The article does not claim that DMT unlocks new sensory abilities to perceive extra dimensions (!). It describes how DMT changes the geometry of phenomenal space, under the assumption of indirect realism about perception. You can certainly study that in a systematic and meaningful way without ever assuming new secret sensory abilities.

That said... higher phenomenal dimensions do exist, and you can experience them on DMT. See this video for a rational explanation of that effect (which is related, but different, from the hyperbolic geometry effect): https://youtu.be/DcGGfahXmQk

Video description:

Many people report experiencing "higher dimensions" during deep meditation and/or psychedelic experiences. Vaporized DMT in particular reliably produces this effect in a large percentage of users. But is this an illusion? Is there anything meaningful to it? What could possibly be going on?

In this video we provide a steel man (or titanium man?) of the idea that higher dimensions are real in a new, meaningful, and non-trivial sense.

We must emphasize that most people who believe that DMT experiences are "higher dimensional" interpret their experiences within a direct realist framework. Meaning that they think they are "tuning in" to other dimensions, that some secret sense organ capable of perceiving the etheric realm was "activated", that awareness into divine realms became available to their soul, or something along those lines. In brief, such interpretations operate under the notion that we can perceive the world directly somehow. In this video, we instead work under the premise that we live in a compact world-simulation generated by our nervous system. If DMT gives rise to "higher dimensional experiences", then such dimensions will be phenomenological in nature.

We thus try to articulate how it can be possible for an experience to acquire higher dimensions. An important idea here is that there is a trade-off between degrees of freedom and geometric dimensions. We present a model where degrees of freedom can become interlocked in such a way that they functionally emulate the behavior of a virtual higher dimension. As exemplified by the "harmonograph", one can indeed couple and interlock multiple oscillators in such a way that one generates paths of a point in a space that is higher-dimensional than the space inhabited by any of the oscillators on their own. More so, with a long qualia decay, one can use such technique to "paint" entire images in a virtual high dimensional canvas!

High-quality detailed phenomenology of DMT by rational psychonauts strongly suggests that higher virtual dimensions are widely present in the state. Also, the unique valence properties of the state seem to follow what we could call a "generalized music theory" where the "vibe" of the space is the net consonance between all of the metronomes in it. We indeed see a duality between spatial symmetry and temporal synchrony with modality-specific symmetries (equivariance maps) constraining the dynamic behavior.

This, together with the Symmetry Theory of Valence (Johnson), makes the search for "special divine numbers" suddenly meaningful: numerological correspondences can illuminate the underlying makeup of "heaven worlds" and other hedonically-loaded states of mind!

I conclude with a discussion about the nature of "highly-meaningful experiences". In light of all of these frameworks, meaning can be understood as a valence effect that arises when you have strong consonance between abstract (narrative and symbolic), emotional, and sensory fields all at once. A key turning point in your life combined with the right emotion and the right "sacred space" can thus give rise to "peak meaning". The key to infinite bliss!