The paradox of Minkowski space: Imaginary unit <i>i</i> is not a number but an action sign
Bibliographic record
Abstract
This work explains an internal contradiction (error) in the current understanding of non-Euclidean Minkowski space. This error happens because the imaginary unit <mml:math display="inline"> <mml:mi>i</mml:mi> </mml:math> in the Minkowski space is considered as a number. In order to solve this contradiction, it is explained in this work that the imaginary unit <mml:math display="inline"> <mml:mi>i</mml:mi> </mml:math> must be consider as an action sign over a vector because only direction of the vector could be imaginary, since imaginary length is nonsense. The concept on the imaginarity of vector refers to the directions of vector (as “plus” or “minus”), but not to the length value and therefore, all numbers could be considered as freely rotatable vectors. Being considered from this position, both the imaginary and real directions (not lengths) of a vector would be consistent for different observers, because they could consider different real axes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".