Te Hihiri o Te Taiao (Chart of Universal Natural Energies) by Dr Te Huirangi Eruera Waikerepuru, based on pre-Colonial knowledge.

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Table of universal scales and phenomena using Fourier transforms

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

Faust, K., & Raes, J. (2012). Microbial interactions: From networks to models. Nature Reviews Microbiology, 10(8), 538–550. https://doi.org/10.1038/nrmicro2832

Davey, M. E., & O’Toole, G. A. (2000). Microbial biofilms: From ecology to molecular genetics. Microbiology and Molecular Biology Reviews, 64(4), 847–867. https://doi.org/10.1128/mmbr.64.4.847-867.2000

Faust, K., & Raes, J. (2012). Microbial interactions: From networks to models. Nature Reviews Microbiology, 10(8), 538–550. https://doi.org/10.1038/nrmicro2832

Flemming et al., 2016. Biofilms: An emergent form of bacterial life. Nature Review Microbiology: https://www.nature.com/articles/nrmicro.2016.94

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

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

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

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/v

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The chart above is the impetus behind the need to decolonise Western academia and where possible, Western society. These statistics reveal the devastating impact of European¹ colonisation on the Indigenous Peoples of Te Moana Nui a Kiwa (Pacific Ocean).

1. It is acknowledged that Rapa Nui also suffered from colonisation by Peruvians.

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From this chart we can see that there is a striking similarity in the languages of people across Te Moana Nui a Kiwa – from Hawai’i to Aotearoa New Zealand in the south and Tahiti in between.

The point of this is to establish cultural and cosmological similarities in Moana and Māori peoples. The terms for sacred, dark/light and Priest reveal. That is important to establish because among these cultures the notion of an interconnected universe is common.

Evidence via the radiocarbon dating record (Wilmshurst, Hunt, Lipo & Anderson, 2011 – see chart below) reveals that there was a rapid period of settlement of the region of Eastern Polynesia (Hawai’i to the north, Aotearoa to the south and Rapa Nui to the east) between 1190 and 1290CE. This is the start of permanent settlement, and it is clear that language and cosmology travelled with the peoples.

Consequently, there is a very strong basis for saying the notion of an interconected universe has been with Polynesians since 1190CE, which is 790 years prior to similar notions being discussed in the West, particularly by Deleuze and Guattari (1987) who are widely cited across several disciplines including Philosophy (Callinicos, 1985), History (Bell & Colebrook, 2009), Science (Bazzul & Kayumova, 2016), Art History (van Tuinen & Zepke, 2017) and the post-Colonial discussion (Huggan, 1989).

The time has come for this acknowledgment to be spread across academia wherever ideas around interconnection are discussed. This is a simple matter of acknowledging precedents.

The important part of this chart lies in the dark blue coloured areas. These are Class 1 sample dates, the most certain of all categories of radiocarbon dating. This is the basis for Wilmshurst et al (2011) giving the period 1190 – 1290CE as the period of rapid settlement.

Of note is the long tail of Class 3 (middle blue colour) sample. While having a wide standard deviation (i.e. dating is in a range rather than specific) these go back around 300BCE in the Marquesas, Aotearoa New Zealand and Rapa Nui. This means that within around century of this date, someone was lighting fires and eating food at this early time. In my view, this is evidence of early exploration of Te Moana Nui a Kiwa.

What we have here are the dates where there is DNA evidence of intermixing between Moana peoples and South Americans. This means that there was contact to the point of raising generations and look at those dates – South Marquesas and Guatemala 1150CE. Colombia features in two periods. All dates except Rapa Nui fall within the period of rapid settlement as given by Wilmshurst et al (2011).

The chart given by Ioannidis, Blanco-Portillo, Sandoval et al (2020) follows below. This is the work of 31 academics across several fields of academia including DNA researchers, Anthropologists and Archeologists.

Native American gene flow into Polynesia predating Easter Island settlement by Ionnadis et al (2020). While there is discusion in the West regarding whether moana peoples went east or South Americans went west, there is ample evidence of voyaging in Polynesia to assert Moana peoples went east. There are Western academics who cite the voyage of Thor Hyerdahl however as Crowe 2018 put it, Hyerdahl drifted to the Tuamotus and was no closer to Rapa Nui than when he set out. The currents near to South America are particularly strong, and require significant skill to navigate, something that has been with Moana peoples since 950CE, which is evidenced by radiocarbon dating.

We now come to two really significant pieces of the thesis – the diffraction of the Samoan concept of Vā against Quantum Theory, and diffracting Electronic Art and the Anthropocene. The Ngaru Whenua Diffractive method in writing consists of honouring the mana or integrity of the authors by using quotations rather than paraphrasing, while looking from one culture through to the other and vice versa. Looking form one culture to another has roots in the diffractive method developed by Haraway and evolved by Barad (2007).

In the chart above, light green represents Moana Peoples while dark green represents the Western European Cultural Hemisphere.

We are now ready to explore the diffraction of the Samoan notion of Vā and Quantum Theory, leading to surprises. However, before we can do that, we must safeguard Indigenous Knowledge by allowing Indigenous forms of knowledge room to breathe. Previously, Indigenous Knowledge had often been constrained to being situated within Western Knowledge frameworks, which harms the integrity of Moana thought. The diagram above represents forms of Moana knowledge while also acknowledging Cartesian Duality – based on the subject/object distinction. Once the Knowledge Dimensions have been scoped, we can then review the diffraction.

The diffraction of Samoan concept of Vā and Quantum Theory. While the authors are contextually addressing different topics, and the words don’t match precisely, what is apparent is the author’s words point in similar directions: the thrust of what they say overlaps in the way of waves. Waves are the origin of the term ‘Ngaru Whenua’ – it refers to a kind of wave (ngaru) pattern made by an island (whenua). That wave pattern was known to traditional Moana navigators and is called diffraction in the West. So my argument here is that waves of knowledge can be seen as passing across each other in a way they overlap while maintaining their distinct form.