Te Wai o te Taiao Flow Dissipation Theory

Te Wai o Te Taiao Flow Dissipation Theory (TWT-FDT) discussion

1. Synopsis

TWT-FDT is being developed by Professor Tom Roa and Dr Mahutoa Pasha Clothier, and was presented in poster form at the Te Pūnaha Matatini Complexity Science annual conference in Ōtepoti Dunedin, Aotearoa New Zealand. Recent work on a full paper resulted in creating the table below. It details a maths and physics process of Fourier transforms, which rely on the complex number √-1. It appears at the large scale strcuture of the universe, in calculations of the Milky Way galaxy, in global weather forecasting models of Earth, the human body, the heart, in molecular oscillations, at nano level and quantum level. This is a scale range from 10^-10 metres all the way up to 10²⁶ metres, an enormous footprint that covers 36 orders of magnitude.

An extraordinary aspect of this research is that both Indigenous groups and Western Science can both be seen as saying that the universe is interconnected. That is an important step in resolving human based climate change, which is largely the c0nsequence of commercialisation and resource exploitation of the environment and species. In an interconnected world, it doesn’t make sense to continue exploitation for the sole reason of driving profit to make wealthy people wealthier.

Row	Phenomena	Physical Scale	Role of Complex Fourier Analysis
1	Large scale structure of the universe	1024 – 1026 metres	The matter density field is defined in Fourier space (Springel et al, 2018); the power spectrum uses complex conjugates (Ivanov et al, 2020), and perturbation theory uses complex kernels (Bender et al, 1999)
2	Milky Way galaxy	Diameter ~ 1021 metres	Spiral density waves described using Fourier modes (Mata-Chávez et al, 2014); galactic potentials are decomposed into complex harmonics (Schaeffer, 2013)
3	Earth	Radius 6.4 x 106 metres	Atmospheric and oceanic waves, and global weather forecasting models use spherical harmonics analysed using Fourier transforms (Wedi et al, 2013)
4	Human body	0-2 metres	Fourier methods used in MRI (Karaman et al, 2015) and CT medical imaging  and signal processing (Zhao et al, 2022)
5	Human heart	Organ size ~ 10-1 m, wavefront thickness ~ 10-3 metres	ECG and cardiac wave propagation are analysed using Fourier transforms, spectral decomposition, and complex eigenmodes (Prasad & Parthasarathy, 2017)
6	Microbial cells and biofilms	~ 10-6 – 10-3 m [1 μm – 1mm]	Fourier-transform infrared spectroscopy (FTIR) is used to characterise microbial cells, strains and biofilms through biochemical spectral fingerprints (Naumann et al., 1991; Helm et al., 1991; Guo & Bocklitz, 2023).
7	Molecular oscillations	10-9 – 10-6 metres	Fourier analysis used for vibrational modes, EM spectra, and signal processing in biological oscillators (Mokari et al, 2023)
8	Nano scale modulations	10-9 metres	Analysis of nano scale pillars and gratings (Paul et al, 2025)
9	Quantum wave fluctuations including Schrödinger	10-10 metres	Wave functions are expanded in complex exponentials (Marconcini et al, 2013)
10	Quantum chromo dynamics – quark interactions in momentum space	10-15 (Hadron radius) – 10-19 m (deep scattering)	Used in quasi Parton distribution functions – non-wave forming (Alexandrou et al 2020, Giraud & Peschanski 2016, Hayashi 2022)

Table references:
Alexandrou, C., Iannelli, G., Jansen, K., & Manigrasso, F. (2020). Parton distribution functions from lattice QCD using Bayes–Gauss–Fourier transforms. Physical Review D, 102, 094508. https://doi.org/10.1103/PhysRevD.102.094508

Bender, C. M., Boettcher, S., & Meisinger, P. N. (1999). PT-symmetric adjoint formulation of quantum mechanics. Journal of Mathematical Physics, 40(5), 2201–2229. https://doi.org/10.1063/1.532860

Giraud, B. G., & Peschanski, R. (2016). Fourier‑positivity constraints on QCD dipole models. Physics Letters B, 760, 287–293. https://doi.org/10.1016/j.physletb.2016.06.033

Guo, S., & Bocklitz, T. (2023). Exploring the steps of infrared (IR) spectral analysis: Pre-processing, (classical) data modelling, and deep learning. Molecules, 28(19), 6886. https://doi.org/10.3390/molecules28196886

Haouat, S. (2014). Schrödinger equation and resonant scattering in the presence of a minimal length. Physics Letters B, 729, 33-38. doi.org

Hayashi, Y. (2022). Renormalon subtraction using Fourier transform: Analyses of simplified models. Journal of High Energy Physics, 2022(6), Article 14408. https://doi.org/10.48550/arXiv.2112.14408

Helm, D., Labischinski, H., Schallehn, G., & Naumann, D. (1991). Classification and identification of bacteria by Fourier-transform infrared spectroscopy. Journal of General Microbiology, 137(1), 69–79. https://doi.org/10.1099/00221287-137-1-69

Insero, G., Santamaria, L., Lucic, V., De Natale, P., Borri, S., & Cappelli, I. (2017). Measuring molecular frequencies in the 1–10 μm range at 11-digits precision. Scientific Reports, 7(1), 12678. doi.org

Ivanov, M. M., Simonović, M., & Zaldarriaga, M. (2020). Cosmological parameters from the BOSS galaxy power spectrum. Journal of Cosmology and Astroparticle Physics, 2020(05), 042. https://doi.org/10.1088/1475-7516/2020/05/042

Karaman, M., Bruce, I. P., & Rowe, D. B. (2015). Incorporating relaxivities to more accurately reconstruct MR images. Magnetic Resonance Imaging, 33(4), 374-384. https://doi.org/10.1016/j.mri.2015.01.003

Marconcini, P., Logoteta, D., & Macucci, M. (2013). Sinc-based method for an efficient solution in the direct space of quantum wave equations with periodic boundary conditions. Journal of Applied Physics, 114(17). https://doi.org/10.1063/1.4828875

Mata-Chávez, M. D., Gómez, G. C., & Puerari, I. (2014). Analysis of the spiral structure in a simulated galaxy. Monthly Notices of the Royal Astronomical Society, 444(4), 3756–3760. https://doi.org/10.1093/mnras/stu1672

Mokari, A., Guo, S., & Bocklitz, T. (2023). Exploring the steps of infrared (IR) spectral analysis: Pre-processing, (classical) data modelling, and deep learning. Molecules, 28(19), 6886. https://doi.org/10.3390/molecules28196886

Naumann, D., Helm, D., & Labischinski, H. (1991). Microbiological characterizations by FT-IR spectroscopy. Nature, 351, 81–82. https://doi.org/10.1038/351081a0

Paul, A., Wever, R., Soman, S., & Pereira, S. F. (2025). Utilizing focused field as a probe for shape determination of subwavelength structures via coherent Fourier scatterometry. Physical Review Applied, 23(2), 024016.  

Prasad, B. V. P., & Parthasarathy, V. (2017). Detection and classification of cardiovascular abnormalities using FFT based multi-objective genetic algorithm. Biotechnology & Biotechnological Equipment, 32(1), 183-193. https://doi.org/10.1080/13102818.2017.1389303

Schaeffer, N. (2013). Efficient spherical harmonic transforms aimed at pseudo-spectral numerical simulations. Geochemistry, Geophysics, Geosystems, 14(3), 751–758. https://doi.org/10.1002/ggge.20071

Springel, V., Pakmor, R., Pillepich, A., Weinberger, R., Nelson, D., Hernquist, L., Vogelsberger, M., Genel, S., Torrey, P., Marinacci, F., & Naiman, J. (2018). First results from the IllustrisTNG simulations: Matter clustering and hierarchy of galaxy luminosities. Monthly Notices of the Royal Astronomical Society, 475(1), 676–698. https://doi.org/10.1093/mnras/stx3304

Wedi, N. P., Hamrud, M., & Mozdzynski, G. (2013). A fast spherical harmonics transform for global NWP and climate models. Monthly Weather Review, 141(10), 3450–3461. https://doi.org/10.1175/mwr-d-13-00016.1

Zhao, H., Liu, Z., Tang, J., Gao, B., Qin, Q., Li, J., Zhou, Y., Yao, P., Xi, Y., Lin, Y., Qian, He., & Wu, H. (2022). Energy-efficient high-fidelity image reconstruction with memristor arrays for medical diagnosis. Research Square. https://doi.org/10.21203/rs.3.rs-2147455/v1

2. Additional contexts

TWT-FDT weaves threads of Te Ao Māori, Quantum Physics and Complexity Science. It utilises Te Kore – Te Pō – Te Ao Mārama, koha (gift) of Dr Te Huirangi Eruera Waikerepuru who often expressed that everything arose from Te Kore The Potential, and that one form of expressing Te Pō was to speak of the many states of Nothing in Te Taiao The Universe.

In TWT- FDT, mathematical unity of the sciences is achieved via the √-1, used in the Schrödinger equation [1, 2] and to map the Mandelbrot Set [3], and in Hilbert space [4] – these are non-trivial locations. Quantum Theory and Complexity Science become semantically interconnected.

In Network Science, the √-1 appears in impedance modelling of power grids, communication networks, and signal flow systems, it is required for modelling signal processing and network traffic analysis. Complex-valued neural networks, which incorporate √-1, can enhance learning in systems with oscillatory or phase-sensitive data improving adversarial robustness in AI systems [5]. The same number, called j in Engineering, is used in electrical engineering, signal processing, control theory, electromagnetics and mechanical systems. This number is a powerful operator, applicable over large and small scales.

The term ‘Dissipation’ is intended to be inclusive of notions of entropy. Four fundamental precepts from maths and science are the foundation of the science in the theory:
1. Gödel’s Incompleteness Theorem
2. The Planck length
3. Hubble Flow and Hubble Friction
4. The Second Law of Thermodynamics

TWT-FDT can generate testable hypotheses, does not interfere with the data set, does not require the addition of the sacred, and unexpected consequences include a connection to ethics which takes three forms. 

3. Kōrero (discussion)

There is a potential for a major advance in thinking around complex systems, due to the integration of pre-colonial Māori cosmology and the interconnection of the sciences. The proposed integration has resulted unexpectedly in imbuing science with an ethic. 

It is important to construct decolonised frameworks that protects mana (integrity) on all sides of cultural debates. Chapter two of the PhD and subsequent book Ocean Diffraction: Indigenous Practices, Quantum Theory, Electronic Art and the Anthropocene perform exactly this task, so Knowledge as Dimensional will be integrated into TWT-FDT.

The engagement with Ahorangi (Professor) Roa is crucial as he is holder of traditional Māori knowledge at significant depths. TWT-FDT is based in the work of Dr Te Huirangi Eruera Waikerepuru, who led Reo becoming an official second language in Aotearoa, along with submissions on the electromagnetic spectrum i.e. Māori Radio and Māori Television. 

Once a developmental phase is completed, we hope to hold meetings nation-wide, and am planning a mini tour of Canadian cities. One-hour sessions with researchers are being considered, using mixed engagement strategies including online resources and local groups sitting in a circle, which greatly improves interaction. The circle idea follows from Nina Czegledy, curator and organiser of many intercultural forums internationally.

4. Te Kore, Te Pō, Te Ao Mārama – Hilbert spaces, dark energy and spacetime

String theory, a mirror universe and quantum memory matrix

At present quantum theory is incomplete in regard to quantum gravity and dark energy, which is to say there are theories but no widespread consensus. String Theory elegantly resolves quantum gravity and provides a statistical-mechanical explanation of Bekenstein-Hawking entropy for a class of black holes. Recent research has found Calabi-Yau manifolds in gravity waves [6] and Feyman integrals [7]. The mirror universe concept put forward by Neil Turok, which integrates CPT (charge, parity and time) symmetry has strengths, however, is currently tied to right- handed neutrinos which to date have yet to be located in data or experiment. A third theory, quantum memory matrix integrates information and topology, and is gaining prominence.

Te Kore. Te Pō, Te Ao Mārama.

Interestingly while each theory uses Hilbert space potentials differently, the relevance of Hilbert spaces, dark energy and dark matter, and four dimensional spacetime is not questioned. There is a mapping here that can be performed, related to Te Kore (the Potential), Te Pō (the Nothing) and Te Ao Mārama (the World of Light) although great care is needed mainly due to a lopsided historical interrelationship where Indigenous and Western cosmologies have been brought in to dialogue. It is important in particular to be citing Māori authors on Māori cosmology and avoid splintering apart what is fundamentally an interconnected world view.

5. Knowledge-based ethics

There is a potential to imbue science with an ethic. It is widely understood that science has not had an ethic over the last seventy years.

5.1 Primary level – basis of knowledge acquisition 

In order to safely allow for a discussion across cultural borders, a consideration of the basis of knowledge acquisition must be made, and in particular knowledge acquisition theories must be extended to become inclusive of Indigenous knowledge, and following the dissolution of the subject/object distinction in 20th century Quantum Theory and Physics.

5.2 Interconnection level

TWT-FDT does not require alteration to the data set and simultaneously, interconnection becomes core to science. We can then easily find segments of science to connect all species and the universal environment in a state of relationship, which constitutes an extraordinarily beneficial platform for ethics. The potential is to connect all of science from the Big Bang to Midwifery through the Schrödinger equation and fractals. Here is one of multiple subject strings: Big Bang – cosmic inflation – quantum fluctuation – Schrödinger – √-1 – fractals – branches – veins & arteries – uterus – midwifery. This is just ten steps.

5.3 Granular level of ethics question resolution 

We can now step towards questions of ethics, where extraordinarily, the kōrero becomes a discussion of the appropriate science to apply. Ethical issues become a matter of finding the appropriate science. 

For example, if it is asked “are the genders equal?” an appropriate response is “according to medical science humans of all genders share 99.9% DNA” [8]. If a further question is asked “are humans connected to nonhuman species,” the response is “yes, the DNA record demonstrates a sliding scale of DNA from chimpanzees at 96% [9] shared through to mice at 86% [10] and trees at 15% shared” [11, 12]. This view coincides with positioning in Indigenous knowledge systems such as knowledge held by Moana peoples. 

Note that the discussion has moved almost imperceptibly from science to ethical considerations. The structure doesn’t supply a singular truth, but rather a discussion around the appropriate science to apply to ethical queries. 

As we are connected to diverse species and the environment, a stance of resource exploitation is no longer tenable to aware individuals. This provides further guidance and an additional imperative regarding the human relationship to the environment, where it can be demonstrated that historically, releasing facts and data has been insufficient to bring about change. 

References

[1]    Yang, C. N. (1987). Square root of minus one, complex phases and Erwin Schrödinger. In C. W. Kilmister (Ed.), Schrödinger: Centenary Celebration of a Polymath (pp. 53–64). Cambridge University Press.  https://doi.org/10.1017/CBO9780511564253.006 

[2]   Kwong, C. P. (2009). The mystery of the square root of minus one in quantum mechanics, and its demystification. The Chinese University of Hong Kong. https://arxiv.org/pdf/0912.3996 

[3]   Douady, A., & Hubbard, J. H. (1985). On the dynamics of polynomial-like mappings. Annales scientifiques de l’École Normale Supérieure 18.2 1985: 287-343. http://eudml.org/doc/82160

[4]   Gagne, M. (2013). Hilbert Space Theory & Applications in Basic Quantum Mechanics. https://www.researchgate.net/publication/304163012_Hilbert_Space_Theory_and_Applications_in_Basic_Quantum_Mechanics

[5]  Yeats, E., Li, H., & Kingery, K. (2021, August). Imaginary numbers protect AI from very real threats. In Proceedings of the 38th International Conference on Machine Learning. Duke University Pratt School of Engineering. https://pratt.duke.edu/news/imaginary-numbers-machine-learning/

[6] Driesse, M., Mogull, G., Sauer, B., Jakobsen, U., & Plefka, J. (2025). Emergence of Calabi–Yau manifolds in high-precision black-hole scattering. Nature. https://doi.org/10.1038/s41586-025-08984-2

[7]   Bönisch, K., Duhr, C., Fischbach, F., Klemm, A., & Nega, C. (2021). Feynman integrals in dimensional regularization and extensions of Calabi–Yau motives. arXiv preprint arXiv:2108.05310. https://arxiv.org/pdf/2108.05310  

[8]. Jorde, L. B., & Wooding, S. P. (2004). Genetic variation, classification and ‘race’. Nature Genetics, 36(11 Suppl), S28–S33. https://doi.org/10.1038/ng1435

[9] Patterson, N., Richter, D. J., Gnerre, S., Lander, E. S., & Reich, D. (2006). Genetic evidence for complex speciation of humans and chimpanzees. Nature, 441(7097), 1103–1108. https://doi.org/10.1038/nature04789

[10] National Human Genome Research Institute. (2010). Why Mouse Matters. https://www.genome.gov/10001345/importance-of-mouse-genome

[11] Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., & Walter, P. (2015). Molecular biology of the cell (6th ed.). Garland Science. 

12. Clothier, M. P. (2025, August 12). Trees are family: DNA, ancestors and whakapapa. planksip. https://www.planksip.org/trees-are-family-dna-ancestors-and-whakapapa/

Knowledge as Dimensional