SCIENCE AS A COLLECTION OF ANSATZES OF HOMOLOGIES WITH FIGURE&GROUND CORRECTIONS

Many English-writing physicists have imported the word "Ansatz" from the German language to mean, roughly, "Let's assume that things are like this, or work like this -- to see what this buys us". (For example, "Let's assume that 'what's out there' can be described as 3-D-in-space and 1-D-in-time -- and see what this buys us." This is like the old "Madison Avenue" line, "Let's run it up the flagpole and see who salutes it.")

I extend "ansatz" to all science to conform with my notion of "The ACTIVITHM" (described on this site), arguing that knowledge does not come without "sticking your neck out". You

  1. impose a PATTERN upon the SYSTEM you're confronting;

  2. search for SUBPATTERNS of this PATTERN;

  3. if these SUBPATTERNS are found, see if these SUBPATTERNS remain INVARIANT UNDER SOME TRANSFORMATION;

  4. if so, define the given SYSTEM in terms of the mathematical GROUP OF TRANSFORMATIONS which this TRANSFORMATION induces.

(I conceived the ACTIVITHM concept in 1961 -- long before I realized the generality of "Ansatz" -- while developing one of my "mathtivities" for kids, which I labeled "Colored Multiplication Patterns -- Colored Conservation Laws".)

I propose that SCIENCE IS A COLLECTION OF ANSATZES.

Unlike assertions by ALTERNATIVE SCIENCE advocates as well as those of religionists who bypass science, my thesis of SCIENCE-AS-ANSATZES DISCONNECTS SCIENCE from DOGMAS, which are declared UNCONDITIONALLY. (I also advocate DISCONNECTING SCIENCE FROM DOGMA by my discussion of "S-SCIENCE VERSUS D-SCIENCE", where "S-SCIENCE" is "Science articulated as STATEMENTS IN THE SUBJUNCTIVE MOOD, as in, 'If this were the case in the Universe, then ....'", and "D-SCIENCE" is "Science articulated as STATEMENTS IN THE DECLARATIVE MOOD, as in 'Since this is the case in the Universe, then ....'".)

And, unlike the typical PHILOSOPHY OF SCIENCE, my treatment of SCIENCE AS ANSATZES can DISCONNECT a critical stage of SCIENCE from facts, in the sense "It's a fact that sitting on a pinpoint hurts." (Thus, pricking of a pin is not an assumption, but SPACE-TIME is.)

Ok. What's the unique PATTERN of a SCIENCE-ANSATZ?

I declare it to be AN ANSATZ OF HOMOLOGIES. And this -- as I'll explain -- DISCONNECTS SCIENCE even MORE from DOGMA and FACT.

As shown in my associated HOMOLOGY TABLE, the form of homology invoked is a statement about the SIMILARITY of the ELEMENT-TO-ELEMENT (or PART-TO-SYSTEM) RELATION for one case to the ELEMENT-TO-ELEMENT (PART-TO-SYSTEM) RELATION for another case. (Example: Fresnel lens compares to convex lens as ramp compares to stairs. In notation, Fresnel lens : convex lens :: ramp : stairs. Again, leg : human :: wheel : vehicle.)

(Please note that the biologist distinguishes the relation of HOMOLOGY from the relation of ANALOGY.)

The homology I suggest for the scientific ansatz is this: model-part M(A) is to model-part M(B) as reality-experience R(A) is to reality-experience R(B), that is, M(A) : M(B) :: R(A) : R(B).

To take a case better fitting our purpose than those in that table, "The bear track in my mental imagery -- M(A) -- is to my image of a bear -- M(B) -- as the ground-track I see -- R(A) -- is to the bear -- R(B) -- that left the track". Even if I find a bear down the trail, I cannot prove that the found bear left "this" track. But it seems plausible.

Please note that we encounter thousands of these homologies every day. So the homologies of science are not different in form from our daily experience -- only different in content.

And this leads to important distinctions between the forms of our experience -- whether CONCRETION or ABSTRACTION or ILLATION (from the Latin "to infer").

So, I think it's important to say that science deals with ansatzes, not dogmas, and not pin-sticking-facts. And that any ansatz deals only with one or more homologies, claiming RELATIONS, NOT ABSOLUTES.

But what is the role of FIGURE&GROUND in SCIENCE-AS-ANSATZ? A MODEL or HYPOTHESIS (or, here, an ANSATZ) can be placed as FIGURE against the GROUND-OF-REALITY. If the MODEL/HYPOTHESIS/ANSATZ explained or predicted REALITY, then FIGURE WOULD MATCH GROUND, as in matching of two congruent geometric structures. But FIGURE-NOT-MATCHING-GROUND homologizes FAILURE-TO-EXPLAIN-OR-PREDICT-REALITY.

In particular, where GROUND STARTS TO SHOW UP BEYOND FIGURE resides the CRITICAL REGION WHICH, SLIGHTLY CORRECTED, MIGHT BE ABSORBED INTO FIGURE -- homologizing wherein MODEL/HYPOTHESIS/ANSATZ might be CORRECTED for EXTENSION -- a process furthered by means of other HOMOLOGIES.

Hence, SCIENCE AS ANSATZES OF FIGURE&GROUND-CORRECTED HOMOLOGIES.

And I further argue that what science is transforms to what scientists claim science to be as a transformation from the SUBJUNCTIVE mode of speech to the INDICATIVE mode of speech. Invoking another homology.

SCIENCE IS : SCIENCE CLAIMED :: SUBJUNCTIVE : INDICATIVE.

And I argue that my model INDUCES CONNECTIONS not hitherto involved.

The quantum theorist and 1963 Nobel laureate, Eugene Wigner, is often quoted as being amazed at the "unreasonable effectiveness of mathematics in the natural sciences", saying also, "This unreasonable effectiveness is a wonderful gift which we neither understand nor deserve."

I propose an "ANSATZ ABOUT THE EFFECTIVENESS OF MATHEMATICS IN THE NATURAL SCIENCES". If you'll help me investigate it, WIN-WIN! If it explains a lot which has been unexplained, we WIN. If it leads to positive results previously unknown, BIG WIN. If it disabuses us of ideas about this particular ANSATZ or other ansatzes, that's also WIN.