A very good start. Kirn and Taibbi certainly understand the total corruption and bankruptcy of journalism and liberals. And the hatred of much of America that animates them.

Anyway… The 1/r^2 law applies to radiation that radiates equally in all directions… ie rufus has the right of it. The total integrated energy will be the same, but the energy density decreases with distance. With light, it’s sometimes more convenient to use power as it relates directly to the net flux of the photons, so the 1/r^2 law decreases the watts/m^2. And in terms of energy/photon, E=h(frequency), so a UV photon has more energy than a radio photon.

The Arecibo message was a focused signal much like the cited example of looking at a flashlight from afar as opposed to a bare light bulb radiating in all directions from the same distance. Eventually, the photon density does decrease with the focused light, but not at the 1/r^2 rate as for the bare light bulb. One can also provide even more “resistance” to distance degradation by using a focused laser source as the photons are now initially all in phase.

As far as detecting weak signals, again as Rufus stated collecting area is important. Exploiting computer processing we can now “make” very large dishes. The obvious example is the VLA in New Mexico where the effective size of the dish is the radius of the array. Now the VLA is somewhat obsolete in that we now routinely use what is called VLBI (Very Long Baseline Interferometry) in which dishes across the globe are linked. Effectively we now have a receiver that is the diameter of the earth itself. There are dreams of putting receivers in space at L2 points to increase the effective diameter even further. The photon density may be low but gather enough photons and you get a measureable signal.

A main sequence star like the Sun peaks its radiation in the visible and follows the standard blackbody curve. It does radiate in the radio, but at much lower value. I’m not sure of the calculation (never done it myself), but I think I read in some SETI material that when the Earth began radiating in the radio some 100 years ago that would have changed the net output spectrum of the Sun as observed from afar in the radio region. ie the Sun would no longer have the standard radio spectrum of a main sequence yellow star. There would be a small peak in the kHz to MHz frequencies totally uncharacteristic of such a star. If one could detect such a peak, it would indicate an unnatural radio source associated with such a star.

https://voyager.jpl.nasa.gov/mission/status/

From: https://www.restaurantnorman.com/does-light-intensity-depend-on-wavelength/ comes this definition: intensity is the amount of energy [received or detected] per unit time per unit area.

But if the energy source is less (flashlight vs. search light), the intensity is also less. So of course the intensity declines if the source is weaker, or the area is greater [over a constant time interval], as it would be at a greater spherical distance. Your “paint-particle-intensity [aka density] is lower on the bigger sphere with the same number of “droplets” covering a larger area.

I understand your first comment (the valley and flashlight), but I don’t think it’s relevant to our discussion. Yes, fewer of my retinal cones are struck by light particles or waves (depends on what day of the week it is 😉 ) but the intensity is the same if the valley is on the surface of a planet with no atmosphere.

Your second comment is relevant, regarding interference. Even in the relative vacuum of space the further something travels the more likely it is to run into something. But I still don’t see what any of this has to do with the inverse square law or distance. The inverse square law matters regarding sensitivity. A 10 foot diameter disc antenna is going to pick up more radiation than a 1 foot diameter disc, just as a 10 foot diameter disc 100 miles from the source will pick up more radiation than one 1,000 miles away, but each, individual unit of radiation is the same. Distance matters regarding the odds of encountering interference, but I don’t think that’s an inverse square law thing, that’s just increased odds because space is not a perfect vacuum.

We still communicate with Voyager 1, right? As long as it has power we can communicate with it.

I think?

Either I misunderstand you or you misunderstand radiation (or there is something completely off in the most basic, fundamental ways I understand radiation).

If we have 2, identical 1 foot diameter spherical balloons covered in identical amounts of wet paint and place both of them inside clear spheres with all the air sucked out (a vacuum) with one clear sphere being 3 feet in diameter and the other being 6 feet in diameter and we pop both balloons the same amount of paint hits the inside of each clear sphere. Even though the paint in the 6 foot diameter sphere travels twice the distance each drop keeps going until it hits something. There is no difference in the amount of paint that gets radiated in either clear sphere.

What is different is the density of the drops splattered. The 6 foot diameter sphere will have more gaps between paint drops than the 3 foot sphere.

In the vacuum of space radio waves (and, I believe, all radiation) travels on forever, or until absorbed by something (which, I think, would always result in heat?).

This is why the part of Mercury’s surface (a rocky planet with no atmosphere) facing the Sun is much hotter than the surface of Mars (another rocky planet with no atmosphere). At a distance of about 4 1/2 times further a lot less solar radiation is “painted” on Mars’ surface than Mercury’s. A solar photon hitting Mercury is identical in force and radiative quality to one hitting Mars, it’s just that a lot fewer hit Mars.