1. Biology Similarity in form, as in organisms of different ancestry.2. Mathematics A one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.3. A close similarity in the crystalline structure of two or more substances of similar chemical composition.
“Homology, then, is the relation between abstract objects (descriptions, or representations of real world objects) where the formal description allows a mapping function between them.”
“Analogous relations are still a kind of isomorphism, but the mapping is not between sets of objects, but between the form of the objects themselves”
“If I discover that Raptor X has enzyme E, then I can infer that all other members of the Raptor group have E as well! That’s an enormous amount of inductive warrant. Interestingly, if I tell you that a raptor is a predator, you cannot infer that all raptors are (some are scavengers). Homology does not license analogical claims. But it may bracket them, as I will later argue. We can summarize the difference here by saying that classifications by homology are inductively projectible, while classifications by analogy are deductive only. Moreover, analogies are generally model-based. The choice of what properties to represent usually depend upon some set of “pertinent” properties, and this is not derived from an ignorance of what matters, or some unobtainable theory-neutrality. In order to measure similarity, you need to know what counts.”
Anamorphic drawings are distorted pictures requiring the viewer to use a special, often reflective device to reconstitute the image.
-phore: Bearer or carrier of.
Euphoria: An excited state of joy, a good feeling, a state of intense happiness.
- A figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable.
- A thing regarded as representative or symbolic of something else, esp. something abstract.
anaphor: 1. a word (such as a pronoun) used to avoid repetition; the referent of an anaphor is determined by its antecedent. 2. An expression refering to another expression. In stricter uses, an expression referring to something earlier in the discourse or, even more strictly, only reflexive and reciprocal pronouns.
The difference between morphic (shape) and phoric (carrier) is a good way of grabbing on to the essential difference between public and private phenomena. Metaphors or other ‘figures of speech’ can have a wide gap between one reference and another. Similarity, as the blog quoted above mentions, is notoriously hard to pin down. The author mentions “Hamming Distance, Edge Number and Tversky Similarity” but these approaches to defining similarity rely on lower level methods of pattern recognition. In all cases, similarity requires some capacity to detect, compare, discern criteria from the comparison, and cause an action which can be detected publicly. In other words, similarity requires that something can generate sensory-motive participation.
The infocentric definitions of similarity do not adequately address the private sense of similarity at all, rather they confine the consequences of theoretical object interactions to demonstrable sets of criteria. Edge number does not apply to something such as whether a feeling is like another feeling or not. To me all of this really highlights the bias of the Western approach of reducing science to the taxonomy of rigid public bodies. The experience even of fluid, gaseous, or plasma phenomena are virtually inaccessible unless reduced to a microcosmic level at which only rigid object properties are considered and all smoothness is abstracted into ‘emergent properties’.
This relates back to the analog and mathematics. If we look at a basic arithmetic operation like 4 x 5 = 20, and get beneath the surface, I think what we might find something like “If four things were just like one thing, then five of those four-ish things would be just like ten two-ish things, or two ten-ish things, which would be one twenty-ish thing”. In a previous post, I got into ratio as the root of reason, and how the radius can be adjusted between tighter and looser rationality. How figurative do you want to get is the question which determines how universal, public, and ‘Western-scientific’ you want to get. Quantitative analysis of course, is the ultimate rationalization, the ultimate reduction of ‘just like’ to ‘exactly the same as’. The ‘=’ condenses all subjectivity into a single semaphore, a flag which refers to precise equivalence, or absolute universal similarity. Similar in all ways that count. What counts is presumed in advance by the Western mind, to be reliable public function, aka objective realism.
Numbers therefore, could be called isophors. Carriers of one to one correspondence. The caliper of the drafting compass of reason is set to minimum tolerance – to the point of points; digital-Boolean logic. At this point, even geometry is superfluous, and computation is revealed to be a spaceless function of connection and disconnection. Whether electronic or mechanical, computers are based on contact and detection first and foremost. Contact (a connection of ranged position) influences physical change (thermodynamic disposition). Despite the assumptions of both AI and QM, I am confident that this is a property of matter, not of vacuum space or ‘information’.
Moving from numbers to geometry and algebra is a matter of making isophors into meta-isophors. We understand that just as a twenty is four fives or five fours, or two tens, so does any number enumerating itself twice is a square, and a squared hypotenuse relates to the square of the sides of a triangle as the squared radius of a circle times pi is its area. The transfer of integers into variables is a squaring of the isomorphic function, making all of mathematics a psychological model of modeling itself. It is no surprise then, that at this point of maximum Western influence over science, we should mistake our own concretely physical experiences of conscious life for a ‘model’ and the world in which we live for a Matrix.
Of course, when all of the logical analysis and quantitative analogs are stripped away, it is only the morphic, the phoric, and the sense to tell the difference which are genuinely real. Logic is not the isophor of sense however, or even a homophor. I would say that maybe logic is the public facing hemisphor of sense. It is the half of sense which can be generalized externally.