I will be following the Challenger class in the 2019 Bridgestone World Solar Challenge this October using a large wall map (based on this post) and some paper pointers. Use the image below to construct your own pointers, writing in the name of your favourite team if it’s missing (see here for a list of all teams). I’m still working on how best to visualise Cruiser class progress.
In the leadup to the 2019 Bridgestone World Solar Challenge in Australia this October, most cars have been revealed (see my recently updated illustrated list of teams), with JU’s reveal a few days ago (see below), and Tokai’s reveal due in a few hours.
There are now 9 international teams in Australia (more than the number of local teams). Eindhoven (#40), Agoria (#8), and part of Vattenfall (#3) are driving north to Darwin, while Top Dutch (#6) have a workshop in Port Augusta (and living quarters in Quorn).
JU’s solar car Axelent (photo credit)
The chart below shows progress in submitting compulsory design documents for the race. White numbers highlight eight teams with no visible car or no visible travel plans:
- #86 Sphuran Industries Private Limited (Dyuti) – this team is probably not a serious entry. I will eat my hat if they turn up in Darwin.
- #63 Alfaisal Solar Car Team – recently, they have gone rather quiet, but they have a working car.
- #89 Estidamah – they have not responded to questions. They also might not turn up, although they have obtained several greens for compulsory documents.
- #80 Beijing Institute of Technology – they never say much, but they always turn up in the end. I don’t expect this year to be any different.
- #4 Antakari Solar Team – they are clearly behind schedule, but they are an experienced team. They will probably turn up. (edit: they have revealed a beautiful bullet car)
- #55 Mines Rabat Solar Team – they seem to have run out of time. Can they finish the car and raise money for air freight? I’m not sure. (edit: it seems that they will attend the Moroccan Solar Challenge instead of WSC)
- #98 ATN Solar Car Team and #41 Australian National University – these teams are obviously in trouble but, being Australian, they should still turn up in Darwin with a car. (edit: both teams have since revealed cars)
Dancing alongside the more serious practitioners of mainstream mathematics are the purveyors of mathematical puzzles and problems. These go back at least as far as Diophantus (c. 200–284), the Alexandrian “father of algebra.” Alcuin of York (c. 735–804) produced a collection of problems that included the the wolf, the goat, and the cabbages (above); the three men who need to cross a river with their sisters; and problems similar to the bird puzzle published by Fibonacci a few centuries later. In more modern times, Martin Gardner (1914–2010) has done more than anyone else to popularise this offshoot of mathematics. It is often called “recreational mathematics,” because people do it for fun (in part because they are not told that it is mathematics).
Particularly popular in recent times have been Sudoku (which is really a network colouring problem in disguise) and the Rubik’s Cube (which illustrates many concepts of group theory, although it was not invented with that in mind). Sudoku puzzles have been printed in more than 600 newspapers worldwide, and more than 20 million copies of Sudoku books have been sold. The Rubik’s Cube has been even more popular: more than 350 million have been sold.
Recreational puzzles may be based on networks, as in Hashi (“Bridges”). They may be based on fitting two-dimensional or three-dimensional shapes together, as in pentominoes or the Soma cube. They may be based on transformations, as in the Rubik’s Cube. They may even be based on arithmetic, as in Fibonacci’s problem of the birds, or the various barrel problems, which go back at least as far as the Middle Ages.
In one barrel problem, two men acquire an 8-gallon barrel of wine, which they wish to divide exactly in half. They have an empty 5-gallon barrel and an empty 3-gallon barrel to assist with this. How can this be done? It is impossible to accurately gauge how much wine is inside a barrel, so that all that the men can do is pour wine from one barrel to another, stopping when one barrel is empty, or the other is full [highlight to show solution → (8, 0, 0) → (3, 5, 0) → (3, 2, 3) → (6, 2, 0) → (6, 0, 2) → (1, 5, 2) → (1, 4, 3) → (4, 4, 0)]. There is a similar problem where the barrel sizes are 10, 7, and 3.
Apart from being fun, puzzles of this kind have an educational benefit, training people to think. For this reason, Alcuin called his collection of problems Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young). Problems like these may also benefit the elderly – the Alzheimer’s Association in the United States suggests that they may slow the onset of dementia. This is plausible, in that thinking hard boosts blood flow to the brain, and research supports the idea (playing board games and playing musical instruments are even better).
The chart below (click to zoom) shows the dates of ten significant written works:
- Plato’s Phaedo
- Euclid’s Elements
- Caesar’s Gallic Wars
- The Gospel of John
- Boethius’ Consolation of Philosophy
- Bede’s Historia Ecclesiastica
- Beowulf (date of writing is approximate)
- Dante’s Divine Comedy
- Shakespeare’s Hamlet
- Jane Austen’s Persuasion
Each work is indicated by a vertical line, which runs from the date of writing to the date of the oldest surviving complete copy that I am aware of (marked by a dark circle). Open circles show some of the older partial or fragmentary manuscripts (these act as important checks on the reliability of later copies).
Two threshold periods (marked with arrow) are worth remarking on. First, Gutenberg’s printing press – after its invention, we still have at least one first edition for many important works. Second, the invention of Carolingian minuscule – many older works were re-copied into the new, legible script after that time. They were then widely distributed to monasteries around Europe, so that survival from that period has been fairly good. In the Byzantine Empire, Greek minuscule had a similar effect.
The Bible is a special case (I have highlighted one particular gospel on the chart). It was copied so widely (and so early) that many ancient manuscripts survive.
In the leadup to the 2019 Bridgestone World Solar Challenge in Australia this October, most cars have been revealed (see my recently updated illustrated list of teams), and the first few international teams (#2 Michigan, #3 Vattenfall, #6 Top Dutch, #8 Agoria, and #40 Eindhoven) have arrived in Australia (see map above). Bochum (#11), Twente (#21), and Sonnenwagen Aachen (#70) are not far behind. Eindhoven (#40) are currently engaged in a slow drive north, while Top Dutch (#6) have a workshop in Port Augusta (and living quarters in Quorn).
Meanwhile, pre-race paperwork is being filled in, with Bochum (#11) and Twente (#21) almost complete. Sphuran Industries from India (#86) is not looking like a serious entrant. On a more positive note, though, Jönköping University Solar Team (#46) is revealing their car later today!
The medieval Propositiones ad Acuendos Juvenes (“Problems to Sharpen the Young”) is attributed to Alcuin of York (735–804), a leading figure in the “Carolingian Renaissance.” He is the middle person in the image above.
Along with the more famous problem of the wolf, the goat, and the cabbage, Propositiones ad Acuendos Juvenes contains the problem of the three men and their sisters. Three men, each accompanied by a sister, wish to cross a river in a boat that holds only two people. To protect each woman’s honour, no woman can be left with another man unless her brother is also present (and if that seems strange, remember that Alcuin was writing more than 1,200 years ago). In Latin, the problem is:
“Tres fratres erant qui singulas sorores habebant, et fluvium transire debebant (erat enim unicuique illorum concupiscientia in sorore proximi sui), qui venientes ad fluvium non invenerunt nisi parvam naviculam, in qua non potuerunt amplius nisi duo ex illis transire. Dicat, qui potest, qualiter fluvium transierunt, ne una quidem earum ex ipsis maculata sit?”
The diagram below (click to zoom) shows the state graph for this problem. The solution is left (per tradition) as an exercise for the reader (but to see Alcuin’s solution, highlight the white text below the diagram).
Miss A and Mr A cross
Mr A returns (leaving Miss A on the far side)
Miss B and Miss C cross
Miss A returns (leaving Misses B and C on the far side)
Mr B and Mr C cross
Mr B and Miss B return (leaving Miss C and Mr C on the far side)
Mr A and Mr B cross
Miss C returns (leaving 3 men on the far side)
Miss A and Miss C cross
Mr B returns (leaving the A’s and C’s on the far side)
Mr B and Miss B cross
Below (click to zoom) is a solar car map of the Netherlands (north, south, east, west), plus the German cities of Aachen & Bochum and the Belgian city of Leuven, which are close enough to the Dutch border to be in the map region. That’s 7 solar car teams in a very small corner of the world! (base map modified from one by Alphathon).