every measurement carries two things: the part you care about and the part you don't. engineers call the ratio between them the signal-to-noise ratio. if the signal has power $P_\text{signal}$ and the noise has power $P_\text{noise}$, then

$$\mathrm{SNR} = \frac{P_\text{signal}}{P_\text{noise}}.$$

because that ratio spans many orders of magnitude, it's usually written in decibels. power goes as the square of amplitude, so measuring amplitudes $A$ instead of powers gives a factor of twenty rather than ten:

$$\mathrm{SNR}_{\text{dB}} = 10\log_{10}\!\left(\frac{P_\text{signal}}{P_\text{noise}}\right) = 20\log_{10}\!\left(\frac{A_\text{signal}}{A_\text{noise}}\right).$$

why it matters more than raw signal

the reason snr is the quantity worth tracking, not the strength of the signal alone, is that it sets a hard ceiling on how much you can actually learn from a channel. shannon's capacity theorem makes this exact: for a channel of bandwidth $B$, the maximum error-free rate is

$$C = B \,\log_2\!\left(1 + \frac{S}{N}\right),$$

measured in bits per second. notice the shape of it. capacity grows only logarithmically in $S/N$: doubling the signal barely moves $C$ once the noise is fixed. if you want to learn faster, cutting $N$ is worth far more than shouting louder.

you don't get a better picture by adding more light. you get it by removing what isn't the picture.

the same math, pointed at attention

i keep coming back to this because it's the cleanest argument i know for guarding what you let into your head. treat a day as a channel. the interesting ideas are $S$; the outrage, the notifications, the ambient churn are $N$. your throughput of anything that compounds is bounded by $\log_2(1 + S/N)$, so the marginal feed, the extra tab, the second scroll all raise $N$ and quietly lower the ceiling on everything else.

averaging helps, which is the one hopeful part. if you can sample the same signal $n$ independent times, coherent signal adds linearly while zero-mean noise adds in quadrature, so

$$\mathrm{SNR}_n = \sqrt{n}\;\mathrm{SNR}_1.$$

patience buys you a $\sqrt{n}$. repetition, revisiting, sleeping on it: these are not stalling, they're integration time. the signal was always there; you just hadn't collected enough of it to see it above the floor.