Phase and Coherence

The concert

Imagine we are in a blimp floating over a great stadium where the Beach Boys are performing a farewell concert. Tens of thousands of people are standing on the grass in front of the stage. The Beach Boys begin to sing their old favorite ballad, Surfer Girl. Audience members link up into long rows, putting their arms across the shoulders of the person on either side, and begin rocking back and forth to the rhythm of the music. From above, we can see that all the rows are rocking to the same beat.

The Beach Boys are the rhythm generator, and each row of people is a pool of neurons. If each individual in the stadium were rocking by himself, it would be difficult for us to see the rhythm of the music. Linked in their long rows, however, the rhythm is clear.

Now we focus on the first three rows.  The first and second rows are both swaying left then right at the same time. They are in phase. If two friends were separated in the two rows, one in front of the other, they would be able to carry on a conversation fairly easily as they rocked from side-to-side.

But the third row started in the opposite direction at the beginning of the song. When the first two rows sway left, they are swaying right.  The rhythm is clearly the same, but two friends in these rows would have a much harder time talking, since they would always be moving in opposite directions. These rows are 180 degrees out of phase.

Whether they are in phase or out, the relationship of the rows remains the same. All are responding to the same rhythm, so their action is coherent.  Knowing the phase angle between the rows, we can always predict which direction anyone in row 2 or 3 will be leaning by watching someone in row 1.

Rows 4 and 5 are unusual.  Row 4 is made up entirely of actors who played munchkins in the Wizard of Oz. None of them is taller than 4 feet. Row 5 is a group of retired basketball centers—all taller than 7 feet. Regardless of the very different amplitudes, we notice that these rows, like the others, are coherent.  Knowing which direction someone in row 1 is leaning, we can accurately predict what direction a munchkin or a center will be leaning.

In rows 6 and 7, however, something different is happening. Someone has lost a child, and there are people searching for it. They are bursting randomly through the rows around them, breaking apart the people in those rows to pass, interfering with the rocking and disrupting the rhythm. They aren’t listening to the music, and when they pass through a row, the people around them cannot pay attention to the song either. These “Beta” neurons, wherever they go, destroy the coherence.  Once a row is ruptured by them, the neurons may end up swaying in opposite directions or lose the rhythm entirely. Ability to predict what direction an individual in these rows will be leaning at any given point in time is nearly zero. Communicate between friends in these rows is very difficult.

Finally, there are several rows which include people with casts on their legs, prosthetic or even missing limbs. They can hear the music and are listening to it—even swaying to it linked in their rows—but they are unable to move as easily as their colleagues. That fact ends up causing the rhythm of the whole row to be disrupted. In these cases, injuries have disturbed the smooth functioning of the row, and our ability to predict what any individual in it will be doing, based on knowing what is happening in row 1, is limited. The ability of the neurons in this pool to communicate easily with the others is also limited.

So we can see that pools of neurons which are resonating to the same rhythm generator can be in phase or out of phase, and this condition will have an effect on the efficiency of their communication. We can also see that, in-phase (synchronous) or out, their actions can still be predictable (coherent), regardless of amplitude of the two pools.  Finally, we can see that the presence of neurons which are performing a function (searching for a child), or neurons which are in some way damaged, can disrupt the phase and coherence of the pool and its ability to communicate smoothly with the others.

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