Vibration number

Winding number

Total energy

1

1

1/10 + 10 = 10.1

1

2

1/10 + 20 = 20.1

1

3

1/10 + 30 = 30.1

1

4

1/10 + 40 = 40.1

2

1

2/10 + 10 = 10.2

2

2

2/10 + 20 = 20.2

2

3

2/10 + 30 = 30.2

2

4

2/10 + 40 = 40.2

3

1

3/10 + 10 = 10.3

3

2

3/10 + 20 = 20.3

3

3

3/10 + 30 = 30.3

3

4

3/10 + 40 = 40.3

4

1

4/10 + 10 = 10.4

4

2

4/10 + 20 = 20.4

4

3

4/10 + 30 = 30.4

4

4

4/10 + 40 = 40.4

Table 10.1 Sample vibration and winding configurations of a string moving in a universe shown in Figure 10.3, with radius R = 10. The vibration energies contribute in multiples of 1/10 and the winding energies contribute in multiples of 10, yielding the total energies listed. The energy unit is the Planck energy, so for example, 10.1 in the last column means 10.1 times the Planck energy.