Measuring Space-Time Geometry over the Ages

Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.Comment: Originally written for the Gravity Research Foundation 2012 Awards for Essays on Gravitation and received Honorable Mentio

Simultaneous aluminum, silicon, and sodium coordination changes in 6 GPa sodium aluminosilicate glasses

We present the first direct observation of high-coordinated Si and Al occurring together in a series of high-pressure sodium aluminosilicate glasses, quenched from melts at 6 GPa. Using ^(29)Si MAS NMR, we observe that a small amount of Al does not have a significant effect on the amount of ^VSi or ^(VI)Si generated, but that larger Al concentrations lead to a gradual decrease in both these species. ^(27)Al MAS NMR spectra show that samples with small amounts of Al have extremely high mean Al coordination values of up to 5.49, but that larger Al concentrations cause a gradual decrease in both ^VAl and ^(VI)Al. Although mean Al and Si coordination numbers both decrease with increasing Al contents, the weighted combined (Al+Si) coordination number increases. Silicon and Al resonances shift in frequency with increasing pressure or changing Al concentration, indicating additional structural changes, including compression of network bond angles. Increases in the ^(23)Na isotropic chemical shifts indicate decreases in the mean Na-O bond lengths with increasing pressure, which are more dramatic at higher Al contents. Recovered glass densities are about 10 to 15% greater than those of similar ambient pressure samples. However, the density increases due to the combined coordination changes of Al and Si are estimated to total only about 1 to 2%, and are roughly constant with composition despite the large effects of Al content on the individual coordinations of the two cations. Thus, effects of other structural changes must be significant to the overall densification. Apparent equilibrium constants for reactions involving the generation of high-coordinated species show systematic behavior, which suggests an internal consistency to the observed Si and Al coordination number shifts

The Effects of Grading Practices on Motivations for Learning at the Middle School Level

The objective of this quantitative survey study was to measure the effect grading traditionally (using averaging) versus non-traditionally (best, most recent evidence) on four types of student motivation. These types of motivation were mastery orientation (learning for learning sake), performance orientation (going for the grade or external recognition), performance avoidance (not wanting to appear incompetent), and mastery avoidance (not wanting to lose what you have). This set of orientations is derived from the goal orientation theory. In this study, 1,652 students and 93 educators between four schools took an anonymous 20-minute online survey. Due to lack of teacher participation, two schools were not used in the study. The survey for the teachers measured grading practices, while the survey for the students measured motivation orientations. There were other questions asked of both teachers and students, but only the aforementioned and demographic data were analyzed. Findings from this study indicate that teachers in School 3 report using traditional averaging significantly more than School 1, who uses the best, most recent evidence more. However, due to the similarities in their other grading practices, the two schools’ mastery orientation scores are not statistically different. School 3 students are statistically more performance oriented, but by a margin that makes one question if classic negative socioeconomics affects are being mitigated as they have double the free and reduced lunch rate. In terms of gender, cis-gendered students are equally motivated regardless of School. However, non-binary students have the lowest scores in mastery and high scores in performance avoidance in School 1 as compared to School 3. Is this because they want to hide, but cannot in this less performance-focused system? The overall finding leads to more questions about specific populations such as non-binary and socio-economically disadvantaged students, but require further research between schools that participate in strictly traditional grading practices and schools such as these studied. However, it seems rather clear that there is a positive incremental step toward refocusing on mastery orientation which has more cognitive benefits as compared to performance and lessens performance avoidance which has negative academic effects

Letter from N. D. Stebbins to John Muir, 1882 Dec 15.

Santa Barbara [/Cala.?] Dec 15/82My good friend Muir’Your postal did not reach me till five days after date. After receiving it as you are away I telegraphed to know of your whereabouts - & found you at San Jose & probably would call on your return – I [xtended?] my ticket (ship) to the next Boat a day or two before leaving I visited the Nat[illegible] [illegible] Room then found Dr. Kellog. on my mentioning your name he said you had been in S.F. & took dinner with him. It would have been a [illegible] to see a man who a loving providence had watched over with such pert[illegible] & shield him from sudden death a thousand times[Page 2]or more. Mr Herbert [Spencer?] & his crowd might laugh with a sneer at such expressions – but I will glory in them. With warmest regards to Mrs Muir & a kiss for the lovely little daughterTruly Ever your Friend N. D. StibbinsPS. I hope in the future to do better on my next visit to [S. F.?]N.D.S--A little more-say to Mrs Muir there was something in the telegram that made me feel towards her as an old familiar friend / I hope so rather than to be [illegible] [with her?]N.D S0108

Letter from N. D. Stebbins to John Muir, 1885 Mar 16.

Santa Barbara, March 16, \u2785.Dear friend Muir:You may be disappointed to find this old octogenarian plus three again in Cal. It is even so for a short time. I came here in Dec. On my way I called at our old friends Dr. and Mrs. Carr. They have a lovely home -- like themselves. I remained with them one night. When I left she spoke of you and yours, especially the little girl, with much affection. You may wonder why I trouble your eyes with my scribbles. I\u27ll tell you. I met with the Natural History Soc. in Santa Barbara, in which I am an honorary member. At one of its meetings I brought up the subject of Prof. Whitney\u27s Calaveras skull and the opinion I had just received from Prof. Dana of New Haven, doubting the verity of the history as given by the prof. or the miners. It has led to a newspaper discussion on the age of man and the truthfulness of this skull being found where Prof. Whitney has published [that, it was] found. I would like to know if you know anything about it? And where can I find Prof. Whitney\u27s statement that the Tuolumne meadows were good grazing lands and already covered with good pasturage. Give me the year of his reports, if you recollect. I recollect your telling me the story when I saw you in Yosemite Valley. If you recollect and can tell me I will be obliged.My furlough runs out in June next, when I expect to return to Mich. I may be obliged to go to San Francisco. If so I would be glad to meet you. Incipient cataract has commenced in my eyes -- please excuse my scribbling. Kindest regards to Mrs. Muir, and a kiss for the little one not only from me but Mrs. Carr at her earnest wish.Ever truly your friend,N. D. Stebbins.If you desire your name will be not known in this discussion. My 83 years celebrated by young ladies from S.B. 3 weeks ago

Letter from N. D. Stebbins to John Muir, 1880 June 21.

[4]the precinct of Montecito. We have no PO in this precinct. I am not strong enough to ramble about much. I wished for your opinion last summer while I was visiting some of the canons in the upper part of S.B. Valley. It is said there are no evidences of the action of glaciers below Monterey in this State. I imagined I saw something that looked like it in New Annie Canon. [illegible] [illegible] Ranch — I would be delighted to see you and learn more of your adventures & [illegible] in what we both feel so enthusiastically about & [illegible] [illegible] of it – if we are called Mountaineers. I have often longed to be with you. How much I wished to be with you when at Alaska – I am nearly an old 79 [illegible]. It is hard work for me to give up the struggle. [illegible] [illegible]. I don’t know now when I shall visit San Francisco[in margin: I may this fall or early winter Wehenever I do I hope to see you. Give my warmest [regards?] to Mrs. Muir Yours truly N.D. Stebbing]—[1]Santa Barbara Cal. June 21/80My dear friend John MuirToday I was more than pleased to have a letter put into my hands which had your autograph attached to it. Some weeks since at one of my calls on a lady friend nearby in conversation your name came up. They said the lady I saw a notice in a ‘paper’ that Mr. Muir was married. That opened my [illegible]. I [illegible] you saying that you loved the mountains & you believed that they loved you. The question arose in my mind [illegible] he got [illegible] from his old loves? I’ll see had wrote to Mr Carr & enquired about your whereabouts - & status! Only a few days [since?] I received an answer confirming the news – glorious news too I intended before this to have written to you &[Page 2][2]congratulated you on your “second sober though” & found one in whom you could love fervently and at the same time know that it was fully appreciated. Nothing like lovely intelligence – don’t you think so? May it last till ripe old age & your ‘[illegible]’ be full of [illegible[ [illegible] and what a blessing! I want to say I have been interested in [reading?] your letters from Alaska published in the Bulletin especially your account of the glaciers & the trip with the great clergy & criticism on their [illegible] [illegible] I have seen some of your articles in previous magazines but I have not seen your book [on Mountain?] St[illegible] – glacier [illegible] [illegible] [illegible]. When will that make its appearance? Your letter to me was put into my hands by a friend at common[3] 00927school & S. School [illegible]. He brought it to me from the [illegible] There was present Mrs. Otis. A. [illegible] Otis. Her husband was formerly publisher at the S.B. [illegible]. He is now engaged for a Seal Co.(?) in Alask. It may be you have seen him as he was in Alaska last summer. I let Mrs Otis look over your letter. She was pleased with it and remarked she would like to write to you – but felt a little de[illegible] about it. She has a fine cultivated mind. A poet. writes for Eastern journals - & some in Cala a lovely character. In many respects like our friend Mrs Carr. I told her after tomorrow she might address you as soon as she pleased, for to night I would write to you & introduce her to you as my friend. I am living some three miles from the Post office i

Letter from N. D. Stebbins to John Muir, 1872 Oct 4 .

I thought these extracts would interest you if you had not seem them - Now I want you to find if possible about the time of the Oolitic period some evidences of the deposits of [coral deleted] cretaceous coral reefs - If any where I should look in the neighborhood of San Luis Obispo where those monstrous marine shells are found - If I can remember I am old fellow & it is not uncommon to find old fools at the present day - The words underscored are found in Prof. Danas\u27 work - I see by an extract from the Occident a San Francisco religious paper Prof Agassiz is now or has been in Cal. if so you will see him. I was amused on reading a criticism (from the same paper copied in our eastern journals) on the reception of Prof Agassiz. I will enclose it perhaps you may not have met with it. If you ever meet with dear old friends Prof & Mrs Carr - give them my best love I feel anxious to know how far Agassiz agrees with your theory of the origins of the canons in the Pacific slope. As I said in my last Moses like I must be content to look on- but you Joshua like be of good [underlined: courage] & [underlined: strong] & the good Lord bless you & fill you with knowledge both of Himself - & Nature Coudersport, Potter Co. Pa. Oct 4 / 72My good friend Muir I have just finished the rading of Mr. Dana\u27s new work on Corals & Coral Islands . He closes up the work by giving his Geological Conclusions I was so amused in seeing how he like the Ann Arbor Prof. (Winchell) in his work on Footsteps of Creation had been misled by Whitney I left I must give you the benefit thinking you may not as yet met with the work so recently pub lished to the world. The Prof. (Dana) gives what he thinks must have been a subsidence in some portion of the Pacific - among others - one he thinks was six thousand miles in length & twenty-five hundred wide reaching from the Sandwich to the Friendly Group [illegible] This subsidence was in progress in all probability during the Glacial era - there origin runs back into the Tertiary[in margin: Will you attend the scientific assn which meets in S.F.? Yours [truly?] N. D. Stebbins] The subsidence connected with the origin of coral islands & barrier reefs of the Pacific - amounted to several thousands of feet perhaps full 10,000, And it may be here repeated that although this sounds large the change of level is not greater than the elevation which the Rocky Mtns, Andes, Alps & Himalayas - since the close of the cretaceous era or the early Tertiary; & perhaps it does not exceed the upward bulging in the Glacial era of part of North America. - The author has presented reasons for believing (Am. J. Sci. /71) that in the Glacial era the watershed of Canada between the River St. Lawrence & Hudson\u27s Bay was raised at least 5,500 feet above its present level (1500 ft) & that this plateau thus elevated was the origin of the great glacier which moved south eastward over New England. This region is the summit of the Eastern arm of the great V-shaped azoic area of the continent, the earliest elevated land of North America; and it is not improbable that the other arm of the V, reaching from 00624Lake Superior & Huron Northwestward, to the Arctic, was raised at the same time to a higher elevation, and was the source of glacial move -ments over the more central portions of the continent. We cannot say Western portions also, since [in margin: his italics] in the first place the facts, according to Prof. J. D [in margin: illegible] Whitney, do not sustain the statement; & in the second, the great mountain ranges of the west would have been a barrier to all influ ences from any central continental elevation, &, besides, the slopes of these ranges, even the Pacific border were higher to the north then now, would have determined the course of all western glacial movements. The idea that the two arms of the great azoic V were raised together, is not without some support. It is there- fore reasonable that late geological history, during the Glacial era after the Mountain chains of the continent had been made & raised to their full height, & the surface crust thickened over all the continent except that of the Azoic nucleus, by successive beds to a thick- ness of thousands of feet, even 35000 by the close of the Paleozioic along the Appalachians, & much beyond this Pacific border, &c Coudersport, Potter Co., Pa.,Oct. 4 \u2772.My good friend Muir,I have just finished the reading of Mr. Dana\u27s new work on Corals and Coral Islands . He closes up the work by giving his Geological Conclusions . I was so amused in seeing how he like the Ann Arbor Prof. (Winchell) in his work on Footsteps of Creation had been misled by Whitney. I felt I must give you the benefit, thinking you may not as yet [have] met with the work so recently published to the world. The Prof. (Dana gives what he thinks must have been a subsidence in some portion of the Pacific. Among others, one, he thinks. was six thousand miles in length and twenty-five hundred wide reaching from the Sandwich to the Friendly group. This subsidence was in progress, in all probability, during the Glacial era, their origin runs back into the Tertiary. The subsidence connected with the origin of coral islands and barrier reefs of the Pacific amounted to several thousands of feet, perhaps full 10,000. And it may be here repeated that although this sounds large the change of level is not greater than the elevation which the Rocky Mountains, Andes, Alps and Himalayas since the close of the cretaceous era in the early Tertiary; and perhaps it does not exceed the upward bulging in the Glacial era of part of North America. The author has presented reasons for believing (Am. J. Sci.\u2771) that in this Glacial era the watershed of Canada between the River St. Lawrence and Hudson Bay was raised at least 5500 feet above its present level (1500), and that this plateau thus elevated was the origin of the great glacier which moved southeastward over New England. This region is the summit of the eastern arm of the great V-shaped azoic area of the continent, the earliest elevated land of North America; and it is not improbable that the other arm of the V, reaching from Lake Superior and Huron northwestward to the Arctic, was raised at the same time to a higher elevation and was the source of glacial movements over the more central portions of the continent. We cannot say western portions also this italics) since in the first place the facts, according to Prof. J. D. Whitney, do not sustain the statement, and in the second, the great mountain ranges of the West would have been a barrier to all influences from any central continental elevation, and besides the slopes of these ranges, even [if] the Pacific border, were higher to the north than now, would have determined the course of all western glacial movements. The idea that the two arms of the great azoic V were raised together is not without some support. It is therefore reasonable that late geological history, during the Glacial era after the mountain chains of the continent had been made and raised to their full height and the surface crust thickened over all the continent except the azoic nucleus, by successive beds to a thickness of thousands of feet, even 35,000 by the close of the Paleozoic along the Appalachians and much beyond this [along the] Pacific border.I thought these extracts would interest you, if you had not seen them. Now I want you to find, if possible, about the time of the oolitic period some evidences of the deposits of cretaceous coral reefs. If anywhere, I should look in the neighborhood of San Luis Obispo where those monstrous marine shells are found. If I can remember -- I am [an] old fellow, and it is not uncommon to find old fools at the present day -- the words underscored are found in Prof. Dana\u27s work. I see by an extract from the Occident, a San Francisco religious paper, Prof. Agassiz is now, or has been in California. If so you will see him. I was amused on reading a criticism (from the same paper, copied in our eastern journals) on the reception of Prof. Agassiz. I will enclose it, perhaps you may not have met with it.If you ever meet with dear old friends Prof, and Mrs. Carr give them my best love. I feel anxious to know how far Agassiz agrees with your theory of the origin of the canyons on the Pacific slope. As I said in my last, Moses like, I must be content to look on, but you, Joshua like,be. of good courage and strong, and the good Lord bless you and fill you with knowledge both of Himself and Nature.Will you attend the scientific assn. whioh meets in S.F.?Yours truly,N. D. Stebbins33

Letter from N. D. Stebbins to John Muir, 1885 Sep 14.

Dowagiac, Mich., Sept 14, \u2785.My dear friend Mr. Muir,A very [interesting] incident occurred this A.M.I got hold of a notice published in a Detroit paper of your account of the glaciers in Alaska, comparing them with those in Switzerland. While my thoughts were occupied with your researches on the Pacific Coast I had handed to me your letter of August 9th, and very much to my gratification.In regard to that Calaveras skull Prof. Dana wrote to me that their ethnologist (I can\u27t call his name) says it doesn\u27t belong to the Post Pliocene age. Prof. Whitney has a friend in Santa Barbara who wrote a couple of articles pub[lished] in S. B. Independent laudatory of his friend, but he couldn\u27t prove to the contrary that the Prof. was deceived by the miners as to the place where that skull was found. Well, it\u27s of little consequence.I am now sorry I did not go up to S. F. last spring before my return to Mich. I thought I would save 600 miles\u27 ride, although the fare was paid to the city. It\u27s an old man now writing to you -- 83 yrs. I fear I will not stay long enough to see that Book .Remember me in warm regards to Mrs. Muir and a kiss for that lovely daughter. I must heartily thank you for your letter, especially your prayers, which I greatly need. And may the everlasting Heavenly Father bless you and yours abundantly with the good things of this life, preparatory for an endless blessedness with Him through the grace of our Divine Redeemer.It is barely possible I may spend next winter in Cal. at Santa Barbara where I have a sister living, if health and strength hold out.Truly your friend,N. D. Stebbins.P. S. I will always be delighted to get a line from you, especially that Book

Letter from N. D. Stebbins to [John Muir], 1884 Jun 6.

Dowagiac, Mich., June 6, \u2784. My greatly respected friend John Muir,It is true that I am still in the land of the living. I imagined yon might be curious to know just so much, as worthless as it is to know it. An old man, past 82 years, quite infirm and becoming blind with all. Still memory keeps me jogging along in the journey of thought, and how often has memory jogged me back to Yosemite Valley and the little or short, but exceedingly pleasant interviews I had with you and our conversations in regard to glacier action which gave such strong evidences of its workings in that wonderful cañon that dropt down when the upheaval took place . Do you recollect when you climbed out and up through the Indian cañon and as you got along to Yosemite falls then you made a prayer for wisdom, on one Sunday! The result was that you found the evidences of glaciers\u27 works in front of you! and settled with me the enigma how the Indian Cañon came to exist, as there was no appearance of a water course ever having passed through it. Well I remember somewhat that [which] I have read in the Overland Monthly of your theory of mountain structure, etc., etc. since some of your experiences with grand-father glaciers, such that those in Switzerland are mere babies--all these hints through the common channel of information, newspapers. Now let me say all these helps have disappeared. When I went to Cal. the last time I left the Overland Monthly with a young friend who died before my return. They are lost and of course the newspapers containing your exploits and scientific theories and investigations. Even the story when you came abreast of ice impossible [to pass] and forbid [ding]your return, when all hope seemed for a time to be gone. Then a sudden inspiration -- truly from your God and Saviour -- helped you over the dangerous precipice in safety. I presume you have never forgotten that escape from that narrow and dangerous trip to the head of one of the ice-fields on Mt. (the name has passed out of my mind at this moment). Are you wondering at what I am driving? In short do you mean that all this knowledge and experience shall be lost to the world? I have consoled myself after losing all that I have seen of your written travels and discoveries that some day you would publish or have one published that would give to the world a complete history of your travels and discoveries and theory of mountain structure, glacier action in cutting out those tremendous cañons along the Sierras, especially Yosemite; and still glaciers discovered by yourself. What! are you going to let all this thrilling experience and knowledge be lost! Now for the animus of this scrawl of a letter. I have been waiting many years to see your book on mountain structure, glaciers, and glacier action and your marvelous exploits and escapes doing justice to your God and His watchful care over you. That book I have not heard was in print! Must I die and all the world with me, ignorant as a world, while a few friends are permitted to know a little -- must it all go into forgetfulness? Now I am quite blind -- can just see these lines I am writing upon with good glasses; still I covet that book on mountain structure and glaciers and glacier action. Must I die never having seen it? If you can find a Dr. Jones, M.D., who formerly practiced medicine in Murphys about 14 miles from the Calaveras Trees in Calaveras Co., a few miles from Table Mountain, who lives now, if alive, in San Francisco, he can tell you all about Whitney\u27s wonderful Calaveras Skull . Dr. Jones told ma that he had often heard the miners tell the story and laugh over the trick they played upon Prof. Whitney in pretending that that skull was found among the gravel diggings under Table Mountain. Whitney didn\u27t make the discovery of glaciers and glacier action on the Pacific slope, and don\u27t you let him steal it from you -- nor LeConte. You owe it to yourself and your friends and the little daughter I hear you have and future generations of yours to have them know who made these scientific discoveries. If I was the means of Dr. Carr\u27s getting you an opportunity to write for the Overland Monthly, let me be now the means in some measure to have a book given to the world such as will do you justice and go down to the end of time with other scientific adventures. (My eyes are badly eclipsed just now). Now, my greatly esteemed friend, do yourself the justice to give the world your knowledge expression, -theory of mountain structure and glacier action, etc., etc. I covet seeing it before I go never to be any more in this life. Hoping to meet you in Heaven where our dear Lord and Saviour is the great centre of all creation and will be eternally, I am ever truly your attached friend. I will enclose my photo for Miss Wanda , with warmest regards for yourself and Mrs. Muir and the little cherub Miss Wanda.N.D. Stebbins.P.S. I had a postal from Mrs. Carr, saying she had been ill. May she live many years to bless the world with her whole-souled, graceful, loving, good-willing, marvelous soul and body