Toomas Karmo: Theological discovery: the witness of John Bradburne (1921-1979)

One of my four Debian GNU/Linux desktops. In upper-left hand corner are the usual operations clocks, disciplined via Network Time Protocol to  perhaps plus-minus 300 milliseconds, showing Ontario civil time in green and UTC in red. Then proceding anticlockwise: Dame Julia's hermitage table in Firenze, perhaps ready for the reception of visitors (Web provenance unknown, sorry, but photo used with her approbation); John Bradburne with patient Joshua (who, apart from being a bugler, kept Muscovy ducks; the photo is from http://www.johnbradburne.com/gallery.php, and bears the copyright notice "(c) John Bradburne Memorial Society", and permission for use has been kindly granted by Celia at the Society); my  photo from 2016-09-25 (SUN) of one, out of tens or hundreds, of honeybees foraging on Symphyotrichum lateriflorus in an Aurora municipal park; and an xterm ("glass Teletype") with some private theological notes. 

Quality assessment: 

On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3'5 is "mediocre pass", 4.5 is "good", and 5/5 is "excellent"): 4/5. Justification: Kmo had time to develop most of the necessary points in reasonable detail.  

Revision history:

• 20160928T1737Z/version 1.3.0; Kmo added a remark noting the daily Bradburne poetry feed on Twitter. Kmo reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.3.1, 1.3.2, 1.3.3, ... . 
• 20160928T1723Z/version 1.2.0: Kmo added notes in photo caption, recording e-mail approvals received from Sister Julia Bolton Holloway and (via the representative Celia, a niece of the martyr) from the John Bradburne Memorial Society. Kmo reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.2.1, 1.2.2, 1.2.3, ... . 
• 20160927T0226Z/version 1.1.0:  Kmo added a remark on the man whose sight was restored upon imploring the intercession of John Bradburne. Kmo reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.1.1, 1.1.2, 1.1.3, ... . 
• 20160926T2128Z/version 1.0.0: Kmo uploaded an adequately polished base version. He reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.0.1, 1.0.2, 1.0.3, ... . 

[CAUTION: A bug in the blogger software has in some past weeks shown a propensity to insert inappropriate whitespace at some late points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

This week, as last week, pressure from the DDO&P heritage-conservation file interrupts my normal rhythm of blogging. I am forced to upload a few hours early, to upload fewer words than is normal on this blog, and to delay once again my concluding remarks in praise of Moise's Elementary Geometry from an Advanced Standpoint. So today I upload nothing on mathematics, but only the necessary new DDO&P material (this task I completed earlier in the day), along with the present rather modest reflection on theology. 

****

We are told that to those who keep asking it will be given, and that those who keep seeking will find, and that to those who keep knocking the door will be opened. There are subtle differences among these three promises.

Indeed this is part of one's reason for taking Christianity seriously. The New Testament offers such numinous depths, or subtleties, as would indeed befit some powerful thinker - subtleties arguably befitting the figure depicted in the New Testament narratives, i.e., arguably befitting a person "who spoke with authority, not in the manner of the legal scholars and the Pharisees". 

Today, I comment not on all three of our Lord's just-cited promises, but on the middle one. 

**** 

I have for months or years been seeking an example of a Catholic hermit to support me in times of anxiety, sadness, or fatigue. I have drawn, and God willing may well in coming weeks, months, or years  continue to draw, solace from the public example and private e-mails of Sister Julia Bolton Holloway. Sister (or Dr, or in former times Prof.) Julia, or "Dame Julia" as I like to call her informally, is the Firenze-based contemporary authority on mediaeval mystic Dame Julian of Norwich. She now ministers to the socially disadvantaged Roma - the "Gypsies" - from her hermitage in the English Cemetery, a little outside the city walls. She writes on an astonishing variety of topics (though not, so far as I know, on Estonia, on mathematics, on physics, on stars, or on DDO&P!), both on Facebook and at http://www.umilta.net. 

Dame Julia notwithstanding, I have been fretting: with my world in a heavy measure governed, from 1950s childhood to the present, by female figures, Dame Julia notably now among them, can I not find - can I not now be allowed to find, might I not now be graciously accorded - some male hermit mentor? 

I think that this past Saturday (I am writing two days later, on a Monday), some casual Web surfing brought in my case the vindication of our Lord's words "Seek and ye shall find." 

****

The essentials are laid out at https://en.wikipedia.org/wiki/John_Bradburne. John Bradburne (1921-1979) was educated at Gresham's in Norfolk (a school, I conjecture, of high and severe traditions). He was awarded, qua  member of the 9th Gurkha Rifles, the Military Cross - not for bashing people up in the Hitler war but for successfully escaping his captors, in operations in or near Malaya. He was received into the Catholic Church in 1947, in Britain. Moving to Africa, he worked with the leprous patients of Mutemwa, 140-some kilometres from present-day Harare. He died as a martyr, near his patients, in the Rhodesia-Zimbabwe military troubles of 1979.

John Bradburne's outlook can fairly be described as Franciscan. He thus has a special affinity both with our current, joyous Holy Father and with the Holy Father's luminous medieval namesake.

Not far from the isolated mountain pool where John Bradburne would take a daily dip stands a granite cross. This is a 1980s donation from a man who, having lost his sight in an accident, regained it upon imploring the intercession of the recently martyred John Bradburne. 

John Bradburne also enters English literary history, as a poet of stature. To my untutored eye, his verse, with its delightfully Victorian resort to rhyme, recalls in its sensibility, although not in its (perhaps timid?) technique, George Manley Hopkins (1844-1889). Bradburne is playful, and to my ear rather demure, where Hopkins is even to the jaded 21st-century reader daring.

Details on the vast Bradburne poetic corpus can be had from a site, maintained by a linguist of high eminence, which I have for my part barely begun to investigate - namely http://www.johnbradburnepoems.com. I have additionally learned from the John Bradburne Memorial Society in Britain that a Twitter account, designated @john_bradburne.com, supplies subscribers with a daily poetry line taken from the database. 

For John Bradburne's life and theological witness, I find value at  http://www.johnbradburne.com, and above all in the 20-plus newsletters (as of today, I have carefully studied the most recent three) at http://www.johnbradburne.com/newsletter.php. 

****

On 2016-09-12 or 2016-09-13, I blogged under the heading "Practical Civics: Pollinators in Richmond Hill Parks". Since uploading that blog entry, I have on one or two occasions managed to see just a single true honeybee here in Richmond Hill. As I remarked on 2016-09-12 or 2016-09-13, wasps and bumblebees are in our specific urban situation rather easy to find, but true honeybees hard.

Sainte Thérèse of Lisieux, it is said, nowadays likes to reveal her availability to people through the medium of roses. I have indeed a kind of vicarious personal experience of this, as I recount toward the end of "Utopia 2184" on my http://www.metascientia.com:

1990s Toronto. Sainte Thérèse. A young man of excellent family. His uncle, or some such, is currently or was not too long ago a bishop, or some such, at no great distance from Toronto itself. When I say bishop or some such, you must understand me to mean definitely a cut above monsignor, no equivocation at all there.

This conversation is happening in a church basement at some not-too-hopelessly-silly Catholic support group, dedicated to meaningful discussions on ahem-ahem this and that. 

The young man intimates that said excellent family contains a husband and wife - not the parents of the young man, as I recollect, but perhaps aunt and spouse, or second cousin and spouse, or something. The couple had, as was common in the twentieth century, lapsed from the Church. Sightseeing in Paris (so the young man explains to us), they made their way to the vicinity of Notre Dame. Funny little shop, I imagine on some obscure side street such as you might get near Île de la Cité or the rue Saint-Jacques. Funny little girl in funny little shop. Selling roses. The couple buy roses, and on impulse enter Notre Dame. That cathedral visit is the beginning of their return to the Catholic faith. Knowing at once that something in their joint life has changed, they turn from Notre Dame to the funny little girl in the funny little shop to thank her. No such girl of course, no such shop. They do try hard, inquiring persistently of the locals.

The story may be true, since the young man telling it to me is, I stress, of excellent family.

As with Thérèse and roses, so for John Bradburne and (people seem to remark on this a lot) bees.

Would I have some encounter with bees, then? 

****

Yesterday, Sunday, I celebrated the cool and bright weather by for the first time exploring an urban flood-plain meadow park in Aurora, on the far side of the Oak Ridges Moraine from Richmond Hill. Would I, perhaps, having on the previous afternoon learned of John Bradburne through serendipitous Web surfing, see  a bee or two - perhaps some lone scouting bee, to match the lone, perhaps scouting, bee I had managed to find some days earlier in Richmond Hill, at a conspicuously colourful flower bed around the bend from my Gentry Crescent digs? 

Sunday's Aurora meadow park sported not goldenrod alone, but also asters - both purple ("New England";    Symphyotrichum novae-angliae, as I gather from the municipal authority's helpful signage) and white (Symphyotrichum lateriflorus). It was in one stand of Symphyotrichum lateriflorus that I first made Sunday's discovery - not a single honeybee, but a great, loud buzzing of them, in their tens, or even in their hundreds. 

**** 

John Bradburne's predecessor John Manley Hopkins has some lines known to everyone. They bear repetition here, as anticipating the variegated and soaring life of John Bradburne: 

Glory be to God for dappled things -   

For skies of couple-colour as a brinded cow;     

For rose-moles all in stipple upon trout that swim;

Fresh-firecoal chestnut-falls; finches' wings;   

Landscape plotted and pieced - fold, fallow, and plough;

And áll trádes, their gear and tackle and trim.  

All things counter, original, spare, strange;  

Whatever is fickle, freckled (who knows how?)     

With swift, slow; sweet, sour; adazzle, dim;

He fathers-forth whose beauty is past change:

Praise Him.

  

Toomas Karmo: DDO&P: Submission to Town Council

Quality assessment:


On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3'5 is "mediocre pass", 4.5 is "good", and 5/5 is "excellent"): 4/5. Justification: There was enough time to make most of the desirable points. 

Revision history: 

• 20160926T1850Z/version 1.0.0: Kmo uploaded base version. He reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.0.1, 1.0.2, 1.0.3, ...  

[CAUTION: A bug in the blogger software has in some past weeks shown a propensity to insert inappropriate whitespace at some late points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

I submitted the following piece of writing to the Town of Richmond Hill Council meeting scheduled for 2016-09-26 (MON) evening, enlisting myself also as a solo speaker in what our Town's administration calls a "Delegation". The Clerks advised, however,  that I should not seek to speak as a Delegation, since my envisaged remarks were to some extent recapitulating my Delegation remarks from last week, and additionally since my detailed Delegation on DDO public outreach would (in Clerks' judgement) be more appropriately made to Mayor and Council later in the political process. 

Clerks did advise that my written submission would be put before Mayor and Council on 2016-09-26 (MON) evening), to enter the public record. 

Clerks and I agreed that I would, provided the Mayor did not raise a fatal objection, be able to speak during Public Forum on 2016-09-26 (MON), before the Council meeting is formally called to order. 

Full particulars on the 2016-09-26 (MON) meeting (all submitted correspondence,  and the agenda, and the minutes, and full Chamber video and audio recordings) are as usual being made available by our Town at http://www.richmondhill.ca. 

0. Preamble

Thank you, Mr Mayor and Council, for this opportunity to speak. 

In the five minutes available to me today, as in the five minutes available to me at Committee of the Whole last week, I will refrain from dwelling on the heritage-conservation fiasco which is the threatened loss of 32 greenspace DDO&P hectares, in the wake of the unjust 2012 and 2014 Ontario Municipal Board settlements. I will, this week as last week, refrain from dwelling on my ongoing inquiry into the physical integrity, within the threatened 32 hectares, of the Oak Ridges Moraine Aquifer cap. (This is a hydrogeological point on which I today, as last week, await promised communications on the one hand from the Town and on the other hand from Ontario's Ministry of Natural Resources and Forestry.) 

Today, as last week, I address only 

the DDO rump-park or remnant-park visioning Staff Report from Planning and Regulatory Services, SRPRS.16.064 and the Staff Report from Community Services, SRCS.16.30. 

1. SRPRS.16.064

You have before you a recommendation that the Janet Rosenberg and Studio 2016 April remnant-park report, comprising Appendix A of SRPRS.16.064, be accepted. I support this recommendation. 

However, I was a little surprised last week to find Committee of the Whole not addressing a troublesome  specific point from the Rosenberg report. While Committee of the Whole discussed costs in general terms, it did not address the question of costs for, specifically, repairs to the Great Dome and Administration Building. As I have in past months remarked to the Town, the figure offered in the Rosenberg remnant-park report, in the 3- or 4-million dollar bracket, conflicts with the deferred-maintenance figure in the approximately 10-million-dollar bracket offered by Prof. Tom Bolton, when he testified under oath at the 2012 Ontario Municipal Board as an expert witness called by my friends the Richmond Hill Naturalists. 

Tonight I remark also on one other respect in which the Rosenberg report could usefully be emended. 

The role of the Royal Astronomical Society Toronto Centre (RASC-TC) at DDO&P has not been wholly constructive. Apart from their failing to develop a programme of "Citizen Science" in their 2008-2016 tenure, they have done nothing to examine the question of increased DDO light pollution, should the developer's ambitions to put 520 or 530 or so homes, with a lane and 14 streets, onto its despoiled 32 hectares come to full, malignant, fruition. The omission is all the more striking because of RASC's avowed commitment to defending "dark skies" across Canada. 

The unhappy record notwithstanding, it cannot be denied  that RASC-TC has also done good things at  DDO, both in the 1935-2008 period and during its 2008-2016 monopoly on DDO astronomy.  I therefore support RASC's plea last week that the Rosenberg report be emended, with the following language.  This is language which RASC-TC to you in a letter dated 2016-09-18, over the signature of Prof.-Emeritus Dr Ralph Chou, and which forms part of last week's Committee-of-the-Whole archive: In 2009, the Royal Astronomical Society of Canada, Toronto Centre, leased the 74-inch telescope and Administration Building from Corsica Developments Inc., and began presenting astronomical outreach programming on the site. By the end of August 2016, over 30,000 visitors were received. 

2. SRCS.16.30

This week, as also last week, I call on Mayor and Council to make a small technical correction: Internet investigation shows that the organization with acronym YRAA is legally not the "York Region Astronomical Association" (as is erroneously written in SRCS.16.30), but the "York Region Astronomy Association". 

This week, as last week, I congratulate the authors of SRCS.16.30 in affirming a core civic value, in their announcing or requesting (in their words) an open and transparent approach to partnership development through the procurement process. 

This week, as last week, I suggest that no one organization or grouping should any longer have an exclusive right to offer DDO programmes. The Town, I respectfully suggest,  now has to promote and foster a diversity of approaches, with a healthy diversity of entities now participating. 

In this context, I recall some of my language from last week: In a fully correct set of decisions on DDO, the principle of non-exclusivity will not only be affirmed, but will be coupled with an affirmation of "Citizen Science". we need more than the DDO weekend educational outreach offered by RASC from 2009 through 2016, and offered up to 2008 by many of us as tour-guide "Dome Speaker" or as tour-guide (with auditorium lecture) "Chief". We need also a programme of research /.../  

I now amplify my language from last week, having between last week and this evening started reaching out both to the DDO Defenders (even while mindful, as always, that they support, and I oppose, the 32-hectare "Observatory Hill" subdivision) and to the (fully and properly conservationist) Richmond Hill Naturalists (DDOD, RHNats). 

(A) We need a programme of astrophysics research. Last week, I mentioned the idea of variable-stars monitoring, with one of the Administration Building roof-dome telescopes, under the ultimate aegis of the American Association of Variable Star Observers. I add tonight a few details on how this might work: 

• A formal observational-astrophysics alliance is set up, perhaps under some guidance from the Town, involving DDOD and RHNats, and additionally  involving any other party (RASC-TC? YRAA?) who wishes to join in. 
• Heading the alliance is some unpaid individual (in the normal university-science jargon, a "Principal Investigator", or "PI") qualified to doctoral level. (This might, as I already mentioned last week, be Dr Ian Shelton from DDOD.) Further technical support is provided by some unpaid individual qualified in astrophysics to at least honours-B.Sc. level, and with a good record of dome work, and with a good record of work  in computer-driven data reduction within the IRAF software package. (I could do this, as could others.) Night-to-night work is performed by the support officer in concert with an unpaid "Citizen Science" team from the community, perhaps comprising five or ten individuals. Of the five or ten, most would not be formally qualified in astrophysics, but would be briefed and trained as necessary by the technical-support officer(s). It would be natural for some of these individuals to be drawn from the rank-and-file membership of DDOD and RHNats. 
• An outlay of between 2,000 CAD and 5,000 CAD would be made on equipment (the sole real expense of the project): a computer in the 500-CAD class, running Linux and maintaining accurate chronometry through Network Time Protocol; and an astronomical CCD camera, generating images in the FITS format for downstream processing within the IRAF software package. 
• The group would seek to work around 5 or 10 half-nights or full nights per month, getting its first publication-quality results, with the PI as lead author, after a shakedown period of 6 or 12 months.  

I add also some minor points, on further types of appropriate programme activity: 

(B) We need to continue, and if possible also modestly to expand, the DDO tradition in meteorology started in or soon after 2009 by RASC-TC. RASC-TC is continuing to operate an automated meteorology installation, the "Vanessa Straumann Memorial Weather Station", with data communicated to the public at http://billlongo.com/DDO/weather/index.htm. One does not want this useful Station to be lost. One would in fact like to see it supplemented, if possible, with a hutch of traditional instruments (including manually operated max-min thermometer, and funnel-equipped manually operated precipitation gauge), as a check on the accuracy of the electronic installation. It would make sense for the hutch to be operated by one or more local schools, under consultation with one or more of  RHNats, DDOD, YRAA, and RASC-TC. 

Operation of traditional instruments would in fact provide high school students with a kind of training that a fully automated meteorological station cannot supply - namely, training in the keeping of laboratory notebooks, and in the mathematical handling of experimental uncertainties

(C) We need eventually to bring the York Region ham-radio community into DDO, optimally within the framework of the Amateur Radio Emergency Service (ARES). A public ham shack at DDO could start by using the existing small shortwave antenna - I presume this is a classic dipole - on the roof of the Administration Building. 

(D) We need to consider using the Administration Building for a programme of mathematics outreach, directed in the first instance at gifted Grade 11 and Grade 12 students in the town. I would be  happy to help a little here, as an unpaid volunteer, and I am perhaps not alone in being happy to help. 

Here is a possible vision: 

• A "Mathematics Self-Help Group", comprising about 10 people, meets upstairs in the Administration Building for one night a week, under the guidance of some mathematically more advanced volunteer. The Group spends most of the evening doing something very humble indeed - namely, homework from school! 
• But there is additionally a rather ceremonial weekly tea, in the ground-floor Administration Building library, in the spirit of a good Cambridge University laboratory. The rule, here as in Cambridge, is that teatime conversations are confined to science.
• Once or twice a month, there is a guest lecture, in the auditorium. (I can happily myself talk on cardinals and transfinite arithmetic - developing, for instance, the standard proof that no set is equipollent with the set of its own subsets, and in this context developing the proposition that the reals are a strictly larger infinite set than the rationals. Or I could, I suppose, somehow talk on Turing machines and undecidability-of-formal-systems. And I think I may be able to rope someone else in to talk on statistics, as a rather distinguished guest lecturer. Further possibilities suggest themselves through the Fields Institute, where I also have or have had one or two minor potential contacts.) 
• At suitable rare intervals, there is even, in the auditorium, a bit of Fun - for instance, a screening of one of the various films detailing Prof. Alan Turing's wartime Bletchley Park code-breaking work. 

Toomas Karmo: DDO&P: (A) Submission to C.O.W.; (B) RASC-TC communication

Quality assessment: 

On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3'5 is "mediocre pass", 4.5 is "good", and 5/5 is "excellent"): 3/5. Justification: Kmo did not have time to make as many points as would be desirable: a lot will have to be done in upcoming Parts E and, as it now appears, F. He did manage (within the framework of the version 1.0.1, 1.0.2, .. process) to do a reasonably polished job. 

Revision history:

• 20160919T1940Z/version 1.0.0: Kmo uploaded base version He reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.0.1, 1.0.2, 1.0.3, ... .  

[CAUTION: A bug in the blogger software has in some past weeks shown a propensity to insert inappropriate whitespace at some late points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

(A) Submission to Town of Richmond Hill
Committee-of-the-Whole 2016-09-19 Meeting

I submitted the following to the Town of Richmond Hill Committee of the Whole meeting scheduled for 2016-09-19 (MON) afternoon, enlisting myself also as a solo speaker in what our Town's administration calls a "Delegation". Full particulars on the meeting are at http://www.richmondhill.ca. 

I will have to blog on this again, somehow, next week, when that meeting is past, and when perhaps a meeting of Council as opposed to Committee-of-the-Whole is impending. 

In the normal cycle of Town business, matters are first aired by the Mayor and all the Councillors at Committee of the Whole, without motions being voted on. One week later, there normally follows a discussion in Council, with the formal taking of votes on formal motions. 

The organization to which I refer in connection with Dr Ian Shelton is the somewhat misleadingly named "David Dunlap Observatory Defenders". This grouping, which I founded late in 2007 but whose doors were later in essence closed to me, signed onto the 2012 Ontario Municipal Board subdivision-on-32-hectares Minutes of Settlement. 

0. Preamble

Thank you, Mr Mayor and Council, for this opportunity to speak. 

In the five minutes available to me today, I will not dwell on the heritage-conservation fiasco which is the loss, to the "Corsica" subsidiary of DG Group (formerly Metrus), of 32 greenspace hectares out of the DDO&P 77-hectare total. I will not dwell on my ongoing attempt to undo this 32-hectare loss, through a possible fresh federal idea involving the Department of National Defence, in a conceivable context of citizen-led reforestation. I will not dwell on my ongoing inquiry into the integrity within the threatened 32 hectares of the Oak Ridges Moraine Aquifer cap. (This is a matter on which I await communications on the one hand from the Town and on the other hand from Ontario's Ministry of Natural Resources and Forestry.) I will not dwell on my now-successful Freedom of Information probe into the developer's tree-felling and archaeology permit work, which should be resulting in the Canada Post delivery of about 68 documentation pages to me later this September. For all these points on which I do not today dwell, I refer you to past postings at my  http://toomaskarmo.blogspot.com. 

Today I address only the DDO rump-park visioning Staff Report from Planning and Regulatory Services, SRPRS.16.064 and the Staff Report from Community Services, SRCS.16.30. 

1. SRPRS.16.064

You have before you a recommendation that  the Janet Rosenberg and Studio 2016 April rump-park report, comprising Appendix A of SRPRS.16.064, be accepted. I concur. In concurring, I note with approbation that the Rosenberg rump-park report correctly refrains from denigrating the ongoing astrophysical research capability of DDO: the report in the version before us is commendably careful to state only, in terse and commendably neutral terms, that "increasing light pollution and new technical advancements elsewhere eventually led the University to focus its research through other facilities".

I do, however, respectfully suggest that in your discussion this afternoon you collectively underscore the importance of getting an accurate cost figure for repairs to the Great Dome and the Administration Building. As I have in past months remarked to the Town, the figure offered in Rosenberg the rump-park report, in the 3- or 4-million dollar bracket, conflicts with the deferred-maintenance bill in the approximately 10-million-dollar bracket offered by Prof. Tom Bolton, when he testified under oath at the 2012 Ontario Municipal Board as an expert witness called by my friends the Richmond Hill Naturalists. 

2.   SRCS.16.30

I call on Mayor and Council to make a verbal correction: where SRCS.16.30 in its present wording has "York Region Astronomical Association". What is actually legally correct is "York Region Astronomy Association". 

I also call on Mayor and Council to consider whether it is right to continue granting exclusive use of DDO to any one organization, as was unfortunately the case with the Royal Astronomical Society of Canada Toronto Centre (RASC-TC) over the period from 2009 through 2016. We have seen two unhappy scenes played out at DDO, under the inappropriate 2009-2016 RASC-TC monopoly - a RASC-TC leader literally chasing an executive member of the David Dunlap Observatory Defenders into the woods; and on another occasion, RASC-TC turning two members of the DDO Defenders, at least one of them on the executive, away on a public tour night, in an unfriendly or even menacing tone. Whatever is now decided regarding DDO, we must see to it that such things - here I recall also my own interruption by RASC-TC heckling in this Chamber on one tense evening some years ago - never get repeated.  

In a fully correct set of decisions on DDO, the principle of non-exclusivity will not only be affirmed, but will be coupled with an affirmation of "Citizen Science". We need more than the DDO weekend educational outreach offered by RASC from 2009 through 2016, and offered up to 2008 by many of us in the DDO astrophysics family, from night to night in our capacities as tour-guide "Dome Speaker" or as tour-guide (with auditorium lecture) "Chief". We need also a programme of research - to take one example, a citizen-science programme of binary-star eclipse timings, under the possible aegis of the American Association of Variable Star Observers, perhaps in one of the two half-metre-class Administration Building telescopes, under the possible guidance of some doctorally qualified Principal Investigator such as Richmond Hill's Ian Shelton. - I add here that in recommending Dr Shelton's participation, I deal with his organization at correct arm's length: I have not yet canvassed him on Citizen Science or SRCS.16.30, and as always I dissent from this misleadingly named organization's signing on to the destruction of 32 greenspace hectares. 

I congratulate the authors of SRCS.16.30 in their invoking a core civic value, in their announcing or requesting "/.../ an open and  transparent approach to partnership development through the procurement process /../". 

I conclude today's remarks by making my own (small) contribution to transparency, by communicating my own (scanty) information on the York Region Astronomy Association, and on related points. 

The database at https://www.can1business.com indicates that YRAA was registered as a corporate entity on 2016-08-08. The database gives also a few other particulars, including a Richmond Hill street address. 

The various e-mails I receive as a member of RASC-TC have not mentioned YRAA. 

YRAA held a first meeting (which I unfortunately missed) on the evening of 2016-09-16 (FRI), in the York Regional Police station at 171 Major Mackenzie Drive West. 

YRAA has a Web site at http://www.yrastronomy.ca. Oddly, however, the site is now without content, and has in the (recent?) past had some content: a Google search retrieves the past content fragment 

Members of the York Region

Astronomy Association want to continue to build on

seven years of 

success at the David Dunlap Observatory, maintaining, 

(with nothing shown by Google beyond that final comma). 

Prominent in DDO outreach, and in RASC astronomy outreach,  and in astronomy outreach at the Richmond Hill Public Library, and therefore possibly connected with the emerging YRAA intiative, and in any case of interest to Town Staff in the context of SRCS.16.30, is amateur astronomer Chris Vaughan. 

I have not yet attempted any communications with Mr Vaughan. 

At  http://astrogeo.ca/about-us--the-ddo.html,  Mr Vaughan promotes what purport to be ongoing tours at DDO. From this same server he disseminates a brochure, under filename astrogeo_brochure_october_13_2014.pdf, promoting DDO tours under his leadership. 

A quick research of Mr Vaughan's background, via LinkedIn, is on the whole encouraging: he holds a 1982 University of Toronto four-year B.Sc. in geology and physics (what in the terminology of other universities would be called "Joint Honours in Geology and Physics"), with additionally an astrophysics minor; and while lacking an astrophysics research record, he nevertheless holds three awards of an astronomy-outreach or amateur-astronomy character,  from RASC-TC, and one from RASC at the national, as opposed to Toronto, level. 

(B) Communication Received from RASC-TC,
Advising of the 2016-09-19 Meeting 

Requests to speak as Delegation, and documents for circulation in Committee of the Whole, are required by 12:00 noon on the day of meeting. 

I put my own request in on the Friday before the meeting. I made my own written submission around 11:59. 

At 10:25, I received, as a member of the Royal Astronomical Society of Canada Toronto Centre (RASC-TC), an e-mail, which I should report here (quoting in part, within the limits governed by the "Fair Use" doctrine in copyright law; I use italics here for all and only the material I quote). 

The mail notes that RASC-TC's governing board will be making a written submission and  that members of the board will attend as observers. 

RASC-TC advises that it will be clarifying its position and path forward, as it does not believe the description of the negotiations in the RH staff report accurately reflects its intentions, nor that its spirit was represented in the negotiation process. 

RASC-TC advises  that its board will also communicate its disappointment with the written description that the negotiations were seemingly not conducted in a manner that put the RASC TC Council's true intentions or interests first, and its surprise that another group was seemingly involved in the discussions.

RASC-TC advises that its board will submit a clarification request that the "History of the Site" in the Introduction of the Master Plan document be updated to more accurately reflect RASC TC's historical and more recent involvement in the DDO, which has been excluded from the timeline in the document.

RASC-TC invites its members to participate in this municipal process, whether by observing the meeting in person, by observing it in Internet live-streaming, by making written submissions, or by speaking from the podium. RASC-TC concludes with a remark that I as an occasionally critical member of RASC-TC find constructive and encouraging:  members are encouraged to share their thoughts and opinions on this and all RASC TC matters.

Toomas Karmo: extract from Victorian humourist Jerome K. Jerome, on Sorrow

One of my four Debian GNU/Linux desktops. In the upper right-hand corner is the usual pair of operations clocks (green for civil time, red for UTC, disciplined  to plus-minus perhaps 300 milliseconds by Network Time Protocol). The four images are stills from a YouTube upload entitled "Three Men in a Boat [Jerome K Jerome] Full Movie- With Subtitles", by YouTube user Gampa Abhinay, under date 2014-02-22. This "Full Movie" is a 1970s British television dramatization of the minor  classic, which captures the spirit of the Jerome K. Jerome's 1887 original even as 1980s-1990s Jeremy Brett captures the spirit of Sir Arthur Conan Doyle's Victorian-through-1920s originals.  Anticlockwise, from lower right: (a) a supper at the landlady's, as the decision is taken, for hypochondriacally fancied reasons of health, to go boating; (b) the upstream Thames journey begins, from Kingston; (c) an unfortunate encounter with a photographer-for-hire (not visible), as the boat sits in a slowly - and, as it turns out, a perilously - filling canal lock; (d) a supper on the water, I suspect somewhere between Kingston and Oxford. 

Revision history:

• 20160919T1802Z/version 1.0.0:  Under pressure from Ontario's DDO&P heritage-conservation file, Kmo uploaded almost 6 hours ahead of his normal weekly schedule, as version 1.0.0. He reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.0.1, 1.0.2, 1.0.3, .. .  

[CAUTION: A bug in the blogger software has in some past weeks shown a propensity to insert inappropriate whitespace at some late points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

It appears that for the next couple of weeks, the David Dunlap Observatory and Park (DDO&P) heritage-conservation file will be so active as to prevent me from blogging at my usual time (Tuesdays in the UTC interval 0001Z/0401Z, corresponding to Monday evenings in Ontario; awkwardly, it looks as though I shall have to be in the public area at Town meetings for a couple of such evenings). And it will for a couple of weeks probably be hard to find the time to wrap up my blogging on Moise's Elementary Geometry from an Advanced Standpoint. 

What to do? 

It is now appropriate to blog four or six or so hours earlier than I normally would, and to continue reporting on DDO&P, and to drop Moise for the time being, and to fill in with some uplifting or entertaining material outside the ambit both of DDO&P and of Moise. 

Accordingly, I today reproduce one of my favourite passages from British literature, from the tenth chapter of Jerome K. Jerome's minor 1887 classic  Three Men in a Boat: 

They awe us, these strange stars, so cold, so clear. We are as children whose small feet have strayed into some dim-lit temple of the god they have been taught to worship but know not; and, standing where the echoing dome spans the long vista of the shadowy light, glance up, half hoping, half afraid to see some awful vision hovering there. 

And yet it seems so full of comfort and of strength, the night. In its great presence, our small sorrows creep away, ashamed. The day has been so full of fret and care, and our hearts have been so full of evil and of bitter thoughts, and the world has seemed so hard and wrong to us. Then Night, like some great loving mother, gently lays her hand upon our fevered head, and turns our little tear-stained face up to hers, and smiles, and, though she does not speak, we know what she would say, and lay our hot flushed cheek against her bosom, and the pain is gone. 

Sometimes, our pain is very deep and real, and we stand before her very silent, because there is no language for our pain, only a moan. Night's heart is full of pity for us: she cannot ease our aching; she takes our hand in hers, and the little world grows very small and very far beneath us, and, borne on her dark wings, we pass for a moment into a mightier Presence than her own, and in the wondrous light of that great Presence, all human life lies like a book before us, and we know that Pain and Sorrow are but the angels of God. 

Only those whose have worn the crown of suffering can look upon that wondrous light; and they, when they return, many not speak of it, or tell the mystery they know. 

Once upon a time, through a strange country, there rode some goodly knights, and their path lay by a deep wood, where tangled briers grew very thick and strong, and tore the flesh of them that lost their way therein. And the leaves of the trees that grew in the wood were very dark and thick, so that no ray of light came through the branches to lighten the gloom and sadness. 

And, as they passed by that dark wood, one knight of those that rode, missing his comrades, wandered far away, and returned to them no more; and they, sorely grieving, rode on without him, mourning him as one dead. 

Now, when they reached the fair castle towards which they had been journeying, they stayed there many days, and made merry; and one night, as they sat in cheerful ease around the logs that burned in the great hall, and drank a loving measure, there came the comrade they had lost, and greeted them. His clothes were ragged, like a beggar's, and many sad wounds were on his sweet flesh, but upon his face there shone a great radiance of deep joy. 

And they questioned him, asking him what had befallen him: and he told them how in the dark wood he had lost his way, and had wandered many days and nights, till, torn and bleeding, he had lain him down to die. 

Then, when he was nigh unto death, lo! through the savage gloom there came to him a stately maiden, and took him by the hand and led him on through devious paths, unknown to any man, until upon the darkness of the wood there dawned a light such as the light of day was unto but as a little lamp unto the sun; and in that wondrous light, our wayworn knight saw as in a dream a vision, and so glorious, so fair the vision seemed, that of his bleeding wounds he thought no more, but stood as one entranced, whose joy is deep as is the sea, whereof no man can tell the depth. 

And the vision faded, and the knight, kneeling upon the ground, thanked the good saint who into that sad wood had strayed his steps, so he had seen the vision that lay there hid. 

And the name of the dark forest was Sorrow; but of the vision that the good knight saw therein we may not speak nor tell. 

Toomas Karmo (Part D): In Praise of Moise's "Elementary Geometry from an Advanced Standpoint"

Quality assessment: 

On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3'5 is "mediocre pass", 4.5 is "good", and 5/5 is "excellent"): 3/5. Justification: Kmo did not have time to make as many points as would be desirable: a lot will have to be done in upcoming Parts E and, as it now appears, F. He did manage (within the framework of the version 1.0.1, 1.0.2, .. process) to do a reasonably polished job. 

Revision history:

• 20160913T1501Z/version 1.2.0: Kmo added a small remark on Moise's proof that in the ordered field which is the reals, the multiplicative identity is strictly greater than the additive identity. Kmo reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented version 1.2.1, 1.2.2, 1.2.3, ... . 
• 20160913T0100Z/version 1.1.0: Kmo supplied the missing material, as five paragraphs under the heading "Moise's discussion of unusual fields". He reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.1.1, 1.1.2, 1.1.3, ... . 
• 20160913T0003Z/version 1.0.0: Kmo uploaded base version, while under time pressure leaving some material out(with a marker flagging his omission). He reserved the right to upload minor (i.e., cosmetic, as opposed to substantive) tweaks over the coming 48 hours, as here-undocumented versions 1.0.1, 1.0.2, 1.0.3, ... . 

[CAUTION: A bug in the blogger software has in some past weeks shown a propensity to insert inappropriate whitespace at some late points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears.]

In general, we find in Moise a careful mathematical formalism, consistent with the ideals of advanced-undergraduate Pure Mathematics, generally undergirded with a further virtue - a professional logician's sense, or at any rate something suitably close to that sense, of logic.

In what remains of this essay, I will discuss his excellence in formalism and logic in detail, mixing into my general approbation also some mild criticisms.

3. Points of Detail from Moise

3.1 Formalism, Outside the Strict Domain of Logic

Uniqueness of identities (and related point regarding inverses): I noted under the photo accompanying my blog posting of 2016-08-29 or 2016-08-30 that my Dalhousie University introduction-to-analysis, in 1971, seems to have laid down as clauses in the definition of a field "There is a unique element which serves as an additive identity, and there is a unique element which serves as a multiplicative identity." Moise does likewise, additionally laying it down that every element has a unique additive inverse, and that every element which is not an additive identity has a unique multiplicative inverse. 

But it suffices to lay down merely "There is at least one element which serves as an additive identity, and there is at least one element which serves as a multiplicative identity, and every element has at least one additive inverse, and every element which is not an additive identity has at least one multiplicative inverse." Given the other field axioms (associativity, commutativity, distribution of multiplication over addition, and the demand that no multiplicative inverse be also an additive inverse) one can then deduce uniqueness of additive identity, uniqueness of multiplicative identity, the existence for every field element a of some unique additive inverse a', and the existence for every field element b which is not an additive identity of some unique multiplicative inverse b'. 

Functions: "a range" versus "the range":  In introducing the concept of a function, Moise is correctly at pains to distinguish image from range. On the reals, the squaring function has as image the nonnegative reals. After going through various preliminaries, Moise makes the correct remark (the emphases on the words "defined" and "is" are his), "/.../we have explained the conditions under which a function is defined, but we have not said what kind of object a function is."  Next, he fills that gap in. For Moise, a function is a set of ordered pairs. He defines "a function with domain A and range B" as a collection f of ordered pairs (a,b) such that (I) for each pair, the first element is in A, and such that (II) for each a in A, a is the initial term of exactly one pair (a,b) in f, and (III) such that the second term of every pair in the collection is in B.

Here, however, it is for clarity necessary to add what Moise neglects to add, namely that (to take an example) the collection of pairs (a,b) of reals such that b is the same entity as a times a (this is a function with, I reiterate, the set of nonnegative reals as its image) is a function with infinitely many different ranges. One of these ranges is the just-cited image set. Another of its ranges is the set of reals (as one indeed might be liable to aver, upon recalling how people everywhere are liable to write, "The squaring function is a function mapping the reals into the reals"). A third of its ranges is the set which is the union of the nonnegative reals and the three-element set {-1, -17, -99}; and so on. In general, on Moise's definition of what a function is, we must not write of "the range" of a function f, but of "a range" of a  function f - with, indeed, the image of f being a range of f, but additionally with any superset of the image of f being a range of f. 

I do gather in my general Mathematics-Department ignorance that on some accounts of function, a function is not a bare set of ordered pairs meeting Moise's conditions, but is a Moise set of ordered pairs along with a range specification. On this competing terminology, we define two different functions when we write on the one hand "g has as domain the reals, and is such that for every x in the reals g(x) is x times x, and g has as range the nonnegative reals" and write on the other hand "h has as domain the reals, and is such that for every x in the reals  h(x) is x times x, and h has as range the reals." 

Degenerate spaces: point P versus singleton {P}:  Moise correctly devotes a short Chapter One section to "The Language and Notation of Sets" before proceeding in his Chapter Two to introduce the idea of a set of points, and to lay down the first five of his postulates. These initial postulates (he uses at this early stage in his book no notion of distance between points, and no notion of betweenness) pertain to a structure in which S is a set of points, and "curly-L" (the set of lines) is a collection of subsets of S, and "curly-P" (the set of planes) is a collection of subsets of S:  "All lines and planes are sets of points"; "Given any two different points, there is exactly one line containing them"; "Given any three different noncollinear points, there is exactly one plane containing them"; "If two points lie in a plane, then the line containing them lies in the plane"; and "If two planes intersect, then their intersection is a line." Now, however, (on p. 45) comes something which is not quite true: "If you check back carefully, you will see that [these five postulates] are satisfied by the 'geometry' in which there is exactly one point P in S, and this point P is both a line and a plane." What Moise should have written instead, with due regard for his earlier section on "The Language and Notation of Sets", is, rather, "If you check back carefully, you will see that [these five postulates] are satisfied by the 'geometry' in which there is exactly one point P in S, and the singleton set {P} is both a line and a plane." 

****

I end this discussion of formalism-outside-the-strict-domain-of-logic on some positive notes.

Moise's discussion of unusual fields: Evidence of care on Moise's part is his treatment of the tiny field, comprising just an additive identity and a multiplicative identity. (This is inevitably a two-element algebraic structure, not a one-element algebraic structure, since a clause in the standard definition of a field - Moise briefly highlights its importance - is that  the additive identity and the multiplicative identity are distinct. - Or rather, being very pure indeed,  with a correct regard for the point I made above, under the heading "uniqueness of identities", we ought to postulate simply "No additive identity is also a multiplicative identity" (i.e., "However big or small may be the set of additive identities, and no matter how big or small may be the set of multiplicative identities, at any rate the intersection of these sets is empty").) Moise carefully gives the usual definitions for addition and multiplication in the two-element structure, and then simply asks his students, in Chapter One, section 1.2 problem set, as problem 19, "Which of the field postulates would hold true?" (A less skilled teacher would, by contrast, somehow hint at the answer, for instance by writing "Prove that all the field postulates hold true.") 

Since Moise is in general careful with fields, and is in general so kind to his students, I felt emboldened to go a little beyond him, as I explained in my blog posting of 2016-08-29 or 2016-08-30: Suppose F is any field - finite or infinite. F might, for instance, be the tiny two-element field which Prof. Edelstein drew to the notice of his 1971-spring-semester special Dalhousie University analysis class. Or F might be the rational numbers with standard addition and multiplication. Or F might be the real numbers with standard addition and multiplication. No matter what F is, we can construct a further field, whose elements are pairs (a,b) of F-elements, as follows: addition is defined in terms of F-addition, as (a, b) schplus (c,d) = (a plus c, b plus d), with (0,0) as an (and, we can quickly prove, as the unique) additive identity element; multiplication is defined in terms of F-multiplication, and the additive inverse "minus" of F, as (a, b) schtimes (c, d) = ((a times c) minus (b times d), (a times d) plus (b times c)), and with (1,0) as the identity element. (The task is to prove that the set of such pairs, with schplus and schtimes, is itself a field.)  - So given the reals, we can construct the complex numbers as pairs of reals; and given Prof. Edelstein's tiny two-element field, we can construct a four-element field as pairs of Edelstein-tinies; and given the just-constructed four-element field, we can construct an eight-element field; and so on.

Having established this result for an arbitrary field F, I for the first time in my life feel rather cheerful about complex numbers, i.e., about the Argand plane. Argand-Schmargand, I now say, in a suitably dismissive tone: any field can with a mildly intricate definition of multiplication be used to generate a new, more elaborate, field, as the the complex numbers with their mildly intricate definition of multiplication are generated from the field of reals. 

It is rather important to be able to say, dismissively, "Argand-Schmargand." For what is the altenative? For years - nay, for decades - I had an inappropriate feeling of superstitious awe regarding the Argand plane, thinking to myself that it conceals some kind of deep, and ultimately debatable, philosophical presupposition, somehow and somewhere. It of course does not at all help that people have historically spoken of "imaginary" numbers, and have loudly insisted that "Imaginary numbers, with Argand-plane sums of imaginary numbers and real numbers, are just as legitimate as real numbers." One becomes uneasy precisely because the insistence is delivered loudly - being delivered, in fact, in the earnest declamatory tones of a government intent on deceiving its electorate, or in the earnest declamatory tones of  a phone-company marketing rep. 

I will also be forever grateful to Moise for distinguishing carefully between the concept of a field with an ordering relation and the more stringent concept of an ordered field. He fortunately asks in the problem sets for a proof that an ordering relation can be imposed on the complex numbers (Chapter One, problem set 1.5, problem 5), while also asking (same problem set, next problem; he gives a hint) for a proof that the field of complex numbers cannot be given an ordering relation that turns it into an ordered field.

And it is good to compare Moise's first edition with his final (third) edition, in their respective treatments of the additive and the multiplicative identity in an ordered field. While the first edition is silent, the third edition helpfully proves as a theorem that in the ordered field which is the reals - in fact, we may add, his theorem holds for an arbitrary ordered field - the multiplicative identity is strictly greater than the additive identity. Moise's comment on this shows the kindly regard he has for potential difficulties amid the less sophisticated ranks within his big cohort of readers (the emphasis on "not" is his): The question here is not whether the real number 1 is greater than the real number 0; everybody knows that it is. The question is whether the statement 1 > 0 follows from the postulates and definitions we have written down so far. If this statement does not follow, then we need another postulate. 

Moise's careful discussion of "The Generalized Associative Law":  Moise, I presume like everyone who introduces the abstract-algebra concept of a field and avers that the reals are a field, postulates the associativity of addition and multiplication in terms of triples: for all a, b, c in the field, (a+b)+c is  postulated to be the same field element as a+(b+c); for all p, q, r in the field, (p times q) times r is postulated to be the same field element as p times (q times r) (with similar in-terms-of-pairs postulates for commutativity of addition and commutativity of multiplication: t + u is postulated to be none other than u + t, and v times w to be none other than w times v, for all field elements t, u, v, w).

One might well imagine a careless author leaving associativity there, taking it it as somehow "evident that", or as something "left to the reader to prove", that for any natural number n, n-fold sums and n-fold products are freely associative.

Moise, on the other hand, fills this in with care, taking fully four pages, with a formal inductive proof, and in the course of his work answering that very necessary question - I imagine it said at the samovar in my imaginary, grubby, Nikolai Ivanovitch Lobachevsky Institute of Socialist Mathematics, on the scarier side of the Urals - "Vot MEENZ 'freely associative'?". He starts his four-page discussion as follows (the emphasis on the word "pairs" is his): 

In practice /.../, as soon as you get past Chapter 1 of anybody's book, you are writing n-fold sums

a1 + a2 + ... + an, 

and n-fold products

a1 a2 ... an, 

for n > 3. We insert and delete parentheses in these sums and products, at will. All this is fine, but it has not been connected up, so far, with the operations that are supposed to be given for pairs of numbers (a,b) and with the associate laws for triplets (a, b, c). It would be a pity if mathematics appeared to be split down the middle, with the postulates and definitions on one side, and the mathematical content on the other. let us therefore bridge the gap between our postulates and the things that we intend to do. 

[To be continued, and perhaps concluded, soon (perhaps next week), as "Part E".]