Attention Is Normalized Accumulated Surprise

The human does not experience the microtime stream. The human experiences its conscious-scale remainder.

We now have the formal ladder:

E(t) = P(t) + iI(t)
R(t) = A(t) / E(t)
S(t) = Log(R(t))

But human attention is not instantaneous surprise.

Attention is not a single raw S(t).

Attention appears after the human system accumulates, normalizes, and resolves a microtime stream of complex surprise into a conscious-scale pointer.

The central definition is:

Human attention is the finite conscious pointer produced when the human system integrates, normalizes, and resolves the microtime stream of complex Reality-surprise into a second-scale object of consciousness.

Shorter:

Human attention is normalized accumulated surprise.

Microtime And Conscious Time

Reality updates beneath consciousness.

For the baseline formal model, use:

epsilon = 10^-12 seconds

That is one picosecond.

Use:

W = 1 second

as the default conscious attention window.

Then:

N = W / epsilon = 10^12

One conscious second contains an enormous number of unconscious updates.

This is not presented as a settled biological claim. It is the formal model’s microtime scale. The essential point is scale separation:

Reality updates at microtime.
Attention appears at conscious time.

Accumulated Surprise

Let K_W be a weighting kernel over the attention window.

The kernel satisfies:

K_W(tau) >= 0
integral K_W(tau) d tau = 1

Windowed accumulated surprise is:

C_W(t) = integral from t-W to t of K_W(t - tau) Log(R(tau)) d tau

In discrete form:

C_n = sum from j=0 to N-1 of w_j S_{n-j}

with:

sum w_j = 1
w_j >= 0

This is the first normalization. It prevents a conscious second from becoming a raw trillion-term explosion.

Renormalization

The system does not hand raw accumulated surprise directly to consciousness.

Define:

Attptr(t) = Nrm(C_W(t))

Attptr(t) is the attention pointer.

One simple demonstration function is:

Attptr(t) = 0 if |C_W(t)| < delta
Attptr(t) = C_W(t) / (1 + |C_W(t)|) otherwise

This does three things:

1. It creates a threshold below which no conscious attention appears.
2. It keeps attention finite.
3. It preserves the direction of accumulated surprise.

The exact renormalization function remains an open parameter of the formal model. The structure does not depend on pretending that the final biological function is already known.

Demand And Location

Attention has intensity:

D_att(t) = |Attptr(t)|

Attention also has direction:

theta_att(t) = Arg(Attptr(t))

The direction is the formal pointer direction in the surprise plane.

Mapping that direction to a named object of consciousness, such as pain, beauty, hunger, threat, opportunity, insult, love, memory, or novelty, requires an additional semantic-address layer.

The core equation gives the pointer.

The semantic layer names what the pointer is pointing toward.

The Key Claim

You do not experience all the surprise of a second.

You experience what remains after the microtime stream has been accumulated, weighted, normalized, thresholded, and renormalized.

That remainder is attention.

Next: Absorption is prediction success.