The power of words

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Sometimes the choice of words that we use to describe something can have a profound impact on how it is received by our listeners.

Most non-mathematicians will not realise that a large part of mathematical proofs are words and not symbols or equations. How can we use such imprecise tools as words to prove things with such abstract and precise meaning? Part of the power of words in this instance is the precise technical meaning that they have come to have over years of use by experts in the field. They can be a shorthand way to refer to countless other proofs and ideas laid down in the field by others.

One fascinating example of the subtlety of words is the adjective “quite”. I have had the experience where Australians have used “quite nice” to downplay the niceness to an acceptable but not extraordinary level, and yet a colleague from northern Europe saw “quite” as meaning “thoroughly” which is more correct from the dictionary. Tricky.

And I find that the emotion of the written word through emails is so much more difficult to navigate than the spoken word with its inflections and pauses.

Blessings

The mystery of words

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I love the way the English language has developed, with all of its complexities and richness. In this series I want to point out some of the beauty and strangeness of our language and hopefully to share some of the power of words.

I recently came across the origin of the word attention. It comes from the Latin root tendere which means to stretch – ad + tendere is to stretch towards. So we then have words like attendant and tenderness which have all grown from this same origin. In fact a tender can mean a ship that provides services to other ships, and a train tender is the carriage towed behind the engine that may carry coal or water! A far cry from the attendant at the hospital!

Tenderness has become one of my favourite attributes of the Divine that I can focus on at this time. And I love the connotations brought up by saying that we focus our attention, or we attend to a matter. Both evoke powerful images for me if I pause and consider them.

By contrast, this root also gives us our words tense and tension, which are seemingly opposite in meaning to the above.

Enjoy!

The Bunjil Creation Story

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(rewritten by Aunty Joy Murphy, Senior Wurundjeri Elder)

A very long, long time ago this beek (land) was like a big empty shell.

Bunjil was given a very important job to make the ngarra (mountains), the yalaks (rivers), all the creatures of the mernda (earth), a koolin (man) and a baggarrook (woman).

Bunjil could not do this alone. After thinking about this for a while Bunjil decided to make six tamboonamons (helpers): a tadjerri (brushtail possum), a turnung (flying mouse-glider), a yubup (green parakeet), a dandan (blue mountain parrot), a djert djert (nankeen kestral) and a tharra (swamp hawk).

Together they worked all yalingbu (day) and all burrun (night) for a long time. Finally Bunjil and his tamboonamons had ela monggi (created) the ngarras, the yalaks and all the creatures. Everyone was barbonneen (happy).

But Bunjil was tired, so tired he couldn’t gamagoen (fly). So Bunjil asked bellin bellin (musk crow) who was in charge of the moornmoots (winds) to help him gamagoen.

Bellin bellin opened one of his moornmoot bags. A big gush of moornmoot blew kalks (trees) out of the beek and into the air but Bunjil’s wings didn’t move. Bellin bellin opened all of the bags. A burt koreen (whirlwind) picked up Bunjil, his two wives Goonawarra and Kurook (two beautiful swans), his son Brinbeal (Rainbow) and his wife the second rainbow, and blew them up into the tharangilkbeh (heavens) to Bunjil’s willam (home).

After a good ngawe (rest), Bunjil felt balit (strong) enough to ela monggi a koolin and a baggarrook.

Bunjil gamagoen down to the beek and perched on the lango (edge) of the birrarung (river of mists). Bunjil scratched the beek and found some soft beg goreen (mud). With his big balit (claws) Bunjil stirred all yalingbu and all burrun. Eventually Bunjil ela monggi a round and long shape. The beg goreen shapes started to shake. A kawang (head) and a tooleroom (body) with dharraks (arms), gurrams (legs) and djeenongs (feet) appeared. Bunjil was excited, this will be the koolin.

More shaking and slowly the koolin stood up. He yann (walked) out of the beg gorreen. Bunjil followed closely and quietly. The koolin ngormi (sat) down on the lango of the birrarung.

Bunjil was dulin (proud) and told his birra (brother) Pally yan (Bat) how he had ela monggi a koolin. But Bunjil was tired and needed to gnawe again.

Pally yan said, ‘You rest my birri, I will ela monggi a baggarrook.’ Pally yan went to the same spot where Bunjil ela monggi the koolin. He found a kalkand hung upside down from a terru gulk (branch) to think about how he would ela monggi a baggarrook.

Pally yan decided to gamagoen over and around the beg goreen. The beg goreen began to shake, Squish, squish, pop, pop noises and then a tooleroom appeared. Pally yan said, ‘Ah, this will be a baggarrook.’

He took a piece of wooegook (stringybark) from the kalk and twisted until it was curly and placed it on the kawang of the tooleroom. Pally yan was excited but wondered how to give murrenda (life) to this tooleroom. He touched the upper part of the tooleroom with the tip of one of his taragos (wings). Pally yan said, ‘C’mon little one, nag ango (breathe).’ Pally yan felt a doorong ting kutini (heart beat).

The baggarrook opened her merrings (eyes), stretched out her dharraks, pushed Pally yan’s taragos away and stood up.

The baggarrook looked around. She saw the koolin and yann towards him. The koolin stood up and held the baggarrook’s marnangs (hand). They ngarrgee (danced) until all the beg goreen had fallen from their toolerooms. They yann away leaving their djinungs koorrngees (foot prints) on the beek.

Pally yan gamagoen to tell Bunjil the good news. Everyone was barbonneen.

(exert from The Little Red Yellow Black Book, fourth edition)

The Uluru Statement from the Heart

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‘Finding the Heart of the Nation’, a book written by Thomas Mayor, explains the process leading up to the formation of the Uluru statement; the culmination of much dialogue and consensus-building forged from more than two centuries of hardship and struggle. The Statement itself, and the Dreamtime artwork that surrounds it, both give testimony to the endurance, resilience, patience, strength, determination and grace of our First Nations People, the Aboriginal and Torres Strait Islanders.

In the coming days and years, we will have the opportunity to support their request for voice, treaty and truth-telling. It is my hope and prayer that all Australians will rally together to ensure that we move forward as a nation with respect, unity and equality. Today is the five year anniversary of the Uluru Statement’s creation and this week is Reconciliation Week. Please consider taking the time to read this important document:

THE ULURU STATEMENT (May, 2017)

We, gathered at the 2017 National Constitutional Convention, coming from all points of the southern sky, make this statement from the heart:

Our Aboriginal and Torres Straight Islander tribes were the first sovereign Nations of the Australian continent and its adjacent islands, and possessed it under our own laws and customs. This our ancestors did, according to the reckoning of our culture, from the Creation, according to the common law from ‘time immemorial’, and according to science more than 60,000 years ago.

This sovereignty is a spiritual notion: the ancestral tie between the land, or ‘mother nature’, and the Aboriginal and Torres Strait Islander peoples who were born therefrom, remain attached thereto, and must one day return thither to be united with our ancestors. This link is the basis of the ownership of the soil, or better, of sovereignty. It has never been ceded or extinguished, and co-exists with the sovereignty of the Crown.

How could it be otherwise? That peoples possessed a land for sixty millennia and this sacred link disappears from world history in merely the last two hundred years?

With substantive constitutional change and structural reform, we believe this ancient sovereignty can shine through as a fuller expression of Australia’s nationhood.

Proportionally, we are the most incarcerated people on the planet. We are not an innately criminal people. Our children are alienated from their families at unprecedented rates. This cannot be because we have no love for them. And our youth languish in detention in obscene numbers. They should be our hope for the future.

These dimensions of our crisis tell plainly the structural nature of our problem. This is the torment of our powerlessness.

We seek constitutional reforms to empower our people and take a rightful place in our own country. When we have power over our destiny our children will flourish. They will walk in two worlds and their culture will be a gift to their country.

We call for the establishment of a First Nations Voice enshrined in the Constitution.

Makarrata is the culmination of our agenda: the coming together after a struggle. It captures our aspirations for a fair and truthful relationship with the people of Australia and a better future for our children based on justice and self-determination.

We seek a Makarrata Commission to supervise a process of agreement-making between governments and First Nations and truth-telling about our history.

In 1967 we were counted, in 2017 we seek to be heard. We leave base camp and start our trek across this vast country. We invite you to walk with us in a movement of the Australian people for a better future.

I believe it is time to walk this way together.

Aboriginal Cosmology

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When we talk about cosmology, we generally assume that astro-physics will inform us about the science of the origin and development of the universe. Modern cosmology is dominated by the Big Bang theory, which brings together observational astronomy and particle physics. However, the more general meaning of cosmology is ‘an account or theory of the universe’. Therefore, it is more appropriate for us to talk about ‘cosmologies’ as many theories exist from all around the world. A grieving child who is told by a parent that ‘Grandma died and has become a star who watches over them’ has begun the gentle art of developing an evolving cosmology.

Many of our readers are aware that we are both trained scientists who enjoy inhabiting the middle ground between science and spirituality (see for example Science and Spirituality and Knowledge and Mystery). We understand that there are many unknowns (and we believe unknowables) in the disciplines of science (including cosmology and the origins of the universe and life itself). Therefore, our own personal cosmology, leans heavily on other disciplines including theology, philosophy and literature.

Western thinking often relies predominately on rational reasoning to gain knowledge and understanding, unable to easily incorporate truth delivered via mythology, dreams, or allegories. However, we have some understanding of learning from myths/legends in our inheritance from the Greeks. Johanna Lambert explains in her book, ‘Wise Women of the Dreamtime’:

In classical Greek myths the Gods or archetypes (Ancestors) have become generalized as universal influences associated with astrological configurations in the sky and supposedly with unchanging characteristics of a universal collective unconscious. In contrast, Aborigines associate these ancestral powers with specific land formations and natural features, and they do not consider their inner psychic landscape to be fixed by generalized collective archetypes. Rather, the Aborigines are inwardly transfigured by the vibrational energies intrinsic to the numerous sacred sites they travel to and from, and they manifest very different characters according to the role they play in the ceremony associated with a particular earthly space.

Comprehending this helps us to appreciate how important the connection and relationship to land/country is for our Australian First Nation Peoples. And, just how traumatic and dislocating the loss of their land (and sacred sites) has been for them. Without an understanding of their cosmology, and respect for their rights to live meaningful lives based on their genuine worldview (and value system or laws), it is hard to imagine Australia being able to reconcile the past and enter the future with unity and hope.

For those readers who would like more understanding, I will finish this piece with a further quote from Johanna Lambert’s book:

In Aboriginal cosmology the Dreamtime epoch concluded; however, the energy and vibrational patterns from the exploits of the great Ancestors congealed the initially limitless space into the topography and forms that we now experience as the material aspect of the universe. The land, its forms and features, as well as the subtle vibrational energy emanating from an earthly place, is the imprint or record of Dreamtime episodes. During the Dreamtime, the Ancestors could transform from humans to animals, until, at the conclusion of this world-creating epoch, they retired to their abode beneath the earth and in the sky. At that time, human and animal became distinct species. However, the emotional, psychological, and psychic characteristics of humans remained symbolized in the physical characteristics and behaviour of the animals. Therefore the Aboriginal worldview can be seen as founded upon a distinct twoness, or fundamental duality at the basis of creation: the Dreamtime epoch that occurred and has concluded, and the earthly creations, or physical reality, that emerged after the Dreaming.

The myths that the Aborigines have transmitted for untold generations were conceived from visualizing what must have taken place in a particular region in order to have the earthly environment take on its shape and condition. Behavioral codes, or Dreaming laws, were subsequently laid down for human society based on this endless array of mythic events and their significance and outcomes.

Wise Women of the Dreamtime

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I have just finished reading a book with this title. Fourteen Aboriginal tales of the Ancestral Powers were collected by a woman called Katie Langloh Parker (between 1896-1918), and Johanna Lambert (in 1993) gathered these sacred stories together with commentary to produce this exceptional book. Neither of these women were/are Aboriginal themselves but both had/have close relationships with Australian first nations people.

For many years (decades now), I have intentionally tried to gain an understanding of Aboriginal worldview, dreamtime stories, law and spirituality. This book has brought to me a fresh opportunity; I can now begin to grasp some of the nuances that have alluded my earlier attempts. Over the next few blogposts, I will endeavour to communicate my fresh realizations to you. Rather than use my own words (given this knowledge is still new-born in my mind), I shall quote from various parts of Lambert’s book attempting to form a consistent narrative of understanding.

The Dreamtime, from which all societal law originated, can be described as a vast epoch that occurred, according to the Aborigines, ‘before time began’. All the Dreamtime stories, or Aboriginal myths, depict events from the Dreamtime, which existed prior to the appearance of the manifest world. This was a period when great mythical powers and beings pervaded infinite space and, with almost incomprehensible intensity and force, lived out their dreams unencumbered by the limits and definitions of embodied existence. The entire contents of universal consciousness – every imaginable physical and psychological characteristic, interaction, and relationship – poured through the dramas of the Dreamtime creative Ancestors.

The exploits and mode of being of the great Ancestors resonate, to a lesser degree, with our experience of dreaming. That is, during our dreams, space and time are unbounded. One’s dreaming self floats in a world beyond the rational, where subject and object, meaning and form merge and separate kaleidoscopically. (Pg 7, ‘Wise Women of the Dreamtime’, ed by Johanna Lambert, 1993)

These two paragraphs help me to value the Dreamtime stories (being a non-Aboriginal Australian) in the context of our global Creation literature ‘library’, which includes a variety of sacred writings/texts. For many cultures around the world, their local Creation stories help determine identity and relational patterns toward deity(ies), self, others, animals, plants, land, water and nature as a whole. However, perhaps none as potently (and intricately) as the Australian Aboriginal Dreamtime stories. I believe we all have something to learn (and gain) by listening carefully to the wisdom contained in these stories held safely in the hands of the longest continuous human culture in the world.

For those of us who hold fast to Christian faith (or perhaps more correctly, are held fast by Christ’s faithfulness), we may consider the reality that in Genesis God/dess is referred to by the word ‘Eloihym’ which translates to ‘The Powers’. Perhaps our indigenous sisters/brothers have something to teach us about this ancient Hebrew name for deity.

Dadirri

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This word is an aboriginal word, from the Ngangikurungkirr language, meaning ‘deep listening’. It is a way of embracing quiet still awareness and allowing nature, country or place to speak to us. Miriam-Rose Ungunmerr believes that dadirri is a gift from Australia’s first nation peoples to the whole nation. She describes it this way, ‘to listen deeply is to connect; it’s the sound of deep calling to deep’.

When I first heard of dadirri, it was a ‘coming home’ experience for me; I realized that this practice of inner deep listening had been of foundational spiritual importance to me since childhood. Although I am not aware of any Aboriginal lineage, it is a well-established pattern for me to sit in nature on the earth and wait quietly for wisdom, encouragement and/or guidance. Hardly a day goes by, (and never a week), without me feeling the need to retreat into nature to listen to the quiet still voice of the Spirit. In the Hebrew sacred text, the creation story says, ‘In the beginning, Eloihym (the Powers) fattened the earth. Ruach, the Spirit, was hovering broodily over the waters’. It is therefore not surprising that our human spirits are nourished and informed when we place ourselves in nature with awareness; listening and waiting. Dadirri invites us into stillness and allows us to experience the depth and knowledge of the spiritual aspects of country without the need for words or complex rituals. In Miriam’s words, ‘Dadirri is the deep inner spring inside of us; we call on it, and it calls on us’.

So, how does it work? I can only answer for myself. I simply find somewhere in nature to walk or sit or lie down. I still myself and make myself aware of the natural surroundings. I give my attention to trees, animals, birds, the ground, water, clouds, the air, the sun, rocks, grass; whatever natural elements I have access to in that place, is what I focus on. I breathe deeply and commit to resting in this place (even if I am walking). It is important to be unhurried so I normally set aside at least half an hour for intentional dadirri. Usually, something in my surroundings will catch my attention (as though a spot-light has been placed on it). It will make me curious and I will look at it carefully and/or listen for any noises or smells associated with it. I may touch it if it is touchable. I allow my memories and my imagination to be freely included in my considerations and I try not to judge anything that comes to my mind. Sometimes this process leads me to profound epiphanies, and sometimes it leads me into deep gratitude for the simplest of nature’s gifts. Nearly always, I come away from these times feeling refreshed and peaceful; knowing that I belong on the earth and am part of a bigger story.

Where can dadirri be done? I live half of my week in the urban centre of a big city (Melbourne) and half of my week on a rural property surrounded by bush and gardens. Both places provide opportunities for me to listen and learn from nature in the way I have described. I have a favourite place in the city which is simply a circular piece of grass surrounded by lemon-scented gums (still young). It is a haven for birds and dogs and small humans. Around the circumference, there are curved bench seats made of steel, and the grass resembles an arena making it easy for me to start the day with anticipation. Dadirri flows easily in this urban space. Equally well, a walk in the Australian bush as the day is awakening or closing, is often an encounter with the Sacred; a walk on ‘holy ground’.

I will leave you with two examples of river dadirri; one of my own (River Wisdom), and one from Miriam-Rose Ungunmerr:

River Wisdom

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Birrarung (the River) reminds me to be forgetful; let forgiveness flow and grace abound.

Creator is more about freedom than goodness; more about the now than the then.

‘See, I am doing a new thing’, says the River passing by,

‘Forget the former things; let go of the past’, it says as it flows to the ocean.

Eloihym’s voice echoes gently in my mind:

‘The new thing springs up. Do you not perceive it?

‘I am making a way in the desert, and streams in the wasteland.’

The River gurgles along playfully, singing,

‘Let go, let go, let it flow, let it flow.’

The saxophone chimes in with agreement,

‘Let the melody flow, a new song, a new song.’

A seagull gives testimony, standing in affirmation, squawking,

‘Let it go sista, let it flow sista, a new song, a new song.’

Plane numbers

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If you were to go walking on the field of numbers you would start as an infant only familiar with a series of dots, the one, two, three of counting. As you grew you would realise that these numbers continue to grow with you. It is not long until you discover numbers that need to be written down to be realised – they are beyond fingers and toes. (At some point you are introduced to zero, a special number indeed. For me it was not the absence of something, rather it was the end of the countdown when your rocket could blast off). Finally, to complete the story of this line of numbers, someone pointed out to you that each number had its pair stretching back in the reverse direction – the negatives. And all of these special numbers, the integers, would dance to the tune of a special set of rules and patterns, which some of us found interesting and engaging, others opaque and confusing.

For the former group, a new world of numbers opened up when we were shown the prime numbers – numbers that could not be broken down into smaller numbers. They were special indeed, and the deeper you looked, the more special they became. Numbers apparently without patterns suddenly had hidden regularities within them. How could that be so? And, with advanced analysis, these primes provided a mystical, magical connection to other apparently unrelated number theories and even fields of science. Heady stuff indeed.

So the number line, as it was called, had infinite length, infinite detail and hidden cycles and patterns. And that was just considering the integers, not the messy bits in between like the fractions and the other gaping holes between the fractions.

Now I would like you to go back to the middle of the number line and look along the line of positive integers, and imagine for me that you can look both left and right and see an infinity of other numbers out on the plane all around you. We give these other numbers the name complex numbers or imaginary numbers but both adjectives are misnomers, they are neither complex nor imaginary.

Now I would like you to walk to the point on our familiar number line midway between zero and one and stand there a moment. If you were to look left and right you would see a line of points stretching out to the infinities in both directions that are the solutions of a special function, the zeta function. Like the primes, they appear to be randomly placed but have some order to them. Like the primes, their placement is related to other fields of mathematical study. But the difference is, unlike the primes which all lie along the number line, we don’t know if all of them lie on this perpendicular line that I have you looking along. So far, after years of study they do all lie on this line, but it only takes one outlier and a beautiful edifice of mathematical study will come tumbling down to be replaced by another one built on its ruins. Some bright spark will discover another non-conformer and another and then someone else will put a limit on how many there are and where to find them and so on it will go.

But for now we can gaze to our left and to our right and imagine the ones we know sitting there nicely lined up for us and realise how much hidden beauty there is in the familiar and the unfamiliar world of mathematics.

Amen.