Oct 13, 2012

Spiritual Approach to Understand the Fourth Dimension

By Marsigit

Fudjack, J. and Dinkelaker, P. (1999) in their “The 'Self' as Hyperbody: Nested Realities and the 'Fourth Dimension'” explained

'The Enneagram as Triple Mandala' to show how mandalas in general are often viewed as comprised of superimposed 'outer', 'inner', and 'innermost' layers, and how these correlate to three approaches to spiritual path - the 'Path of Renunciation', the 'Path of Transformation', and the 'Path of Realization'.

They described that from the liminocentric structure of the Enneagram as Symbol - the manner in which the outermost figure (which is a circle) is identical to the innermost, secret figure (also a circle) - we infered the presence of (nine) Spiritual Qualities.

Further, as attributes of the Self, these can be considered transcendental qualities that pre-exist the characterological 'flaws' or 'defects' around which the Ego-traits that characterize the 9 Enneatypes are constellated.

They inscribed that in Buddhist, Hindu, and Sufi path-of-realization teachings, these Spiritual Qualities are likened to 'hidden jewels'.

They explained that in the Path of Realization teachings of the MAHAUTTARATANTRA SHASTRA this metaphor branches off into nine similar metaphors, related to nine Qualities, and also into parallel motifs that play a central role in the KALACAKRA texts - the idea of a 'hidden kingdom', profound 'buried' or 'hidden' teachings (terma), and a yet-to-be-born universal monarch.

In term of the literal status of spiritual truth, Fudjack, J. and Dinkelaker, P. (1999) the METAPHORS themselves seem to insist on the literal and physical status of what they represent; the image of wheels falling from the sky, individuals waking from dreams with pages of physical texts in hand, or actual fruits - all seem to want to depict acts of embodiment, in which some THING comes literally out of nothing.

They elaborated that the seeming insistence, in 'path of realization' teachings, on the literal nature of spiritual truth has a somewhat fundamentalist ring to it.

They delivered the question, “Is it sufficient (as we previously suggested) to argue that what is being represented is simply the RETURN of the seeker from the spiritual 'heights', to an embodied existence in the ordinary, mundane world? Or is this too facile an explanation?

Fudjack, J. and Dinkelaker, P. (1999) strived to uncovered that the truths that are being expressed should not be construed as MERELY literal but also have a function simultaneously at two other 'levels of meaning' that are sometimes called 'figurative', and 'transcendental', in which, they might more aptly be considered 'super-literal' truths - and by this we mean to suggest statements that are literally true, but in a reality at a higher level of description.

They found that for the OBJECTS that are symbolized by the 'path of realization' metaphors under discussion are ones that exist not exclusively in mundane (ego-based) reality, nor in some 'other', separate reality, however, they exist in a 'super-reality' or 'sur-reality' that CONTAINS the mundane world, but also extends beyond it - in the same way in which two-dimensional planes are contained within three dimensional cubes; borrowing a term from contemporary science, we shall use the word 'hyperspace' to describe such a reality.

Fudjack, J. and Dinkelaker, P. (1999) found also that realities can be likened to 'spaces' having a certain number of specifiable 'dimensions'; if the reality in which one exists has an n-dimensional space, then a reality that has n+1 or more dimensions can be said to constitute a 'hyperspace' with respect to it.

Further, bodies in n-dimensional space will, of course, have n (or fewer) dimensions; so bodies that need n+1 dimensions to be adequately described can only fully 'exist' in the appropriate n+1 dimensional hyperspace - and we can refer to them as 'hyperbodies'. Accordingly, from a 3-dimensional perspective, a 4-dimensional cube is, by this definition, a 'hypercube'.

Fudjack, J. and Dinkelaker, P. (1999) found that “self” can be perceived as Hyperbody, with 'Qualities'. Then, they explained that the 'Self' (in the Jungian sense of the word) is a HYPERBODY with respect to the typological space in which mundane personality resides; the words that Jung uses to refer to the Self - such as the 'philosopher's stone', for instance - all seem to suggest that this is the case.

Furthermore, according to them, Jung's images are consistent with the 'Path of Realization' Buddhist metaphors that we have been considering in this series: - the 'precious jewel hidden in the lotus', and its variants.

They noted that all fall under the rubric of metaphors pointing to the appearance of what we have called the 'superfluous ninth', metaphors dealing with the production of 'spiritual body'.

Fudjack, J. and Dinkelaker, P. (1999) learned that 'The treasure', as Edward Edinger succinctly puts it, 'is the Self, the suprapersonal center of the psyche'; and the 'Qualities' that characterize this hyperbody (which is sometimes called 'vajra body' in Tibetan Buddhism) - its attributes or facets, as it were - are more likely to appear in the lesser-dimensioned ego-based 'mundane' reality as 'contradictions' or 'conflicts', and sometimes 'mysteries' and 'paradoxes', than as simple 'traits'.

Accordingly, the word 'vajra' refers to a pure, unobstructed space that is the quintessence of emptiness.

They perceived that this space is somehow also capable - however paradoxical this might at first seem - of presenting itself in solid form.

Next, they delivered the question, “Isn't it a similar quality, after all, which is the one that we find perennially fascinating when we experience it in mundane jewelery - the fact that jewels are transparent and invisible - nearly nonexistent - but nonetheless adamantine, impenetrable?”.

Fudjack, J. and Dinkelaker, P. (1999) found that the 'qualities' of the Self are likely to appear just as elusive as the light reflected from the FACETS of a jewel; and they will manifest as contradictions, paradoxes, and mysteries in the lesser-dimensional Ego-space which is the home of our mundane 'personalities' simply because some of the attributes of objects in an n+1 dimensional space will remain inaccessible ('ineffable') in n-dimensional spaces; and these contradictions indeed form the CORE of mundane pesonality.

At the bottom of the 9 EnneaTypes are 9 characterological riddles that point to the hidden presence of the 'Self'. To show those contradictions, Fudjack, J. and Dinkelaker, P. (1999) toke a simple example of the level-specific nature of 'qualities', volume as an attribute of objects in 3-dimensional physical space.

In 2-dimensional space the concept of volume has no meaning - although there is an equivalent concept ('area'). So a 2-dimensional being might, from the concept of 'area', the quality with which she is familiar, EXTRAPOLATE the existence of a similar quality ('volume') in 3-dimensional space.

However, they perceived that she will not, however, be able to directly experience it in the (2-dimensional) objects to which she is privy; it will seem like a theoretical 'construct' to her, although it is a palpable 'quality' to those of us capable of experiencing in 3-dimensional space.

Three Types of Meaning (Literal, Figurative, and Transcendent) were described by Fudjack, J. and Dinkelaker, P. (1999) as follows:

“In her book on Shambhala, LePage correlates what she calls the 'three planes of reality' (physical, psychic, and spiritual) with the three types of 'meaning' about which the nineteenth century French mystic Edouard Schure spoke. Schure reported that the ancient Egyptians had a language which expressed their thought at three levels simultaneously - The first was literal, the second symbolic and figurative, the third sacred and hieroglyphic. At their wish, the same work assumed a literal, a figurative or a transcendent meaning. This language had a singular eloquence for the adept, for, by means of a single sign, it evoked the principles, causes, and effects radiating from divinity into blind nature, in the human consciousness and into the world of pure spirit”.

Relating to the “’Superfluous' Nature of Hyperobjects”, Fudjack, J. and Dinkelaker, P. (1999) elaborated as follows:
“The notions of 'hyperspace' and 'hyperobject' are handy concepts when it comes to trying to specify the relationship between 'transcendent' objects (eg, the Self), their 'qualities' (eg, the 'Spiritual Qualities' of the individual), and coming to understand how such qualities might manifest at the mundane level of reality in which we normally abide (eg, as 'characterological defects', around which 'personalities' form). The word 'hyperspace' is a relative term. In using it one is simply referring to a reality that has more dimensions than the base-line reality with which one is primarily concerned. A three-dimensional space, for instance, is a 'hyperspace' for the flatlander caught in a two-dimensional existence. The term 'hyperspace' is basically just a scientific substitute for the religious notion of a 'transcendent reality', although it is useful because it specifies that it is by virtue of additional DIMENSIONS that such a reality transcends ordinary reality. And it also treats transcendence as a relative term. No space is 'absolutely' transcendent, only relatively so with respect to some other particular space. The notion of a 'hyperobject' is similarly useful, particularly in the context of a discussion about the nature of symbols. A hyperobject is simply an object IN hyperspace - ie, an object with more dimensions than one can directly detect if one is a being in a lesser-dimensional reality. So for the two-dimensional flatlander, a three-dimensional cube is a 'hyperobject'. The flatlander cannot see it. Or perhaps we should say that the flatlander can't see ALL OF IT - as he can see it only AS a square. Or that he sees 'its reflection' in two-dimensional space, or its 'shadow', or a collapsed version of the object - a dumbed-down (or dimensioned-down) version. We might even call this version of the object a 're-presentation' of it - ie, a symbol. As beings in three-dimensional space, we humans cannot directly preceive a four-dimensional 'hypercube'. But such a thing 'exists', and can be described, and we can talk about its 'qualities', even if we are not in a position to directly experience them. Scientists do it all the time. According to mathematicians, the figure to the left is what a four-dimensional 'hypercube' looks like in three dimensional space. In the same way in which a three-dimensional cube has six square faces, the four-dimensional hypercube is comprised of eight three-dimensional cubes, one of which is completely hidden from view (because each of its six sides interfaces with another cube that obscures our vision, no matter what angle we might try to look at it from).

Fudjack, J. and Dinkelaker, P. (1999) then also elaborated the relation among Hyperbody, Coagulatio, and the Birth of 'Inner' Children as follows:

“For Edinger, who follows Jung in this regard, the Crucifixion is a 'coagulatio' symbol, representing the particular stage in the inner 'alchemical' process of individuation in which concretization takes place. Coagulatio is an embodiment or incarnation that is mythologically linked with desire, a 'fall from heaven', and with 'Saturnine' evil (that is associated with 'materiality'). Honey, Edinger tells us, is 'an agent of COAGULATIO'. Interestingly, honey, as we've seen, was one of the nine alternate metaphors for the 'hidden jewel' in the 'path of realization' text, the MAHAUTTARATANTRA SASTRA. Edinger quote's Jung's discussion of Dorn's use of honey - Thereby the mixture acquired the property not only of eliminating impurities but of changing spirit into body, and in view of the proposed conjunction of spirit and the body this seemed a particularly promising sign. To be sure, the 'sweetness of the earth' was not without its dangers, for as we have seen ... the honey could change into a deadly poison. According to Paracelsus it contains 'Tartarum', which as its name implies has to do with Hades. Further, Tartarum is a 'calcined Saturn' and consequently had affinities with this malefic planet. Embodiment can be construed as a 'fall'. The lowly circumstances of Christ's birth correspond to the ordinary and commonplace aspects of being concretely real. The events of the Passion also apply. Christ's condemnation and execution with criminals present him as a willing carrier of evil. His carrying the cross represents the realization of the burden of one's being. The outstanding image is the crucifixion itself - being nailed to matter. In alchemical terms, the cross represents the four elements from which all manifest being is made. FIXATIO is one of the synonyms for COAGULATIO”

Interestingly, Fudjack, J. and Dinkelaker, P. (1999) learned that if the fourth dimension does indeed 'wrap around' onto the zero-dimension, the joining would seem to occur somewhere BETWEEN the 3rd and 4th dimension.

Accordingly, in 'fractal geometry' (which we might call the 'geometry of liminocentric structures') one is permitted 'fractional' dimensions. You can have objects that are 2-dimensional, and 3-dimensional; but you can also objects that are 1.5-dimensional, or 2.73-dimensional.

Is it possible that the turning point, the place where the dimensional wrapping occurs, is at the fractional dimension equal to 'pi'? Pi was at one time approximated as 22/7ths (or 3 1/7, which equals 3.142857).

If then, they emphasized, dimensions have this kind of chinese-box relationship with each other, then 3 1/7 turnings of the 'wheel' (or 'circumabulations' of the 'mandala') might take us not only into the center, but also shoot us full-circle back out to our starting point at the periphery; and what can we say of objects IN realites that have this kind of involuted structure, or the 'qualities' that they possess?

Fudjack, J. and Dinkelaker, P., 1999, The 'Self' as Hyperbody: Nested Realities and the 'Fourth Dimension'


  1. Lumaurridlo
    S3-PEP 2018

    Sains sebagai dimensi keempat dari Iman, Islam, dan Ihsan secara hirarkis mestinya tetap berada pada posisinya.Analogi 4 dimensi terhadap sebuah rumah adalah Iman sebagai pondasi Islam sebagai tiang, tembok dan atau pagar beserta partisi-partisinya, ihsan adalah atapnya. Sains berada dimana? sains dapat diletakkan sebagai salah satu jenis pintu dan atau jendela untuk masuk atau keluar ke atau dari satu kesatuan ruang tersebut.sains dalam sejarahnya banyak menjadi pintu masuk ke Rumah begitupun sains dalam sejarahnya menjadi jalan keluar dari kenyamanan hidup dan tetap tinggal di rumah.

  2. Diana Prastiwi
    S2 P. Mat A 2018

    Fudjack dan Dinkelaker menemukan bahwa kenyataan bisa disamakan dengan ruang yang memiliki dimensi tertentu. Jika kenyataan mempunyai dimensi ruang, maka kenyataan mempunyai n+1 atau dimensi yang lain bisa diganti dengan hyperspace. Ajaran agama erat kaitannya dengan dimensi dan path of realization yang didalamnya terdapat hal hal fundamental dan kokoh. suatu keadaan atau suatu peristiwa itu selalu mempunyai tugas dan fingsi masing-masing. Kita segaia umat beragama dalam ini percaya dan yakin bahwa Allah SWT menciptakan semau yang ada dialam semesta ini memiliki tugas dan fungsinya masing-masih.

  3. Bayuk Nusantara Kr.J.T

    Secara spiritual, saya dapat memahami dimensi-dimensi berdasarkan ciptaan-ciptaan Tuhan. Dimulai dengan dimensi nol yaitu benda mati karena merak tidak dapat bergerak, seperti batu. Kemudian dimensi satu yaitu benda hidup yang terlihat statis namun bergerak, seperti tanaman karena tanaman dapat menguasai benda yang ada dibawahnya yaitu benda mati namun terbatas. Kemudian dimensi dua yang tidak statis dan mampu bergerak pada bidang datar yaitu hewan, karena hewan dapat menguasai dua dimensi dibawahnya. Kemudian dimensi 3 yaitu manusia. Manusia mampu menguasai 3 dimensi dibawahnya. Diatasnya lagi adalah makhluk tak kasat mata namun diyakini keberadaannya, yaitu malaikat dan jin. Karena Jin dapat menguasai 4 dimensi dibawahnya. Hingga dimensi tak hingga yaitu dimensi Tuhan. Karena Tuhan melingkupi segalanya

  4. Fabri Hidayatullah
    S2 Pendidikan Matematika B 2018

    Terdapat berbagai macam pendekatan untuk memahami dimensi keempat, salah satunya ialah melalui pendekatan spiritual. Beberapa filsuf menyatakan bahwa di dalam ajaran realisasi Agama Buda, Hindu dan Sufi, kualitas spiritualnya dihubungkan dengan sesuatu yang sangat berharga dan tersembunyi. Mereka menjelaskan bahwa desakan yang tampak dalam ajaran realisasi tersebut, pada arti sifat yang sebenarnya pada kebenaran spiritual memiliki seperti lingkaran fondamentalis.

  5. Dini Arrum Putri
    S2 P Math A 2018

    Dimensi ke empat berbicara tentang spirtualitas. Menurut saya, tidak ada yang bisa menilai dan memandang bagaimaba dimensi ke empat itu karena berhubungan dengan nilai nilai agama, namun tergantung pada persepsi setiap orang. Dan untuk bisa memahami dimensi ke empat dimulai dengan pendekatan spritual yaitu belajar untuk bisa terus dekat dengan Tuhan dan belajar sesuai dengan ruang dan waktunya.

  6. Amalia Nur Rachman
    S2 Pendidikan Matematika B UNY 2018

    Apabila kita mengkaitkan antara dimensi keempat dengan pendekatan spiritual, adanya ajaran budha, hindhu, sufi merupakan contoh realisasi ajaran dari kualitas spiritual. Berbeda halnya jika dikaitkan dengan matematika, dimensi keempat seperti hypercube empat dimensi yang terdiri dari delapan kubus tiga dimensi, salah satunya adalah benar-benar tersembunyi dari pandangan (karena masing-masing enam sisi interface dengan kubus lain)

  7. Septia Ayu Pratiwi
    S2 Pendidikan Matematika 2018

    Pendekatan sprititual terhadap dimensi keempat berhubungan dengan keyakinan terhadap ajaran spiritual seperti adanya ajaran Budha, Hindu, Sufi, dan lain sebagainya. Manusia hanya mampu memhaami 3 dimensi seperti dimensi ciptaan-ciptaan-Nya di dunia ini, namun manusia tidak bisa memahami dimensi keempat secara konkrit karena dimensi keempat hanya milik Tuhan karena Dia yang bisa dapat mencakup seluruh dimensi tanpa terkecuali.

  8. Rosi Anista
    S2 Pendidikan Matematika B

    Dalam tulisan di atas, Fudjack dan Dinkelaker menemukan bahwa realitas dapat disamakan dengan ruang yang memiliki sejumlah dimensi tertentu jika kenyataan di mana seseorang ada memiliki ruang n dimensi, maka realitas yang memiliki dimensi n +1 atau lebih dapat dikatakan merupakan 'ruang hypers' sehubungan dengan itu.

  9. Janu Arlinwibowo
    PEP 2018

    Keyakinan atau spiritual merupakan suatu pemahan yang dapat membantu setiap manusia untuk memahami dimensi waktu. Seringkali waktu berjalan begitu cepat, namun apa yang dihasilkan sangat minimal, sehingga waktu memberikan efek penyesalan pada manusia. Bagaimana spiritual dapat membuat manusia berdamai bahkan bersahabat dengan waktu?
    Jelas dalam islam menyebutkan, keuntungan seseorang itu adalah ketika kualitas hidupnya lebih baik dari kemarin. Sangat jelas dalam hal ini bahwa waktu menjadi suatu skala untuk menentukan kualitas. Dengan mamahaminya dengan baik maka umat beragama akan dengan bijaksana memperhatikan waktu demi waktu untuk selalu meningkatkan kualitas hidup.
    Islam mengajarkan bahwa terdapat hikmah dalam setiap kejadian. Tegas dalam surat Al-Insyirah menyebutkan bahwa setelah kesusahan pasti ada kemudahan. Jika di ekstensifkan maka terkandung arti bahwa tidak ada sesuatu yang sia-sia (apa yang telah ita lakukan) karena pasti setelah usaha keras (kesusahan) pasti akan memberikan hasil yang menggembirakan. Ini adalah konsep dimana manusia diajarkan untuk tidak menyalahkan waktu, mengajarkan untuk tidak menyesal, dan berandai-andai tentang masalah lampau. Tetapi harus berusaha dengan keras setiap satuan waktu dan menatap kedepan seiring dengan berjalannya waktu.
    Adanya waktu yang abadi, waktu dunia dan waktu akhirat. Ketika manusai memahami ini maka akan membuat manusia memaksimalkan waktunya di dunia untuk mempersiapkan waktunya saat di akhirat. Dalam Islam dikabarkan bahwa kehidupan abadi kelak menanti semua manusia di akhirat sementara di dunia hanya sementara, maka bersibuklah untuk menyiapkan kehidupan abadi. Lagi-lagi waktu menjadi skala perhitungan, dimana waktu yang lebih lama (abadi di akhirat) memiliki nilai yang lebih dibading yang hanya sebentar (hidup di dunia).

  10. Rona Happy Mumpuni
    S2 Pendidikan Matematika D

    Setelah membaca artikel di atas, saya mendapatkan kesimpulan bahwa manusia hidup dalam empat dimensi. Dimensi pertama yaitu benda hidup yang terlihat statis namun bergerak, seperti tanaman karena tanaman dapat menguasai benda yang ada dibawahnya yaitu benda mati namun terbatas. Kemudian dimensi kedua yang tidak statis dan mampu bergerak pada bidang datar yaitu hewan, karena hewan dapat menguasai dua dimensi dibawahnya. Kemudian dimensi ketiga yaitu manusia. Manusia mampu menguasai 3 dimensi dibawahnya. Diatasnya lagi adalah makhluk tak kasat mata namun diyakini keberadaannya, yaitu malaikat dan jin. Karena Jin dapat menguasai 4 dimensi dibawahnya. Hingga dimensi tak hingga yaitu dimensi Tuhan. Dari keempat dimensi tersebut, dimensi keempat yang sulit dipahami oleh manusia. Salah satu pendekatan yang dapat digunakan untuk memahami dimensi keempat adalah pendekatan spiritual.

  11. Vera Yuli Erviana
    NIM 19706261005
    S3 Pendidikan Dasar 2019

    Assalamualaikum Wr. Wb.
    Fudjack dan Dinkelaker menemukan bahwa kenyataan bisa disamakan dengan ruang yang memiliki dimensi tertentu. Sejatinya ada berbagai macam pendekatan yang bisa digunakan untuk memahami dimensi keempat, salah satunya adalah dimensi agama atau spiritual. Islam mengajarkan bahwa pasti ada hikmah di balik suatu kejadian, dan problem yang diberikan tidak akan melebihi kadar kemampuan seseorang.