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The concept of infinity has a long and troubled history. Thus it is a promising concept with which to explore rejection, disagreement, controversy and acceptance in mathematical practice. This paper briefly considers four cases from the history of infinity, drawing on social constructionism as the background social theory. The unit of analysis of social constructionism is conversation. This is the social mechanism whereby new mathematical claims are proposed, scrutinised and critiqued. Minimally, conversation is based on the two roles of proponent and critic. The proponent puts forward a proposal, which is reacted to and evaluated by those in the role of critic. There is a continuum of contexts in which such conversations take place from inner conversations the mathematician has within themselves, and casual face-to face interactions between mathematicians at the chalkboard, all the way to the formal responses of referees and editors to submitted journal papers. Such responses vary from unconditional acceptance, partial acceptance through to outright rejection. There may be disagreements between proponents and critics, among those in the joint role of critic, and broader, community-wide disagreements and controversies, according to specific mathematical proposal and the critical judgements of it.

The rich and complex concept of infinity has a long and troubled history, and it is probably the most controversial concept in mathematics. Thus it is a promising concept with which to explore rejection, disagreement, controversy and acceptance in mathematical practice. This paper briefly considers four cases from the history of infinity, the last two as yet largely undiscussed in the history and philosophy of mathematics.

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My intention in proposing CT here and elsewhere (Ernest 1991, 1998) is endorsing 1 and 2 and rejecting 3. CT is a descriptive theory applicable to past mathematical practices. As such it is an empirical theory that needs to be tested in practice. Second CT is intended as a philosophical theory of knowledge creation within a social constructionist philosophy of mathematics. However I do not believe that a prescriptive methodology of mathematics is desirable or possible. Human ingenuity continues to overcome the strictures of past practices, as the history of infinity illustrates.

What this brief case study shows, and the role of infinity illustrates, is that there can be legitimate disputes and disagreements within mathematics that are irresolvable. Completed infinities are welcomed, accepted and studied on one side, and wholly rejected and delegitimised on the other. In this case mathematics resembles philosophy, where some problems and disputes are never overcome, being based on incompatible conceptual frameworks used to address intractable philosophical problems. However, in mathematics itself, as opposed to the philosophy of mathematics, such disagreements are much rarer.

This paper has explored the reception of contributions concerning or involving infinity in four short case studies using CT. The case of Saitoh shows what can happen if the conversation never spreads beyond a small circle close to the author. Such a restricted conversation can conceivably be helpful in the generation of new ideas. Whether this restricted conversation has yielded any serious critiques, such as in the preceding paragraphs, is unknown in the case of Saitoh. However, without submission to a formal institutional conversation that warrants results the proposals will not be subjected to rigorous critique, and will normally not be accepted as a contribution to the body of mathematical knowledge.

This paper explores the range of interactions of proponents and critics, and the roles adopted within the controversial history of infinity. Rejection, disagreement and acceptance have been accommodated within the descriptive framework of CT, presented as a tool for understanding the social mechanisms of knowledge generation and validation. As such it offers greater verisimilitude than the traditional logical reconstruction of concepts and proofs that smooths out the actual disagreements, detours and redefinitions that occurred in the history of mathematics and which led to our modern theories (Lakatos 1962).

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D. Eric Maikranz self-published The Reincarnationist Papers in 2009. Due to his difficulties to find a literary agent to have his book adapted into a film, he announced a campaign in the first edition of the book, offering to his readers a commission to someone who successfully pitched a film adaptation of his book to a Hollywood producer. By eighteen months, he received an email from Rafi Crohn, a junior executive at a Hollywood production company who found his book in a Nepalese hostel. (Maikranz paid the commission to Crohn in December 2019.)[citation needed] Crohn then commissioned Ian Shorr and Todd Stein to write an adaptation.[clarification needed] The screenplay was voted onto the Black List in 2017.[6]

In his review for Variety, Peter Debruge called the film "Matrix-meets-The Old Guard wannabe" and wrote: "The more you start to nitpick this movie, the more innumerable its plot holes appear, until the whole thing collapses in on itself."[33] Justin Chang of the Los Angeles Times said: "The script doesn't reincarnate so much as it recycles, drawing freely on the nested realities of Inception, the free-your-mind metaphysics of The Matrix and the amnesiac-assassin[34] revelations of the Jason Bourne movies. Maybe watch one of those tonight instead."[35] Robert Daniels of RogerEbert.com gave the film 0.5/4 stars, saying that "rather than crafting a high-concept science-fiction marvel, Fuqua's Infinite relies on shoddy VFX and ropey world-building for the worst film of his career."[36]

Cryptocurrency is beginning to play a key role in certain precincts of this new world. However, its role in shaping the metaverse has been complicated by the big declines of the crypto winter throughout 2022.

The Sandbox is a virtual world with native tokens to transact with in-game digital assets. SAND can be earned and spent within the Sandbox, just like MANA in Decentraland, another metaverse coin that appears on this list.

Whether the metaverse delivers on its goals or not remains a question as to which games, platforms and applications will rise above others. At the moment, SAND is one of the biggest players in this space.

That said, the more obscure metaverse tokens may not have liquidity for fiat trading pairs. Therefore, traders may be required to first purchase a bigger cryptocurrency before subsequently swapping it into the more niche metaverse token they desire.

It is a film that is discontent to be simply one thing and does not fit categorically into any one box. It is meta, both a production and a story about the process of producing. It is both a play and a movie, a comedy and a tragedy.

Of the entire sample, only 60 and 14 % were familiar with the concepts of systematic and narrative reviews respectively. The majority claimed to know about meta-analysis (58 %) but when invited to explain the difference between a systematic review and a meta-analysis, only five respondents (6 %) offered an adequate explanation. Two-thirds of the sample (66 %) chose not to answer this question. Only 43 % of the sample had ever read a Cochrane review. One-fifth (24 %) had never heard of a Cochrane review. Similarly, 35 % had never read a systematic review in any journal. 17dc91bb1f