dorsal/arxiv
View SchemaThe Principle of Synergy and Isomorphic Units
| Authors | Edgar Paternina |
|---|---|
| Categories | |
| ArXiv ID | physics/0010022 |
| URL | https://arxiv.org/abs/physics/0010022 |
Abstract
A solution to the part and whole problem is presented in this paper by using a complex mathematical representation that permits to define the Holon concept as a Basic Unit System that remains itself in spite of complex operations such as integration and derivation. This can be done because of the remarkable isomorphic property of Euler Relation. We can then define a domain independent both of the observer and the object, as within it, the object is embedded. We will then be able to have a Quantum Mechanics solution without the "observer drawback", as Karl R. Popper tried to find all his life but from the philosophical point of view and which was Einstein main concern about QM too. A unit that has always similar or identical structure or form, despite even complex operations such as integration and derivation, is the ideal unit for the new sciences of complexity or just the systems sciences too, where structure or form, wholeness, organization, and complexity are main requirements. A table for validating the results obtained is presented in case of the pendulum formula.
{
"annotation_id": "3a876438-5a2d-4042-af6f-73b06d4846a0",
"date_created": "2026-03-02T18:00:32.419000Z",
"date_modified": "2026-03-02T18:00:32.419000Z",
"file_hash": "45909867449d51b47fef395a49db4c3b7948bdc03bd34b30d0faa4429737aa6f",
"private": false,
"record": {
"abstract": "A solution to the part and whole problem is presented in this paper by using\na complex mathematical representation that permits to define the Holon concept\nas a Basic Unit System that remains itself in spite of complex operations such\nas integration and derivation. This can be done because of the remarkable\nisomorphic property of Euler Relation. We can then define a domain independent\nboth of the observer and the object, as within it, the object is embedded. We\nwill then be able to have a Quantum Mechanics solution without the \"observer\ndrawback\", as Karl R. Popper tried to find all his life but from the\nphilosophical point of view and which was Einstein main concern about QM too. A\nunit that has always similar or identical structure or form, despite even\ncomplex operations such as integration and derivation, is the ideal unit for\nthe new sciences of complexity or just the systems sciences too, where\nstructure or form, wholeness, organization, and complexity are main\nrequirements. A table for validating the results obtained is presented in case\nof the pendulum formula.",
"arxiv_id": "physics/0010022",
"authors": [
"Edgar Paternina"
],
"categories": [
"physics.gen-ph"
],
"title": "The Principle of Synergy and Isomorphic Units",
"url": "https://arxiv.org/abs/physics/0010022"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1335e3df-65ec-444d-af11-3aa074423b99",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}