALLOWS THE MOST ARTICULATE CLAIMS AND DESCRIPTIONS OF ANY MODEL I KNOW OF.
  2. THESE CLAIMS AND DESCRIPTIONS CAN BE FORMULATED FOR TESTING BY THE NEW TOOL OF MAGNETOENCEPHALOGRAPHY (M.E.G.) (anon!).

These two properties make WIN-WIN any CP-hypothesis I propose. If critics answer ARTICULATE claims for a CP-hypothesis by ARTICULATE counterclaims, we can learn something, no matter "who wins the claim game". Furthermore, a good test (for results "positive" or "negative") is always revealing.

Approximating the CP thesis: THE BRAIN MAKES MAPS (ICONIC PATTERNS) OF REALITY TO GUIDE OUR BEHAVIOR.

This is suggested in a "classic" 1983 experiment on rats and in other experiments cited below.. (If you disagree with the interpretation of this experiment, please articulate your counterclaims.)

Given your understanding of the description of this experiment (and perhaps the others), I'll appeal to this understanding to explain how some cognitive hypotheses (CHs) can be tested. But, first, an explanation (as promised above) of MAGNETOENCEPHALOGRAPHY (M.E.G.).

(from p. 351, The Frontiers of Complexity, The Search for Order in a Chaotic World, 1995, by Peter Coveney and Roger Highfield) "The [M.E.G.] measurement relies on the rapidly changing magnetic field generated by the electrical activity within the conscious brain. Called magnetoencephalography, or MEG [to be compared with the long used but limited, electroencephalography or EEG], the method was first demonstrated in 1968 when David Cohen at the Massachusetts of Technology showed that it was possible to record magnetic signals generated when currents flow in the brain. The technique avoids the principal problem of using EEG, which is the blurring of electrical signals due to intervening tissue. Magnetic fields pass through nonmagnetic materials such as brains without any distortion, enabling us to monitor rapid changes in neural activity to within a millisecond."

In a description of M.E.G. operations, this "reality-mapping" facility of the brain seems revealed in brain-scannings. ( As one researcher remarks, in Coveney & Highfield, "It is absolutely astounding .... We can see the brain working in real time.") But, in this case, a nonhypocampal mapping locale was found: "... a part of the brain that is involved in forming a mental picture or map, [is] situated in the fissure between the parietal and occipital lobes. This region of the brain was revealed [by scannings] when subjects were asked to imagine navigating through their own homes." (Questions: Is the mapping locale different in rats and humans? Or can the parietal-ocipital locale be confirmed in rats also? Can rats be fitted with microchips which telesignal brain activity?)

Both the rat experiment and the human-mental-navigation experiment seem to confirm the CH. Let's formulate CH-based experiments for both types.

For the rat type, I can presently sketch two types of experiment. Both use my asserbility measure, which I discuss in detail elsewhere (and is easily explained by a homology: asserbility measure: statements:: probability measure: events).

The simplest tentative formulation of its logical structure is:

  1. "If hypothesis H is the case, then prediction P is the case;
  2. prediction P is confirmed;
  3. then hypothesis H is 'confirmed'."
That is, "If H, then P; P; then H."

Stated thus, the form is tautologically "invalid" (not true by form). This form is usually known by the misleading label, "fallacy of asserting the consequent" (FAC), as in the last clause. But we change "H is confirmed" to read "H is magnified", meaning that the asserbility measure deriving form H increases above a "base-line" of 1/2 to 7/8.

To see what, in general, happens, let's specify "H" and "P", and imagine repetitions of the experiment.

Let H become a specialization of CH: THE RAT'S BRAIN CREATED A FIRST-TRIAL MAP OF THE LOCATION OF THE TANK-TOWER. And let P become: THE RAT SWIMS DIRECTLY TO THE TOWER AND CLAMBERS ON IT. Given this formulation of "If H then P; P confirmed; then H", the asserbility measure A changes,A: 1/2 -> 7/8.

(Formula: In general, for i hypotheses and j confirmed predictions, A = 1 - 1/2(sup i) + 1 + 1/2(sup(i+j)).)

Now, imagine using another rat, with the argument becoming, "If H, then P1 & P2; P1 & P2; then H" -- meaning "both rats DO IT"; then A:1/2 -> 7/8 -> 15/16. In general, if n rats "won our bets", A becomes (2-to-nth power - 1)/(2-to-nth power).

Obviously, as n increases, FAC approaches the asserbility (A = 1) of a valid conclusion (say, for logic aficionados, modus ponens). Such results for this type of experiment would gain considerable credibility for CH.

In the second type of experiment, I suppose that a microchip rmbedded in the rat can signal to a scanner. The essential prediction, P, here is: RAT-NAVIGATION-SCAN MATCHES (LIKE-PATTERNS) -- by approrpriate modification -- HUMAN-SCAN. (Or you improve the hypothesis.) I assume you can see how to formulate this in asserbility terms.

So I turn now to my formulation of COGNITIVE HYPOTHESES (CHs) regarding ancient problems -- and how they might be M.E.G.-tested. Problems:

Can the Plato-Scholastic universals recognition process be CH-explained as a neurological limit-sequence process?