system
Given the following post, respond as if you're commenting on Reddit:
human
Why are astronomers focused on creating giant telescopes as opposed to giant arrays of smaller telescopes (lets ignore radio telescopes for now)?

One would think it would be cheaper to use Interferometry than build something like the ELT?

Or am I missing something about how hard it is to combine the signals?
gpt
Radio interferometry is staggeringly easier to do than optical interferometry.  To do interferometry, you need full information about the incoming wave so you can set up the interference, i.e. you need the amplitude and the phase/timing of the wave in order to combine it later.  For radio, the frequencies are low enough that we can record the signals on hard media, precisely timestamp it, and combine the data whenever we want.  The first VLBI stuff done in the 70's/80's actually used cassette-style tapes which were later played back simultaneously.

Optical interferometry is a whole different ballgame.  Radio is in the hundreds of GHz at most; optical is several PHz (petahertz = one quadrillion hertz).  We don't have a time standard that fast, nor can we record an astronomical source quickly enough to take advantage of such a time standard.  So, we have to combine the light as it is collected and make an interferogram that way.  This requires very carefully controlling the path length each light beam travels so that the combined light is coherent and generates an interference pattern.  Note that you must do this to within a fraction of the wavelength of light - the CHARA array on Mt. Wilson controls the path length to nanometer precision, and has to do this over its several hundred meter baseline.  Doing this across the radius of the Earth like you can with radio is a total pipe dream.

Also consider that an interferometer is not the ideal choice for all science.  While no instrument is sensitive to anything smaller than the resolution provided by its longest baseline (for single-aperture telescopes, this is the diameter of the primary optic), an interferometer is also insensitive to anything larger than that resolved by its smallest baseline.  For example, say you have a 10-meter telescope, and an interferometer which has a 100-meter and a 300-meter baseline.  The 10-meter telescope might only resolve scales of 0.01" or larger, say, but the interferometer in the same wavelength range will only effeciently detect objects which are between 0.0003 and 0.001" in size.  It can't see a galaxy 10' across, but the big telescope can.