The Paradox of dual TARDISes: Exploring the Intriguing Possibilities

Within the Doctor Who universe, the concept of a TARDIS landing inside another poses a fascinating paradox. While the show does not provide a definitive answer, several interpretations based on series lore open up a realm of intriguing possibilities.

Time Vortex and Dimensional Stability

The TARDIS is a time machine that exists in a different dimension. If one TARDIS were to land inside another, it could theoretically create a spatial anomaly. Despite the TARDIS being designed to handle complex dimensional physics, the mechanics of such a scenario remain largely unexplored in the series. This has led to a myriad of interpretations and theories among fans and scholars.

The Potential for Nested Realities

There are instances in the series where characters have encountered multiple TARDISes or TARDIS-like structures. In some scenarios, the TARDIS has been shown to create pocket dimensions or alternate realities. Therefore, landing inside another TARDIS could result in the creation of a new, nested reality. These incidents suggest that the interaction between TARDISes might lead to the formation of alternate dimensions, further deepening the mystery surrounding their inter-dimensional nature.

Exploration of Time Loops

The show often plays with time loops and paradoxes. If the Doctor were to land inside their own TARDIS, it could lead to a time loop scenario where events repeat or diverge in unexpected ways. The Doctor's complex timelines and various incarnations provide ample room for such scenarios to play out.

Narrative Device

Ultimately, if a TARDIS were to land inside another, it would likely serve as a narrative device for the show. This scenario could be used to explore themes of identity, time, and space, consistent with the show's history of engaging with complex philosophical questions. The Doctor's journeys and encounters with various TARDISes could serve as a metaphorical representation of the continuous unfolding of time and its paradoxes.

Mathematical Possibilities

It has happened at least three times, with the most recent instance being when a TARDIS went back in time and materialized inside its past self. Another notable occurrence in the Third Doctor's TARDIS and a third in the Tremas/Master's TARDIS.

The concept of a TARDIS materializing inside another can be mathematically viable. You don't even need "dimensional engineering" - it can be achieved in three or even two dimensions with fractal geometry. A simple example is the 2-dimensional "Koch Snowflake," which has an infinitely long perimeter enclosed within a finite area. By folding the Koch Snowflake through the third dimension, you can make it escape the previous enclosure while remaining intact.

Since placing a TARDIS inside itself is mathematically the same as placing it outside itself, all you have to do is upscale the equivalent of the folding of the snowflake to at least four dimensions. We can’t visualize "folding space" in four dimensions, but it makes sense at least mathematically. This concept has roots in science fiction by authors like Robert A. Heinlein and Arthur C. Clarke, who wrote about it before 1963.

While the exact outcome of a TARDIS landing inside another TARDIS is not explicitly defined in Doctor Who, it opens up many intriguing possibilities within the show's established rules regarding time and dimensions. The TARDIS's paradoxical nature and the potential for nested realities continue to captivate audiences, making each new encounter a thrilling exploration of the unknown.

Conclusion

The idea of a TARDIS landing inside another is both a Doctor Who fan-favorite topic and a rich source of philosophical exploration. Whether it leads to time loops, the creation of alternate realities, or simply serves as a narrative device, the concept remains an exciting part of the show's lore.