5.1 The Revelation of Weber-Fechner

“Why in childhood, a summer vacation feels as long as a lifetime; while in old age, ten years pass like sand through fingers? This is not just psychology; this is geometry. Our consciousness is a logarithmic ruler; it compresses not only light and sound, but also time itself. It is precisely this compression that allows us to maintain a linear dignity when facing an exponentially exploding universe.”

The Mathematical Signature of Physiology

19th-century psychophysicists Weber and Fechner discovered an iron law governing all senses:

$$S=k\ln I$$

Sensory intensity ($S$) is the logarithm of physical stimulus intensity ($I$).

• Decibels of hearing.

• Magnitude of vision.

• Pressure of touch.

They all follow this law.

In the third book of Vector Cosmology, we interpreted this as “information decoding.” But from the “axiology” perspective of the fifth book, this law reveals life’s ultimate defense against “time inflation”.

Countering Exponential Explosion: Fighting Poison with Poison

Recall our evolution equation: The universe’s total budget (speed of light/computational power) grows exponentially with intrinsic time $\tau$:

$$I(\tau )=c(\tau )\propto e^{\lambda \tau }$$

If our perception were linear ($S\propto I$), we would face a disaster:

• At birth: The world is slow.

• In adulthood: The world is 10 times faster.

• In old age: The world is 100 times faster. We would be unable to think or react, because the frequency of external events exceeds our processing bandwidth.

But evolution (or that higher-dimensional us) was extremely clever in choosing logarithmic perception.

We put the exponentially growing physical input $I(\tau )$ into the logarithmic function $\ln (\cdot )$:

$$S(\tau )=k\ln (e^{\lambda \tau })=k\lambda \tau$$

A miracle occurs.

The exponential ($e$) and logarithm ($\ln$) cancel each other out.

That violently accelerating physical time is restored in our subjective consciousness to a smooth, uniform, linearly flowing river.

We feel that “every second is equal in length” because we are using a constantly shrinking “psychological ruler” to measure a constantly expanding “physical universe.”

This is the highest manifestation of life’s homeostasis in the time dimension.

The Relativity of Time Density

This also explains why “new experiences” can lengthen life.

Weber’s law has another corollary: Just Noticeable Difference (JND) is proportional to the current total.

$\Delta I\propto I$.

This means that the more you have (the larger $I$), you need more increment ($\Delta I$) to feel “change.”

Mapping to the sense of time:

• Childhood: Your total memory ($I$) is small. Each new day ($\Delta I$) accounts for a large proportion relative to the total. The increment $\ln (I+\Delta I)-\ln (I)$ is significant. So time is slow, thick.

• Adulthood: Your total memory ($I$) is large. The same day ($\Delta I$) thrown into the ocean creates no waves. The logarithmic increment approaches zero. So time flies.

Conclusion:

Physical time is fair to everyone (Chronos).

But Logarithmic Time is different for everyone.

If you want to “live long,” extending physical lifespan through health preservation is only a lower strategy.

The upper strategy is “resetting the base.”

Explore unknown fields, learn completely new skills, love strangers.

These actions create heterogeneous $v_{int}$ that cannot be simply added to the old $I$; they open new logarithmic coordinate axes.

Only innovation can reverse the accelerated depreciation of psychological time.

Conclusion: We Are the Deceleration Glass of Time

The Weber-Fechner law is not just a mechanism of senses; it is the shield of consciousness.

The universe ($e$) tries to throw us out, tries to tear us apart with exponential acceleration.

And we ($\ln$) create an “inertial reference frame” by bending our perception.

In this reference frame, we don’t feel the universe’s gallop. We only feel gentle breeze and peaceful years.

We are the deceleration glass of time.

Through this glass, we filter that bizarre, ever-changing high-energy universe outside into a warm, gentle “human world” suitable for human habitation.

Since our perception is logarithmic, what properties will the logarithmic function exhibit when we approach that infinitely distant endpoint ($\Omega$ point)?

Does it imply that for subjective consciousness, the endpoint can never be reached?

This leads to the theme of the next section: Zeno’s Eternity. We will see why, in the logic of logarithms, life is an endless flight.