# Transmathematica 2021 - The 3rd International Conference on Total Systems

5th July 2021, 12.45 - 18.00 London Time. Online via Zoom.

The meeting will be recorded and uploaded to YouTube.

Zoom link: <expired>

**Call for Papers (closed)**

The Transmathematica conference accepts papers on any subject within the scope of the Transmathematica Journal. That is, it accepts papers from any discipline in the arts, humanities and sciences that deal with total systems or with new or adventurous mathematics. Total systems have no exceptions, so they always work. This is of interest to Computer Science, Mathematics, Physics, Philosophy and many other disciplines. Papers on transmathematics or any of the transciences are especially welcome.

*Presenting new papers*

Papers should ideally be submitted as PDFs using the Transmathematica Journal’s submission process but authors may submit conference papers by email to the Editor in Chief. The journal's usual Article Processing Charge of £300 applies but there is no charge for attending the virtual conference.

Papers should be submitted as soon as possible. All accepted papers will be published in the Transmathematica journal.

The conference committee will endeavour to give publication decisions within two weeks of submission. Authors are encouraged to submit early, to gain publication approval, and then to spend time improving their papers, up to the production-ready deadline.

*Presenting old papers*

As an alternative to presenting new papers, one author per Transmathematica paper, accepted for publication after the last conference, may have a presentation slot to speak, on any topic, but without an associated publication. This option is free of charge.

*Attending the virtual conference*

There is no charge to attend the virtual conference.

**Audio-Visual Presentations**

Conference presentations will be made by Zoom. Presenters may speak to camera and share their screens. Speakers will be invited to practice their Zoom presentation before the conference. Participants may record the presentation. The conference will make an official recording which will be posted on YouTube shortly after the conference. Recordings may record participants Zoom identity, chat, camera view and shared screen.

**Conference Committee**

Dr Walter Gomide, Department of Philosophy, Federal University of Mato Grosso (UFMT), Brazil.

Dr Tiago Reis, Federal Institute of Education, Science, and Technology of Rio de Janeiro, Brazil.

Dr James Anderson, Transmathematica Editor in Chief, England.

The conference committee may call on all of the Transmathematica journal’s Editorial Team and other experts for peer reviews.

**Deadlines (closed)**

Submission of full papers, as PDFs, for peer review by June 6th 2021. After this date papers may still be submitted but there is no guarnatee that they can be reviewed in time for conference registration. Papers that are too late for the conference may be considered as regular journal submissions.

Conference registration ends June 30th 2021.

Production Ready Papers, June 30th 2021. Papers received after this date may be scheduled as regular Transmathematica journal papers.

The Transmathematica journal accepts submissions at any time and has discretion to redirect papers to the conference issue. The journal’s Article Processing Charge is £300.

**Conference Registration (closed)**

*Presenting new papers:* the covering letter with your submitted paper should say that you wish to attend the online conference. You will then be contacted with details of how to join the online meeting.

*Presenting old papers:* one author per Transmathematica journal paper, accepted for publication after the last Transmathematica conference, may make a presentation without an associated paper. Email the Editor in Chief to say that you wish to join the online conference as a presenter. You will then be contacted with details of how to join the online meeting.

*Participants:* email the Editor in Chief to say that you wish to join the online conference as a participant. You will then be contacted with details of how to join the online meeting.

**Conference Programme Monday 5th July 2021**

5th July 2021, 12.45 - 18.00 London Time. Online via Zoom.

The meeting will be recorded and uploaded to YouTube.

Zoom link: <expired>

Peer reviewed papers will be published before the conference, so that participants can get the most out of the conference by being fully informed about the presentations they may wish to attend and the questions they may wish to ask. Participants may wish to email authors before the conference to ask questions or arrange private meetings. See the email links in each paper.

*Embargo:* Transmathematica will not make any public comment about conference papers until the close of the conference on 5th July 2021.

Each presentation will start on the hour. Presenters are advised to present for 30 minutes and allow 15 minutes for questions. There will then be a break for 15 minutes before the next presentation.

**12.45 Welcome Address - Dr James Anderson**

After welcoming participants, I will explain how the online conference works. I will then report on the Transmathematica Society, Transmathematica Conference, and Transmathematica Journal. I will announce arrangements for the next conference in 2023.

**13.00 Fracterm Calculus - Jan Aldert Bergstra**

**13.45 Brea**k

**14.00 Construction of the Transreal Numbers from Hyperreal Numbers - Tiago dos Reis**

We construct the transreal numbers and arithmetic from subsets of hyperreal numbers. In possession of this construction, we propose a contextual interpretation of the transreal arithmetical operations as vector transformations.

**14.45 Break**

**15.00 The Number Nullity and the Indeterminate - Walter Gomide**In this talk I will consider nullity as the superposition of all real numbers. This fact is the "cause" of the possibily of seeing nullity as the concept of indeterminacy, expressed in transreal numbers.

**15.45 Break**

**16.00 Foundations of Transmathematics – Turtles All The Way Down - Dr James Anderson**

“Turtles all the way down” refers to an ancient concern with recursive definitions. Transmathematics has developed a chain of total definitions all the way from the physical world to the calculus of transnumbers. We review this chain and improve the handling of logic and the definition of a transet.

Earlier we introduced the perspective simplex, or perspex, as a monad that describes: the shape and motions of objects in three dimensional space; how objects look in the abstract four dimensions of perspective space; a computer instruction that instructs a super-Turing machine that may describe the motions of a human or direct the motions of a robot; an artificial neuron that provides a super-Turing machine for the instruction to execute on. The perspex is described in a continous space with selection, which provides a mecahnism to categorise continuous properties into discrete symbols and, thereby, describes how a brute physcial object may operate in the physical world and reason both somatically and linguistically.

Transmathematics is at an early stage of development and revises its defintions quickly. The total systems that have survived to the present day have been arranged according to one or more organisational principles. Transreal arithmetic arranges that its arithmetical operations are syntactically total and are consistent with real analysis. Transcomplex and the emerging transquaternion arithmetic further arrange that their transnumber spaces are obtained from the transreal number line by rotations that sweep out a ball, together with the point at nullity. The emerging Trans-Dedekind Cuts are totalised over all cuts, including the two partially empty cuts, which correspond to positive infinity and negative infinity, and the fully empty cut, which corresponds to nullity. The Trans-Dedekind Cut is a sufficient basis for all transnumber systems but to totalise all sentences of arithmetic we must have a total logic and a total set theory. Trans-Boolean logics and transets have been developed but we now revise their role in the chain of definitions.

The usual Classical or Boolean logic is already total. This logic is stated in terms of the explicit truth values True, T, and False, F, together with implicit handling of the semantic values Contradiction and Non-Existence. We are now content to adopt the usual logics as a foundation for transmathematics. However the usual set theories are not entirely satisfactory, for our purposes, so we revise the notion of a transet.

We adopt the usual set-builder notation but write the usual sets in square brackets and then use these to define transets, written in Latin braces. Thus transets are a meta language built on sets. Transets employ four semantic values which appear as the sets: Just True [T], Just False [F], Contradiction, C = [T F] and Gap, G = []. As usual a set, s, appears as s = [x | f(x)], which means that x is a member of the set s if and only if the membership predicate f(x) is True and not False. We now extend this definition to say that x is a member of the transet {x | f(x)} if and only if the membership predicate, f(x), is Just True and not Just False and not Contradiction and not Gap. Thus x is a member of the transet {x | f(x)} if and only if the set [f(x) | T] = [T]. Thus transets can be built on the sets of any set theory, have unlimited comprehension over all membership predicates, f(x), and are immune to all set paradoxes by construction.

**16.45 Break**

**17.00 Discussion**

**18.00 Closing Address - Dr James Anderson**