[syhprum (OP)]

strowgers telephone exchangers could well have been the peak of pre-electronic computing, in my town a large building was mostly devoted to such a device.
How many lines could a typical system control and how large is a modern replacement ?.
 

[evan_au]

In the early days of the telephone, the physical wiring was a significant constraint.
Here is a photo of an early 5,000-line telephone exchange in Sweden:

5000_line_exchange.png (497.01 kB . 529x540 - viewed 2822 times)
Those exchanges needed to be on the physical path between each user.

Today, telephone exchanges are connected via the internet (either public internet, or a network internal to an organisation).
- The "exchange" is really a database, so that if you identify who you want to communicate with, it can inform the other party (or parties) of an incoming call, and tell you where to send the speech (or images), direct over the internet.
- The internet needs to connect the two parties, but the exchange does not need to be anywhere near the physical path
- So today's telephone exchanges can handle millions of users

The really modern equivalent of the telephone exchange is Facetime, Zoom or Microsoft Teams...

[syhprum (OP)]

What leaves my house is a coaxial cable which brings in my internet on a 350 Mhz carrier and and four twisted lines that have 50 v on them open circuit to provide a telephone service where do they go ?

[evan_au]

What leaves my house is a coaxial cable

This is called Hybrid Fiber Coaxial (HFC) technology. Standards governing this are provided by DOCSIS.
Modern versions of DOCSIS use large parts of the spectrum up to (and beyond) 1GHz to carry data in both directions.
- Data can be voice, video, internet, etc
- Typically many people on the same street share the same section of coaxial cable.
- This electrical signal is converted to optical fiber at the "head end", where it is carried back to a central location, where it can connect into the internet.
See: https://en.wikipedia.org/wiki/DOCSIS

four twisted lines that have 50 v on them open circuit

This technology is called Plain Old Telephone Service (POTS), and dates from the 1880s.
These twisted wires carry voice signals (up to 3kHz) back to a local telephone exchange perhaps 1-5km from your home.
In modern implementations, this is digitized in the local exchange, and then transmitted to the rest of the world over optical fiber.
See: https://en.wikipedia.org/wiki/Plain_old_telephone_service

The other common telephone technology you didn't mention is Cellular Mobile, where the voice is digitized in your handset, and the "last mile" is carried over wireless signals back to a base station 0.5-5km from your home. There the data is put into optical fiber, and carried back to a more central location.
See: https://en.wikipedia.org/wiki/Cellular_network#Mobile_phone_network