Resonance is defined as the harmony of frequencies (vibrations) of two different materials.

A simple example from ordinary experience will give us an idea of what physicists mean by "atomic resonance". Imagine yourself and a child at a playground where there are swings. The child sits on the swing and you give him a push to get him started. To keep the swing moving, you have to keep pushing it from behind. But the timing of these pushes is important. Each time the swing approaches you, you have to apply the force of the push just at the right moment: when the swing is at the highest point of its motion towards you. If you push too soon, the result is a collision that disturbs the rhythmic momentum of the swing; if you push too late, the effort is wasted because the swing is already moving away from you. In other words, the frequency of your pushes must be in harmony with the frequency of the swing's approaches to you.

Physicists refer to such a "harmony of frequencies" as "resonance". The swing has a frequency: for example it reaches you every 1.7 seconds. Using your arms you push it every 1.7 seconds. Of course if you want, you can change the frequency of the swing's motion, but if you do, you have to change the frequency of the pushes as well, otherwise the swing will not swing right.

Just as two or more moving bodies can resonate, resonance can also occur when one moving body causes motion in another. This type of resonance is often seen in musical instruments and is called "acoustic resonance". It can occur, for example, among two finely-tuned violins. If one of these violins is played in the same room as the other, the strings of the second will vibrate and produce a sound even though nobody is touching it. Because both instruments have been precisely tuned to the same frequency, a vibration in one causes a vibration in the other.

The resonances in these two examples are simple ones and are easy to keep the track of. There are other resonances in physics that are not simple at all and in the case of atomic nuclei, the resonances can be quite complex and sensitive.

Every atomic nucleus has a natural energy level that physicists have been able to identify after lengthy study. These energy levels are quite different from one another but a few rare instances of resonance between atomic nuclei have been observed. When such resonance occurs, the motions of the nuclei are in harmony with one another like our examples of the swing and violin. The important point of this is that the resonance expedites nuclear reactions that can affect the nuclei.

Investigating how carbon was made by red giants, Edwin Salpeter suggested that there must be a resonance between helium and beryllium nuclei that facilitated the reaction. This resonance, he said, made it easier for helium atoms to fuse into beryllium and this could account for the reaction in red giants. Subsequent research however failed to support this idea.

Fred Hoyle was the second astronomer to address this question. Hoyle took Salpeter's idea a step further, introducing the idea of "double resonance". Hoyle said that there had to be two resonances: one that caused two heliums to fuse into beryllium and one that caused the third helium atom join this unstable formation. Nobody believed Hoyle. The idea of such a precise resonance occurring once was hard enough to accept; that it should occur twice was unthinkable. Hoyle pursued his research for years and in the end he proved that his idea was right: there really was a double resonance taking place in the red giants. At the exact moment two helium atoms resonated in union, a beryllium atom appeared in the 0.000000000000001 second needed to pro- duce carbon. George Greenstein describes why this double resonance is indeed an extraordinary mechanism:

There are three quite separate structures in this story-helium, beryllium, and carbon-and two quite separate resonances. It is hard to see why these nuclei should work together so smoothly…Other nuclear reactions do not proceed by such a remarkable chain of lucky breaks…It is like discovering deep and complex resonances between a car, a bicycle, and a truck. Why should such disparate structures mesh together so perfectly? Upon this our existence, and that of every life form in the universe, depends.

In the years that followed it was discovered that other elements like oxygen are also formed as a result of such amazing resonances. A zealous materialist, Fred Hoyle's discovery of these "extraordinary transactions" forced him to admit in his book Galaxies, Nuclei and Quasars, that such double resonances had to be the result of design and not coincidence. In another article he wrote:

If you wanted to produce carbon and oxygen in roughly equal quantities by stellar nucleosynthesis, these are the two levels you would have to fix, and your fixing would have to be just about where these levels are actually found to be…A commonsense interpretation of the facts suggests that a super intellect has monkeyed with physics, as well as chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.

Hoyle declared that the inescapable conclusion of this plain truth should not go unnoticed by other scientists.

I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars.