1. New Didactic Tools  4. Entropy: Bridging the Gap 
2. Exploring Phase Space  5. The Sophomore Phase Transition 
3. Adventures in space  6. There is Nothing New ... 
* This paper was read at the Gordon Research Conference on "Physics in Research and Education",
How to explain physics using little math?
Help comes from Hardware and Theory:
Use Live Simulation and Intuitive Geometry (of phase space) as didactic tools. 
To give an example:
Applet Sinai 
Most have hyperspherical phase space volumes (except LJ and spin lattice) 
Phase space:
Explore the simple but surprising properties of nspheres 
(2) 
Applet Harddisks Note the density of the velocity component v_{x} 
Projecting constant densities on hyperspherical surfaces down onto
one axis we find, depending on dimension,
(see Fig. 2)
p_{2}(x)  =  
p_{3}(x)  =  
p_{4}(x)  =  
p_{5}(x)  =  
p_{12}(x)  =  
Thus the MaxwellBoltzmann distribution
may be derived solely from the geometry of highdimensional spheres.
Applet Harddisks Watch the density of the velocity component v_{x} as N is increased. 
Applet Hspheres

(3) 
Applet Boltzmann

Applet Entropy1

[`moron'=nitwit, `sophos' = the wise one]
In addition to the above, some further truths are attainable in the course of the third term:
In the 18th century, higher education, including mathematics, was reserved to men.
The Italian art critic and `popular science writer' Francesco Algarotti found it unbearable that one half of humanity should not be able to grasp the impact of Newton's revolution.
So he sat down and wrote a bestselling book in which he sketched Newton's ideas using plain language only. Instead of formulae he invoked similes and intuitivegeometrical arguments.
Newtonianism for the Ladies: How to explain physics using absolutely no math  


Francesco Algarotti, the ''Swan of Padua'' 