Telescopes and Consultation

If we work together we can see better than if we work separately!  This post describes the Science behind how many telescopes can combine power if they work as one,  and then translates that understanding into a lens looking at why "consultation" has so many similar properties.

 

Picture of  The Very Large Array radio telescope in New Mexico. ( as seen in the movie Contact )

Since the time of Galileo, astronomers have always looked into the heavens using telescopes,  devices which let us see further than our own eyes.

Originally, telescopes were made using mirrors or lenses,  and used regular light of the type we can see.  But the light our eyes can see is only a tiny sliver of the whole spectrum of electromagnetic radiation that extends way above blue and way below red.

 So  astronomers figured out how to make telescopes that could "see" in the radio part of the spectrum,  the same way your radio "picks up" stations.

Two problems limited them.  The first is one of size, called "aperture".   The bigger the telescope, the further you can see, because it collects more energy.  The second problem is fuzziness and is called "resolution".  That's described by how close two things can be in space and still be able to see that they are two things, not one larger fuzzy thing.

 It turns out that the bigger the telescope, the better resolution it has.

 So, people made bigger and bigger telescopes. Then new problems showed up, namely, that it is really difficult to make a large telescope and keep it in the right shape so it doesn't bend and distort the image, and second, its really expensive to make larger and larger telescopes.

But almost as magic, there's a way around those problems.  It turns out that you don't need to have the entire aperture filled with sensors -- you can get most of the information you want if you just sample the aperture space with a few small patches.

That's what you see in the picture at the top -- there are many small dishes ( separate radio telesopes ) that span a larger area, the effective aperture of a sort of meta-telescope comprised of all the smaller individual telescopes.

 The signals from each of those radio telescope fragments or chunks are all collected together in a central point and a process called "aperture synthesis" figures out how to combine them into a single better image.

 Once people figure that out, they realized you did not even need long cables. You could just record the signals separately on magnetic tape ( then ) and mail them to some central place to be processed.  You can put one station in Chile and another in Sweden and get a "baseline" of the diameter of the Earth resulting in a huge improvement in resolution. That's called Very Long Baseline Arrays.

But the way to combine all the signals to extract the most information about what is really out there is subtle.

There is a trick -- not only the SIGNAL amplitude  had to be captured, but the signal PHASE had to be  captured.   This is subtle but crucial -- without it the whole process fails.  The very "same" signal, if you look at just amplitude, turns out to be a very different signal if you include phase information.

It turns out that there are THREE important ways to look at a signal or to encode information in one: amplitude,  frequency, and phase.      Right now we make radios using only amplitude modulation (AM) and frequency modulation (FM) which have different benefits -- AM stations go a long way but are noisy,  FM stations go a short way but are not noisy,   Nature however also uses phase modulation (PM) but its more complicated to build radios that way, so its not done.

I'd note in passing that frequency and amplitude can be measured in the classical Western Science paradigm of not being concerned about relationships to context or the outside world.  Phase information however, by definition, requires paying attention to context to have a baseline to compare a signal to , and is more Eastern Science in nature, more holistic.

 So what?  What can we learn from this about putting many people into a room, into a conversation, and having them share perspectives that each sees individually, ad coming up with a single coherent larger better understanding of some subject?

 A lot.   The Science gives us a model that works, a pattern, that we can port to human meetings. What re the key parts of SEEING from fragments in the presence of NOISE, distortions built into each receiver and telescope such as flaws in the lens or construction, twisting of metal girders due to weight or wind loading,  and bandwidth limitations on the the individual receivers ( each of which has a finite size aperture so it is absolutely limited in what strength signal it could ever possibly see, and what resolution it could ever possibly obtain, even if it took pictures forever and tried to combine them.)

(1)  do NOT reject any signal -- you need all you can get for total collected energy

(2)  do NOT attempt to just add up the signals and divide by the number of signals (N)  to come up with an average signal, because that loses almost all the information, even though it will reduce noise, because each receiver has different noise so the dividing by N step reduces noise by a factor of N. 

(3)  do NOT select a "best" signal and reject the rest.    It is true that "seeing conditions" will vary from receiver to receiver,   some with clouds, some with turbulent atmosphere fuzzing up the picture, so that some individual pictures will be in that sense "better", clearer, sharper than others, and some will look like mirages with everything blurry.     And it is true that high-speed modems run at much high speeds than was once thought theoretically possible by actually being aware of how noisy the line is at any given millisecond and speeding up transmission when "the seeing is good" and slowing it down when it's not so good.  But that still is not the best you can do.

(4) you need a sophisticated process to "combine" the information from each receiver, there is no way around that.     One obvious fact is that the telescopes may be turned different ways, East versus West, so you have to rotate the images to some common reference frame before you even attempt to combine them.  In other words,  there is nothing wrong with each image, but it has been affected by the way the observer is pointing when the image was taken.    If you simply try to slide the images on top of each other, they will most definitely not "fit".    You need to back out, or correct for the viewpoint of the observer before you even begin to combine what the observers saw. 

There are other mathematical factors involving phase of signals, which are too complex to explain easily.  

The point is, it is "hard" to combine the separate readings, the separate thing the different receivers see,  so as to extract the most information and reduce the impact of individual telescopes' built in distortions, weather, etc.   It is doable, but it is hard

(5) In fact it turns out that you can figure out an image even better than "theoretically possible" from many images by very advanced statistical processing,   a technique which is used on satellite images of Mars.  That's called "hyper-resolution" and  a subject for another post.

(6) Making many small separate receivers and spreading them out as far as possible maximizes the information you collect and reduces the noise  You need as much diversity as possible in that vein.  This is far better than trying to make a single super receiver that is bigger than all the others.  The resolution of an aperture is mathematically simply given by the formula D/f, where D is the diameter of the dish or lens and f is the frequency of signal being used.  Twice the D gives you twice the resolution.  To get maximum resolution you want signals coming from different countries, not just different sides of your own property.

(7) It's obvious, but the equivalent of "humility" is required -- no one signal is automatically better than any other, no one signal can possibly span the truth,  only when one "listens to" all of the other signals in the room does the truth emerge. 

 (8) Repeating the comment above -- This can be done but it's hard.  That's why we are all taking lessons in "consultation", after all!!  It's not immediately obvious how to rise above individual percpeptions and views,   correct for context, rotate images so they are all the same way up, sort out signal from noise including self-declaration of weak spots or fuzzy spots in one's own thinking, and put it all together into an emergent picture of Truth.