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Oor argitekte en minibustaxi’s
"The problem of infinity was famously captured by the German mathematician, David Hilbert (1862-1943). He proposed the Infinite Hotel, now known as Hilbert's Hotel, as an illustration of how to deal with treating infinity as a number. This hotel has an infinite number of rooms and despite being always full it can cater for any number of extra guests that arrive.
If a guest arrives at the hotel even though it is full, the guest will be given a room. How? No problem: everyone shifts to the next room. The person in room 1 moves to room 2, the person in room 2 moves to room 3, and so on. Since the hotel is infinite, there will always be a next-door to move into. This leaves room 1 free for the newly-arrived person to move into.
The same happens when any number of guests arrive, requesting rooms. If thirty turn up, the receptionist gets everybody to shift to the room thirty numbers down - the person in room 1 moves to room 31; the person in room 2 moves into room 32, and so on. The newly-arrived group will take rooms 1 to 30.
But wait, wasn't the hotel full already? Yes, but this shows how infinity can't be regarded as a number in the normal sense, because infinity plus a finite number is still infinity. The possible scenario gets still more bizarre.
Imagine that an infinite number of guests arrive. Would the hotel be able to accommodate them? No problem in the Infinite Hotel. The receptionist get everybody to move to the room which is double the room number they have already, so that the person in room 1 moves to room 2, the person in room 3 moves to room 6, and so on for ever. This leaves all the odd-numbered rooms free, and since there are an infinite number of them, there will be no problem in accommodating an infinite number of guests.
As much as it would be useful in Florence in August, Hilbert's hotel will never be available other than as a way of showing that two times infinity (or, in fact, any finite number times infinity) is still infinity."
(Ronald Green, Nothing matters, Winchester: Iff Books, 2011, p 226-227).
In 'n ander bron word hierdie hotel ook beskryf. "Hilbert even imagined an infinitely large couch load of visitors arriving unexpectedly. It's bad enough to have a conventional coach, but this one (thanks to some strange manipulation of reality) manages to cram in an infinite number of people looking for bed and board" (Brian Clegg, A brief history of infinity, London: Robinson, 2003, p 238).
Die genoemde bus laat my spontaan dink aan 'n doodgewone minibus, wat blykbaar altyd plek vir nog passasiers het. Dit is dalk hoe die bogenoemde dertig mense onverwags by die hotel aangekom het. Daar is 'n geneigdheid om laat, dus eers wanneer Hotel Hilbert vol is, op te daag. Deesdae mag niemand egter weggewys word nie. Die laatkommers veroorsaak klaarblyklik groot ongerief, want almal wat reeds in die hotel was, moet na 'n ander kamer skuif. Ter wille van versoening moet dit maar verduur word. 'n Enkele mens per kamer, soos hierbo beskryf, klink onrealisties. Hotel Hilbert kan egter erkentlik teenoor inheemse kultuur wees deur baie mense in elkeen van die oneindige getal kamers te akkommodeer.
Dit lyk asof hierdie hotel optimaal by die nuwe Suid-Afrika aangepas het. Dit is die soort woonplek waarmee behuisingsuitdagings suksesvol die hoof gebied kan word. Die analogie van die minibus en die hotel, wat albei altyd nog plek het, kan egter aanleiding tot gevaarlike gevolgtrekkings gee. Hierdie scenario kan rampspoed meebring as dit goedsmoeds op 'n land toegepas word, bv as geredeneer word dat Suid-Afrika 'n onbeperkte getal inkommers kan huisves. Ons is reeds goed met gewelddadige verswelging bekend. Die volgende golf kan uit veral die res van Afrika kom.
Voertuie en hotelle moet ontwerp word sodat hulle by plaaslike behoeftes aanpas. Dit geld ook gemeenskapsentrums. In die nuwe Suid-Afrika is daar kort-kort 'n berig oor 'n ramp (vuur, water, onrus, ens) wat talle mense uit hulle huise dryf. Daar word dan gesê: Die ontheemdes word intussen in die gemeenskapsentrum gehuisves. Dit gaan hier om 'n onbeperkte getal mense wat 'n onbepaalde tyd in bv 'n saal, met 'n beperkte getal toilette en dalk geen kookgeriewe nie, woon. Die vraag wat telkens by my opkom, is: Hoe beplan professionele argitekte sulke potensieel multifunksionele gemeenskapsentrums vir die nuwe Suid-Afrika? Dit is 'n vrugbare tema vir navorsing, bv vir 'n gevorderde graad in argitektuur.
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