Jigsaw 19, Series 3, Report No.4

Duly completed yesterday.

There had been a panic, with a flowery piece from the lower right hand quadrant having gone missing, with no trace on the carpet below. And the odd piece has been missing from these jigsaws in the past: maybe the quality control on these specials is not what it is on the mass-produced puzzles, even though they come from the same, very respectable, manufacturer?

However, on this occasion, the missing piece turned up, blue back up, which made it more visible, on the carpet, the next day. Perhaps something had turned it over or otherwise disturbed it.

PS 1: interested to read about the troubles at Starbucks over freeloaders. Starbucks being a chain which I have rarely if ever used, but it would clearly have been a good pick twenty years ago. However, I have occasionally been irritated where 'community' spaces have been invaded by rather too many people who are clearly just there for the warmth and/or the free wifi. For example, Olle & Steen or the Royal Festival Hall. Hard to strike the right balance between community spirit and making money. Hard for a not very well paid barista to show a quiet & decent homeless person the door when it is cold outside. And I see from reference 3 that there was a bit of trouble on this same front back in 2018. Not to mention all the other vicissitudes that I guess are more or less inevitable in a large and successful company - with a growth rate that puts even Wetherspoon's to shame. But I don't think that Wetherspoon's is yet into franchises. While Starbucks has given up on Australia.

PS 2: for reasons too longwinded to be rehearsed here, I am presently revisiting projective geometry, a subject to which I was first introduced near sixty years ago and I am finding reference 4 to be pitched at just about the right level, despite being a translation from the German. First point, the first pages of reference 4 seem a very long way from the first pages of reference 5, a book which I have owned, largely unread, for a very long time. Both contain the principle of duality, that is to say the symmetrical and reciprocal relationship between points and lines in the plane - but what has happened to all the fans of lines from points, all the projectivities to be found in reference 4? Inspiration for which came from the (re)discovery of perspective during the European Renaissance - which last was very much the starting point for the Gallivan essay noticed at reference 6. I look forward to revelation. Second point, I have been very impressed how great complexity emerges from a small number - four - of very innocuous looking axioms. There are people, for example, who take a great interest in the number of points contained in a finite projective plane. It seems that this number cannot be 92, 93 or 110 - amongst others. Another example of this sort of thing which comes to mind is/are the Mandelbrot sets, one of which is snapped above, derived from only moderately complicated rules. One might say a tribute to the generative power of human language - while some might say a tribute to the power of the divinity, some aspects of which are revealed by human language. I prefer to keep the divinity out of it - but I think I had better let this matter rest for now.

PS 3: Wednesday morning: I have just come across the term 'structural deficit' in the FT and wondered what exactly it might be. Bing turned up all sorts of stuff from places I have never heard of - but also the helpful reference 8 - both accessible and coming from a respectable source. So I now know what a structural deficit is - and have been reminded that UK government borrowing is indeed on the high side. We do need to bear down on it - with how fast being a matter for nice judgement - if you want to stay in power.

References

Reference 1: https://psmv5.blogspot.com/2025/01/jigsaw-19-series-3-report-no3.html.

Reference 2: Starbucks cracks down on freeloaders to reverse sales decline: Coffee chain launches plan to get more paying customers back in stores as it reports fewer transactions - Gregory Meyer, Financial Times - 2025.

Reference 3: https://en.wikipedia.org/wiki/Starbucks.

Reference 4: Projective Geometry: From Foundations to Applications – Albrecht Beutelspacher, Ute Rosenbaum – 1998.

Reference 5: Axiomatic projective geometry - Goodstein, Primrose - 1953.

Reference 6: https://psmv5.blogspot.com/2025/01/weaver-two.html.

Reference 7: https://en.wikipedia.org/wiki/Mandelbrot_set. '... The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules. It is one of the best-known examples of mathematical visualization, mathematical beauty, and motif....'.

Reference 8: The budget deficit: a short guide - Matthew Kemp, House of Commons Library - 2025. To be found at https://researchbriefings.files.parliament.uk/documents/SN06167/SN06167.pdf.

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