Another way to quieten the default network

If the default network is busiest when the mind wanders into self-related thought, then any practice that trains attention to stay with the present should change its activity. Contemplative traditions have been training exactly that for more than two thousand years. Since the 2000s, imaging studies have begun to show what happens in the brain when they do.

The second finding in Brewer’s study is the important one for this book. The default network was not simply turned down. In experienced meditators its central hub was more tightly coupled to the networks that monitor and control attention. That is a picture of a system under better regulation, not of a system switched off.

A cycle of wandering and noticing

During focused-attention meditation, such as attending to the breath, the mind wanders, the meditator notices, attention is brought back, and focus is held for a while before the next drift. Hasenkamp and colleagues asked meditators to press a button each time they noticed their mind had wandered, and found that the phases of this cycle engaged different networks: the default network during mind-wandering, the salience network at the moment of noticing, and executive networks when attention was shifted back and held (Hasenkamp et al. 2012).

That cycle can be modelled as a two-state Markov chain. In each minute, a mind that is on task drifts away with probability $p_\text{drift}$; a wandering mind notices and returns with probability $p_\text{notice}$. In the long run the share of time spent wandering is $p_\text{drift}/(p_\text{drift} + p_\text{notice})$ and the average episode lasts $1/p_\text{notice}$ minutes.

# Mind-wandering as a two-state chain, one step per minute:
# on task --(p_drift)--> wandering --(p_notice)--> back on task.
def chain(p_drift, p_notice, minutes=20):
    share = p_drift / (p_drift + p_notice)         # long-run share of time wandering
    episode = 1 / p_notice                         # mean length of one episode, minutes
    catches = minutes * (1 - share) * p_drift      # episodes started (and noticed) per session
    return share, episode, catches

for label, d, n in (("untrained (calibrated to 46.9 %)", 0.30, 0.34),
                    ("noticing faster", 0.30, 0.60),
                    ("noticing faster, drifting less", 0.20, 0.60)):
    share, ep, c = chain(d, n)
    print(f"{label:37s} wandering {100 * share:3.0f} %, "
          f"episode {ep:.1f} min, {c:.1f} catches per 20 min")
# untrained (calibrated to 46.9 %)      wandering  47 %, episode 2.9 min, 3.2 catches per 20 min
# noticing faster                       wandering  33 %, episode 1.7 min, 4.0 catches per 20 min
# noticing faster, drifting less        wandering  25 %, episode 1.7 min, 3.0 catches per 20 min

The middle line shows something meditators often report and find discouraging. When noticing improves, the number of “catches” in a session goes up, not down, because each episode ends sooner and a new one can begin. More catches early in training are a sign that the skill of noticing is growing. Only when drifting itself becomes less frequent does the number fall again. Chapter 8 turns this into a daily log.

Two routes, two kinds of stability

Chapters 3 and 4 have described two quite different ways of reducing the dominance of the default network: a pharmacological change at the 5-HT_2A receptor, and the training of attention. The second kind is the only kind this book recommends, and the reasons can be stated in terms of stability and control as well as law and safety.

A simple way to describe a quantity that is pushed about by noise but pulled back towards a set point is the Ornstein–Uhlenbeck process, $dx = -k(x – \mu)\,dt + \sigma\,dW$. Here $\mu$ is the level the system returns to, $k$ how quickly it returns, and $\sigma$ how strongly it is jostled.

import math

def profile(mu, k, sigma):
    """Ornstein–Uhlenbeck process dx = −k (x − mu) dt + sigma dW (minutes).
    Returns the spread of x, the half-time to return after a push,
    and the share of time spent more than 1 unit away from mu."""
    sd = sigma / math.sqrt(2 * k)
    half = math.log(2) / k
    tail = math.erfc(1 / (sd * math.sqrt(2)))      # P(|x − mu| > 1)
    return sd, half, tail

# Illustrative parameters only (see the hypothesis box): x is a stand-in for
# DMN-dominated, self-referential processing, in arbitrary units.
cases = {
    "ordinary waking":                     (1.0, 0.5, 0.40),
    "trained attention (endogenous)":      (0.8, 1.0, 0.40),
    "acute receptor-driven state (exog.)": (0.6, 0.1, 0.80),
}
print("state                                 mean  spread  half-time  time > 1 unit away")
for name, (mu, k, s) in cases.items():
    sd, half, tail = profile(mu, k, s)
    print(f"{name:37s} {mu:4.1f}  {sd:6.2f}  {half:6.1f} min  {100 * tail:12.1f} %")
# state                                 mean  spread  half-time  time > 1 unit away
# ordinary waking                        1.0    0.40     1.4 min           1.2 %
# trained attention (endogenous)         0.8    0.28     0.7 min           0.0 %
# acute receptor-driven state (exog.)    0.6    1.79     6.9 min          57.6 %

In this description, training attention lowers the set point a little and, more importantly, raises $k$: the mind returns faster from wherever it is pushed, and large excursions become rare. The acute pharmacological state is described as a lower set point with much weaker restoring force and much larger fluctuations: the state is less constrained, which is what “higher entropy” means, and it is not under the person’s control for its duration. That is a model of why one route builds a skill that stays with a person in daily life, while the other produces a temporary state whose course is set by chemistry.

The method of listening

The author teaches a method for singers based on the Śūraṅgama Sūtra’s description of “turning the hearing inward” (反闻闻自性), discussed in the second book of the 5D Library. As a meditation it is a form of focused attention on sound and on the act of hearing itself, and so belongs with the practices reviewed here. It has not been studied with brain imaging, and nothing in this chapter should be read as evidence that it has any particular effect on the brain.