notes: on cognition and computation; conceptual accessibility; and a formal approach to metaphorical analysis 1

metaphor

too much time and effort is spent arguing the merits and pitfalls of individual metaphors, when the root cause – a failure to adequately define and formalise ‘metaphorical-analysis’ – remains unaddressed

Undoubtedly, metaphor is innate to human experience, and cognition.

‘There is something that it is’ to intuitively perceive and consider universal phenomena by metaphor – to consider one kind of universal phenomenon in terms of the characteristics of another almost-entirely different kind of phenomenon 2.

–how can that be?

–what do metaphors tell us about cognition? 3

–what might metaphors tell us about universal phenomena? 4

Equally, ’there is also something that it is’ to insufficiently define :

  1. What it is to perceive and consider by metaphor – what it means to do so, and perplexingly;
  2. How to set about it, in an ‘as objective and volitional manner as possible’ 5

The result, is that almost any conversational use of metaphor (particularly conversations where explicit specificity is valued: scientific discourse, for example) can quickly become distracted, then immersed, in ’the wrong stuff’

such as the case of the metaphor of ‘cognition as computation’

actualmetaphormetaphormetaphorthingthingnot the actual metaphorcommon subset of concernsmetaphorthingset-of-all concernsset-of-all concerns

figure 1: metaphor

—what might be done?

metaphorical analysis

—what do we even mean?

Consider some phenomena B, as metaphor C.

When we consider phenomena B, as metaphor C :

  1. We aren’t saying B is literally C; or that B and C are absolutely the same
  2. We are saying some part of B and C is the same; that B and C relate by some partial, fractional equivalence

Given two sets-of-all circumstances: some elements of both B and C are included – are equivalent; and some elements of B and C are not.

CBset-of-all concernsset-of-all concernsCBset-of-all concernsset-of-all concernsCBACBACBsubset-of-common concernsCB

figure 2: metaphorical analysis

The above case and figure makes clear – we don’t need to know which elements specifically are included in our metaphor, to recognise that some elements aren’t; so arguing against a metaphor by the fact some elements don’t apply, is problematic - we ought to expect it.

—how do we minimise the chance of focusing on ’the wrong stuff’?

—how might we define which elements are included?

analytical refinement

same but different

Curiously, this same pattern can be used to interrogate phenomenal composition in several ways (see the pattern below): consider ‘general-special’

CCCCBBBBsubset-of-common concernsCBset-of-all concernsset-of-all concernsset-of-all concernsCBset-of-all concernsset-of-all concernsset-of-all concernsCCBBCCCCCCCCBBfractional accounti ii iii iv v vi BBAACCAAAACBACBACBsubset-of-common concernsCBAAAAthemanual.iothemanual.ioAAAAinheritisolatevii universal phenomenaCCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAspecificityabstractioncommonesotericnavigationdirectionCCBBAAancestor descendent relationancestordescendentinherit potentialconstraints propagatetimeviiiAAAAAAAAcommonalitydistortionunifiedcontinuousisolateddiscontinuousfractional accountingBCCCunifiedde-duplicatedcontinuousCCCCBBBCCCCCCCisolatedplurally enumerateddiscontinuousAAAAAAAAAAAAAAAAAAAAAAAAactual metaphorthingmetaphorsets-of-all concernsset-of-common concernsthingmetaphornot the actual metaphorgeneralisationBCsets-of-all concernsset-of-common concernsBCdistinctiongeneralisationmetaphorcontextually, objectively, similar entry-point to common constituentcontextually, objectively, dissimilar entry-point to common constituentcontinuousdiscontinuousbcdefgeneral special distinctiongeneral-casespecial-casegeneralised termjargongeneralisationspecialisationpatterndomainlanguagesimplifyambiguitycontextcomplicatetrunkbranchconstraintconstrainedCCCCBBBBAAAAainterfaceimplementationrelation

figure 3: the pattern

–how does this relate to cognition and computation?

what is a computer?

on seeing past distractions

What is a computer?

  1. The origin of the term was a person who performed computations
  2. We commonly use the term to refer to electronic silicon devices, which also perform computations
  3. $\ldots$

Consider 1 (a person who performed computations) and 2 (electronic silicon devices, which perform computations) as two special-cases of computer (noting that: there are more kinds, and we might expect more in the future)

Consider each (1, 2) as a set-theoretic set-of-all-respective-circumstances (B, C: figure 4), with intersect (A: figure 4). The intersection includes all that is common – the relative general-case – between both special-cases.

remember: we don’t need to know what is common, to know that some elements aren’t common; so we ought to be cautious when framing arguments by elements which aren’t {possibly; probably; demonstrably} common, at least

  1. This kind of (set-theoretic) analysis is such that the intersect between two arbitrary special-cases is always smaller than both, individually ($[\;|A| < |B|\;], [\;|A| < |C|\;]$: figure 4)
  2. Further, if we imagine a hypothetical set-of-all computers, whereby each computer is represented by a set-of-all respective circumstances (of each special-case), we might rightly imagine the intersect (E: figure 4) between all – the ’essential general-case’ – is smaller still ($|E| < |A|$: figure 4); its’ elements simpler, and more abstract, than the material implementation of {each; any} special-case
name

figure 4: essential general case

This ’essential general-case’ – the resultant set of the intersect between all kinds of computer (with simpler, more abstract elements than any material implementation individually) – is a good approximation for our computer metaphor (sufficiently-equivalent for this example), and importantly, more explicitly frames the importance of ignoring special-case details from the metaphor itself.

extra note: typo $|A|<|E|$ corrected to $|E|<|A|$ 🤦🏻‍♂️

going deeper

—what came before x, and how do we think of x in those terms?

figure stack analysis #todo

  • phenomenal decomposition (down)
  • compositional reframing (up)

working results, for brevity

Essence :

  1. Space-of-all-potential {container; substrate; alignment; composition}
    1. Conditionality {constraint; finiteness; sufficiency}
    2. Relativity {proximity; sequence; structure; scope}
    3. Mutation {increment; change; behaviour}
  2. Phenomenal {temporal; compositional} evaluation upon intersection; continuation

Substance {energy; matter} :

  1. Intersection
  2. Cumulative intersection
  3. Persisted cumulative intersection
    1. Scope: {intrinsic; extrinsic}
      1. {Temporal; compositional} reference frame
    2. Cycle {intrinsic: continuability; extrinsic: side-effect, catalyst, replicator} 6

Biology {replication; encapsulation; autonomy; etc} :

#todo i’ll fill in details here following contact/ feedback

definitions

defining cognition and computation in terms of what came before (a sketch)

When we look past the phenomenal, contextual differences between each special-case of computation (from present silicone etc, through people, to ‘what came before’), and consider the underlying essential commonality (the set-theoretic intersect of each set-of-all-respective-circumstances), we might arrive at the following description of one aspect of the computation cognition metaphor.

computation

  1. Computation is conditional evaluation of conditions; a computer conditionally evaluates conditions
  2. A system (is) {conditionally continuable} {conditional sequence; conditional sequencer; conditionally sequences}
    1. Conditional continuability includes {period/ cycle interrupt; output -> input}
    2. Parallelisation is asynchronous high-dimensional sequencing
  3. A computer system (is) {conditionally continuable} {conditional evaluation of arbitrarily dimensional condition-sequences}

or thereabouts – this description is aspectual, and extendable; extended by other fundamental mechanisms, cycles, cache, scope, etc

cognition as computation

  1. A neurone is a condition (chemical gradient/ threshold)
    1. Plural neurones are compound conditions
  2. Cognition conditionally evaluates conditions
    1. Cognition includes environmentally asynchronous arbitrarily-dimensional sequential evaluation
  3. Stimulus organism response is conditionally continuable, conditional response

#tbc i have much much more here, but i’m looking to air this framing of metaphorical-analysis at this time. please contact for more

More to the point, this description of cognition is composed by phenomenal mechanics common across universal {scale/ level/ scope}, including relative phenomenal priors; and so we might say that this aspect of cognition is (circumstantially) inevitable – it requires no leap of universal or evolutionary capability. It is, like all phenomena, composed and composable, so extensible; in the way that distinct perspectives of the same physical phenomenon are composed and extensible, so composable, together.

that there is more to say about cognition than this one aspect, does not render this aspect invalid anymore than one of any arbitrarily-plural valid perspectives of the same physical phenomenon might render the others invalid

What is important, is that legitimate {aspects; perspectives} relate and reconcile together – we ought to expect to compose our understandings in this manner

so the final point, i suppose: is that this essential general-case is the very essence not just of implementation-agnostic comprehension, cognition and computation, but of life, and the universe itself

  1. separately, if the origin of the term computer is a person, how does computation not relate to cognition?! 🤓 ↩︎

  2. Though not quite ↩︎

  3. and maps ↩︎

  4. and territory ↩︎

  5. {Formal; grounded; ‘high-dimensionally coherent’} ↩︎

  6. Maps to {function; category-theory; fourier; turing; etc} ↩︎