Hyper-Greco-Latin Cube

Hyper-Greco-Latin Cube

 

The sixty-four groups of six digits following form a Hyper-Greco-Latin Cube. You can consider the last three columns to represent the X, Y and Z coordinates of the cube. In an experimental design, each of the six columns can be used to denote an experimental variable at four levels. Each level of each variate occurs sixteen times with each level of each of the others, and (I think) four times with each pair of values of two other variates.

You can then analyse whatever variate you are measuring with a classic Analysis of Variance, providing six factors with three degrees of freedom, and 45 degrees of freedom for the residual.

(I don’t need to say that you would, of course, assign the four levels of each variate at random, using a suitable random number source)

 

1 1 1 1 1 1               3 4 4 1 2 1              4 2 2 1 3 1           2 3 3 1 4 1

4 3 4 2 1 1               2 2 1 2 2 1              1 4 3 2 3 1           3 1 2 2 4 1

2 4 2 3 1 1               4 1 3 3 2 1              3 3 1 3 3 1           1 2 4 3 4 1

3 2 3 4 1 1               1 3 2 4 2 1              2 1 4 4 3 1           4 4 1 4 4 1

 

4 4 3 1 1 2               2 1 2 1 2 2              1 3 4 1 3 2           3 2 1 1 4 2

1 2 2 2 1 2               3 3 3 2 2 2              4 1 1 2 3 2           2 4 4 2 4 2

3 1 4 3 1 2               1 4 2 3 2 2              2 2 3 3 3 2           4 3 2 3 4 2

2 3 1 4 1 2               4 2 4 4 2 2              3 4 2 4 3 2           1 1 3 4 4 2

 

2 2 4 1 1 3               4 3 1 1 2 3              3 1 3 1 3 3           1 4 2 1 4 3

3 4 1 2 1 3               1 1 4 2 2 3              1 3 2 2 3 3           4 2 3 2 4 3

1 3 3 3 1 3               3 2 2 3 2 3              4 4 4 3 3 3           2 1 1 3 4 3

4 1 2 4 1 3               2 4 3 4 2 3              1 2 1 4 3 3           3 3 4 4 4 3

 

3 3 2 1 1 4               1 2 3 1 2 4              2 4 1 1 3 4           4 1 4 1 4 4

2 1 3 2 1 4               4 4 2 2 2 4              3 2 4 2 3 4           1 3 1 2 4 4

4 2 1 3 1 4               2 3 4 4 2 4              1 1 2 3 3 4           3 4 3 3 4 4

1 4 4 4 1 4               3 1 1 4 2 4              4 3 3 4 3 4           2 2 2 4 4 4

 

Electric Motorway

I ran this letter off the cuff in January 1995, and left it at that. On consideration I would substitute ‘diesel’ for ‘turbo’ throughout. Volvo are just now (2013) marketing the V60 hybrid which was ‘in the air’ in 1995! It might be better to take over the inside lane, rather than the outside, or even to develop a separate one-lane (each way) motorway for Heavy goods vehicles only.

Letter in New Scientist 25/Feb/1995 p 84

Your Correspondent Fenton Robb makes some valuable suggestions on the introduction of electric vehicles (letters 7January and 11 February), but other approaches are possible and may not need government support.

Volvo, the car and truck manufacturer is experimenting with a battery-powered vehicle equipped with a clean efficient turbine/generator for topping up on other than local journeys.

I regularly travel between Paris and Calais via the A1 and A26 autoroutes. The outer lanes of these motorways are filled with heavy trucks travelling nose-to-tail at their maximum permitted speed of 90kilometers per hour, slowing down on each upward slope, and braking hard on each descent. Occasionally, a lorry driver maddened by boredom pulls into the inner lane, and car brake lights blossom for several minutes as he crawls past a colleague. A few hundred metres away, sleek TGVs and Eurostar trains slide by, picking up their power from overhead lines, and returning energy to the grid when braking.

If a catenary power system was filled to the slow lane of these motorways, and corresponding pick-ups were fitted to heavy turbo-electric goods vehicles with regenerative braking, potential and kinetic information could be conserved. Given auto-steering using buried cables (already existing in prototype), speed control using distance sensors already available, and possibly computer safety monitoring, truck drivers could turn on to the autoroute at Calais, and awake after a good night’s sleep at Marseilles, with fully charged batteries and full fuel tanks.

Since these autoroutes are run by efficient, cost-conscious private companies, no taxpayer’s contributions would be needed. Capital installation costs would soon be covered by economic user charges. Operators would gain in speed, safety, reliability and reduced employees’ health and welfare charges. Finally, the private motorist would have less chance of becoming the filling in a steel sandwich, or being kippered in diesel fumes.