Monday, 29 August 2016

Toomas Karmo: Remark in Lieu of Forthcoming Part C of Essay-in-praise-of-Moise

Perpetually at my desk is the obituary, from Toronto's Globe and Mail of 2003-02-07, of  Prof. Max Edelstein (written by his daughter, the British Columbia mathematician Leah Keshet). Prof. Keshet and I have been in correspondence in recent years, and I am inexpressibly grateful to her for the gift of two books from her distinguished father's personal library. - Prof. Edelstein, as my teacher in a special analysis course at Dalhousie University in the 1971 spring semester, conceived the perfect method of teaching. There was no exam. There was no mid-term. There were not even any problem sets, in the normal sense. The sole requirement was that we, the students in his tiny cohort, would write our own textbook, proceeding from hints and questions and challanges handed out by Prof. Edelstein in blue spirit-duplicator coursenotes. My own textbook, which I have kept carefully and have now also sent in photocopy to Dalhousie University, starts with the definition of a field, soon proceeding to a run of theorems. It is just like the first chapter of the wonderful Moise. But I do notice a tiny blemish, common to Prof. Edelstein and the immortal Moise. We really should not say, in postulating the additive identity, 'There exists a unique 0 such that for every element a in the field, 0 + a = a" (and likewise for the mulltiplicative identity). It suffices to say "There exists at least one element 0 such that for every element a in the field, 0 + a = a" (and similarly for the multiplicative identity). Uniqueness is then something we prove, from the field postulates (both in the case of the additive identity and in the case of the multiplicative identity). - The shiny ceramic sphere, with its blue, green, and red triangles, persuades me that in spherical geometry, in contrast with Euclidean plane geometry,  isosceles triangles with a common apex can fail to be similar: the equal base angles of my red isosceles triangle, in particular, on the far side of the sphere, are obtuse, in startling contrast with the equal-and-acute base angles of my blue isosceles triangle, and in startling contrast with the equal-and-acute base angles of my green isosceles triangle. 




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 do a reasonably complete and (within the framework of the version 1.0.1, 1.0.2, .. process) reasonably polished job. 

Revision history:



  • UTC=20160830T0233Z/version 2.0.0: Kmo managed to get rid of the point-form outline and to a proper upload. He reserved the right to do tiny cosmetic, nonsubstantive, tweaks over the coming 48 hours, as here-undocumented versions 2.0.1, 2.0.2, 2.0.3, ... .  
  • UTC=20160830T0003Z/version 1.0.0: Kmo lacked  time to be thorough, and so uploaded mere point-form outline. He resolved to get this (admittedly short) blog posting correctly polished by 20160830T0401Z .




[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.]





Here is a mere public-service announcement. 

I had no time this week for writing up "Part C" of my essay praising Moise, but I hope to write it up next week (with upload in the normal four-hour interval, in this case the four-hour interval UTC=20160906T0001Z/20160906T0401Z). 

In the mean time, readers may wish to follow me in proving an easy general result pertinent to Moise's first chapter, on fields. (The result emerges quickly from thinking about Moise, although Moise does not himself include it in the chapter problem sets.)  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. 

Toomas Karmo (=VA3KMZ): Moral-Uplift Images Pertinent to Radio and Department of National Defence

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 do a reasonably complete and (within the framework of the version 1.0.1, 1.0.2, .. process) reasonably polished job. 

Revision history:



  • UTC=20160830T1339Z/version 2.1.0; Kmo added a small remark on jamming of Red Army signals in 1991 August. - He reserved the right to make tiny, cosmetic, nonsubstantive tweaks over the coming 48 hours, as here-undocumented versions 2.1.1, 2.1.2, 2.1.3, ... . 
  • UTC=20160830T0157Z/version 2.0.0: Kmo finished converting the point-form outline into coherent prose. He reserved the right to make tiny, cosmetic, nonsubstantive tweaks over the coming 48 hours, as here-undocumented versions 2.0.1, 2.0.2, 2.0.3, ... . 
  • UTC=20160830T0002Z/version 1.0.0: Kmo was unable to get everything finished, and uploaded a mere point-form outline. He resolved to get the writing and polishing into an adequate state by 20160830T0401Z. 
   
[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.]


Imitating my practice on earlier occasions, I once again show a screenshot of one of my (at all times foufold) Debian GNU/Linux desktops.

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Here, as in previous screenshots, I show in the upper right-hand corner a pair of operations clocks - green for Toronto civil time, and red for UTC - generally attaining a precision tighter than plusminus 200 milliseconds. These clocks are disciplined over Network Time Protocol essentially once in 24 hours, on essentially all occasions against that peer of tock.utoronto.ca and chime.utoronto.ca which is tick.utoronto.ca.

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Today I have caused two Debian GNU/Linux /usr/bin/xterm windows to show excerpts from some flat-ASCII private study notes on radio.

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The two depicted rigs are from "back Home", i.e., from Estonia. They saw civic service in the most serious European crisis since the 1939/1945 war, in 1991 August. (European history has thus just this month, in 2016 August, passed a quarter-century milestone.)

In the 1991 crisis, Estonia, Latvia, and Lithuania regained their interwar independence. The Ukraine of 1991 August attained, or moved to attaining, the independence which many of its brave people had sought in vain during the post-1917 Bolshevik-Menshevik civil war. And similar developments, of a generally promising character, occurred elsewhere that anxious August, in the now-imploding USSR.

At the onset of the crisis, a putsch had temporarily removed M.S.Gorbachev (1931-) from Kremlin power - leaving, however, B.N.Yeltsin (1931-2007) able to play a constructive role, in defiance of the absurd would-be junta.

The Red Army, prima facie putsch-supporting, had occupied terrain at the base of the Tallinn Television Tower. Pro-independence Estonian personnel in the tower were asserting that if this facility - crucial to Estonian public broadcasting, and to Estonian peacetime communications abroad - came under Red Army attack, they would respond by activating their building's halon fire-suppression system. They would thereby in one stroke be both ending their own lives and demonstrating to world opinion the firmness of Estonian political resolve.

Had the widely feared attack occurred, events could (I now in hindsight suggest) have escalated out of control, ultimately to the grief not of Estonia alone but of many nations.

It was therefore essential for authorities in Estonia's principal nucleus of government, Tallinn's Toompea citadel, to monitor the radio traffic of Red Army units within Estonia; to monitor public broadcasting services in Russia and the West; and to maintain their own external communications, inbound and outbound. There was additionally some mission-critical jamming of Red Army signals.

The rig on the left (so explains http://raadiosoda.blogspot.com) is a model of an HF ("high frequency", "shortwave") receiver used widely in the USSR army and navy, and available also to USSR hams, and kept in production from 1948 right up to 1981: Tema väga oluliseks omaduseks oli äärmiselt suur töökindlus. Seade ei läinud praktiliselt mitte kunagi täielikult rikke ja mõne raadiolambi halb töötamine sai uue vastu väljavahetamisega kiiresti kõrvaldatud. ("Its exceptionally relevant feature was its extreme robustness. The set would practically never get so out of order as to be beyond repair. A deficiency in some valve would be quickly remedied, by swapping the old valve out for a new one.")

This set was used at Toompea for monitoring public broadcasts, both  within the USSR and outside it; for receiving ham-operator situational reports; and for monitoring the movements of a Red Army Pskov (I suspect, a paratroop) division.

The homebrew transceiver on the right (so explains http://raadiosoda.blogspot.com) was used by a Tartu ham, the either-then-or-eventual ES5MC, in support of the Tallinn-Vilnius intergovernmental hotline. My lookup today, in the Toronto afternoon of 2016-08-29, at http://www.qrz.com indicates that ES5MC (Mr Arvo Pihl) is still licensed under that callsign. Mr Pihl is indeed shown in my http://www.qrz.com database lookup to have an e-mail adress on the Estonian equivalent of Canada's ham-radio rac.ca server, namely erau.ee.

At the lower right is the most photogenic, though not necessarily the most operational, part of the the Toompea facilities, the 1360-1370 "Pikk Hermann" ("Tall Hermann") tower.

An English writeup correspoding to the just-cited http://raadiosoda.blogspot.com may be found at http://estonianelectronicwarfare.blogspot.com.

Further, an English writeup of Pikk Hermann, placing it into its wider architectural and governmental context, can be found on the Estonian parliamentary Web server, at http://www.riigikogu.ee/en/visit-us/toompea-castle/tall-hermann-toompea-towers/.

****

In the centre image is a small part of a many-hectare thing I have seen on dozens of occasions from the VIA train window, namely the antenna farm on the Tantramar Marshes outside Sackville, New Brunswick.

It is a standing joke in radio engineering that an antenna farm is optimally sited on a mountaintop salt marsh. Tantramar has the desirable radio-reflective salty (and so electrically conductive) salt water, although it is, alas, at no considerable elevation.

The main user of the farm was Radio Canada International (RCI). The RCI shortwave service was discontinued, in favour of an Internet service with a reduced number of languages, in 2012. But according to https://en.wikipedia.org/wiki/CKCX, this same antenna farm was also used under time-share arrangements by Radio Japan, China Radio International, the Voice of Vietnam, the BBC World Service, Deutsche Welle, and Radio Korea. The same source indicates that the farm was demolished in 2014.

Kipling writes, in a poem that attracted the admiration even of T.S. Eliot,

Far-called, our navies melt away; 
On dune and headland sinks the fire. 

My last train-window glimpse of the imposing setup was in the summer of Mum's death, in 2011.










Toomas Karmo (=VA3KMZ): Open Letter re DDO&P DND (Department of National Defence) Implications

This map, ultimately from materials published by the Town of Richmond Hill in a hyperlink tree rooted at http://www.richmondhill.ca/subpage.asp?pageid=DDO_park, documents the 72-hectare David Dunlap Observatory and Park (DDO&P) "Trapezoid" and the 5-hectare DDO&P "Panhandle". The "Panhandle" (in white) is to become part of the envisaged approximately 45-hectare rump park. The remaining approximately 40 hectares of the rump park is that part of the Trapezoid which is here coloured green. Also shown is the envisaged, but to many of us entirely unacceptable,  approximately 32-hectare subdivision (with its lane, its 14 streets, its stormwater sump, and its 520-plus homes). The northern edge of the Trapezoid, along Hillsview Drive, is around 1.2 km long. The Trapezoid is bounded on the east by Bayview Avenue and on the west by the CNR "Bala Subdivision" line. This is a line with some DND relevance, but now most prominent in the public mind as the GO commuter line, running on about 30 km of not-quite-straight railbed to Toronto Union Station. (As the crow flies, the distance is more like 20 km.)  Yonge Street lies a little west of the railway, about 1 km to the west of the Panhandle.



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 do a reasonably complete and (within the framework of the version 1.0.1, 1.0.2, .. process) reasonably polished job. 

Revision history:


  • 20160912T1810Z/version 2.1.0: Kmo added points on Toronto-Ottawa landline and Toronto-Ottawa satellite links, and on the suitability of the DDO Administration Building roof for solar-panel arrays, and on the ability of the USSR to run a large radio installation without trimming back too much woodland. He reserved the right to upload minor, cosmetic and nonsubstantive, tweaks over the coming 48 hours, as here-undocumented versions 2.1.1, 2.1.2, 2.1.3, ... . 
  • 20160830T0122Z/version 2.0.0: Kmo finished uploading a reasonably polished version, and accordingly deleted his point-outline material. He reserved the right to upload minor, cosmetic and nonsubstantive, tweaks over the coming 48 hours, as here-undocumented versions 2.0.1, 2.0.2, 2.0.3, ... . 
  • 20160830T0001Z/version 1.0.0: Kmo uploaded base version, unfortunately in part merely in point-outline form. He resolved to polish things adequately by 20160830T0401Z. 


[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.]

0. Background



Some of my readers, particularly at the Department of National Defence (DND), will be unfamiliar with the David Dunlap Observatory and Park (DDO&P) land-conservation file.

I have blogged on this file extensively in the last month and a half, as follows: 

  • on 2016-08-22 or 2016-08-23, under the title "Open Letter re DDO&P Breach-of-Aquifer Question (Town et al)" 
  • on 2016-08-15 or 2016-08-16, under the title "Failure of 2016-08-14 Archdiocese-Outreach Effort (Pertinent to DDO&P Conservation)"
  • on 2016-08-15 or 2016-08-16, under the title "Failure of 2016-08-14 Muzzo-Outreach Effort (Pertinent to DDO&P Conservation)"
  • on 2016-08-15 or 2016-08-16, under the title "RASC-TC Leadership Change, and Further RASC-TC Statement on DDO&P"
  • on 2016-08-08 or 2016-08-09, under the title "Muzzo-family/Toomas Conciliation Project (DDO&P and Convict)"
  • on 2016-08-08 or 2016-08-09, under the title "DDO&P Karen-and-Toomas Reconciliation Project"
  • on 2016-08-08 or 2016-08-09, under the title "Commentary on Useful RASC-TC Editorial on DDO&P Conservation Case"
  • on 2016-08-01 or 2016-08-02, under the title "Open Letter re DDO&P to Town Council, Addressing the 2016-07-29 Concerns of Councillor Karen Cilevitz " (but fortunately the comments by Councillor Cilevitz, arguably inconsistent with the Municipal Code of Conduct in its call for Councillors to be courteous toward the public, have since been removed - I presume by her - from her Facebook page) 
  • on 2016-07-25 or 2016-07-25, under the title "Open Letter re DDO&P to Muzzo and DeGasperis Families, and Others"
  • on 2016-07-22, under the title "CIVIC EMERGENCY: RASC Pulls out of DDO 2016 September"



The posting of 2016-07-22 incorporates, under the section heading "1. Background to the 2016-07-22 RASC Crisis", a full set of descriptive references to my earlier DDO&P-pertinent http://toomaskarmo.blogspot.com blog postings. I do here apologize for not having had the time to set up a proper indexing formalism for http://toomaskarmo.blogspot.com. If time were to permit, I would have to create a hyperlink index of all my principal blog topics, imitating the model of Sister Laurel O'Neil at http://notesfromstillsong.blogspot.com. Sister O'Neil's right-hand column, some distance down her page, is headed "Labels". Here are given appropriate subject references, running from such alphabetically early headings as "Abba John Colobos" and "Abuses of Canon 603" all the way down to such alphabetically late headings as "white martyrdom" and "wordliness". 


1. Update:
Ongoing Oak Ridges Moraine Aquifer Cap Investigation


Before today embarking on my main DDO&P topic, I should give a short update on my topic from 2016-08-22 or 2016-08-23, the "Open Letter re DDO&P Breach-of-Aquifer Question (Town et al)". 

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As of UTC=20160829T2131Z, I had no information from the Town regarding its state of knowledge on the physical integrity of the aquifer cap. The Town had, however, assured me at the end of the previous week that it was working on a reply, and that it would contact me once it had consulted an appropriate member of its Staff. This official was due back from holiday by 2016-08-29. I for my part thanked the Town for their constructive communication, remarking that I had directed a parallel enquiry to Ontario's Ministry of Natural Resources and Forestry, noting to the Town that the Ministry undertakes to answer queries in 15 days, and stressing to the Town that accuracy in our aquifer-cap question is preferable to speed. 


2. Fresh Considerations: DDO&P and the Department of National Defence




2.1: Background Regarding Greater-Toronto-Area Resilience


From http://www.yorkregion.com/news-story/1434067-video-aurora-house-holds-secret/ (the Aurora Banner, 2012-03-23, under headline "Aurora house holds secret") one can see the alarmingly modest scale of Cold War efforts for the civil defence of Toronto. In an era in which the United Kingdom had rudimentary UKWMO ("Warning and Monitoring Organization") bunkers across the country, in at least many instances at some such tight spacing as 20 kilometres, it rather appears that Toronto civil defence was to be coordinated from a single Aurora bunker, at 220 Old Yonge Street. The bunker possessed a (surely inadequate) hundred or so phone lines, plus a map room and assorted minor auxiliaries.

The 220 Old Yonge property has at some point subsequent to 2012 been put up for sale. Whether a buyer has been found I do not know.

My experience in Melbourne civil defence, as an early-1980s volunteer in the State Emergency Service (under the Government of Victoria) suggests a similarly modest scale of disaster preparation in Australia.

The Toronto and Melbourne examples are to be contrasted not only with Cold-War-era UKWMO, but still more tellingly with Switzerland. Perhaps it was in part because Switzerland was serious about civil defence in the two troubled decades following World War I that it managed to avoid Austria's sad 1938 fate.

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Disaster scenarios are, admittedly, different now from what planners faced in the eras of Anschluss and Cold War. The immediately plausible threats are no longer of a self-evidently extreme character. if we leave the most dramatic of the various possibilities aside today (therefore today staying silent about, in particular, a possible repeat of the Carrington Event, as discussed at https://en.wikipedia.org/wiki/Solar_storm_of_1859 and http://science.nasa.gov/science-news/science-at-nasa/2009/21jan_severespaceweather/), then two special vulnerabilities suggest themselves:
  • there could be a repeat of the 2003-08-14 blackout, for instance in winter, under the stress of some region-wide ice storm paralleling the storms of 1998 January and 2013 December
  • there could be an Internet degradation, for instance from military or terrorist hostilities occurring far outside Canada
DND will have performed some risk appraisals in connection with at least the second of these two scenarios.  Although I cannot for my part claim to be at all well read, I nevertheless do offer the following scenario points here (subject to correction, either by DND itself or by competent others): 

  • The worldwide Domain Name Service (DNS) root name servers - one, no doubt physically distributed over multiple machines,  governs URL-to-and-from-IP-address translation for the entire *.com domain; another does this job for the entire *.ca domain; a third does this job for the entire *.uk domain; and so on  - are a point of Internet vulnerability. They indeed have been asserted (whether accurately or inaccurately, I do not know)  to have already, in some recent year, come under attack. 
  • The DNS root-level servers aside, DNS is vulnerable from a conceivable subversion of the Network Time Protocol. The problem here is that routers are, for compelling engineering reasons, barred from updating their routing tables in the event of chronometry inconsistencies.
  • Toronto has in past years (I was told this by an appropriate professional around 2000 or 2005) had essentially one single Internet chokepoint - i.e., one single building, the loss of which would isolate Toronto from the world's Internet backbones. 
  • If this single chokepoint has since that time been replaced with multiple chokepoints, the number of such present chokepoints at any rate cannot, for compelling reasons of engineering and economics, be large. 
The two vulnerabilities are not guaranteed to be independent. 

On the one hand, a grid failure has Internet implications - notably when the backup systems for routers fade away, with their diesel generator fuel running out or their battery banks running down. 

And conversely, an Internet degradation may in turn affect the "SCADA" control systems in power stations, triggering a collapse of the grid. - I was given an assurance to the contrary by a professor some years ago at the Royal Canadian Institute, in a Sunday-afternoon lecture series. But I am now reluctant to believe him. If the Internet and the grid are decoupled, as the professor cheerfully asserted when I approached him at post-lecture mix-and-mingle time, then how (I now ask) has it been possible for USA SCADA (or similar) power-plant systems to be remotely hacked? 


2.2: General National-Resilience Implications of Radio


Governments planning for continuity of operations need VHF/UHF radio at all levels. This much they have probably had since soon after the Hitler war. Indeed I believe that some thought has even been given to VHF/UHF disaster planning at the humbler, mere university level: I think a friend of mine has to some degree raised the question of VHF/UHF links for coordinating, in a situation where Internet and grid (and of course landline and cellular telephone)  fail, the disaster-recovery efforts of the University of Toronto downtown, Mississauga, and Scarborough campuses.

Something else, however, is needed too. And this is a thing easily overlooked.

Disaster planning requires attention to radio  links beyond the VHF/UHF horizon, i.e., to distances in excess of (nominally) 50 kilometres. How, in a disaster degrading the Internet, can Toronto-based municipal, provincial, and federal authorities be guaranteed links with over-the-horizon Kingston and Windsor? And how, above all, can they be guaranteed links with Ottawa?

It would be foolish to rely on chains of VHF/UHF repeater stations, with communications handled through intricate sequences of relay points. The only robust solutions over Ontario distances, now even as before the Hitler war, lie in the HF ("high-frequency", "shortwave") regime - or still lower, in the MF ("medium-frequency", including and flanking the AM broadcast band) regime; or lower again, in the exotic marine-relevant LF ("low-frequency") regime.

Admittedly, there is likely to be a government emergency land-line link, whether in fiber or in copper, between Toronto and Ottawa, separate from the commercial telecommunications infrastructure. But here we run into the same problem of a repeater-station chain as besets long-haul VHF/UHF.

The Victorians ran telegraph copper all the way across the Atlantic seabed without repeaters. In compensation, however, they had to endure an impossibly low bandwidth, permitting them on the order of 10 just words per minute. At faster speeds, the dots and dashes in their Morse blurred together. What the modern copper-engineering tradeoff is between high bandwidth and paucity of repeaters I do not know.  For fiber optics, we have of course bandwidth adequate for government needs - data, voice, and more -  but at the high price of a repeater every 100 kilometres or so.

Additionally, landline is vulnerable to sabotage, and to seismic events.

One hopes that government has, apart from dedicated Toronto-Ottawa landline, a dedicated Toronto-Ottawa satellite link.  However, satellite, too, has its vulnerabilities, as in military and solar-storm scenarios. For satellites in lowish, rather than in geosynchronous, orbits, there is also the emerging "space junk"  vulnerability: https://en.wikipedia.org/wiki/Kessler_syndrome.

For HF and below, the principal vulnerabilities are jamming (but this is nowadays addressed, if it has to be addressed, through burst transmission technology), and Sun-driven ionospheric disturbance. As one goes to lower and lower frequencies, and therefore to longer and longer wavelengths, reliability of communications in the face of ionospheric disturbance increases.

HF is conventionally defined as extending from 3 MHz to 30 MHz. The less distance-capable VHF runs from 30 to 300 MHz, with 300 MHz marking the lower boundary of UHF.

Perhaps governments can at present operate with only a minor HF capability. In future decades, however, as Canada's security situation deteriorates under the twin impacts of climate change and fossil-fuels shortfalls, more will be needed. The principal operational HF-or-lower requirement in the troubled 2020s, or at any rate in the troubled 2030s, 2040s, 2050s, and beyond, will be the high-gain antenna farm, with appropriate directionality. Such antenna farms, with their feedlines and transmitters and receivers, are appropriately located at the edges of Canadian cities. From the suburban HF-or-lower rigs, VHF/UHF links can be run down into the actual urban nuclei of government - in Toronto's case into the Premier's offices beside the University of Toronto downtown campus; into downtown police headquarters; and into the existing Toronto-based Emergency Operations Centre, with its existing radio desks. The result would be that communications could be established between a Toronto nucleus of government and some corresponding nucleus in, say, Ottawa with just three hops: from the Premier's office (e.g.) on VHF/UHF, out to the HF-or-lower setup, with its antenna farm, in the Toronto suburbs; then out on, say, an HF wavelength of around 40 metres or 80 metres to a corresponding HF antenna farm in the Ottawa suburbs; and then on down, with VHF/UHF, to some appropriate situation room housing the Federal cabinet.

Amateurs using HF get by with antenna farms of a rather modest scale. At the University of Toronto Hart House Amateur Radio Club, around 2005 or 2010, I worked two-way Morse with the USA, and on a few happy occasions also with Europe, on that glorified copper clothesline which is the dipole. For government, however, more is needed, on a physical scale no longer modest. The 40-mere dipole, appropriate for telegraphing Europe on just over 7.0 MHz, is physically about 20 metres long, and so could fit (in its for-us-optimal north-south orientation, for strong east-west response) onto the Hart House roof.

In government, however, reliability is paramount. To get through at the appropriate times of day even with a balky ionosphere, officials need something like the log-periodic, the "curtain", or the rhombic design.

For concreteness, let us take the rhombic. At http://www.w8ji.com/rhombic_antennas.htm we find the suggestion that for the 40-metre amateur band (a good choice for Toronto-to-Ukraine in the evening, and for Toronto-to-Ottawa in the morning), "414 feet" is an appropriate overall length. In SI units, to two significant figures, this becomes 130 metres.

But government will surely also want to transmit on a wavelength close to the 80-metre (circa 3.5-MHz) ham band. That would for its part require an antenna farm about 260 metres across at its widest point, i.e., along the major diagonal of the rhombus.

There might additionally be some need for robust government transmissions on a wavelength close to the amateur 160-metre band (in other words, around 1.8 MHz). In that daunting case, the major diagonal of the four-mast rhombus would have to stretch to a length of around 520 metres. (Does one perhaps at this point add intermediate, insulated, masts, to keep the long runs of horizontal wire from snapping under their own weight? Or does one abandon rhombic for curtain - or for some beaming configuration, optimally over watery ground, of vertical-antenna masts?)


2.3: DDO&P Implications of National-Resilience Radio


These HF (or, if we want also something close to the 160-metre ham band, even MF) arrangements are  perhaps not too difficult in Ottawa. One Ottawa possibility is an old federal facility, the Experimental Farm. And I know from direct inspection that there is plenty of open farming country around the notorious old Cold War "Diefenbunker", municipally within Ottawa boundaries, and in fact in rural Carp, near the blink-and-you-have-missed-it hamlet of Kinburn.

In Toronto, the task becomes harder. An open site is needed, 20 or so kilometres outside the immediate prospective downtown blast-and-infestation zone (ensuring that the HF capability stays up even if downtown administration is destroyed), and yet not blocked from downtown Toronto by any significant hills.

In our problematic built-up environment, DDO&P proves perhaps the best site available.

Admittedly, some thought will have to be given also to the University of Toronto Mississauga and Scarborough campuses, with their open spaces, and to the various facilities - there is one even in outlying King City - of Environment Canada.

With DDO&P, at any rate, we have a wide terrain, allowing an abundant spread of multiple rhombics for multiple frequencies and multiple beam directions, and space to spare for such possible further requisites as a heliport.

Conveniently also, DDO&P is bounded by a passenger railway and a principal traffic artery (many-lane Bayview Avenue), and is just an easy walk away from Yonge Street.

Additionally, DDO&P offers something perhaps not available elsewhere, namely a heavy masonry structure with free lab space.  In the DDO Administration Building basement are three big rooms which over the period 1935/2008 respectively served as a woodworking shop, as an optics shop, and as a metal-machining shop. On the upper floor of the Administration Building is an erstwhile photographic darkroom, whose multiple large sinks could be repurposed for life science - notably in a time of pandemic, or of other regional biohazard. Adjacent to the erstwhile darkroom are two large rooms, each capable of accommodating lab benches for 5 or 10 workers.

The most important asset from a DND-radio perspective, however, is the electronics lab, on this same upstairs level. Around the lab runs an abundance of shelving or cabinet space, appropriate for a busy electronics-repair facility. In the centre of the room is a long two-sided bench, topped in slate for soldering, and with space for 6 - or even for 10 or 12 - individual soldering stations.

There remains space in this big room for some to-me-indeterminate number of desks. Admittedly, desk space is available also in a set of conventional offices on the same (upper) floor, and in a similar set of conventional offices on the ground floor.

The Administration Building roof, apart from three telescope domes, is flat, and communicates with lower floors by staircase rather than by utility ladder. These architectural features would benefit personnel installing or maintaining photovoltaic arrays.

A planning scenario now suggests itself. I offer it as a possible point of departure for DND analysts working in concert with Parks Canada, with the Province, and with the Town of Richmond Hill:
  • DND embarks on discussions with the would-be DDO developer, DG Group (formerly Metrus) subsidiary Corsica. DND points out that an acquisition would relieve the developer of its growing public-relations embarrassment, while at the same time serving the national interest over coming decades. 
  • DND acquires the prospective 32-hectare subdivision land on fair terms from the developer, conceivably in a land-swap context. 
  • DND does as little as possible with the land in the short term, mindful of the imperative to minimize peacetime defence expenditure. In the short term, DND welcomes citizen groupings to undertake the slow, hard work of reforestation.
  • DND puts into place legal machinery ensuring that in an emerging national crisis, it can with the full cooperation of the Town of Richmond Hill erect any necessary antenna farm on its 32-hectare terrain, and if necessary even put radio installations onto the 45-hectare Town-of-Richmond-Hill rump park, and can erect any needed outbuildings on its 32-hectare terrain, and can requisition any needed lab and solar-panel space in and on the DDO Administration Building. (In general, the erection of a rhombic requires some trimming in whatever forest may in future be present, and yet  - so I conjecture, subject to correction - is unlikely to require a wholesale clear-cut. My discussions with an ex-Soviet specialist, " Mr/Miss/Mrs DEF", this summer are instructive. Mr/Miss/Mrs DEF had seen what was perhaps the principal long-distance HF jamming facility of the USSR, used rather unsuccessfully by the USSR authorities to try to block reception of VOA, BBC, Radio Free Europe, and the like by the USSR citizens. Although this malign transmitter installation radiated far more power than any Canadian government could want for its Toronto-Ottawa link, the scrub forest - the ground was swampy, and so that Siberian scrub included birch - was left rather largely intact.) DND and the Town are in making these contingency plans guided by the precedent set in the Hitler war, in which DND as a DDO on-the-grounds guest carried out research into magnetism (in some such field as the degaussing of naval vessels, as a precaution against magnetic mines) - housing its then personnel, in fact, in what was later to become a DDO building, the extant 1960s-onwards "Radio Shack". 




Monday, 22 August 2016

Toomas Karmo (Part B): 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"): 4/5. Justification: Kmo had time to do a reasonably complete and (within the framework of the version 1.0.1, 1.0.2, .. process) reasonably polished job. 

Revision history:


  • UTC=20160825T0311Z/version 1.2.0: Kmo looked again at his lettering of the rapid (Pappus) proof of pons asinorum, and found that he had at 20160823T0203Z got this wrong! How very annoying. Perhaps the work at 20160823T0203Z was the result of fatigue. Now corrected. - Kmo retained the right to make nunsubstantive tweaks, as here-undocumented version 1.2.1, 1.2.2, 1.2.3, ..., over the coming 48 hours. 
  • UTC=20160823T0203Z/version 1.1.0: Kmo repaired a very bad error, in which he completely mixed up his lettering in the rapid (Pappus) proof of pons asinorum. He also at some point a little earlier than this repaired other significant errors, involving incorrect lettering of figures. - Kmo retained the right to make nonsubsantive tweaks, as here-undocumented versions 1.1.1, 1.1.2, 1.1.3, ... , over the coming 48 hours. 
  • UTC=20160823T0003Z/version 1.0.0: Kmo uploaded base version. He retained the right to make nonsubstantive tweaks, as here-undoumented versions 1.0.1, 1.0.2, 1.0.3, ... , over the coming 48 hours .       

   
[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 anticipation of follow-on writing, I have now added the necessary "Part A" to last week's title, and the requisite "Part B" to this week's. Additionally, I have now added to "Part A" the necessary section heading, "1. Introductory Comments, on the Inadequacy of Traditional Geometry Textbooks". - I now continue in this "Section 1", for the reader's convenience repeating my last two sentences.] 

One could not agree more. But now what, by way of "clear and distinct abstract reasoning", do we actually encounter in traditional presentations of Euclidean geometry, such as in that disappointing 1919 Godfrey-and-Siddons? 

Early on, in fact as Godfrey-and-Siddons "Theorem 12", there is the familiar "pons asinorum" proposition regarding triangles that are either isosceles-and-not-equilateral or equilateral: If two sides of a triangle are equal, the angles opposite to these sides are equal. It is given that ABC is a triangle which has the length AB the same as the length AC. The proof is now via the familiar "S.A.S.", in Godrey-and-Siddons's exposition "Theorem 10": If two triangles have two sides of the one equal to two sides of the other, each to each, and also the angles contained by those sides equal, the triangles are congruent. To make S.A.S. applicable, the unhappy pair of authors consider a line bisecting the Theorem 12 triangle at A. Here they say, "Let it cut BC at D." 

But (Moise rightly presses this question) how do we know the existence of such a point D? The postulates offered in Godfrey and Siddons do not suffice for an existence proof. 

A similar problem, involving an unsubstantiated existence claim, occurs with the Godfrey-and-Siddons discussion of an actual method for bisecting an angle (I quote verbatim, except that for maximum clarity I reletter): "From PQ, PR cut off equal lengths PX, PY"; "With centres X and Y and any convenient radius describe equal circles intersecting at Z." If the existence of equal-length segments PX, PY is charitably granted (this itself requires some discussion), there nevertheless remains the leap to the assertion that point Z exists. How, in general, do we know that given any points X and Y in Euclidean 2-space, there is some distance r such that the circles at X and Y, of radius r, have at least one point Z in common? 

****

Turning now to the Godfrey-and-Siddons proof of the underlying "Theorem 10", the "side-angle-side" congruence principle used in proving their Theorem 12, we find a further gap, of an interestingly different kind. Their proof begins, "Apply triangle ABC to triangle DEF so that A falls on D, and AB falls along DE." Their notion of "applying" conceals subtleties. We in fact need to note (as I think, on my cursory revisit to their book this week, Godfrey and Siddons fail to note) two different situations in Euclidean 2-space. 

(a) Triangles ABC and DEF may possibly be such that through some combination, in some order, of zero or more within-the-Euclidean-plane translations of ABC and zero or more within-the-Euclidean-plane rotations of ABC, the vertices and angles of ABC and DEF may be brought into coincidence - as at least one of  the conceivable correspondences ABC-DEF, or ABC-DFE, or ABC-EDF, or ABC-EFD, or ABC-FDE, or ABC-FED. In this case, let ABC and DEF be called "within-Euclidean-plane superposable". 

Since the just-proffered definition says "zero or more", not "one or more", it is trivially true that for every triangle ABC, ABC and ABC are within-Euclidean-plane superposable. This small fact will soon prove helpful, as a lead-in to Pappus's improvement on Euclid's "pons asinorum" page. 

(b) Triangles ABC and DEF may possibly be such that through some combination, in some order, of zero or more within-the-Euclidean-plane translations of ABC and zero or more within-the-Euclidean-plane rotations of ABC and zero or more within-the-Euclidean-plane reflections of ABC through some line, the vertices and angles of ABC and DEF may be brought into coincidence - as at least one of the conceivable correspondences ABC-DEF, or ABC-DFE, or ABC-EDF, or ABC-EFD, or ABC-FDE, or ABC-FED. In this case, let ABC and DEF be called "congruent". 

The concept of congruence proffered here matches the traditional plane-geometry textbook concept of congruence, but (this is my main point) is looser than the concept of triangles that are within-Euclidean-plane-superposable. 

If triangles ABC and DEF are congruent, and yet are not within-Euclidean-plane-superposable, then ABC can admittedly be brought into coincidence with DEF by taking ABC out of the Euclidean plane, and flipping it over in Euclidean 3-space, and returning it to the Euclidean plane, and doing some translations and/or rotations within the plane. 

The distinction is slurred over by Godfrey and Siddons, who unfortunately write of figures (for instance, triangles) that "when applied to one another can be made to coincide (i.e. fit exactly)": such figures, they add, "must be equal in all respects", and "figures which are equal in all respects are said to be congruent". This language is unfortunate. "Can be made to" is not spelled out. The meaning must be "can be made to by a process of translation and rotation in Euclidean 3-space, not necessarily just in Euclidean 2-space". But how is the hapless reader supposed to divine that meaning? 

When we leave two-dimensional Euclidean geometry for Euclidean solid geometry, the problem ramifies, becoming an illustration of the topic of "handedness", or (after an ancient Greek root) "chirality" - important in electromagnetics, and if we are not careful leading us into the terrifying world of hyperspace. 

For consider two modest solids. One is a Roman "R", with its various straight and curved strokes of some nonzero width, and with the whole letter of some nonzero thickness. The other is a Cyrillic "ya" (the backwards R, the last letter of the Russian alphabet), of the same volume, with matching segment lengths and matching arc radius and matching angles, and so on - being in fact a three-dimensional mirror image of the given R. 

The R and the ya are in a straightforward sold-geometry sense - analogous to what we have already developed for Euclidean plane geometry - not only congruent, but even superposable. (As in the two-dimensional case superposition is to be achieved by rotations and translations in 2-space, so in this present, Euclidean solid-geometry, case superposition is to be achieved by rotations and translations in 3-space.) 

Imagine, now, the R and the ya to be decorated, each with one small hemispherical dimple in its front surface, where the oblique stroke meets the bowl. If the tiny dimples are scooped out in such a way that the R and the ya remain mirror images, then the two solids are in a straightforward sense congruent-and-yet-not-superposable. 

This is like the difference in electromagnetics between a right-handed coil and a left-handed coil. A mirror-image pair of such coils, subject to identical conditions of time-varying magnetic flux, will by Faraday's law of induction develop equal-but-opposite voltages across their terminals. 

It seems that similar examples can be found in stereochemistry. The picture of amino-acid "enantiomers" at the beginning of https://en.wikipedia.org/wiki/Chiral is suggestive. 

The language of Godfrey and Siddons notwithstanding, there is no sense in which the dimpled R and the dimpled ya "can be made to coincide" - unless, indeed, we leave Euclidean 3-space for the terrifying, unvisualizable, world of Euclidean 4-space. 

A more satisfying approach to the "Theorem 12" of Godfrey and Siddons is one pioneered a couple of decades after Godfrey and Siddons, by Harvard authority George David Birkhoff (1884-1944; he is considered one of the major American mathematicians of his era). Birkhoff was writing for a school-mathematics community, as a collaborator with educator Ralph Beatley, in a book bearing the title Basic Geometry. Their third and final edition was printed, if not earlier, then at any rate in 1959, at the publishing house Chelsea. A sign of excellence is that this same edition was reissued in 2000 by the American Mathematical Society, under ISBN 978-0-8218-2101-5. 

Introduce (says Birkhoff-with-Beatley; I paraphrase from memory) S.A.S. as a postulate, in the form "Let triangles ABC and DEF be congruent in the sense that AB and DE are of equal lengths, and AC and DF are of equal lengths, and the internal angles at A and D are of equal measure; then the sides BC and EF are of equal lengths, and the sides CA and FD are of equal lengths, and the internal angles at B and E are of equal measure, and the internal angles at C and F are of equal measure." 

We can now rapidly prove "Theorem 12", without recourse to the problematic claim that a bisector of the apex angle intersects the triangle base. If sides AB and AC are of equal length, triangle ABC satisfies the S.A.S. postulate, in that ABC is congruent with itself (in the protasis, we innocently take D to be A, cunningly take E to be C, cunningly take F to be B); with S.A.S. assumed, and with the S.A.S. protasis found to be satisfied, each part of the apodosis can now be asserted. In particular, the internal angle at B is now guaranteed to have the same measure as the internal angle at C. 

Moise has not only the virtue of rigour, but the virtue of classical erudition. For in pointing this terse proof out, and remarking that Euclid's proof runs by contrast to the length of a whole printed page, he addes that the terse proof was known in antiquity to Pappus. 

Moise has also a third virtue, namely the ability to be witty at the expense of computer scientists. He points out that the simple proof weas inadvertently rediscovered in a comp-sci lab: 

Not many years ago - or so the story goes - an electronic computing machine was programmed to look for proofs of elementary geometric theorems. When the pons asinorum theorem was fed into the machine, it promptly printed Pappus' proof on the tape. This is said to have been a surprise to the people who had coded the problem; Pappus' proof was new to them. /.../ if you want a machine to get the idea that the triangles /... / in the SAS postulate are supposed to be different, you have to say so explicitly. It didn't occur to anybody to do this, and so the machine proceeded, in its simple-minded way, to produce the most elegant proof. 

What I have just just quoted is from pp. 105 and 106 of Moise's final, third, edition, published in 1990. The first edition, from an earlier era in computing, has the same anecdote, but with some additional disparaging remark on "vacuum tubes". 

****

I have the time and patience to cite one further example of Godfrey-and-Siddons's logical failings, concerning their already-cited notion of "equality". I have quoted them as asserting that figures that can be made to coincide are "equal in all respects". Well, as they say around the samovar in my imaginary Nikolai Ivanovitch Lobachevsky Institute of Socialist Mathematics (across that imaginary potholed Siberian street from the "Alexandr Stepanovitch Popov Institute of Heroic Radio"): "Vot MEENZ 'equal'?"

[To be continued next week, I hope, as "Part C". - To anticipate a little, "equal" has to be unpacked in the manner of mathematical logician Frege, with "x equals y" having just one correctly clear meaning: "x is the same object as y". I guess I will be citing here Frege's dictum that the only acceptable mathematical sense for "equals" is the one in which the heavenly body Hesperus "=", i.e., is the same planet as, the heavenly body Phosphorus: the thing you occasionally see in the evening sky, and are wont to call Hesperus, is the same entity, being the planet Venus, as the thing you occasionally see in the morning sky, and are wont to call Phosphorus.] 

Toomas Karmo: Operations Clocks and Sherlock Holmes (Moral Uplift)




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 do a reasonably complete and (within the framework of the version 1.0.1, 1.0.2, .. process) reasonably polished job. 

Revision history:



  • UTC=20160823T0121Z/version 1.1.0: Kmo made a rather subsantial change, adding a quotation from Sir Arthur Conan Doyle's enervating description of London in the August heat. - Kmo retained the right to make nonsubsantial tweaks, as here-undocumented versions 1.1.1, 1.1.2, 1.1.3, ... , over the coming 48 hours. 
  • UTC=20160823T0002Z/version 1.0.0: Kmo uploaded base version. He retained the right to make nonsubstantive tweaks, as here-undoumented versions 1.0.1, 1.0.2, 1.0.3, ... , over the coming 48 hours.       

   
[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.]




On 2016-08-08 or 2016-08-09, I uploaded to this blog a minor article, with screenshot, on the theme of "operations clocks". Depicted in the screehshot was a Battle of Britain operations clock from RAF Uxbridge, north of London, and also my own pair of Debian GNU/Linux operations clocks, for civil time and UTC. The point of my little blogging exercise was to show how computer graphics can supply moral uplift. 

Today I do something similar. 

Here again is the RAF Uxbridge bunker clock, plus my own pair of operations clocks.

I also today go to a little trouble to display a "glass teletype", or Debian GNU/Linux /usr/bin/xterm window, showing study notes from my sporadic efforts to learn about Law. 

In the upper left-hand corner I today show an image I have been using for moral uplift every few weeks or months, from Einstein's Princeton office. 

Today I am chiefly concerned, however, to draw attention to the remaining two images in the desktop screenshot, at the bottom left and at the bottom centre. Both relate to Sherlock Holmes. 

Even the more casual students of Baker Street (I among them) are aware that the definitive ciné incarnation of the immortal fictional detective is no longer Sir Basil Rathbone (1892-1967). Satisfying though that star of British wartime cinema continues to be, pride of place must now instead be accorded to Jeremy Brett (1933-1995). Brett's portrayals of Holmes at Granada Television (in 41 episodes, from 1984 to 1994), unlike Sir Basil Rathbone's, are breathtaking in their fidelity to the original "Canon" texts. Only occasionally are there large divagations from what Sir Arthur Conan Doyle wrote. These divagations must themselves be considered faithful to the author's guiding conception. An instance: the screen version of Cardboard Box supplies details on Christmas at Number 221B, showing Holmes making a most touching gift of a cycling cape to Dr Watson, as he takes Mrs Hudson's advice regarding shops and presents.  (The original is set, instead, in the hottest part of summer: It was a blazing hot day in August. Baker Street was like an oven, and the glare of the sunlight upon the yellow brickwork of the house across the road was painful to the eye. It was hard to believe that these were the same walls which loomed so gloomily through the fogs of winter. Our blinds were half-drawn, and Holmes lay curled upon the sofa, reading and re-reading a letter which he had received by the morning post. For myself, my term of service in India had trained me to stand heat better than cold, and a thermometer at ninety was no hardship. But the morning paper was uninteresting. Parliament had risen. Everybody was out of town, and I yearned for the glades of the New Forest or the shingle of Southsea. A depleted bank account had caused me to postpone my holiday, and as to my companion, neither the country nor the sea presented the slightest attraction to him. He loved to lie in the very centre of five millions of people, with his filaments stretching out and running through them, responsive to every little rumour or suspicion of unsolved crime.

In the bottom-left  image is Jeremy Brett grappling with the sinister Prof. Moriarty, at the brink of the Reichenbach Falls in Switzerland. The image repays a meditation of the kind more conventionally prompted by Pilgrim's Progress or by biographies of saints. The crusader for justice, the villain, the mortal combat: it is an allegory of the struggle taking place inside each of us, as we confront our own private demons of sensuality, or of depression, or of timidity, or (are you reading this, you would-be subdivision developers at DDO&P?) of avarice. Few better illustrations can exist for those much-quoted words from Arhipelag Gulag: " /.../ the line dividing good and evil cuts through the heart of every human being. And who is willling to destroy a piece of his own heart?" 

In the bottom-centre image is a more tranquil thing. Here there is a mockup, in a contemporary London museum, of the fictional 221B Baker Street hearth, in the fictional 221B Baker Street upstairs sitting-room. There is in many of us a Country of the Mind in which Queen Vicky's Golden Jubilee is behind her and her Diamond Jubilee still ahead; where Scotland Yard is, despite its fumbling inefficiencies, incorruptible; where the triumph of Science over Superstition is a given, even in the Adventure of the Devil's Foot; and where a real domestic hearth harbours a real domestic fire. 

Toomas Karmo: Open Letter re DDO&P Breach-of-Aquifer Question (Town et al)

My cellphone photo from Bayview Avenue from a bus window in the (very dry) afternoon of 2016-08-10, showing a part of the despoiled 32 DDO&P hectares, in the vicinity of the projected stormwater sump. The Town and other authorities will have to consider whether there has been a breach of the Oak Ridges Moraine Aquifer cap, in a scenario feared in the Ontario Municipal Board 2012 and 2014 testimony of hydrogeologist Mr Garry Hunter. Visible in the background is some of the remaining forest, slated to become a rump park in the possession of the Town.




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 do a reasonably complete and (within the framework of the version 1.0.1, 1.0.2, .. process) reasonably polished job. 




  

Revision history:


  • UTC=20160823T0001Z/version 1.0.0: Kmo uploaded base version. He retained the right to make nonsubstantive tweaks, as here-undoumented versions 1.0.1, 1.0.2, 1.0.3, ... , over the coming 48 hours .  - He drew this blog posting to the notice of pertinent authorities, mainly municipal, provincial, and federal, in a private e-mail under timestamp UTC= 20160823T231357Z.




[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.]





1. Preamble, with Legal Background


I write with a question for the Town of Richmond Hill, pertaining to what has in recent years been Canada's weightiest heritage-conservation case, the 77-hectare David Dunlap Observatory and Park (DDO&P). 

In writing, I cc other involved parties. 

Foremost among these others are (a) the provincial and federal authorities, and (b) the team of the would-be DDO&P developer (who seeks to build 14 streets, a lane, and a stormwater sump, with 520-plus homes, thereby destroying about 32 of the total 77 hectares). 

I write as a 2006 November through 2008 June DDO staffer. 

I write at a time of increased activity in my DDO&P file, as already noted by many of my readers earlier this month, in a private e-mail headed "20160810T155131Z". It is helpful to recall the pertinent part of that e-mail today. On 206-08-04, I was notified through Canada Post, by Ontario's Information and Privacy Commissioner, that the desire of the Regional Municipality of York would be granted: I would, as a Freedom-of-Information applicant, be given all my requested paperwork regarding the aspiring developer's archaeology and tree-removal permits. In this 2016-08-04 paper communication, I was reassuringly told that an objection lodged by some unspecified third party was now being dismissed, as an unsuccessful appeal. With the appeal duly out of the way, I expect the pertinent documents to arrive in papermail in mid-September. As I noted in that e-mail headed "20160810T155131Z", I will upon receipt of the documents be able to proceed further with my analysis of the developer's legal position. 

****

I note for everyone, today as in essence also on previous occasions, the following further points of legal background: 

  • I have spent the bulk of my life savings on this DDO&P conservationist casework, to an amount of 500,000 CAD or 550,000 CAD - for the most part at two long Ontario Municipal Board (OMB) hearings, in 2012 and 2014, in support of the Richmond Hill Naturalists. 
  • I am now accordingly too poor to justify the expense of a lawyer. 
  • I am prepared to defend myself in court, speaking without a lawyer, if sued or prosecuted. 
  • I use the Web, notably  http://toomaskarmo.blogspot.ca (also known as http://toomaskarmo.blogspot.com) as a vehicle for making the details of the DDO&P case publicly visible. I do this in part as a precaution against a nightmare scenario, in which my mild autism renders me temporarily tongue-tied or temporarily panic-stricken when I reluctantly undertake my own advocacy in the courtroom. 


2. DDO&P Hydrogeological Background


The Oak Ridges Moraine Conservation Act (2001) accords partial protection to the environmentally sensitive Moraine. (The sensitivity is in part due to the fact that from the Moraine originate the Humber, Don, and Rouge rivers, all running from the Moraine down into the Lake Ontario that provides Toronto with drinking water.) If the map at https://en.wikipedia.org/wiki/Oak_Ridges_Moraine delineating the Moraine is accurate, then the DDO&P northern boundary lies something less than 10 kilometres (perhaps 4 kilometres or 6?) south of the Moraine's southern limit. It therefore seems to me that the Oak Ridges Moraine Conservation Act (2001) does not directly govern DDO&P. I am anxious, however, to be corrected regarding my understanding of the Act, by the Government of Ontario, if I am mistaken. 

The Act is not the end of the story. 

Running under DDO&P is the Oak Ridges Moraine Aquifer (ORMA). Hydrogeologist Mr Gary Hunter testified at OMB in 2012 and 2014, as an expert witness summoned by my friends the Richmond Hill Naturalists, that there was some risk of the envisaged subdivision-development activity at DDO&P breaching the ORMA cap. All analysts of the case must, therefore, keep a sharp eye on the terrain, as the developer proceeds with excavation of the envisaged stormwater sump (in land-planning language, with the envisaged "stormwater management pond") and with related engineering works. 

Fortunately, monitoring is easy, since the sump and its surrounds are visible from Bayview Avenue. 

The July and early August of 2016 were unusually dry. This, then, presented good conditions for monitoring the possible upwelling of groundwater, such as might conceivably come from some kind of injury to the ORMA cap. In the afternoon of 2016-08-10, two or three or so days before the long dry spell ended, I took six photos of the ongoing engineering works, from a bus. Three of these show water. Of the three, I attach one to this present e-mail, displaying it also in the posting of this e-mail in the above-cited blog.  

3. Question for the Town


I now make the following formal query of the Town, trusting that as I am trying to serve the public interest nobody will be very angry with me. I make my query as part of my effort to understand the legal case: 

  • Is the ORMA cap either (a.a) known by the Town to be injured or (a.b) known by the Town to be not injured? Or is it, rather, the case that (b) the Town does not presently know the status of the ORMA cap - i.e., does not presently know it to be injured, and does not presently know it to be not injured? 


I respectfully ask the Town to respond in e-mail by 2016-08-29 (MON) 14:00 EDT (i.e., by UTC=20160829T1800Z), either (1.1) with a direct answer to this query or (1.2) with a request to be allowed more time to pursue any necessary investigations, and optionally also (2) with any additional commentary or elucidation for me that the Town may at this point consider proper. 

I will take it, unless instructed otherwise, that the Town's upcoming e-mail communication to me is fully public. By "fully public" I mean here that I am free to paraphrase it in my above-cited blog, and to quote it there in part or in whole, and to make any other reasonable use of it (for instance, to forward it to more senior levels of government, or to forward it to environmental-advocacy organizations). 

I would additionally welcome any pertinent e-mail comments from anyone else, and most notably from

  • Ontario's Ministry of Natural Resources and Forestry
  • Ontario's Ministry of Municipal Affairs and Housing
  • Ontario's Environmental Commissioner 
  • the developer's team (which I presume, unless advised otherwise, still to be under Mr Michael Pozzebon, at the DG Group (formerly Metrus) subsidiary "Corsica") 

Monday, 15 August 2016

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

Under the writing tools and triangle and compasses is my photocopy of the unsatisfactory 1919 Godfrey-and-Siddons
Elementary Geometry: Practical and Theoretical. Under that is some paper from my work on the Real Thing,
the third (1990) edition of Edwin E. 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: I had to make this installment of my essay shorter than would have been desirable, since time was running out. 

Revision history:




  • UTC=20160823T0002Z/version 1.2.0: Kmo improved title, adding a necessary "Part A", and added a necesssary section heading. 
  • UTC=20160816T1355Z/version 1.1.0: Kmo corrected a really bad mistake. He had unthinkingly asserted that every isosceles-but-not-equilateral triangle has exactly two dominant angles. (If the equal angles, at the base, are each less than 60 degrees, then the isosceles triangle has exactly one dominant angle, at its apex.)   - He retained the right to make nonsubstantial tweaks, as here-undocumented versions 1.1.1, 1.1.2, 1.1.3, ...., over the coming 48 hours. 
  • UTC=20160816T0004Z/version 1.0.0: Kmo uploaded base version. He retained the right to make nonsubstantive tweaks, as here-undoumented versions 1.0.1, 1.0.2, 1.0.3, ... , over the coming 48 hours .       

  
[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.]



1. Introductory Comments, on the Inadequacy  of Traditional Geometry Textbooks

There is a line somewhere in liturgy about "all who bring hope to this world".

English-reading devotees of undergraduate mathematics know that among those who bring hope is the still-living Prof. Michael Spivak (1940 - ), in his rigorous presentation of univariate calculus. 

Many will additionally know at least a little of Spivak's contemporary, Tom Mike Apostol (born 1923, departed this life 2016-05-08), who expounds univariate and multivariate calculus in a bold two-volume work. It takes a radical defiance of classroom convention to develop integral calculus (the study of single-variable Accumulations) before univariate differential calculus (the study of single-variable Rates). But Prof. Apostol did, I suspect in his process somehow - this is a bit I have not yet glanced at - underscoring the inevitability of the "Fundamental Theorem", which ties those two branches of calculus together (asserting the Accumulation, from x=a to x=b, of rate-of-change-in-F, to be none other than F(b) - F(a)). 

How many, on the other hand, know of Edwin E. Moise (1918-1998), as a correctly rigorous expositor of geometry?

****

Geometry has long been in a bad state. 

A little earlier this summer, aware that one of the leading twentieth-century mathematicians was University of Toronto geometer Harold Scott MacDonald Coxeter (1907-2003), I cracked open a library copy of some appropriate book. This was perhaps Coxeter's 1961 Introduction to Geometry. Ai-ai-ai-ai-ai, and oy veh. Here was an "Introduction" in the sense in which some Nobel laureate - some Claude Cohen-Tannoudji - might write an "Introduction to Quantum Mechanics". 

And yet I had persistently in my mind the uneasy, almost heretical, thought that it might be geometric truths, not algebraic truths, that are fundamental. I was therefore determined to keep working, even in the teeth of discouragement. 

****

We come up here against a mystery, a mysterium tremendum ac fascinans. Everyone connected, however weakly, with the world of science must have at least a few nightmarish thoughts. I wonder, admittedly as a non-biologist, whether we might not some day have to reject wide swathes of the Theory of Evolution, even while continuing to profess the veracity of the fossil record. 

Here, for instance, is a beehive in August. The young worker bees are inside, building their comb and tending to their queen's larvae. On the landing board arrives an older scouting worker bee, approaching the end of her so-brief summer life. In addition to her minuscule load of nectar or pollen, she bears Information, of a character potentially vital to the winter survival of her "colony" (in the specialized language of apiculture), or in more mundane language her city. 

Making her way inside, into the warm darkness, she starts her dance. 

I believe the dance was deciphered by Karl Ritter von Frisch (1886-1982; Nobel Prize in Physiology or Medicine, 1973, with Tinbergen and Lorenz): the nature of her discovered nectar-and-pollen source, and its direction and distance, get duly communicated to her attentive colleagues. After a short while, ten or twenty or more of those colleagues are briefed, almost in a tiny simulacrum of the RAF. Having understood, they fly forth on their own massive foraging, to the correctly indicated destination, perhaps even two or three or four or (in extreme cases) five or more kilometres away. 

That collective foraging - perhaps it will be on a hundred-metre long stand of goldenrod along some sunny highway edge, just coming into its late-August bloom - will turn the tiny initial donation of pollen or nectar into a winter resource big enough to underpin the survival of the entire 60,000- or 30,000-citizen metropolis. 

How, I uneasily ask, could Darwinian selection explain such a remarkable attainment, involving as it does even the use of symbols? 

****

And a little more to the present point, I have, in my admitted capacity as the Village Idiot in all things scientific, intermittent nightmarish thoughts on Mathematics. 

Could it be that progress in physics is currently being blocked, somewhere, by a dearth of mathematical machinery sufficiently close to underlying physical realities - even as the physics of the Greeks was frustrated by their lack of a formalism for describing those centrally important Rates which are accelerations? Should we, perhaps, be using the Interval Arithmetic of https://en.wikipedia.org/wiki/Interval_arithmetic rather than the familiar infinite-precision real number line to handle laboratory measurements? Might it, perhaps, be even some kind of subtle error or oversimplification to formulate quantum mechanics - beset as it is with problems of philosophical interpretation  - in terms of that familiar, tidy, Argand complex-number plane? 

Might there even (this is one of the ultimate nightmares) be some sense in which the mathematics of physics has to start from geometry, with our so slick, so facile contemporary algebra becoming a mere ancillary? 

****

So, as I say, I was wrestling with the "mysterium tremendum ac fascinans", finding Coxeter too advanced to permit safe flying. 

I had, to be sure, logged a total of 203 hours, 3 minutes over the period 2009-05-05/2009-08-25 from working the Elementary Geometry: Practical and Theoretical of G.Godfrey and A.W.Siddons (3rd edition; Cambridge University Press, 1919). But this was a vexing experience, which in the end felt only moderately better than time-wasting busy-work. 

Geometry, it is said, trains the intellect in rigour. Well, do allow me some comment. 

I try to keep an occasional eye on two small institutions which might mark a way forward for Catholic tertiary education, as our cultural decline morphs over the next few generations into a Dark Age. I have already cited the two in my blog posting from the first week in 2016 July, headed "Part E" of "Is Science Doomed?", under section heading "Practicalities of Triage: Education in a Catholic Setting". 

(1) At Our Lady Seat of Wisdom Academy in rural Ontario, mathematics, notably including euclidean geometry, is celebrated in the following terms, in a discussion somewhere under the "Academics" tab at https://www.seatofwisdom.ca:  Mathematics, primarily via Calculus, Statistics and Euclidean Geometry, leads the mind to clear and distinct abstract reasoning, prescinding from matter. 

(2) From the other institution, the rather rural Wyoming Catholic College, comes an almost identical sentiment, on a Web page  - http://www.wyomingcatholiccollege.com/academics/Curriculum/mathscience/index.aspx - decorated with a proof either of the Pythagorean Theorem ("If a triangle is a right triangle, the area of a square erected on the side opposite a dominant angle equals the sum of the areas of the squares erected on the other two sides") or of its converse ("Only if a triangle is a right triangle does the area of a square erected on the side opposite a dominant angle equal the sum of the areas of the squares erected on the other two sides"; by "dominant angle", I mean here "Any angle of the given triangle than which there is none greater in that triangle" - so that every triangle which is isosceles-and-not-equilateral has either exactly two dominant angles or exactly one dominant angle, and every equilateral triangle has three dominant angles, and every triangle outside the two just-cited special cases has exactly one dominant angle).  Wyoming Catholic College writes as follows, with reference to "Arithmetic and Geometry":  /.../ its highly logical structure and freedom from the imprecision of material being makes it ideal for elementary training in reasoning, where the beauty of mathematics both inspires wonder and makes evident the human mind's thirst for understanding. 

One could not agree more. But now what, by way of "clear and distinct abstract reasoning", do we actually encounter in traditional presentations of Euclidean geometry, such as in that disappointing 1919 Godfrey-and-Siddons? 

[To be continued next week, in the upload scheduled for the four-hour UTC interval 20160823T0001Z/20160823T0401Z. This entire essay will have to run over something like two or three or four installments, therefore probably finishing either late in August or at some point in September.]