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44 might recover their former Fertility, if they were again peopled with Men and Cattle; in as much as about thoe Places there grows fine Gras, epecially from 60 to 65 Degrees. In the great Bay, which in the Sea Carts goes under the Name of 's River, and at preent is called the Bay of Good Hope (from the Danih Colony ettled near the Entrance of this Inlet) there are on both Sides of the Colony many good Pieces of for the grazing and paturing Numbers of Cattle, beides Plenty of Proviion, which the Sea as well as the Land yields. Trees or Woods of any Conideration are rarely met with; yet I have found in mot of the Bays Underwoods and Shrubs in great Quantity, epecially of Birch, Elm, and Willows, which afford ufficient Fuel for the Ue of the Inhabitants. The larget Wood I have een is in the Latitude of 60 and 61 Degrees; where I found two or three Fathom high, omewhat thicker than a Man's Leg or Arm: mall  grow alo here in abundance, the Berries of which

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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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 town and its external aspect, was as striking as it was full of pain. With the exception of the dull high street, which had the usual characteristics of a small agricultural market town, some sombre mansions, a dingy inn, and a petty bourse, Marney mainly consisted of a variety of narrow and crowded lanes formed by cottages built of rubble, or unhewn stones without cement, and from age, or badness of the material, looking as if they could scarcely hold together. The gaping chinks admitted every blast; the leaning chimneys had lost half their original height; the rotten rafters were evidently misplaced; while in many instances the thatch, yawning in some parts to admit the wind and wet, and in all utterly unfit for its original purpose of giving protection from the weather, looked more like the top of a dunghill than a cottage. Before the doors of these dwellings, and often surrounding them, ran open drains full of animal and vegetable refuse, decomposing into disease, or sometimes in their imperfect course filling foul pits or spreading into stagnant pools, while a concentrated

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 of every species of dissolving filth was allowed to soak through and thoroughly impregnate the walls and ground adjoining.

These wretched tenements seldom consisted of more than two rooms, in one of which the whole family, however numerous, were obliged to sleep, without distinction of age, or sex, or suffering. With the water streaming down the walls, the light distinguished through the roof, with no hearth even in winter, the virtuous mother in the sacred pangs of child-birth, gives forth another victim to our thoughtless civilization; surrounded by three generations whose inevitable presence is more painful than her sufferings in that hour of travail; while the father of her coming child, in another corner of the sordid chamber, lies stricken by that typhus which his contaminating dwelling has breathed into his veins, and for whose next prey is perhaps destined, his new-born child. These swarming walls had neither windows nor doors sufficient to keep out the weather, or admit the sun or supply the means of ventilation; the humid and putrid roof of thatch

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Rh There are also Spiders, Flies, and Wasps. They know nothing of any venomous Animals, as Serpents and the like; nor have they any Snakes, Toads, Frogs, Beetles, Ants, or Bees; neither are they plagued with Rats, Mice, or any such Vermine.

Greenland Sea, abounds in different Sorts of Animals, Fowls and Fihes, of which the Whale bears the Sway, and is of divers Kinds, Shapes and Sizes. Some are called the Finned Whales, from the Fins they have upon their Back near the Tail; but thee are not much valued, yielding but little Fat or Blubber, and that of the meaner ort; they conit of nothing but lean Fleh, Sinews and Bones. They are of a long, round and lender  Rh

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Page:Atlas of the World’s Languages in Danger.pdf/10

Christopher Moseley

Nine years have passed since the previous edition of this Atlas was published. Nine years have also passed since the death of Professor Stephen Wurm of the Australian National University, who edited the first two editions. They marked the first attempt to plot on maps the locations of the languages that were most in danger of extinction within the foreseeable future. Both those editions highlighted particular areas of the world where linguistic diversity was being seriously depleted.

This project was born of a concern for the loss of diversity in this most basic human resource. It parallels the increasing concern over the loss of the world’s biological diversity, and for related reasons: the loss of isolated and self-sustaining habitats in the face of encroaching urbanization, economic concentration and the consequent homogenization of human cultures.

By its very nature, this Atlas tends to become outdated more rapidly than an ordinary language atlas would do. What is plotted on these maps are the most fragile linguistic balances – languages in danger of disappearing, even disappearing from one edition to the next.

The present edition is a logical progression from the second edition of 2001, which was divided into five parts: an introduction detailing developments in the study of endangered languages since the first edition; a description of the phenomenon of language endangerment and the death of languages; a short report on efforts by the scientific community to describe and record endangered languages; a fairly detailed overview of language endangerment in all major parts of the world; and a small atlas of some fourteen maps, some completely new and some others revised from the previous edition.

What the 2001 edition called ‘major parts of the world’ could be defined as those areas where the pressure on minority languages was the greatest, to put it in the simplest terms. This edition, however,


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Malaya Agreement 1948, as the case may be, shall be registered as a citizen of Singapore under the provisions of this Constitution.

61. (1) A citizen of Singapore who is a citizen by registration or by naturalization shall cease to be such a citizen if he is deprived of his citizenship by an order of the Government made in accordance with the provisions of this Article.

 * (2) The Government may, by order, deprive any such citizen of his citizenship if the Government is satisfied that the registration or certificate of naturalization—

 * (a) was obtained by means of fraud, false representation or the concealment of any material fact; or

 * (b) was effected or granted by mistake.

 * (3) The Government may, by order, deprive any such citizen of his citizenship if the Government is satisfied that that citizen has, within the period of five years after registration or naturalization, been sentenced in any country to imprisonment for a term of not less than twelve months or to a fine of not less than five thousand dollars or the equivalent in the currency of that country and has not received

a free pardon in respect of the offence for which he was so sentenced.

 * (4) No person shall be deprived of citizenship under this Article unless the Government is satisfied that it is not conducive to the public good that that person should continue to be a citizen of Singapore; and no person shall be deprived of citizenship under paragraph (b) of clause (2) or under clause (3) of this Article if the Government is satisfied that as a result of the deprivation he would not be a citizen of any country.

 * (5) This Article shall not apply to any person who has been naturalized as a citizen of Singapore under the provisions of the Federal Constitution.

62. (1) Where a person has been enrolled as a citizen of Singapore under the provisions of Article 56 of this Constitution and the Government is satisfied that the enrolment—

 * (a) was obtained by means of fraud, false representation or the concealment of any material fact; or

 * (b) was effected by mistake,

the Government may by order cancel the enrolment.

 * (2) Where under this Article a person's enrolment as a citizen of Singapore is cancelled that shall not discharge him from liability in respect of anything done or omitted before the cancellation, but except as regards anything so done or omitted he shall as provided in the Federal Constitution revert to his former status as a citizen of Malaysia.

63. (1) Before making an order under Article 61 or 62 of this Constitution, the Government shall give the person against whom the order is proposed to be made notice in writing informing him of the ground on which the order is proposed to be made and of his right to have the case referred to a committee of inquiry under this Article.


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Introduction expands the coverage to virtually the entire inhabited world, regardless of the density of endangered languages, while varying the scale of the maps to accommodate and acknowledge those areas where the linguistic diversity is greatest, or under the greatest threat.

The five years between the appearance of the first two editions were marked by an explosion in awareness of and research into language endangerment. This was due to several factors. My predecessor, Stephen Wurm, in the Introduction to the previous edition, pointed to a number of ventures that appeared alongside the first edition of this Atlas, including both publications and organizations in support of threatened languages. For a number of years previously, several international forums had been calling attention to the threat to the world’s pool of species diversity, and clearly this created a public mood that also encouraged an interest in preserving the diversity of human language and material culture. Thanks to the devotion of linguists in many countries, for the first time in human history it had become possible, at least in theory, to accurately catalogue and locate every language known all over the world. The compendium the Ethnologue: Languages of the World (Lewis, 2009), published by SIL International at regular intervals since 1951, is one of the most extensive efforts of this kind, and the Encyclopedia of the World’s Endangered Languages (Moseley, 2007) is one of the most recent. The only languages omitted were those belonging to the remaining handful of uncontacted peoples in the most inaccessible regions of the world.

Uncontacted languages are not the same as endangered languages, of course. But from the moment contact is established with the outside world, it must be assumed that the (previously) uncontacted group is not initiating the contact, but rather has been ‘discovered’, and that the discoverers represent a much larger speech community, probably an international one, and one which, at the very least, has sufficient infrastructure to organize such an expedition. One must also assume that the contacting side has an interest in either the speech community or the land it occupies. Commercial expansion and exploitation are frequently the motive behind such explorations and incursions.

Such first contacts are rare nowadays, but not unknown. There are also cases where the speakers deliberately repulse any attempt at contact, such as the speakers of Sentilese on Sentinel Island in the Andaman group in India, and certain Amazonian groups. In the twenty-first century, when a traditional way of life among hunter-gatherer peoples is a rarity, it is prized and championed by advocacy groups such as Survival International.

From the point of view of the linguistic researcher, this is a double-edged sword. The trained linguist must be sensitive and alert not only to linguistic factors so as to be able to accurately describe and transcribe the language (usually with the help of a bilingual intermediary) but also to non-linguistic and cultural factors, ignorance of which might alienate the group being studied and make cooperation impossible. Nowadays professional linguists, whether their aims are missionary or purely research-oriented, receive a thorough training in field methods. This in itself is an important factor in the future preservation of the world’s threatened languages.

What constitutes an endangered language, then? Linguists differ in their assessments of what exactly endangerment is, and the degrees of danger implied (see the writings of Joshua Fishman, 1991, 2000, a pioneer in this field of study, on the ways of assessing the viability of a language for revitalization), but the simplest definition that can be given is the following: a language is endangered if it is not being passed on to younger generations.


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Atlas of the World’s Languages in Danger There are many complications, nuances and uncertainties associated with this definition. For example, a language may be thriving in the home environment, but not taught in the schools. In such cases, the language is not likely to be a written one, so that oral transmission is the norm. A language may be the vehicle of an economic underclass whose breadwinners are forced to go elsewhere to seek work – and when they do move into a larger speech community, they may not be able to retain everyday use of their own language. Circumstances vary from region to region, as will be seen from the discussions in this book, but a common thread running through those discussions is that endangered languages lack prestige – even in the eyes of their speakers; they lack economic power and independence; they lack a stable infrastructure; and in most cases they also lack literacy. That is why it is an important mission of the United Nations Educational, Scientific and Cultural Organization (UNESCO) to locate and publicize those languages, for the common awareness of humankind and the common good of its Member States.

Between the first and second editions of this Atlas, rapid strides were made in the coordinated study of language endangerment on a worldwide basis. Work on severely endangered languages in various parts of the world was carried out under a contract between the Intangible Cultural Heritage Section of UNESCO and the Permanent International Committee of Linguists (CIPL), enabled by a series of grants. Grants have also been provided for language documentation and rescue projects by the Linguistic Circle of Copenhagen; the Volkswagen Stiftung in Germany; the British-based Foundation for Endangered Languages; the Endangered Languages Fund in the United States of America; and the Languages of the Pacific Rim Project directed from Kyoto, Japan. The funding of research in the field has been placed on a much firmer footing since the establishment in 2002 of the Hans Rausing Endangered Languages Project, based at the School of Oriental and African Studies (SOAS), University of London.

The revival of recently or even long-extinct languages is becoming a topical issue in many parts of the world, with the descendants of the last speakers clamouring for materials on their ancestral languages in order to gain an insight into how they sounded and functioned, and to relearn them at least in part so that they can use words and phrases as symbols of their reawakened identity. In Australia, for example, several dying or extinct languages have been revived and already have several dozen speakers, with more and more members of the respective ethnic communities learning their ancestral tongues.

Nations in which a major world language of colonial expansion is the dominant one, but which harbour small languages whose territory is shrinking, have often found it hard to come to terms with their indigenous heritage, and have not devoted sufficient attention to the field of safeguarding language. This is true not only of Australia, Canada and the United States, where English has swept all before it, but also of Lusophone Brazil and the Spanish-speaking world generally. That is one reason why this international volume fills such a pressing need: there is an obvious benefit in comparing the situations of loss of diversity and taking steps to redress the balance.

The history of mapping the world’s languages is almost as recent as that of the awareness of language endangerment – indeed, they go hand in hand. Not only does this edition of the Atlas provide a more complete coverage of the world’s surface than the previous editions, but the maps have been prepared in a completely different way. For the first time, this Atlas is being made available in both print and online versions, and the contributors have plotted the data interactively, making use of an interface developed by UNESCO and based on the Google Maps


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waited to let the forty cows go past, each of them pausing to lick the forehead of the strawberry cow that leaned over the gate of her stall and lowed continually concerning her newly-born white calf. But so slow they were in their wanton, obedient movement to the milking-shed that we turned and found another path, and thus surprised a pond lying deep among tansy flowers, grey nettles and billows of conquering bramble and brier.

The farmyard was always dusty, or deep with ridgy mire, from the trampling of men and horses and cows in the streets that wound among its cart-lodges, stables, stalls, milking-sheds and barns all glowing with mature tiles, and ricks gleaming with amber thatch. But in a corner lay unused, older than them all, the long-headed and snaky-bodied pond. We learned to know that pond.

Sometimes, when summer has honoured the water with a perfect suit of emerald green, that pond shows itself to be a monstrous, coiled, primæval thing, lying undisturbed, and content to be still and contemplative. Often has the monster been driven away—by draining; often has it returned, still a green, coiled, primæval being that disappears suddenly in November and leaves a soft, dark

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 pool. Some have ventured to intrude upon the monster, to fish for the sleepy carp which are found when it has been driven from its nest of purple mud; but they fish in vain.

The solitary, dying ash tree at the edge of the pond seems, by day, when the monster is powerful there in the summer, to be but the skeleton of an old victim; or, in the winter, the sad and twisted nymph of the water. But every night, like any dreaming child or musing lover, though not perhaps so happily, is it let into a varied, strange, exalted paradise.

You may see it—on still evenings when the mist prevails over all things except the robin's song, and makes even that more melancholy—or when the songs of many nightingales besiege, enter and possess the house and the deserted farmyard—or when the cold and entirely silent air under a purple November sky chills the blood, so that friendship and hope and purposes are all in vain as in an opiate dream—then you may see the ash-tree take heart. It has the air of one going home upon a lonely road that will not end in loneliness. Those bare and stiff, decaying branches are digits pointing homeward through the sky; the tree forgets the monster at its feet and the children who laugh and the supremacy of the buildings round about. It might seem, with those extended branches, to be a self-torturing and aspiring fanatic who had endured thus for uncounted days and nights, and has his vision at last. For, when night is perfect, the tree exults, and though it is perhaps not joyous, it is as one of those great sorrowful temperaments—of soldier, or explorer, or humorist—so active and inexorable that they

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 may claim kinship with the truly joyous ones. If it is still sad, it is "endiademed with woe." How large and satanic it is beside the heavy rounded oaks and the stately, feminine elms and the lovely limes.

Even so might a philosopher heighten and lord it, travelling in Charon's ship along with deflated tyrants and rhetoricians and bold and crimson animals born to eat provinces and to poison worms; even so, Ossian and Arthur and Cuchullain and Achilles triumph over men that were yesterday on thrones and chariots.

Often have I seen the tree, and it alone, giving character to the whole valley and filling the land as a bell fills a cathedral or as the droning of a bee fills a lily.

My little thoughts seem to be drawn up among the black branches like twittering birds going to rest in some high cliff that is a chief pillar of the fabric of the night. Half dead and threatened though it be, surely the spirit of it, which is to many a broad and tragical night as the arm of a great painter to his picture, will survive not only me and my words but the tree itself. I have approached it on some moonlit midnights, when the sky was so deep that the tall oaks were as weeds at the bottom of an unfathomed sea, and it has stood up erect and puissant, as if it were the dreamer at one with all he sees, in a world of blind men with open eyes. Then, as the autumn dawn arrived it was still looking towards Orion; defrauded, indeed for a time of its vision, but not of its glory. The swaying cows wandered to the milking

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Page:CTRL0000034607 - Deposition of Ali Alexander, (Dec. 9, 2021).pdf/68

68 And so, what I have seen since then is a video that I believe to be true, and which he says, Hey, guys, you can't be here. Go to Lot 8, that's where Trump said he's going.

Right.

And so, that was a tool of rhetoric by speaker. At that point I have to believe that Alex but Alex can be naive and innocent and he could have believed that.

That's fine. We saw a text message earlier you saw where Caroline Wren told you—

What time was it at?

12:59, POTUS not walking. Do you remember that?

Yeah. And that's what—my true belief is that the President was not coming.

Right. So at that time you knew it wasn't true, as far as you knew that the President—when Mr. Jones said that the President was coming, you knew at that time he wasn't coming. Is that right?

It would have seemed logistically improbable.

I'm asking what you understood at the time that he wasn't coming.

Yes. My understanding was that it was logistically improbable to the nth degree. And again, I already told this committee that in my professional opinion, there was no way for Trump to ever come.

I heard you. I heard you.

And so, did you ask Mr. Jones at the time why are you saying that President Trump is coming?

No. I'm observ—I have tear gas in my eyes. I'm not thinking about correcting him. And again, we're engaged in tools of rhetoric to get people out of the conflict zone. And so, if Mr. Jones said that there are aliens on the other side, I would


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Rh the yōgīs of the Vaishṇava orders have usually been more agreeable and less ambiguous than those of the Śaiva community.

We must briefly consider now the religious teachings of the Bhagavad-gītā and the Nārāyaṇīya, and then turn to the inscriptions and contemporary literature to see whether we can find any sidelights in them. We begin with the Bhagavad-gītā, or The Lord's Song.

The Bhagavad-gītā purports to be a dialogue between the Pāṇḍava prince Arjuna and Kṛishṇa, who was serving him as his charioteer, on the eve of the great battle. In order to invent a leading motive for his teaching, the poet represents Arjuna as suddenly stricken with overwhelming remorse at the prospect of the fratricidal strife which he is about to begin. "I will not fight," he cries in anguish. Then Kṛishṇa begins a long series of arguments to stimulate him for the coming battle. He points out, with quotations from the Upanishads, that killing men in battle does not destroy their souls; for the soul is indestructible, migrating from body to body according to its own deserts. The duty of the man born in the Warrior-caste is to fight; fighting is his caste-duty, his dharma, and as such it can entail upon him no guilt if it be performed in the right spirit. But how is this to be done? The answer is the leading motive of Kṛishṇa's teaching. For the maintenance of the world it

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 sheds. The little bats ran to and fro in the air and made their little snipping and drumming sounds. It was light; but the ash tree was not utterly cast down; it still walked in the way of the stars; it was inscribed in solemn characters upon the sun that rode up red in the mist.

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Page:CTRL0000034607 - Deposition of Ali Alexander, (Dec. 9, 2021).pdf/69

69 support that, because that would get people away from tear gas, away from conflict.

Right. Because what attracted people is the fact that President Trump was there in your mind, right? That they would go to where he said President Trump was?

If Trump was coming to Lot 8, a lot of people would come to Lot 8.

Right. Because as we talked earlier we talked about President Trump's words, we are not talking about Brandenburg in the Supreme Court. The people who were there were Trump supporters, right?

There are a lot of people and a lot of evidence to suggest that the reason that we saw no counter protesters is that they were in the crowd, too.

There. The majority of the people you saw there were Trump supporters from everything that you saw?

They purport themselves to be Trump supporters. I sometimes do not feel safe, which is why I said me, and Owen Shroyer, and Alex Jones are all in the security bubble. And we are stuck together. There is no exiting the security bubble. We are in the security bubble and we are at the mercy of whatever those gentlemen tell us to do.

Right, okay. And so, at any point did you ever talk to Mr. Jones where he is getting the information that President Trump—

No.

You never asked him?

No. That would be improbable. I have tear gas in my eyes. I'm suffering from a traumatic event. My event is being barred from happening. And I'm just thinking about how do I save human lives, you know.

And part of that would be it sounds like at least Mr. Jones was saying that President Trump was coming.

Mr. Kamenar. Counsel, I think he's asked and answered your question. You've


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title: The Heart of England/Chapter 10


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80 is necessary that men should do the works of their respective castes, and these works do not operate as karma to the detriment of the future life of their souls if they perform them not from selfish motives but as offerings made in perfect unselfishness to the Lord. This is the doctrine of Karma-yōga, discipline of works, which is declared to lead the soul of the worshipper to salvation in the Lord as effectually as the ancient intellectualism preached in the Upanishads and the Sāṃkhya philosophy. But there is also a third way to salvation, the way through loving devotion, or bhakti, which is as efficacious as either of the other two; the worshippers of Śiva had already preached this for their own church in the Svētāśvatara Upanishad. Besides treating without much consistency or method of many incidental questions of religious theory and practice, Kṛishṇa reveals himself for a few instants to Arjuna in his form as Virāj, the universal being in which all beings are comprehended and consumed. Finally Arjuna is comforted, and laying the burden of all his works upon Kṛishṇa, he prepares in quiet faith for the coming day of battle.

There are four main points to notice in this teaching. (1) The Supreme God, superior to Brahma, he who rules by grace and comprehends in his universal person the whole of existence, is Vishṇu, or Hari, represented on earth for the time being by Kṛishṇa Vāsudēva. The author

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70 asked it several times.

Mr. Okay. Fair enough.

Mr. Kamenar. And he said he hasn't talked to Jones to explain—

 * BY

How about after the fact? Did you ever have a conversation with Mr. Jones why he said at the time at the Capitol Grounds that President Trump was coming?

I don't recall that Alex Jones and I have had a conversation about a play by play of the traumatic event, no.

Okay, so no. Okay.

 * BY

Let's go back to Exhibit 26, page 236. You're on that page already.

Mr. Kamenar. What's the page?

Mr. . 236.

The Witness. I was on the page, I'm sorry.

 * BY :

That's okay.

And it looks like you're testing a Jordan Harrison, do you see that part of the page?

Yes.

And there are messages to say make the wild protest. I am assuming the wildprotest.com page, a blank page. First, who is Jordan Harrison?

Jordan Harrison is a web vendor that I frequently use for computer-related stuff. I had no computer access.

And who was in control of the wildprotest.com website?

It was a Stop the Steal website.

And why are you telling Jordan Harrison to make the web page blank at the


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78 .). Their teachings are not the same in details, though on most main points they agree; for they belong to different sections of the one religious body. Leaving aside the Bhagavad-gītā for the moment, we note that the Nārāyaṇīya relates a story that there were born four sons of Dharma, or Righteousness, viz. Nara, Nārāyaṇa, Hari or Vishṇu, and Kṛishṇa. In other places (I. ccxxx. 18, III. xii. 45, xlvii. 10, V. xlviii. 15, etc.) we are plainly told that Nara is a previous incarnation of Arjuna the Pāṇḍava prince, and Nārāyaṇa is, of course, the supreme Deity, who in the time of Arjuna was born on earth as Kṛishṇa Vāsudēva, and that in his earlier birth Nara and Nārāyaṇa were both ascetic saints. This tradition is very important, for it enables us to see something of the early character of Nārāyaṇa. He was an ancient saint of legend, who was connected with a hero Nara, just as Kṛishṇa was associated with Arjuna; and the atmosphere of saintliness clings to him obstinately. Tradition alleges that he was the ṛishi, or inspired seer, who composed the Purusha-sūkta of the Ṛig-vēda (X. 90), and represents him by choice as lying in a yōga-nidrā, or mystic sleep, upon the body of the giant serpent Śēsha in the midst of the Ocean of Milk. Thus the worship of Vishṇu, like the worship of Śiva, has owed much to the influence of live yōgīs idealised as divine saints; though it must be admitted that

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Rh makes no attempt to reconcile the fatalism implied in the old theory of karma-saṃsāra with his new doctrine of special and general grace: he allows the two principles to stand side by side, and leaves for future generations of theologians the delicate task of harmonising them. (2) Three roads to salvation are recognised in principle, the intellectual gnosis of the old Upanishads and the Sāṃkhya, the "way of works" or performance of necessary social duties in a spirit of perfect surrender to God, and the "way of devotion," continuous loving worship and contemplation of God. In practice the first method is ignored as being too severe for average men; the second and third are recommended, as being suitable for all classes. (3) The way of salvation is thus thrown open directly to men and women of all castes and conditions. The Bhagavad-gītā fully approves of the orthodox division of society into castes; but by its doctrine that the performance of caste-duties in a spirit of sacrifice leads to salvation it makes caste an avenue to salvation, not a barrier. (4) The Bhagavad-gītā has nothing to say for the animal-sacrifices of the Brahmans. It recognises only offerings of flowers, fruits, and the like. The doctrine of ahiṃsā, "thou shalt do no hurt," was making much headway at the time, and the wholesale animal-sacrifices of the Brahmans roused general disgust, of which the Buddhists and Jains took

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71 time on January 6th?

Because I believe he has access to it.

No. Why are you telling him, Mr. Harrison, who has access to wildprotest.com, to make it blank?

Because my event had been prevented from happening because there was a Capitol riot. There was no—there was not going to be an event. And I did not want to be subject to the defamation, and libel, and slander that I have since been subject to confusing my efforts to deescalate with people who did deplorable things, horrible things.

I failed to mention that Mr. Raskin has joined the deposition.

Staying in the same exhibit, Exhibit 26, I'm going to page had 170.

. I just have one quick question. Mr. Alexander, do you know who Mr. Harrison works for or does he own his own web vending company?

Mr. Alexander. I think he owns his own company.

Mr. Kamenar. What's the next exhibit?

Mr. . Exhibit 26, page 170.

 * BY

And this is a message from Ms. Wren so kind of on the same lines of what you said to Mr. Harrison about making the web page blank, Ms. Wren writes you and said can we take down the coalition partners page on the website? This is on January 7th. So is she -- which website is she referring to?

I'm sorry, what's the time stamp?

Looks like January 7, at 11:35 a.m. She says quote, unquote, "Yo, crazy day yesterday. Can we take down the coalition partners page on the website, please." And it looks like you replied "yes." And then it looks like she replies "thanks." Is she referring to marchtosaveamerica.com?


text:
Page:The Heart of England.djvu/93

found only two satisfying places in the world in August—the Bodleian Library and a little reedy, willowy pond, where you may enjoy the month perfectly, sitting and being friendly with moorhen and kingfisher and snake, except in the slowly recurring intervals when you catch a tench and cast only mildly envious eyes upon its cool, olive sides. Through the willows I see the hot air quiver in crystal ripples like the points of swords, and sometimes I see a crimson cyclist on a gate. Thus is "fantastic summer's heat" divine. For in August it is right to be cool and at the same time to enjoy the sight and perfume of heat out of doors. In June and July the frosts and east winds of May are so near in memory that they give a satisfaction to the sensation of heat. In September frosts and east winds return. August, in short, is the month of Nature's perfect poise, and I should like to see it represented in painting by a Junonian woman, immobile, passionless and happy in a cool-leaved wood, and looking neither forward nor backward, but within.

Far off I see a forest-covered hill that says "Peace" with a great, quiet voice. From the pool and towards the hill runs a shining road, with some of its curves visible for miles, which I have not followed and dare not follow, because it seems to lead to the Happy Fields.

title: Page:The Heart of England.djvu/93


text:
Page:Hindu Gods and Heroes.djvu/84

82 advantage for the propagation of their teachings.

I have previously spoken of the solitary passage in the Chhāndōgya Upanishad in which Kṛishṇa's name is mentioned, as receiving the teachings of Ghōra Āṅgirasa, and it will now be fitting to see how far these teachings are reflected in the Bhagavad-gītā. Ghōra compares the functions of life to the ceremonies of the dīkshā (see above, p. 68): and this is at bottom the same idea as the doctrine of karma-yōga preached again and again in the Bhagavad-gītā. "Whatever be thy work, thine eating, thy sacrifice, thy gift, thy mortification, make of it an offering to me," says Kṛishṇa (IX. 27); all life should be regarded as a sacrifice freely offered. Then Ghōra continues: "In the hour of death one should take refuge in these three thoughts: 'Thou art the Indestructible, Thou art the Unfailing, Thou art instinct with Spirit.' On this there are these two verses of the Ṛig-vēda:

Thus upward from the primal seed From out the darkness all around We, looking on the higher light, Yea, looking on the higher heaven, Have come to Sūrya, god midst gods, To him that is the highest light, the highest light."

In the Bhagavad-gītā (IV. 1 ff.) Kṛishṇa announces that he preached his doctrine to Vivasvān the Sun-god, who passed it on to his

title: Page:Hindu Gods and Heroes.djvu/84


text:
Page:CTRL0000034607 - Deposition of Ali Alexander, (Dec. 9, 2021).pdf/72

72 No. I'm just trying to read the prior text messages to figure it out because I did not know because it could be the website you just mentioned, because we were running two different websites. So it could have been that website, but it doesn't say here in the prior text messages but it could have been that one.

What websites did you have control of on January 6th?

I'm aware—right now, I'm aware of Stop the Steal U.S. so three, Stop the Steal.US, wildprotest.com, and then the marchtosaveamerica.com, I believe.

So when she says can he take it down the coalition partners page, is it your testimony here it is either the wildprotests.com or marchtosaveamerica.com?

Excuse me?

When she says take down—can we take down the coalition partners pages on the website, please, it could have been wildprotest.com or marchtosaveamerica.com?

It could have been.

You don't remember which one it was?

Whatever one had a coalition partners page.

Mr. Should we take a break? It is 12:30. It is up to you all.

Mr. I am just going to open the floor up to the members to ask follow-up questions. Any questions from the members? That's a negative. And any follow-on questions for counsel?

Let's go on recess then, I believe this is the lunch recess.

Mr. How long will that be 30 minutes?

Mr. . Yes. Just come back at 1 o'clock p.m.

[Recess.]


text:
Page:CTRL0000034607 - Deposition of Ali Alexander, (Dec. 9, 2021).pdf/73

73 [1:10 p.m.]

 * BY :

Mr. Alexander, I just want to go back before we move on to the next topic. And before we start, I would like to announce that no members are on. And that Mr. left the deposition as well.

Mr. Kamenar. No members?

Mr. No members. That's correct.

 * BY

Can you go to Exhibit 26, page 238 again. The text messages with Ms. Kimberly Fletcher?

I'm sorry. What page is that?

It's going to be 238.

238?

That's correct. So on the bottom half of the page where you say, "POTUS is not ignorant of what words would do." Just very clearly explain to us what do you mean by what his words would do?

Mr. Kamenar. That has been asked and answered.

Mr. What do you mean by—what would his word do?

Mr. Kamenar. I mean, if you want to speculate.

 * BY

You're saying it. I am just asking what you mean by your words.

Yeah, I've already been asked this question and given the record an answer and I don't want to give a contrary answer.

So when you—Mr. Alexander, I'm going to ask you the question again.


text:
Page:Hindu Gods and Heroes.djvu/85

Rh son the patriarch Manu; elsewhere in the Mahābhārata (XII. cccv. 19) the Sātvata teaching is said to have been announced by the Sun. Ghōra in his list of moral virtues enumerates "mortification, charity, uprightness, harmlessness, truthfulness"; exactly the same attributes, with a few more, are said in the Bhagavad-gītā to characterise the man who is born to the gods' estate (XVI. 1-3). Ghōra's exhortation to think of the nature of the Supreme in the hour of death is balanced by Kṛishṇa's words: "He who at his last hour, when he casts off the body, goes hence remembering me, goes assuredly into my being" (VIII. 5; cf. 10). These parallels are indeed not very close; but collectively they are significant, and when we bear in mind that the author of the Bhagavad-gītā is eager to associate his doctrine with those of the Upanishads, and thus to make it a new and catholic Upanishad for all classes, we are led to conclude that its fundamental ideas, sanctification of works (karma-yōga), worship of a Supreme God of Grace (bhakti) by all classes, and rejection of animal sacrifices (ahiṃsā) arose among the orthodox Kshatriyas, who found means to persuade their Brahmanic preceptors to bring it into connection with their Upanishads and embellish it with appropriate texts from those sources. Very likely Kṛishṇa Vāsudēva, if not the first inventor of these doctrines, was their most vigorous propagator.

title: Page:Hindu Gods and Heroes.djvu/85


text:
Page:CTRL0000034607 - Deposition of Ali Alexander, (Dec. 9, 2021).pdf/74

74 Well, this is the fourth time you've asked me, but I already have an answer on the record an hour ago. And I would feel very uncomfortable exposing myself to that legal liability. I am under oath. I acknowledge that I'm under oath. And I had to recontextualize it here 11 months later for y'all in my first answer. So the fourth one wouldn't—

So he was not ignorant that his words would lead to the rioters attacking the Capitol?

, you know, a fifth time. I would really just like to stick with my first answer, if you're okay with that.

And as the rioters are attacking the Capitol, you're not going to denounce them? Is that what you're saying to Ms. Fletcher?

On that separate text message you've already asked me that, too. And I actually remember said that I denounced all the people who performed vandalism, all of the people who performed violence. I didn't denounce the people who were on the grass and peacefully assembled. And a lot of people wanted to lump them in together. And I just don't believe that that is equal treatment under the law. I am a little civil libertarian on some of those issues. I believe that each individual should, you know, have their fair day in court. And to denounce everybody and lump them in with people who committed violent acts is not fair.

So show me where you're saying I denounce the people that are going in and vandalizing—why would it make sense to denounce people who are not breaching the Capitol?

That happens in politics all the time—

I'm trying—

I am really glad, and I appreciate the stenographer letting me finish my


text:
Page:Relativity (1931).djvu/89

HE basal principle, which was the pivot of all our previous considerations, was the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion. Let us once more analyse its meaning carefully.

It was at all times clear that, from the point of view of the idea it conveys to us, every motion must only be considered as a relative motion. Returning to the illustration we have frequently used of the embankment and the railway carriage, we can express the fact of the motion here taking place in the following two forms, both of which are equally justifiable:

(a) The carriage is in motion relative to the embankment.

(b) The embankment is in motion relative to the carriage.

In (a) the embankment, in (b) the carriage, serves as the body of reference in our statement

title: Page:Relativity (1931).djvu/89


text:
Page:Relativity (1931).djvu/90

 of the motion taking place. If it is simply a question of detecting or of describing the motion involved, it is in principle immaterial to what reference-body we refer the motion. As already mentioned, this is self-evident, but it must not be confused with the much more comprehensive statement called “the principle of relativity,” which we have taken as the basis of our investigations.

The principle we have made use of not only maintains that we may equally well choose the carriage or the embankment as our reference-body for the description of any event (for this, too, is self-evident). Our principle rather asserts what follows: If we formulate the general laws of nature as they are obtained from experience, by making use of

(a) the embankment as reference-body,

(b) the railway carriage as reference-body,

then these general laws of nature (e.g. the laws of mechanics or the law of the propagation of light in vacuo) have exactly the same form in both cases. This can also be expressed as follows: For the physical description of natural processes, neither of the reference-bodies $$K$$, $$K'$$ is unique (lit. “specially marked out”) as compared with the other. Unlike the first, this latter statement need not of necessity hold a priori; it is not contained in the conceptions of “motion” and “reference

title: Page:Relativity (1931).djvu/90


text:
Page:Relativity (1931).djvu/91

 body” and derivable from them; only experience can decide as to its correctness or incorrectness. Up to the present, however, we have by no means maintained the equivalence of all bodies of reference $$K$$ in connection with the formulation of natural laws. Our course was more on the following lines. In the first place, we started out from the assumption that there exists a reference-body $$K$$, whose condition of motion is such that the Galileian law holds with respect to it: A particle left to itself and sufficiently far removed from all other particles moves uniformly in a straight line. With reference to $$K$$ (Galileian reference-body) the laws of nature were to be as simple as possible. But in addition to $$K$$, all bodies of reference $$K'$$ should be given preference in this sense, and they should be exactly equivalent to $$K$$ for the formulation of natural laws, provided that they are in a state of uniform rectilinear and non-rotary motion with respect to $$K$$; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (e.g. those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity. In contrast to this we wish to understand by the “general principle of relativity” the following

title: Page:Relativity (1931).djvu/91


text:
Page:Relativity (1931).djvu/92

 statement: All bodies of reference $$K$$, $$K'$$, etc., are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion. But before proceeding farther, it ought to be pointed out that this formulation must be replaced later by a more abstract one, for reasons which will become evident at a later stage.

Since the introduction of the special principle of relativity has been justified, every intellect which strives after generalisation must feel the temptation to venture the step towards the general principle of relativity. But a simple and apparently quite reliable consideration seems to suggest that, for the present at any rate, there is little hope of success in such an attempt. Let us imagine ourselves transferred to our old friend the railway carriage, which is travelling at a uniform rate. As long as it is moving uniformly, the occupant of the carriage is not sensible of its motion, and it is for this reason that he can without reluctance interpret the facts of the case as indicating that the carriage is at rest, but the embankment in motion. Moreover, according to the special principle of relativity, this interpretation is quite justified also from a physical point of view.

If the motion of the carriage is now changed into a non-uniform motion, as for instance by a

title: Page:Relativity (1931).djvu/92


text:
Page:Relativity (1931).djvu/93

 powerful application of the brakes, then the occupant of the carriage experiences a correspondingly powerful jerk forwards. The retarded motion is manifested in the mechanical behaviour of bodies relative to the person in the railway carriage. The mechanical behaviour is different from that of the case previously considered, and for this reason it would appear to be impossible that the same mechanical laws hold relatively to the non-uniformly moving carriage, as hold with reference to the carriage when at rest or in uniform motion. At all events it is clear that the Galileian law does not hold with respect to the non-uniformly moving carriage. Because of this, we feel compelled at the present juncture to grant a kind of absolute physical reality to non-uniform motion, in opposition to the general principle of relativity. But in what follows we shall soon see that this conclusion cannot be maintained.

title: Page:Relativity (1931).djvu/93


text:
Page:Relativity (1931).djvu/94

F we pick up a stone and then let it go, why I does it fall to the ground?” The usual answer to this question is: “Because it is attracted by the earth.” Modern physics formulates the answer rather differently for the following reason. As a result of the more careful study of electromagnetic phenomena, we have come to regard action at a distance as a process impossible without the intervention of some intermediary medium. If, for instance, a magnet attracts a piece of iron, we cannot be content to regard this as meaning that the magnet acts directly on the iron through the intermediate empty space, but we are constrained to imagine—after the manner of Faraday—that the magnet always calls into being something physically real in the space around it, that something being what we call a “magnetic field.” In its turn this magnetic field operates on the piece of iron, so that the latter strives to move towards the magnet. We shall not discuss here the justification for this incidental conception, which is indeed a somewhat arbi-

title: Page:Relativity (1931).djvu/94


text:
Page:Relativity (1931).djvu/95

 trary one. We shall only mention that with its aid electromagnetic phenomena can be theoretically represented much more satisfactorily than without it, and this applies particularly to the transmission of electromagnetic waves. The effects of gravitation also are regarded in an analogous manner.

The action of the earth on the stone takes place indirectly. The earth produces in its surroundings a gravitational field, which acts on the stone and produces its motion of fall. As we know from experience, the intensity of the action on a body diminishes according to a quite definite law, as we proceed farther and farther away from the earth. From our point of view this means: The law governing the properties of the gravitational field in space must be a perfectly definite one, in order correctly to represent the diminution of gravitational action with the distance from operative bodies. It is something like this: The body (e.g. the earth) produces a field in its immediate neighbourhood directly; the intensity and direction of the field at points farther removed from the body are thence determined by the law which governs the properties in space of the gravitational fields themselves.

In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance

title: Page:Relativity (1931).djvu/95


text:
Page:Relativity (1931).djvu/96

 for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body. For instance, a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo), when they start off from rest or with the same initial velocity. This law, which holds most accurately, can be expressed in a different form in the light of the following consideration.

According to Newton’s law of motion, we have

where the “inertial mass” is a characteristic constant of the accelerated body. If now gravitation is the cause of the acceleration, we then have

where the “gravitational mass” is likewise a characteristic constant for the body. From these two relations follows:

If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a

title: Page:Relativity (1931).djvu/96


text:
Page:Relativity (1931).djvu/97

 given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable choice of units we can thus make this ratio equal to unity. We then have the following law: The gravitational mass of a body is equal to its inertial mass.

It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as “inertia” or as “weight” (lit. ‘‘heaviness”). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity.

title: Page:Relativity (1931).djvu/97


text:
Page:Relativity (1931).djvu/98

E imagine a large portion of empty space, so far removed from stars and other appreciable masses that we have before us approximately the conditions required by the fundamental law of Author:Galilei. It is then possible to choose a Galileian reference-body for this part of space (world), relative to which points at rest remain at rest and points in motion continue permanently in uniform rectilinear motion. As reference-body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus. Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room.

To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a “being” (what kind of a being is immaterial to

title: Page:Relativity (1931).djvu/98


text:
Page:Relativity (1931).djvu/99

 us) begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion. In course of time their velocity will reach unheard-of values—provided that we are viewing all this from another reference-body which is not being pulled with a rope.

But how does the man in the chest regard the process? The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor. He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth. If he release a body which he previously had in his hand, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment.

Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of

title: Page:Relativity (1931).djvu/99


text:
Page:Relativity (1931).djvu/100

 course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field.

Ought we to smile at the man and say that he errs in his conclusion? I do not believe we ought to if we wish to remain consistent; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws. Even though it is being accelerated with respect to the “Galileian space” first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity.

We must note carefully that the possiblility of this mode of interpretation rests on the fundamental property of the gravitational field of giving all bodies the same acceleration, or, what comes to the same thing, on the law of the equality of inertial and gravitational mass. If this natural law did not exist, the man in the accelerated chest would not be able to interpret the behaviour of

title: Page:Relativity (1931).djvu/100


text:
Page:Relativity (1931).djvu/101

 the bodies around him on the supposition of a gravitational field, and he would not be justified on the grounds of experience in supposing his reference-body to be “at rest.”

Suppose that the man in the chest fixes a rope to the inner side of the lid, and that he attaches a body to the free end of the rope. The result of this will be to stretch the rope so that it will hang “vertically” downwards. If we ask for an opinion of the cause of tension in the rope, the man in the chest will say: “The suspended body experiences a downward force in the gravitational field, and this is neutralised by the tension of the rope; what determines the magnitude of the tension of the rope is the gravitational mass of the suspended body.” On the other hand, an observer who is poised freely in space will interpret the condition of things thus: ‘‘The rope must perforce take part in the accelerated motion of the chest, and it transmits this motion to the body attached to it. The tension of the rope is just large enough to effect the acceleration of the body. That which determines the magnitude of the tension of the rope is the inertial mass of the body.” Guided by this example, we see that our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass. Thus we have obtained a physical interpretation of this law.

title: Page:Relativity (1931).djvu/101


text:
Page:Relativity (1931).djvu/102

 From our consideration of the accelerated chest we see that a general theory of relativity must yield important results on the laws of gravitation. In point of fact, the systematic pursuit of the general idea of relativity has supplied the laws satisfied by the gravitational field. Before proceeding farther, however, I must warn the reader against a misconception suggested by these considerations. A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen. Now we might easily suppose that the existence of a gravitational field is always only an apparent one. We might also think that, regardless of the kind of gravitational field which may be present, we could always choose another reference-body such that no gravitational field exists with reference to it. This is by no means true for all gravitational fields, but only for those of quite special form. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.

We can now appreciate why that argument is not convincing, which we brought forward against the general principle of relativity at the end of Section XVIII. It is certainly true that the observer in the railway carriage experiences a jerk forwards as a result of the application of the

title: Page:Relativity (1931).djvu/102


text:
Page:Relativity (1931).djvu/103

 brake, and that he recognises in this the non-uniformity of motion (retardation) of the carriage. But he is compelled by nobody to refer this jerk to a “real” acceleration (retardation) of the carriage. He might also interpret his experience thus: “My body of reference (the carriage) remains permanently at rest. With reference to it, however, there exists (during the period of application of the brakes) a gravitational field which is directed forwards and which is variable with respect to time. Under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards direction is continuously reduced.”

title: Page:Relativity (1931).djvu/103


text:
Page:Relativity (1931).djvu/104

E have already stated several times that classical mechanics starts out from the following law: Material particles sufficiently far removed from other material particles continue to move uniformly in a straight line or continue in a state of rest. We have also repeatedly emphasised that this fundamental law can only be valid for bodies of reference $$K$$ which possess certain unique states of motion, and which are in uniform translational motion relative to each other. Relative to other reference-bodies $$K$$ the law is not valid. Both in classical mechanics and in the special theory of relativity we therefore differentiate between reference-bodies $$K$$ relative to which the recognised “laws of nature” can be said to hold, and reference-bodies $$K$$ relative to which these laws do not hold.

But no person whose mode of thought is logical can rest satisfied with this condition of things. He asks: ‘‘How does it come that certain refer-

title: Page:Relativity (1931).djvu/104


text:
Page:Relativity (1931).djvu/105

 ence-bodies (or their states of motion) are given priority over other reference-bodies (or their states of motion)? What is the reason for this preference? In order to show clearly what I mean by this question, I shall make use of a comparison.

I am standing in front of a gas range. Standing alongside of each other on the range are two pans so much alike that one may be mistaken for the other. Both are half full of water. I notice that steam is being emitted continuously from the one pan, but not from the other. I am surprised at this, even if I have never seen either a gas range or a pan before. But if I now notice a luminous something of bluish colour under the first pan but not under the other, I cease to be astonished, even if I have never before seen a gas flame. For I can only say that this bluish something will cause the emission of the steam, or at least possibly it may do so. If, however, I notice the bluish something in neither case, and if I observe that the one continuously emits steam whilst the other does not, then I shall remain astonished and dissatisfied until I have discovered some circumstance to which I can attribute the different behaviour of the two pans.

Analogously, I seek in vain for a real something in classical mechanics (or in the special theory of relativity) to which I can attribute the different behaviour of bodies considered with respect to

title: Page:Relativity (1931).djvu/105


text:
Page:Relativity (1931).djvu/106

 the reference-systems $$K$$ and $$K'$$. Newton saw this objection and attempted to invalidate it, but without success. But E. Mach recognised it most clearly of all, and because of this objection he claimed that mechanics must be placed on a new basis. It can only be got rid of by means of a physics which is conformable to the general principle of relativity, since the equations of such a theory hold for every body of reference, whatever may be its state of motion.

title: Page:Relativity (1931).djvu/106


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Page:Relativity (1931).djvu/107

HE considerations of Section XX show that the general principle of relativity puts us in a position to derive properties of the gravitational field in a purely theoretical manner. Let us suppose, for instance, that we know the space-time “course” for any natural process whatsoever, as regards the manner in which it takes place in the Galileian domain relative to a Galileian body of reference $$K$$. By means of purely theoretical operations (i.e. simply by calculation) we are then able to find how this known natural process appears, as seen from a reference-body $$K'$$ which is accelerated relatively to $$K$$. But since a gravitational field exists with respect to this new body of reference $$K'$$, our consideration also teaches us how the gravitational field influences the process studied.

For example, we learn that a body which is in a state of uniform rectilinear motion with respect to $$K$$ (in accordance with the law of Galilei) is executing an accelerated and in general Rh

title: Page:Relativity (1931).djvu/107


text:
Page:Relativity (1931).djvu/108

 curvilinear motion with respect to the accelerated reference-body $$K'$$ (chest). This acceleration or curvature corresponds to the influence on the moving body of the gravitational field prevailing relatively to $$K'$$. It is known that a gravitational field influences the movement of bodies in this way, so that our consideration supplies us with nothing essentially new.

However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body $$K$$, such a ray of light is transmitted rectilinearly with the velocity $$c$$. It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest (reference-body $$K'$$). From this we conclude, that, in general, rays of light are propagated curvilinearly in gravitational fields. In two respects this result is of great importance.

In the first place, it can be compared with the reality. Although a detailed examination of the question shows that the curvature of light rays required by the general theory of relativity is only exceedingly small for the gravitational fields at our disposal in practice, its estimated magnitude for light rays passing the sun at grazing incidence is nevertheless 1·7 seconds of arc. This ought to manifest itself in the following way.

title: Page:Relativity (1931).djvu/108


text:
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 As seen from the earth, certain fixed stars appear to be in the neighbourhood of the sun, and are thus capable of observation during a total eclipse of the sun. At such times, these stars ought to appear to be displaced outwards from the sun by an amount indicated above, as compared with their apparent position in the sky when the sun is situated at another part of the heavens. The examination of the correctness or otherwise of this deduction is a problem of the greatest importance, the early solution of which is to be expected of astronomers.

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the

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 case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

Since it has often been contended by opponents of the theory of relativity that the special theory of relativity is overthrown by the general theory of relativity, it is perhaps advisable to make the facts of the case clearer by means of an appropriate comparison. Before the development of electrodynamics the laws of electrostatics were looked upon as the laws of electricity. At the present time we know that electric fields can be derived correctly from electrostatic considerations only for the case, which is never strictly realised, in which the electrical masses are quite at rest relatively to each other, and to the co-ordinate system. Should we be justified in saying that for this reason electrostatics is overthrown by the field-equations of Maxwell in electrodynamics? Not in the least. Electrostatics is contained in electrodynamics as a limiting case; the laws of the latter lead directly to those of the former for the case in which the fields are invariable with regard to time. No fairer destiny could be allotted to any physical theory, than that it should of itself point out the

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 way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.

In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course of natural processes, the laws of which are already known when a gravitational field is absent. But the most attractive problem, to the solution of which the general theory of relativity supplies the key, concerns the investigation of the laws satisfied by the gravitational field itself. Let us consider this for a moment.

We are acquainted with space-time domains which behave (approximately) in a “Galileian” fashion under suitable choice of reference-body, i.e. domains in which gravitational fields are absent. If we now refer such a domain to a reference-body $$K'$$ possessing any kind of motion, then relative to $$K'$$ there exists a gravitational field which is variable with respect to space and time. The character of this field will of course depend on the motion chosen for $$K'$$. According to the general theory of relativity, the general law of the gravitational field must be satisfied for all gravitational fields obtainable in this way. Even though by no means all gravitational fields

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 can be produced in this way, yet we may entertain the hope that the general law of gravitation will be derivable from such gravitational fields of a special kind. This hope has been realised in the most beautiful manner. But between the clear vision of this goal and its actual realisation it was necessary to surmount a serious difficulty, and as this lies deep at the root of things, I dare not withhold it from the reader. We require to extend our ideas of the space-time continuum still farther.

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ITHERTO I have purposely refrained from speaking about the physical interpretation of space- and time-data in the case of the general theory of relativity. As a consequence, I am guilty of a certain slovenliness of treatment, which, as we know from the special theory of relativity, is far from being unimportant and pardonable. It is now high time that we remedy this defect; but I would mention at the outset, that this matter lays no small claims on the patience and on the power of abstraction of the reader.

We start off again from quite special cases, which we have frequently used before. Let us consider a space-time domain in which no gravitational field exists relative to a reference-body $$K$$ whose state of motion has been suitably chosen. $$K$$ is then a Galileian reference-body as regards the domain considered, and the results of the special theory of relativity hold relative to $$K$$. Let us suppose the same domain referred to a

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 second body of reference $$K'$$, which is rotating uniformly with respect to $$K$$. In order to fix our ideas, we shall imagine $$K'$$ to be in the form of a plane circular disc, which rotates uniformly in its own plane about its centre. An observer who is sitting eccentrically on the disc $$K'$$ is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body $$K$$. But the observer on the disc may regard his disc as a reference-body which is “at rest”; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. Nevertheless, the space-distribution of this gravitational field is of a kind that would not be possible on Newton’s theory of gravitation. But since the observer believes in the general theory of relativity, this does not disturb him; he is quite in the right when he believes that a general law of gravitation can be formulated—a law which not only explains the motion of the stars correctly, but also the field of force experienced by himself.

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 The observer performs experiments on his circular disc with clocks and measuring-rods. In doing so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to the circular disc $$K'$$, these definitions being based on his observations. What will be his experience in this enterprise?

To start with, he places one of two identically constructed clocks at the centre of the circular disc, and the other on the edge of the disc, so that they are at rest relative to it. We now ask ourselves whether both clocks go at the same rate from the standpoint of the non-rotating Galileian reference-body $$K$$. As judged from this body, the clock at the centre of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to $$K$$ in consequence of the rotation. According to a result obtained in Section XII, it follows that the latter clock goes at a rate permanently slower than that of the clock at the centre of the circular disc, i.e. as observed from $$K$$. It is obvious that the same effect would be noted by an observer whom we will imagine sitting alongside his clock at the centre of the circular disc. Thus on our circular disc, or, to make the case more general, in every gravitational field, a clock will go more quickly or less quickly, according to the position in which the clock is situated (at rest). For this reason it is not

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 possible to obtain a reasonable definition of time with the aid of clocks which are arranged at rest with respect to the body of reference. A similar difficulty presents itself when we attempt to apply our earlier definition of simultaneity in such a case, but I do not wish to go any farther into this question.

Moreover, at this stage the definition of the space co-ordinates also presents unsurmountable difficulties. If the observer applies his standard measuring-rod (a rod which is short as compared with the radius of the disc) tangentially to the edge of the disc, then, as judged from the Galileian system, the length of this rod will be less than 1, since, according to Section XII, moving bodies suffer a shortening in the direction of the motion. On the other hand, the measuring-rod will not experience a shortening in length, as judged from $$K$$, if it is applied to the disc in the direction of the radius. If, then, the observer first measures the circumference of the disc with his measuring-rod and then the diameter of the disc, on dividing the one by the other, he will not obtain as quotient the familiar number $$\pi = 3.14 \ldots$$, but a larger number, whereas of course, for a disc which is at rest with respect to $$K$$, this operation

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text: Harmonium (Stevens)/Infanta Marina

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 would yield $$\pi$$ exactly. This proves that the propositions of Euclidean geometry cannot hold exactly on the rotating disc, nor in general in a gravitational field, at least if we attribute the length 1 to the rod in all positions and in every orientation. Hence the idea of a straight line also loses its meaning. We are therefore not in a position to define exactly the co-ordinates $$x$$, $$y$$, $$z$$ relative to the disc by means of the method used in discussing the special theory, and as long as the co-ordinates and times of events have not been defined we cannot assign an exact meaning to the natural laws in which these occur.

Thus all our previous conclusions based on general relativity would appear to be called in question. In reality we must make a subtle detour in order to be able to apply the postulate of general relativity exactly. I shall prepare the reader for this in the following paragraphs.

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HE surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a “neighbouring” one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing jumps.” I am sure the reader will appreciate with sufficient clearness what I mean here by “neighbouring” and by “jumps” (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum.

Let us now imagine that a large number of little rods of equal length have been made, their lengths being small compared with the dimensions of the marble slab. When I say they are of equal length, I mean that one can be laid on any other without the ends overlapping. We next lay four of these little rods on the marble slab so that they constitute a quadrilateral figure (a square), the diagonals of which are equally long. To ensure the equality of the diagonals, we make use of a

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 little testing-rod. To this square we add similar ones, each of which has one rod in common with the first. We proceed in like manner with each of these squares until finally the whole marble slab is laid out with squares. The arrangement is such, that each side of a square belongs to two squares and each corner to four squares.

It is a veritable wonder that we can carry out this business without getting into the greatest difficulties. We only need to think of the following. If at any moment three squares meet at a corner, then two sides of the fourth square are already laid, and as a consequence, the arrangement of the remaining two sides of the square is already completely determined. But I am now no longer able to adjust the quadrilateral so that its diagonals may be equal. If they are equal of their own accord, then this is an especial favour of the marble slab and of the little rods about which I can only be thankfully surprised. We must needs experience many such surprises if the construction is to be successful.

If everything has really gone smoothly, then I say that the points of the marble slab constitute a Euclidean continuum with respect to the little rod, which has been used as a “distance’’ (line-interval). By choosing one corner of a square as “origin,” I can characterise every other corner of a square with reference to this origin by means

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84 Now what are the teachings of the Nārāyaṇīya? It appears to contain two accounts. In the first we have the story of king Vasu Uparichara, who is said to have worshipped the Supreme God Hari (Vishṇu) in devotion without any animal-sacrifices, in accordance with doctrines ascribed to the Āraṇyakas, i.e. the later sections of the Brāhmaṇas, including the older Upanishads. This fully agrees with the standpoint of the Bhagavad-gītā. The second account gives the story of a visit paid by the divine saint Nārada to a mysterious "White Island," Śvēta-dvīpa, inhabited by holy worshippers of God who are, strangely enough, described as having heads shaped like umbrellas and feet like lotus-leaves and as making a sound like that of thunderclouds ; they are radiant like the moon, have no physical senses, eat nothing, and concentrate their whole soul on rapturous adoration of the spirit of God, which shines there in dazzling brightness to the eye of perfect faith. Nārāyaṇa there reveals himself to Nārada, and sets forth to him the doctrine of Vāsudēva. According to this, Nārāyaṇa has four forms, called mūrtis or vyūhas. The first of these is Vāsudēva, who is the highest soul and creator and inwardly

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 of two numbers. I only need state how many rods I must pass over when, starting from the origin, I proceed towards the “right” and then “upwards,” in order to arrive at the corner of the square under consideration. These two numbers are then the “Cartesian co-ordinates” of this corner with reference to the “Cartesian coordinate system” which is determined by the arrangement of little rods.

By making use of the following modification of this abstract experiment, we recognise that there must also be cases in which the experiment would be unsuccessful. We shall suppose that the rods “expand” by an amount proportional to the increase of temperature. We heat the central part of the marble slab, but not the periphery, in which case two of our little rods can still be brought into coincidence at every position on the table. But our construction of squares must necessarily come into disorder during the heating, because the little rods on the central region of the table expand, whereas those on the outer part do not.

With reference to our little rods—defined as unit lengths—the marble slab is no longer a Euclidean continuum, and we are also no longer in the position of defining Cartesian co-ordinates directly with their aid, since the above construction can no longer be carried out. But since

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 there are other things which are not influenced in a similar manner to the little rods (or perhaps not at all) by the temperature of the table, it is possible quite naturally to maintain the point of view that the marble slab is a “Euclidean continuum.” This can be done in a satisfactory manner by making a more subtle stipulation about the measurement or the comparison of lengths.

But if rods of every kind (i.e. of every material) were to behave in the same way as regards the influence of temperature when they are on the variably heated marble slab, and if we had no other means of detecting the effect of temperature than the geometrical behaviour of our rods in experiments analogous to the one described above, then our best plan would be to assign the distance one to two points on the slab, provided that the ends of one of our rods could be made to coincide with these two points; for how else should we define the distance without our proceeding being in the highest measure grossly arbitrary? The method of Cartesian co-ordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies. The reader will notice that

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 the situation depicted here corresponds to the one brought about by the general postulate of relativity (Section XXIII).

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CCORDING to Gauss, this combined analytical and geometrical mode of handling the problem can be arrived at in the following way. We imagine a system of arbitrary curves (see Fig. 4) drawn on the surface of the table. These we designate as $$u$$-curves, and we indicate each of them by means of a number. The curves $$u = 1$$, $$u = 2$$ and $$u = 3$$ are drawn in the diagram. Between the curves $$u = 1$$ and $$u = 2$$ we must imagine an infinitely large number to be drawn, all of which correspond to real numbers lying between 1 and 2. We have then a system of $$u$$-curves, and this ‘‘infinitely dense” system covers the whole surface of the table. These $$u$$-curves must not intersect each other, and through each point of the surface one and only one curve must pass. Thus a perfectly definite value of $$u$$ belongs to every point on the surface of the marble slab. In like manner we

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 imagine a system of $$v$$-curves drawn on the surface. These satisfy the same conditions as the $$u$$-curves, they are provided with numbers in a corresponding manner, and they may likewise be of arbitrary shape. It follows that a value of $$u$$ and a value of $$v$$ belong to every point on the surface of the table. We call these two numbers the co-ordinates of the surface of the table (Gaussian co-ordinates). For example, the point $$P$$ in the diagram has the Gaussian co-ordinates $$u = 3$$, $$v = 1$$. Two neighbouring points $$P$$ and $$P'$$ on the surface then correspond to the co-ordinates

$$\begin{align} P: \qquad & u, v \\ P': \qquad & u + du,\ v + dv \end{align}$$,

where $$du$$ and $$dv$$ signify very small numbers. In a similar manner we may indicate the distance (line-interval) between $$P$$ and $$P'$$, as measured with a little rod, by means of the very small number $$ds$$. Then according to Gauss we have

where $$g_{11}$$, $$g_{12}$$, $$g_{22}$$, are magnitudes which depend in a perfectly definite way on $$u$$ and $$v$$. The magnitudes $$g_{11}$$, $$g_{12}$$, and $$g_{22}$$ determine the behaviour of the rods relative to the $$u$$-curves and $$v$$-curves, and thus also relative to the surface of the table. For the case in which the points of the surface considered form a Euclidean continuum with reference to the measuring-rods, but only in this case, it is possible to draw the $$u$$-curves and

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 $$v$$-curves and to attach numbers to them, in such a manner, that we simply have:

Under these conditions, the $$u$$-curves and $$v$$-curves are straight lines in the sense of Euclidean geometry, and they are perpendicular to each other. Here the Gaussian co-ordinates are simply Cartesian ones. It is clear that Gauss co-ordinates are nothing more than an association of two sets of numbers with the points of the surface considered, of such a nature that numerical values differing very slightly from each other are associated with neighbouring points “in space.”

So far, these considerations hold for a continuum of two dimensions. But the Gaussian method can be applied also to a continuum of three, four or more dimensions. If, for instance, a continuum of four dimensions be supposed available, we may represent it in the following way. With every point of the continuum we associate arbitrarily four numbers, $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$ which are known as “co-ordinates.” Adjacent points correspond to adjacent values of the coordinates. If a distance $$ds$$ is associated with the adjacent points $$P$$ and $$P'$$, this distance being measurable and well-defined from a physical point of view, then the following formula holds:

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 where the magnitudes $$g_{11}$$, etc., have values which vary with the position in the continuum. Only when the continuum is a Euclidean one is it possible to associate the co-ordinates $$x_1 \dots x_4$$ with the points of the continuum so that we have simply

In this case relations hold in the four-dimensional continuum which are analogous to those holding in our three-dimensional measurements.

However, the Gauss treatment for $$ds^2$$ which we have given above is not always possible. It is only possible when sufficiently small regions of the continuum under consideration may be regarded as Euclidean continua. For example, this obviously holds in the case of the marble slab of the table and local variation of temperature. The temperature is practically constant for a small part of the slab, and thus the geometrical behaviour of the rods is almost as it ought to be according to the rules of Euclidean geometry. Hence the imperfections of the construction of squares in the previous section do not show themselves clearly until this construction is extended over a considerable portion of the surface of the table.

We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which “size-relations”

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 (‘‘distances” between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined “size” or “distance,” small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

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E are now in a position to formulate more exactly the idea of Minkowski, which was only vaguely indicated in Section XVII. In accordance with the special theory of relativity, certain co-ordinate systems are given preference for the description of the four-dimensional, space-time continuum. We called these “Galileian co-ordinate systems.” For these systems, the four co-ordinates $$x$$, $$y$$, $$z$$, $$t$$, which determine an event or—in other words—a point of the four-dimensional continuum, are defined physically in a simple manner, as set forth in detail in the first part of this book. For the transition from one Galileian system to another, which is moving uniformly with reference to the first, the equations of the Lorentz transformation are valid. These last form the basis for the derivation of deductions from the special theory of relativity, and in themselves they are nothing more than the expression of the universal

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 validity of the law of transmission of light for all Galileian systems of reference.

Minkowski found that the Lorentz transformations satisfy the following simple conditions. Let us consider two neighbouring events, the relative position of which in the four-dimensional continuum is given with respect to a Galileian reference-body $$K$$ by the space co-ordinate differences $$dx$$, $$dy$$, $$dz$$ and the time-difference $$dt$$. With reference to a second Galileian system we shall suppose that the corresponding differences for these two events are $$dx'$$, $$dy'$$, $$dz'$$, $$dt'$$. Then these magnitudes always fulfil the condition.

The validity of the Lorentz transformation follows from this condition. We can express this as follows: The magnitude

which belongs to two adjacent points of the four-dimensional space-time continuum, has the same value for all selected (Galileian) reference-bodies. If we replace $$x$$, $$y$$, $$z$$, $$\sqrt{-1}ct$$, by $$x_1$$, $$x_2$$, $$x_3$$$$x_4$$, we also obtain the result that

is independent of the choice of the body of refer-

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 ence. We call the magnitude $$ds$$ the “distance” apart of the two events or four-dimensional points.

Thus, if we choose as time-variable the imaginary variable $$\sqrt{-1}ct$$ instead of the real quantity $$t$$, we can regard the space-time continuum—in accordance with the special theory of relativity—as a “Euclidean” four-dimensional continuum, a result which follows from the considerations of the preceding section.

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LBERT EINSTEIN is the son of German-Jewish parents. He was born in 1879 in the town of Ulm, Würtemberg, Germany. His schooldays were spent in Munich, where he attended the Gymnasium until his sixteenth year. After leaving school at Munich, he accompanied his parents to Milan, whence he proceeded to Switzerland six months later to continue his studies. From 1896 to 1900 Albert Einstein studied mathematics and physics at the Technical High School in Zurich, as he intended becoming a secondary school (Gymnasium) teacher. For some time afterwards he was a private tutor, and having meanwhile become naturalised, he obtained a post as engineer in the Swiss Patent Office in 1902, which position he occupied till 1909. The main ideas involved in the most important of Einstein’s theories date back to this period. Amongst these may be mentioned: The Special Theory of Relativity, Inertia of Energy, Theory of the Brownian Movement, and the Quantum-Law of the Emission and Absorption of Light (1905). These were followed some years later by the

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N the first part of this book we were able to make use of space-time co-ordinates which allowed of a simple and direct physical interpretation, and which, according to Section XXVI, can be regarded as four-dimensional Cartesian co-ordinates. This was possible on the basis of the law of the constancy of the velocity of light. But according to Section XXI, the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co-ordinates when a gravitational field is present. In connection with a specific illustration in Section XXIII, we found that the presence of a gravitational field invalidates the definition of the co-ordinates and the time, which led us to our objective in the special theory of relativity.

In view of the results of these considerations we are led to the conviction that, according to

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text: Harmonium (Stevens)/Domination of Black

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 the general principle of relativity, the space-time continuum cannot be regarded as a Euclidean one, but that here we have the general case, corresponding to the marble slab with local variations of temperature, and with which we made acquaintance as an example of a two-dimensional continuum. Just as it was there impossible to construct a Cartesian co-ordinate system from equal rods, so here it is impossible to build up a system (reference-body) from rigid bodies and clocks, which shall be of such a nature that measuring-rods and clocks, arranged rigidly with respect to one another, shall indicate position and time directly. Such was the essence of the difficulty with which we were confronted in Section XXIII.

But the considerations of Section XXV and Section XXVI show us the way to surmount this difficulty. We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss co-ordinates. We assign to every point of the continuum (event) four numbers, $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$ (co-ordinates), which have not the least direct physical significance, but only serve the purpose of numbering the points of the continuum in a definite but arbitrary manner. This arrangement does not even need to be of such a kind that we must regard $$x_1$$, $$x_2$$, $$x_3$$, as “space” co-ordinates and $$x_4$$ as a “time” co-ordinate.

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 The reader may think that such a description of the world would be quite inadequate. What does it mean to assign to an event the particular co-ordinates $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$, if in themselves these co-ordinates have no significance? More careful consideration shows, however, that this anxiety is unfounded. Let us consider, for instance, a material point with any kind of motion. If this point had only a momentary existence without duration, then it would be described in spacetime by a single system of values $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$. Thus its permanent existence must be characterised by an infinitely large number of such systems of values, the co-ordinate values of which are so close together as to give continuity; corresponding to the material point, we thus have a (uni-dimensional) line in the four-dimensional continuum. In the same way, any such lines in our continuum correspond to many points in motion. The only statements having regard to these points which can claim a physical existence are in reality the statements about their encounters. In our mathematical treatment, such an encounter is expressed in the fact that the two lines which represent the motions of the points in question have a particular system of co-ordinate values, $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$, in common. After mature consideration the reader will doubtless admit that in reality such encounters con-

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