This is an interesting analysis of some outstanding features of Pirahã culture and language from a point of view of cross-cultural and developmental psychology in the spirit of Piaget. It goes against attitudes and assumptions that belong to what Lakatos would have considered the hard core of the contemporary research programme in anthropology. Research that does this runs a high risk of being rejected if not immediately by the editors of trusted and reputable journals then by referees. Together with the similarly tradition- and convention-burdened attitude by teachers and grant providers, this blocks fundamental progress in science. In distinction from several other reviewers of this article, I regard it as most commendable that valuable articles that go against generally accepted assumptions within a field of research have a chance in Qeios. Based on developmental psychology, the author provides a convincing explanation for Everett’s reported experience that adult Pirahãs, as distinct from their children, fail to acquire the skill of counting even if they try hard. They have been brought up in a non-counting culture, and the human mind appears to be open for learning to count only during childhood. Unused developmental windows cause arrested developments. Once it is clear that Pirahãs have no concept of number, it goes without saying that they do not distinguish between singular and plural. However, the author mentions the absence of a plural separately and considers it erroneously as typical of less advanced languages. Just consider that there is no general plural in East Asian languages (Chinese, Korean, Japanese, Vietnamese, Thai). The presence of an obligatory plural is typical of antiquated, over-grammaticalized languages. Most European languages force their speakers to express number for all countables (plural vs. non-plural in French and, more widespread, singular vs. non-singular), some also in adjectives and verbs. Obligatory distinctions in gender, even in arbitrary grammatical gender, are even more inutile. Such obligatory distinctions are minimal in creole languages. Over history, languages tend to become as complicated as its speakers can handle. Simplification pressure comes from second language speakers. This is why the structure of creole languages is particularly simple and utile, and why Malay/Indonesian, Mandarin Chinese, and English have become simplified. Pirahã is neither particularly simple and regular, nor is it over-complicated. Page 2-5, 7, 17, 30, 32, 37: The author claims repeatedly that certain unspecified “categorical color terms” are absent in Pirahã. However, there are no universal color categories, and the way in which Pirahãs speak about color is familiar in particular from precolonial African languages that basically use words for black, white and red with the associated meanings of ‘dark’, ‘light’ and ‘blood’ respectively. (The English word “red” has also been traced back to an Indo-European word for ‘blood’.) It would have been more interesting to learn whether the Pirahãs have a word for ‘color’. If they have none, they may really lack this concept, but this has not been made clear. Quotation from page 4: “Pirahã culture constrains communication to non-abstract subjects which fall within the immediate experience of interlocutors. This constraint explains a number of very surprising features of Pirahã grammar and culture: the absence of numbers of any kind or a concept of counting and of any terms for quantification, the absence of color terms, the absence of embedding, the simplest pronoun inventory known, the absence of “relative tenses”, the simplest kinship system yet documented, the absence of creation myths and fiction, the absence of any individual or collective memory of more than two generations past, the absence of drawing or other art and one of the simplest material cultures documented, and the fact that the Pirahãs are monolingual after more than 200 years of regular contact with Brazilians and the Tupi-Guarani-speaking Kawahiv.” (Everett 2005a, p. 621)”Here, it is reasonable that the immediate experience constraint leads to a simple kinship system, the absence of creation myths, fiction, and a memory of more than two generations past. However, it remains unclear how the same constraint would lead to an absence of number, of color terms, of embedding and of “relative tenses”. Further, the claim that Pirahã has “the simplest pronoun inventory known” is not at all tenable. Delete this. The pronoun system (not described in this article) is actually free from unnecessary complications, but this holds for the most widely used pronoun system, that of Chinese, as well. It is rather interesting that according to one description, Pirahã has even a specific pronoun for animals under water and another one for non-aquatic animals.  Page 4, 6, 21: While distinctions in tense and aspect of verbs, such as future II, perfect, past perfect, and conditional I and II (page 21) may not be grammaticalized in Pirahã, the author fails to consider that other utile distinctions are. Consider the quote from Everett: “No one should draw the conclusion from this paper that the Pirahã language is in any way ´primitive´. It has the most complex verbal morphology I am aware of and a strikingly complex prosodic system.” (page 6). The author does not mention this, but it is primarily evidentiality that is grammaticalized in Pirahã. This lends prominence to statements about self-perceived events. It can be noted that to these belong even one’s dreams. On the other extreme, it lends obscurity to myths and fiction. It also lends obscurity to religion, but not to ghosts which can be heard. Here, it appears that the Sapir-Whorf hypothesis of linguistic relativity would offer a reasonable explanation for Pirahã attitudes. Pages 31, 33, 34: The author should be excused for the unusual expression “nature peoples”. This appears to be a translation of German “Naturvölker”, which has a positive connotation and lacks a good equivalent in English. English “primitive peoples” refers to the same peoples, but with a negative connotation. “Indigenous peoples” reflects a colonialist view. Qoutation from page 34: “The first words which a child learns are words for the basic categories and not those for superordinate categories. He or she will learn cat and dog before learning animal … (Hill & Arbib 1984, p. 285)”.  This is a false teaching. This was demonstrated to me by my daughter, who, before she had any words, used a grunt first when referring to a pig, then to a dog and a month or so later, with a questioning expression, to a tiny red dot that was moving. It was a kind of spider. Qoutation from page 34: “The Pirahã language however has flexions, up to 16 endings per verb, usually three or five. Therefore, it is thinkable that Pirahã language did not emerge with the onset of Homo sapiens but was preceded by some more elementary languages. This would not exclude the possibility that some main characteristics of the Pirahã language may trace back to either the onset or the early beginning of Homo sapiens.”This may be considered as naïve. No language, not even any feature of a language can be traced back more than 10 000 years. References: Clean the list from literature that is not actually mentioned. As for Oesterdiekhoff, G. W. (2018b). ”Evolution of mind and language. Learning from the Pirahã case”, Anthropos, 113, 1, 195-216: Tell the readers in the Introduction that the present article is an extended version of this former one. (In response to another reviewer)

General commentIn this article, standard cosmology is criticised, an alternative is brought in and terrestrial experiments for testing central aspects of it are proposed. A particular research question is not really made explicit. In section 4, an experiment with a Sagnac interferometer is described. This has in the present version been extended by a similar experiment with a Mach-Zehnder interferometer (section 4.1). Thereby the focus of the article is moved to these experiments. However, these are not even mentioned in the present Abstract, and sections 1-3 are also concerned with other aspects of cosmology. Various shortcomings of standard cosmology are there in effect replaced by various different shortcomings of a sketchy model in which supermassive black holes in the centre of galaxies rotate their local ‘superfluid space’ (or ‘ether’), which is claimed to be the physical origin of galactic rotation curves, as described in previous articles by Šorli et al. Although their outcome is uncertain, the described experiments lend the article some weight. Specific commentsThe Abstract needs to be rewritten since it still reflects deficiencies that have already been amended in this version. It is also necessary to mention the planned experiments described in section 4, which test a unique aspect of Šorli’s cosmological model.Passage prior to Section 1.1, beginning with “In addition, whether the expansion of space would cause the cosmological redshift as a kind of Doppler effect is questionable”: This reflects a misunderstanding. The cosmic redshift is usually considered as a Doppler effect (caused by relative motion). This is what the FLRW metric suggests. It is alternatively considered as an effect of a uniform expansion of “space”. In this case, there arises no Doppler effect (except from proper motion). However, the redshift-distance relation is noticeably different between these alternatives. This difference is reduced if dark energy is introduced. In your response, you wrote “I know the idea of time-invariant space is unusual”. However, this idea is not so unusual, and I meant to criticize primarily the denial of the physical existence of time and the claim that the universe itself is timeless. Middle of section 1.1: Like most readers, I have no doubt about the physical reality of proper time. It can be expressed as the number of periods of a standard radiation. Spatial distance can be expressed as half the number of waves of the same radiation sent towards a mirror and reflected back. If anything, it might be reasonable to deny the physical existence of one-way distances and – in the absence of time – that of any spatial distances. I recognize that you are not alone in your view of time, but time cannot “emerge from a timeless law that governs change” (Barbour [5]) simply because there can neither be any change nor can anything emerge in the absence of time. 2nd passage of section 4: “Today we know that the local ether around the Earth moves and rotates with the Earth…”: Neither here nor elsewhere it is advisable to mention a minority point of view and present it as if it was the view of the majority. Titles of sections 4 and 4.1: The unproven assertions expressed here presuppose a positive outcome of the planned experiments. They need to be replaced by titles that remain adequate even if the outcome should be negative. Last statements before sections 4.1 and 5: In ref. [13], dark energy is, surprisingly, considered as “the fundamental primordial field of the universe”. Dark energy from areas around a galaxy is said to push towards its center, where the dark energy density has its minimum. This difference in dark energy density is considered to generate gravity. However, dark energy is nothing else than a fudge factor invoked in big bang models in order to compensate for the discrepancy between the apparent redshift-distance relation and the different one predicted by the original FLRW metric. Rising the status of this error to that of a fundamental primordial field makes everything much worse, in particular in an allegedly bijective approach. In section 4.1, there should be an introduction to Mach-Zehnder interference. I do not think that the rotation of the motor will have the expected effect, but I consider it worthwhile to do the experiments and it is an advantage to have the expected results described beforehand.Minor comments Last statement before section 1.1: Gravitational > CosmologicalMack-Zender > Mach-ZehnderList of references: bring the info into the same order – either in that of [7] or [13].

This article is critical of the standard big bang model of the universe. This is laudable since this model suffers from deficiencies of several kinds. It is true that we lack any direct evidence for the expansion of the universe. For a recently proposed attempt that could be mentioned and scrutinized here, see [1]. What has been measured is the gravitational redshift. This needs to be distinguished from the cosmological redshift. The latter was originally described as a Doppler effect, and one can claim that such an effect was never observed in an expanding space. It is clear that the cosmic microwave background radiation is a homogeneous radiation that cannot reasonably have its origin at the surface of last scattering in the recombination era. The claim that it has is a symptom of the relic radiation blunder [2]. Your bijective approach is sound but sparingly explained here. (In my perspective, it represents an inductive approach, which allows existential statements whose truth can be asserted. Universal statements or ‘laws of nature’ can at best be asserted to be well-founded or still tenable rather than ‘true’.)While I expect a comeback of a stationary cosmology as well, I think Section 3 is not convincing, at least not for those who are unfamiliar with your prior publications. The topic of Section 4 is too specific. It should better be kept for a separate article in which the planned experiment may be described.  Specific commentsAfter “The expansion of universal space has never been observed or measured”, where [1] could be mentioned, it is said that “The claim that the gravitational redshift is proof of universal expansion is a cognitive simplification outside the realm of scientific thought.” However, such a claim is uncommon in standard cosmology, in which the alleged expansion of the universe is associated with a cosmological redshift, which is strictly distinguished from the gravitational one. Consider whether you should substitute “cosmological redshift” for the next nine occurrences of “gravitational redshift” and/or delete some of the statements. (Cosmologies in which the cosmological redshift is explained as a gravitational effect are not widely known.)Substitute “homogeneous and isotropic” for “uniform throughout space”. We can hardly observe at other places - and check the following: “CMB is the radiation of the entire universal space”, “That the entire space radiates it” and “The entire space emanates this radiation”. These utterances do not rhyme well with a bijective approach.“The FLWR metric is not valid for Euclidean space”: The FLRW metric presupposes a Euclidean proper space (which neither expands nor shrinks).Statements such as “the universe itself is timeless”, “time has no physical existence”, “the universe develops in a time-invariant space” and “time is an emergent physical reality”, will not as easily find acceptance as you imagine. Minor commentsFLWR → FLRW (unless you insist on the first)“phycological” → “psychological”“Hartle and Hawking”: add reference nr. “Lamiakea” → “Laniakea”List of references: Use one and the same referencing system throughout.  References in this review[1] C Wang, K Bolejko, GF Lewis, Ap J 940: 16 (2022)[2] H Traunmüller, F1000Research 9, 261 (2021)