Short Notes on Various Papers, 2023

Feb 14 2023 · LastMod: Mar 11 2023

2023-03-11 D. A. Lavis, The Concept of Probability in Statistical Mechanics

Logic/Theoretical CS

Weihrauch, Zhong, Is wave propagation computable or can wave computers beat the turing machine (2002)

2023-02-10

Weihrauch, K., & Zhong, N., Is wave propagation computable or can wave computers beat the turing machine? (2002) https://doi.org/10.1112/S0024611502013643) .

A cited paper showed that there exists some computable initial conditions for the 3d dimensional wave equation s.t. the unique solutions are not computable. The notion of computability here is that of Type-1 computability, the traditional one involving primitive recursive sets.

There is an extended notion of computability, called Type-2 computability, of which the details can be found in the nLab entry. The main result of the paper is that the wave propagation doesn’t seem to be able to beat the type-2 Turing machine, while it can beat the type-1 universal Turing machine. This notion of computability is worth to be noted. The partial combinatory algebra of Type-2 computability formalizes Brouwer’s notion of choice sequences. This more or less means that only with Type-2 computability, analysis and topology are possible. In

Andrej Bauer, Realizability as connection between constructive and computable mathematics, in T. Grubba, P. Hertling, H. Tsuiki, and Klaus Weihrauch, (eds.) CCA 2005 - Second International Conference on Computability and Complexity in Analysis, August 25-29,2005, Kyoto, Japan, ser. Informatik Berichte, , vol. 326-7/2005. FernUniversität Hagen, Germany, 2005, pp. 378–379.

Bauer argues that (Type-2) computable mathematics is the realizability interpretation of constructive mathematics. However since I know basically nothing about recursion theory and realizability, it would be wise that I stop here, at least for the time being.

An important questions that I wasn’t able to find the answer:

Is type-2 Turing machine implementable?

Cybernetics/Information/Adaptation and Self-Organizing Systems

D. A. Lavis, The Concept of Probability in Statistical Mechanics

2023-03-11

See the separate post.

Ryabko, Reznikova, The Use of Ideas of Information Theory for Studying “Language” and Intelligence in Ants (2009)

2023-03-04

See the separate post.

Mind/Cognition

Andre Roch Lecours, Yves Joanette, Linguistic and other psychological aspects of paroxysmal aphasia (1980)

2023-02-13

Andre Roch Lecours, Yves Joanette, Linguistic and other psychological aspects of paroxysmal aphasia (1980) https://doi.org/10.1016/0093-934X(80)90034-6 . This is the famous paper, a clinical case report on the case of Brother John. It was claimed that for Brother John, Aphasic spells occurred without modification in consciousness and without involvement of behaviors other than those related to oral and written speech and language. He uses tricks deliberately to hide the fact of a spell. He is capable of adequate manipulation of relatively complex tools, and of adequate recognition of things and events on the basis of nonlinguistic auditory, visual or tactile information. He has also proven capable of carrying on with previously given - via language - instructions. During the episodes he knows in advance that linguistic incapacitation shall progressively come to an end, since he will keep a transistor radio with himself in deliberate assessment of his oral comprehension capacities.

In his Origins of the Modern Mind, Merlin Donald will use this as a proof case for the thesis that without language one is still capable of thinking, but it should be noted that for philosophers of language, the notion of ’language’ is not merely that of written, oral language, and not even that of internal language, ‘speech occuring inside one’s mind’.

It is unclear what is the precise notion of consciousness appearing here. It was claimed that Brother John remains aware of severe language perturbation, but judging others to be aware of something involves the working of theory of mind in the observer. Furthermore, how can it be legitimate to equate Brother John’s behavior during his aphasia spell with what is narrated, with spoken or written language, afterwards: of course he didn’t ’think’ he should find a hotel when he was unable even to think in terms of language. However, these are philosophical problems that can be seen as rather sophistic, so it is admissible to ignore them. It seems that remains conscious here simply means

  1. One is not sleeping or in a coma.
  2. One is seen to be somehow normal, in the sense that the behaviour would not seem too strange,

A rather suprising fact is that Brother John has proven capable of carrying on with previously given, sometimes several weeks before, instructions. This naturally leads to the conclusion that an instruction given via language, when comprehended and stored in memory, doesn’t need to be decoded and presented in language to affect the mind and to lead to an action of the agent.

While Brother John knows that the spell has occured during the episodes, he doesn’t know right off if a given attempted utterance or written production of his is adequate or not.

“I know that certain words I say are not correct, but I do not know which ones and I do not know how I pronounce them. Sometimes, instead of talking nonsense, I prefer not to talk at all.”

It also seems that, some utterances are given, without any conscious awareness.

It occasionally occurs, in the course of a long spell, he utters a short hackneyed segment in English, a language of which he has very rudimentary knowledge at best: he remains unaware of this and does not remember about it once the spell is over.

The crucial thing here is that what is it that Brother John is unaware of during episodes. Brother John claims that

  1. Inner and overt expression are proportionally affected throughout his dysphasic spells.
  2. Coherent thought remains possible in the presence of dysphasia affecting inner as well as overt expression, in spite of partial or complete incapcacity to evoke particular lexical words specifically embodying this thought.

The problem for Brother John was that, he experienced difficulty in finding his words. If one read through the paper, he will find that the problem is always that of lexical ability, but not that of syntactic or even grammatic ability. Brother John can even do rudimentary arithmetic computations presented conventionally with symbols, while he cannot read the numbers.