A small signal can be detected over vast distance if one has means to separate the signal from the noise.
I have off and on dabbled with amateur radio. Mastering the skills has been fun. But just contemplating the improbability of the mechanisms delights me.
Imagine if I put a 60 watt lightbulb on my roof and folks across the ocean notice its reflection in the clouds. That would be amazing, no?
I can send 60 watts of radio energy to my roof to have it reflect off of ionospheric clouds and be heard overseas. Radio is special this way.
Radio signals are precise. A light bulb scatters energy every which way but not radio.
Radio receivers expect that precision. They discard the part of the signal that does not meet expectation.
What's left is me tapping out my message from one electrical appliance to another with nothing but the natural world between them.
See What is Radio
Big Data usually means digging through billions of digital droppings to find the signal accidentally encoded within. Its an accomplishment of sorts but unlikely to have the world changing impact of radio.
The weak signal might just be the noise. Study of noise in observations allows Statisticians to determine when Correlation Can Mean Causation.