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Did you mean: Why HN screw with titles?

PS: Title as of this comment is “Why 56k the fastest dial up modem speed”

The "is" is missing from the title (Why is 56k).

I wish HN just autofilled the Title field after the URL field has changed during submission (but still allowed users to edit the title).

I assume whoever typed it in just missed a word.
Because with the power to control us comes the feeling that they should control us.
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TIL: Phone networks already carried digital signals in the 60s. I absolutely did not expect that.
"Fast-forward to 1962. Ma Bell begins using T-1s to connect its switching centers. T-1s are a digital communications link, not analog. The entire phone network goes digital. In a modern phone network, the only analog communication is between an individual house's phone line and the phone company's box."

This is misleading. The phone network used analog links (typically microwave relay) for long distance almost exclusively for many years (into the 80s) after the introduction of T1. T1 itself is not terribly well suited to very long distance links though and can only be pressed into it with repeaters every mile or so.

Hence towers with dishes on the outside. Long perplexed why they had canvas stretched across, and didn't point up: https://en.m.wikipedia.org/wiki/Microwave#/media/File%3AFraz...
Our Charter Spectrum “cable” connection goes over a microwave link like this.

How do I know? Well, we had a pretty big wildfire a couple years ago that burned a microwave tower a couple hours away. The official response was that they couldn’t get internet back in town until they rebuilt the tower. Our internet was down for a couple weeks until it was safe enough for them to get back to the tower site.

Microwave relay links predate spaceflight and even when comms satellites became a thing, it made (and still makes) little sense to beam regional TV/radio/phone up to geosynchronous and back, due to cost and latency. There was no good replacement to terrestrial microwave until fiber optic became a thing.

In a very real sense microwave relays are the direct descendant of the optical telegraph (aka "clacks" in Discworld lingo).

> Long perplexed why they had canvas stretched across

Its a radome, used to protect the antenna from weather.

130VDC on the copper, apparently.

Had "the second longest T1 in the service area" for a while there. BellSouth declined to renew the contract in 2008, the business folded, etc. In 2013 I was digging through the old building, and the T1 line card in the wiring closet was still powered.

Nowadays the relay boxes all the way into town are mostly hanging open or have been repeatedly run over. I wonder how much of the rest of that infrastructure they just abandoned in place.

the 130V was to power either repeaters or the smart jack.
>The phone network used analog links (typically microwave relay) for long distance almost exclusively for many years (into the 80s) after the introduction of T1

The reason should be obvious. Digging long distance trenches and all of the property buying/leasing and right of ways/easements and all of the other fun stuff makes it a total nightmare. Radio broadcast just makes much more financial sense as well as logistically.

Were the microwave links really analog signaling?
The Long Lines network used frequency modulation and frequency division multiplexing and was completely analog. It was really only advancements in semiconductor lasers and optical fiber manufacturing that drove its abandonment.
> The phone network used analog links (typically microwave relay) for long distance

Those microwave links represent layer 0 in the connection which is by definition always analogue, the same is/was true for T-1 which used alternate mark inversion [1] signalling over a 4-wire circuit. It is the type of signal carried over the link which decides whether it is considered "digital" or "analogue". T-1 carried 24 time-divided PCM channels ("digital"), microwave links could and can carry both frequency-divided multiplexed analogue channels ("analogue") as well as time-divided PCM or packet-switched channels ("digital").

[1] https://en.wikipedia.org/wiki/Bipolar_encoding#Alternate_mar...

Computers are old. The future is here, it's just unevenly distributed. I take a self-driving car multiple times a week yet anyone outside my bubble hasn't ever ridden one and thinks that technology doesn't work yet. I have conversations with an LLM, but people on the other side of the world don't even have laptops or reliable Internet access. Military people have jetpacks to move around on. Inequality is as old as dirt, unfortunately.
It also strikes me how much the old phone network, and its cultural aspects, have faded into the past - particularly when I drive past some derelict bit of telecom infrastructure. Even 30 years ago, it was amusing to watch kids try to deal with a rotary-dial phone. Now even landlines are an endangered species, and area codes are barely relevant. Finding a working telco pay phone these days would be like finding a unicorn.

Meanwhile, on a random roadtrip through rural Illinois yesterday, I was seeing "5G UC" on my cell phone, out in the middle of nowhere. Unevenly distributed, indeed!

>Finding a working telco pay phone these days would be like finding a unicorn.

Even if I found one, I would only be able to make a collect call. I never carry loose change on me, and I haven't had a calling card in decades.

There used to be a way to pay with credit card IIRC?
Not that I was ever exposed to. Calling cards were just account numbers with a monthly statement. If you used a credit card for that, then maybe, but to me paying with a credit card suggests a per call transaction. That I have not experienced. But the world is a bigger place than just me, so maybe it was available in other areas?
> Inequality is as old as dirt

Yes

> unfortunately

No. Perfect equality means that nobody can excel in anything, anywhere and any time. With perfect equality comes stagnation. If you happen to know Rush' song "The Trees" you'll know what I'm talking about:

Now there's no more oak oppression For they passed a noble law And the trees are all kept equal By hatchet, axe, and saw

It is not so much inequality which can be a problem but the fact that the lower bounds can be too low for an acceptable quality of life. As long as the lower bounds are high enough - above the "poverty line" - there can be inequality without that being a problem in and of itself.

Another thing which can be a problem is the reason for there being inequality, e.g. when some rule or custom creates artificial limits for some people but not for others ("discrimination").

For a society to thrive you want people to make the best of their possibilities and to use their capabilities to the fullest extent. With that you automatically get inequality because not everyone has the same possibilities and capabilities, e.g. a farmer on a rock-infested piece of glacial detritus will not be able to produce bumper crops even if he is at least as capable as the farmer in the river delta who can not leave his wooden shoes outside without them sprouting roots and growing leaves. On that same river delta a capable farmer will be able to more reliably produce good crops than one who has never heard of crop rotation. If you take the most productive developer in your company and provide him with a fully equipped tool shop he will not be able to produce as good a widget as would the most experienced mechanic who in his turn would not be as productive a developer. Both can do their best to reach their local optimum but the developer will most likely see that result in higher earnings than the mechanic will.

Inequality is not a problem. Equity - forced equality as personified by the "they" in the lyrics to "The Trees" - is a problem.

Great point. The distinction between equality and equity is an important one, with the canonical image for it for me being the one with the fence*. Where inequality today looks like billionaires throwing parties and doing drugs on their own private island at one end, and people living in tents and going hungry, also doing drugs, but with no hope at the other end, it's not the inequality itself that's the problem, it's that the lowest end of the spectrum is so utterly bleak that people have to steal and commit crimes to survive that's the problem.

* https://www.researchgate.net/profile/Shrehan-Lynch/publicati...

Telecommunications were the first application for nearly every principle and technology now used in computers.

In the 1930s, Claude Shannon was trying to optimize the phone network's automatic switching fabric built out of millions and millions of relays when he, more or less by accident, proved that switching circuits are equivalent to Boolean algebra, in a deep sense, and so the appropriate arrangement of switches, can compute anything that can be computed.

The first major commercial application for the vacuum tube was not in radio, but in amplifying long-distance telephone links. They would quickly find use in frequency multiplexing telephone lines, too. [1]

Similarly, one of the first applications of vacuum tubes as a high-speed electronic switch was for multiplexing telegraph lines, and much of the initial research on high-reliability low-power tubes able to switched fully on without damage began, with the telephone and telegraph companies.

The first computers were built out of relays and vacuum tubes specially designed for telecommunications.

The transistor was invented at Bell Labs. The planned application was the telephone network. The very same year, the theory behind modern error correcting codes was developed at Bell Labs too. These find extensive use today in data storage in computers, but the original goal was arbitrarily accurate transfer of telegraph data over noisy links.

Digital transmission of photographs dates to the late 1920s too; they wanted to send images over extremely noisy long-distance telegraph links. So record the intensity of light over each spot of the image on paper tape. Then send the tape over the wire. And reverse on the other end. [2]

I've come to understand the computer revolution as really the story of the telecommunication revolution. Computers serendipitously came about with advances in telecommunications, enabled by the same technologies, and indeed, often driven by the needs of telecommunications. (One of the very first applications for a computer in an embedded context - dating to the late 1950s in experiment - the telephone exchange, of course.)

[1] https://long-lines.net/tech-equip/misc/Graybar103-0693.jpg

[2] http://www.hffax.de/history/html/bartlane.html

At one time teletype switching was done in centers where the incoming line was connected to a tape punch. The operator tore the tape off the punch, read the destination address punched at the beginning of the tape, and put the tape on a tape reader connected to an outgoing line to another center closer to the destination. https://en.wikipedia.org/wiki/Tape_relay

IP routers now do this faster.

I'd argue that they were also invented specifically to do specific mathematical calculations. Many predecessors of the modern computer were designed to do math. Some examples:

The ENIAC was invented to do mathematical calculations for the army.

Blaise Pascal invented a mechanical calculator to do arithmetic in 1642. Leibniz improved on his design and made his own version in 1673. However, not many of either version were made, as it was still cheaper to just do the addition, subtraction, multiplication, and division yourself.

Herman Hollerith invented a punch card tabulating machine and patented it in 1884. It was used to process the 1890 US Census. It could increment counters to do addition and multiplication, but its main purpose was to assist with processing large amounts of data using punch cards, the way SQL databases are used today.

In 1930, Vannevar Bush invented a machine called the Differential Analyzer, which was an analogue computer that could solve differential equations by integration. You could store functions in it by adjusting gears. The purpose was to be able to automatically calculate things like the position of a projectile moving through the air after n seconds without having to calculate it by hand.

Most of this I got from the book ENIAC, The Triumphs and Tragedies of the World's First Computer, which touches on all these predecessors to the computer.

The idea of the Semantic Web dates to about 1945 and Vannevar Bush, in As We May Think. Douglas Engelbart (Mother of All Demos) cites Bush as a major influence.

Bush was Claude Shannon's graduate advisor.

I sometimes wonder how much crazy stuff these people didn't write down because they only knew how to make little bits of it happen with current tech.

Isn't Morse code technically a digital signal, albeit with an extremely low bit rate?
Yes. It's sloppy PWM with a non-ASCII character code. It's optimized for human encoding/decoding rather than machine; the pulse widths are not globally uniform like they would be in a machine-oriented code, which is what I mean by "sloppy."
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To nitpick, the 53.3k limit only affected US Robotics' pre-V.90 standard called X2, due to how much power they would require, which violated FCC rules. K56Flex (the competing 56k protocol), and later the ratified V.90 standard didn't have this problem and you could achieve carrier speeds of 56,000 bps.

This distinction was getting lost to time even back then with everyone just assuming it was some arbitrary FCC limit. This post from NANOG in 1998 explains it: https://archive.nanog.org/mailinglist/mailarchives/old_archi...

What's crazy is how badly I was waiting to upgrade from X2 to K56Flex just to get the 3kbps, which was like a life-altering speed difference back then!
I’ll go to my grave thinking wow 3.2 kilobytes is a good connection!
3.2kbps is the maximum rate of symbols (i.e. 3200 baud). So K56Flex squeezes one extra bit per symbol.
I don't know how it worked but I never saw better than 53/54k with v.90 or v.92. Maybe there was more going on.
It really depended a lot of how clean your pair was, and sometimes even what kind of switch you were homed on.

Like channel banks prior to the D4 and a 1AESS would very likely have a marked difference to your speeds.

Once, for a short while, I was getting around 110kbps reported from my modem (obviously it was doing compression).

It couldn’t do it for binary, but it still was noticeable with HTML and email.

It didn’t last long. Whatever accidental phone line + ISP magic enabled it was quickly “fixed”.

https://en.wikipedia.org/wiki/Microsoft_Point-to-Point_Compr...

but PPP compression wouldnt explain modem reporting faster speed. Btw I never saw PPP compression enabled in the wild either.

I had a nice US Robotics (or probably 3Com by that point) hardware modem, I have always assumed it was a feature in there somewhere.

Maybe it was PPP instead. It was the effective link speed, not something measured with a download tool.

This would have been ‘97 or so, so my memory is hazy.

Ahh the 56K modem wars - each group swore either by USR or K56Flex and were incompatible with each other until V90 standard came along - some modems could be firmware upgraded (USR) others not that used discrete components.
I'm pretty sure my external modem had a firmware update that took it from 53kbps to 56k flex
Growing up, I lived in the boonies. Even with a 56k modem, the fastest it could go was 33.6k. I got to learn all of the info from the TFA when I was a trying to find out why. That’s also when I learned that some companies had full T1 lines all to themselves for a whopping ~1.5Mbps. Until some makes a call or sends a fax when your top speed drops 64k per phone line being used. It’s also why ISDN didn’t connect at 128k but at 112k since it just used two “bonded” lines of the T1
Twin bonded ISDN lines were my only option for anything faster than 33.6k. “You too could have had 128k for the low monthly price of $250 + cost of two phone lines + cost of equipment + labor”. When I finally moved to somewhere that had cable (and cable internet at 1.5mbps) I vowed never to return to the sticks.

Then Elon came along… Starlink is probably one of the most useful inventions next to the lightbulb, DC current, Solar Cells, Toilets, desalination/ro and the WWW. I’ve gotten 100mb+ out in places where you have no cell service, no humans, no life, and no way of contacting anyone if in trouble. Starlink kept the connection no problem.

I’m excited for the future if we can just get over our differences. XR, Starlink, EV’s, Highspeed rail, Electric planes, Mars…

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While we're making suggestions: don't bring up "derangement syndrome" if you want to be taken seriously. You ironically used it in a sentence appealing for less polarization. The comment was fine without.
Refusing to point out a problem does not make it disappear. I consider it clear as daylight that some people react irrationally to certain individuals whether those be Musk or Trump or anyone else. That phenomenon seems to be relatively new, e.g. in the times of Reagan there were many who clearly did not like the man but that never led to much more than "Ronald Raygun" and similar expressions and Bush - just as contentious - became "Shrub" but even then the reactions were not nearly as - to use a popular term - 'triggered' as they have become lately.
No, the meme is new. There is no new phenomenon deserving of such a term. Yes, I can point to ridiculous things people said about Trump and call it TDS. It's still just a cynical, myopic, partisan take on a subset of behavior from a subset of people, wrapped up in a cute term, meant to dehumanize the opposition. It's propaganda.
I just dont see how starlink makes money in the long term, without massive government subsidy like Iridium gets. Elon's seeming unwillingness to play nice with the federal government in regards to this harms Starlink's ongoing viability.

Technically, it's a pretty neat trick - architecturally, it works just like any cellular network, except the power is moving, not the subscriber.

The government has been trying to subsidize ISPs to expand broadband to more rural areas, but that has been a failure compared to Starlink which actually exists.
The same government that refused to pay up until they had their arms twisted?

The unwillingness is from the government

> You too could have had 128k for the low monthly price of $250 + cost of two phone lines + cost of equipment + labor”.

+ per minute billing from your telco and your ISP.

Oh man, so true. $350 worth of internet hourly charges when my mother was livid and asked me what the hell I was doing all the time online running up a bill like that.

I simply replied “Air Warrior 3”.

T1's were so mind numbingly expensive and ISDNs always seemed like a cheaper but insulting value. Same bandwidth as two modems, I ended up holding out for 'broadband' and making due with two phone lines for a few years.
> Until some makes a call or sends a fax when your top speed drops 64k per phone line being used.

That wasn’t how it worked. You could have a T1 with certain channels configured for voice and others for data, but the configuration was static — you didn’t get to use the bandwidth from the voice channels when they were idle.

> It’s also why ISDN didn’t connect at 128k but at 112k since it just used two “bonded” lines of the T1

ISDN bearer channels were 8-bit clean. If you bonded both channels of a BRI, you had a 128kbps data path. What you typically couldn’t use was the 16kbps D channel, which was used for signaling.

Correct. And IIRC, IDSL was just ISDN with all three channels dedicated to data. Yielding 144kbps at phenomenal distances from the CO.
IDSL was an ISDN bearer with Frame Relay running on top, it basically didn't use the channelization scheme at all - and IIRC had different framing than a real BRI line.
IDSL used HDLC natively as a frame format. You could run Frame Relay on top of that (or PPP.) Line coding was standard 2B1Q in North America (same as a “regular” ISDN BRI.)
Some ISDN TAs supported data-over-voice for 56kbps per channel. Useful in areas where data calls has per-minute charges but unlimited local "voice" calls were included in the monthly charges.
Right, and some TAs supported data notifications over the D channel. There was also 144kbps IDSL which made use of the D channel bandwidth. And a bunch of other variations.

But, the fundamental channel width was 64kbps and ISDN data calls were not routinely connecting at 56kbps due to robbed-bit signaling, which the GP comment claimed.

Seems like the article failed to address the architectural reason why any of these details were relevant. A modem is a point-to-point communicating device and the signal has to be carried between two arbitrary points on the telephone network. DSL isn't really fundamentally different from a 56k, but the architecture is superior: DSL only goes to the other end of a wire, then the encapsulated IP traffic is forwarded elsewhere. 56k hit a wall because circuit switching has fundamental disadvantages. Packet switching allowed us to get past that.
56k was not relevant for point to point communicating between arbitrary points on the network though. 56kbps dial-up worked in an asymmetric fashion with a fully digitally connected modem on one end (eg the ISP). Station to station analog modem standards capped out at 33.6k.

> DSL isn't really fundamentally different from a 56k

There's a great deal of additional integrated digital signal processing to make DSL work that was too costly for consumer modems at the time. I wouldn't agree with this assessment. And other than operating on phone lines for last mile it is completely different on all the layers and uses completely different equipment.

> 56k hit a wall because circuit switching has fundamental disadvantages. Packet switching allowed us to get past that.

There were circuit switched networks far faster than 56k, so not sure this had much to do with any inherent limitation.

Packet switching has obvious advantages for network utilization and was a necessary evolution but I don't think it is relevant to any 56k limit or the revolution in DSP that make multi-megabit over copper pairs possible.

As you said, the DSP revolution was not scientific it was economic. They always knew how to do it, for decades, but it was unholy expensive. VLSI economically enabled DSL but it was a thing that they knew they wanted to do, and knew how to do, for decades. DSL technology was perfected before the 56K modem was even invented.
> They always knew how to do it, for decades

Unless we're limiting to the purely theoretical this is quite the hyperbole and in that case applies equally well to the 56k modem.

Size and heat are also factors. The process nodes did not exist in the 70s and early 80s to produce the integrated circuits necessary. VLSI technically enabled DSL.

The idea that somehow the difference between 1960s integration and 1990s is "purely economic" is pretty silly. If only they threw trillions of dollars more into research in the 60s would we have had the Intel Pentium then rather than 30 years later, maybe, but that is a useless line of reasoning. Someone has to actually do the "science".

You need to actually design and produce a suitable line card equivalent for every subscriber that will support DSL speeds without taking up the space of an airport for it and the cooling. That didn't exist for decades before DSL was rolled out (which started barely a decade after it was patented).

> DSL technology was perfected before the 56K modem was even invented.

Considering that DSL standards continued to evolve after the 56K modem was obsolete this is also hyperbole.

The other thing not yet mentioned which is pretty fundamental is that DSL eschews the 3.3khz bandwidth of POTS.

I mentioned this article to my retired AT&T engineer wife, and she blurted out "Robbed-bit signaling!"

https://en.wikipedia.org/wiki/Robbed-bit_signaling

Unrelated, but I highly recommend anyone visiting Seattle check out the Connections Museum, open on Sundays only. It has several different genuine analogue and early digital telephone exchange frames saved from being scrapped from genuine telephone exchanges. They turn them on and you can actually call from one phone to another inside the museum. The museum itself actually shares a building with a real telephone exchange. Lots of old books, technical journals and schematics too.

I just thought to post this since when I visited in September, some actual retired telecoms engineers were part of the tour group. One had been involved in the development of submarine cable technology.

Technically only the not yet functional DMS-10 is digital, everything else is analog. The 3ESS is a stored program, computer controlled analog switch - it uses the same remreed technology the 1AESS used to set up call links.

Out of all of those however, panel is my favorite however, it sounds amazing to listen to, both the equipment and what the line sounds like. A call between a panel and the number 1 xbar sounds amazing, nothing quite sounds like revertive pulse signaling.

Interestingly enough, there were three switches made that used RP internally - Panel, 7A Rotary and 1XBAR - and if you go find video of the 7A Rotary, you'll see it sounds almost exactly like panel, because the unique sounds of the rotary sequence switches both exchanges use.

Is the fact that the museum isn't available 85% or the week intentional irony or something?
It's all unpaid volunteers, and I think the museum is free if i recall correctly
I will second this. It's super cool and the volunteers there love showing people stuff and have lots of enthusiasm for it
That was great. Never knew exactly where the 56k number came from.

When 56k modems first came out I was able to get full speed, and it was a great upgrade. Then we moved and I could never pass 28.8 or so.

Turns out in their infinite wisdom in the new development we moved to the phone company divided things up even more so they could get two lines out of what should have been one. 28 + 28 = 56.

I don’t know if they were using some sort of compression or something so that it wasn’t audible on voice calls but it meant a modem was capped forever.

The wait for cable internet was interminable (it came before DSL).

Usually this meant the new neighborhood was put behind a subscriber loop carrier (SLC) which added an extra analog/digital conversion. Voice calls were getting digitized locally, sent across a T1 (only 4 wires needed, instead of 96-192), and back to analog to the normal frame at the CO. The effect of this was the telltale sign of carrier speeds only hitting 26,400 bps.
That’s basically the kind of thing I suspected. Thanks!

I wonder if that config screwed them when it came time to try to sell DSL. It still wasn’t available years later when I moved out.

This brings back a lot of memories, but I think what I lament the most is that this was really the end of American soup-to-nuts engineering in telecom. At the end of the 56k production and the start of G.Lite DSL, all this engineering started going to China to save money. Long gone are the days of Radio Shack and companies EE's designing, prototyping, testing, and manufacturing electronics. Sad.
No mention of dual speed models like Diamond, which would use two 56k lines simultaneously?
That could even be done with two completely separate modems.
Not really, as with using something like the diamond that was hidden by the driver.
Indeed, PPP has a multilink feature which an bond packets from multiple modems into a single bitstream. Both the client (your machine - Windows 98 could do it) and your ISP needed to support it.

I remember trying this a few times while at my parents' store. My dad would tell me which phone line I could use that day - either the dedicated line used to process credit cards (if they were closed), or a spare line off the PBX. But occasionally, I was allowed the use of both - and luckily had a pair of PCMCIA modems with the dongles in different places - and could get speeds well above 56k.

Diamond called theirs 'shotgun technology' iirc. I used a pair of USR external modems cobbled into a shotgun configuration via a linux proxy to manage our internet connection, but we got DSL shortly after (and surprisingly early for the rural location we were in).
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This article glances at, then misses the fundamental technical reason why modems topped out at ~ 56kbps: that’s really all the bandwidth that is available on a POTS line, due to the bandpass filter, the ADC on the other end, companding, and engineering practices that led the Bells to maintain their lines to the standards of an analog voice conversation.

The robbed-bit signaling thing is really a red herring: it was a problem, but not THE problem. At the time analog 56kbps modems were popular, it was already possible to negotiate 64kbps/8-bit clean DS0 channels over T1 — you just needed a PRI or an inter-machine trunk to do so.

In fact, if you were an ISP at the time, you generally needed those modems connected to T1 PRIs or IMTs anyway to support your ISDN customers economically. (My memory may be getting fuzzy on this, but I also remember that certain access concentrators with k56/v.90 digital modems would only negotiate the higher analog speeds on a PRI or IMT bearer channel.)

What there was absolutely no appetite to do, on the part of the voice carriers, was beef up the bandwidth available on POTS lines by developing new ADCs, getting rid of companding, or engaging in labor-intensive “facilities grooming”[0] for a POTS subscriber, in the way they routinely did for T1[1] circuits.

0 - Telcos call their lines and equipment “facilities.” Grooming, in the context of outside plant (telco terminology for the physical cabling that goes to subscribers) means to select wire pairs that exhibit good noise and echo characteristics and to remove elements, like poor splices and bridge taps, that impede performance.

1 - T1s, unless delivered to a customer via an optical transport network, use the same copper lines as analog POTS lines. Originally, T1s required two pairs (four wires). This eventually was replaced with HDSL4 (two pairs, but better distance and repeater characteristics,) then HDSL2 (single pair.) As the names suggest, the encoding used was a DSL variant.

And even for 56kbps, you need to have the ISP end talk digitally to the telco, so that you don't get the noise (including from the DAC) of the local loop on the ISP end. That's really what pushes the SNR far enough down to make it work (and why the uplink is only 33.6kbps; I guess they didn't want to try to make a separate modulation for that direction).
The article mentioned using an 8bit ADC. Could a 16bit ADC be used on BOTH sides and achieve 112kbps?
No because you still have to modulate the signal to get it to/from a house, and modulation schemes are where you squeeze maximum bits per second into available analog bandwidth within the limits imposed by Claude Shannon.

The article didn't talk about modulation schemes and I wish it had.

Sure, with other changes. You would still have to:

* Select (or repair) “good” pairs that didn’t have poor echo, impedance, noise, etc. characteristics.

* Not compand the resulting PCM sample with mu/alaw companding.

* Provide an atomic bearer channel from the telephone switch to the ISP that was at least 112kbps.

* Develop a modem encoding scheme that could take advantage of the extra bandwidth.

At this point, you’ve reinvented a really crappy version of DSL that could be user-signaled to call different networks (i.e., phone numbers.)

The other option, the one that people selected, was to use the copper facilities but bypass the phone switch and its associated audio and in-band signaling shenanigans. That was/is xDSL.

When I was in highschool I lived in a rural town of about 7000 people that had an analog telephone exchange. I read about the bandwidth limitations, and a friend of mine and I decided to test them over a local and long distance call. The long distance one cut out pretty much exactly at the frequency the spec said it should, but the local one could transmit and receive much higher frequencies, presumably because it had its own circuit and wasn't multiplexed with other ones. (That led to a lot of unrealized fantasies about creating a homemade super modem for local connections.)
Assuming the local call wasn’t on a party line, your lines were probably served by an analog switch or maybe on the same line card of something like a DMS-100. What you described wouldn’t work on “modern” digital switch.
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Here is a much shorter explanation. PSTN voice calls go over 64 kbps digital links (e.g. G.711 uLaw codec, 8 kHz sample rate).

56 kbps pushes close to the theoretically available channel bandwidth.

That's all there is to it: information coding theory.

To get more than around 56 kbps from modems, you would need more fidelity from the underlying lines: a wider-band, lower noise pure copper end-to-end connection, or higher bitrate codecs.

I was never able to exceed 24kb/s with my "56k" modem. I came to find out that the phone company (in Austin TX) was using a single pair to service more than one customer in my apartment complex. Naturally, whatever piece of equipment they used to accomplish this stymied faster modem speeds.

I finally installed an ISDN. That was delightful. Not only did it allow me to have two lines - one for voice and one for data - the netgear RT-338 ISDN router automatically dialed my ISP instantaneously. It felt like I was always connected because I didn't have to wait for a modem handshake. Speeds were more than twice as fast as what I could get with my analog modem. However, by far the MOST IMPORTANT thing (and mostly the reason I installed the ISDN in the first place) is that my latency took a nosedive allowing me to become an LPB with a 50ms ping time on QuakeWorld. >:-D

(Shoutout to Charlie S. from OuterNet, Austin's best ISP in the 90's)

What is an LPB?
Low Ping Bastard
Back in the day LPB was someone with low pings (remember dial up was 150 to 300ms sometimes) and they'd have an upper hand on games before they were "unlagged" with prediction code.
A common lament among the dead 15 years ago in real time online gaming...low ping bastard/bitch, basically just saying the only reason you got the kill is because your ping is 60ms and mine is 250ms.
I worked on ISDN drivers and firmware at a job back in the late 1990s. One of the optimizations I implemented eliminated a memory copy by the 68302 which improved ping times from ~30ms to ~16ms. The good old 68000 is not exactly the fastest at memory copies...
Seems like an oversight that the extra stuff the 68302 added wouldn't have been a DMA block copy or something.
I am, no doubt, a beneficiary of your work. You have my sincere gratitude! :-)
You likely had something called a 'pair gain' installed - which worked much like DSL, by using a high frequency FM carrier over the audio frequencies to provide a second phone line on the same pair. These things were largely gone by the mid 90's - and were not that common in the first place.
They plagued Australian homes up through the late 2000's unfortunately

Fucking Telstra

Yup, we built a new house in Australia in 2001 and thought we were being so forward thinking by getting a 2nd phone line for the modem/fax. Of course it ended up being done using a pair gain and we were stuck at 33.6k.
Back in the late 90s friend had ISDN installed at his apartment and it was glorious. Compared to dialup it was like high speed internet. We used some Mac app that basically gave you access to all the cracked software you could have ever wanted.
You could also bond the two channels together for a 128K connection - installed Linux to get the bonding to work on my ISDN card as Windows 3.1 For Workgroups knew nothing about it.
My understanding from discussions about modems in the mid 1990s was that the bandwidth limit for POTS-to-POTS modems was about 36kbit/s, because the signal has to go DAC (modem) -> ADC (telco) -> DAC (telco) -> ADC (modem), and the modems at either end are not synchronized with the telco’s digital path.

The thing that allowed speeds to increase to 56kbit/s was digital connections at the ISP end: typically the ISP would get a T1 or E1 circuit fed into a box that would act as 24 modems, but purely digital and synchronized with the telco. So the signal now went Ascend MAX (isp) -> T1 (telco) -> DAC (telco) -> ADC (modem), providing much less quantization noise.

Boils down to the fact that a phone line to a house was built with a a certain amount of bandwidth for a human voice, implemented with a lowpass filter of 4 kHz. But the article doesn’t explain or show why the magic 4 kHz number was chosen.
There are no filters and cable is not BW limited, otherwise ADSL wouldnt work on same wiring.
See the section Long, long ago
“Ultimately, they settled on approximately 3.2 kHz.” doesn’t really explain who made this decision, when, or why.

All we get is “Long ago, when the phone networks were still completely analog, when the first real phone networks were being built, the engineers that were designing them faced a decision.” Who were those engineers? What company? How did they test what would be adequate bandwidth?

Ohhhh, is _this_ where the 7-bit transfer settings came from? That always seemed a weird number to me (unless a bit was instead repurposed as a parity bit).
On second though, probably not; the same 7/8 bit settings plus parity and stop are available on non-POTS-dependent serial ports as well.
Whatever the wire protocols were that were responsible, the fact that UUNet exposed it is why we all had to deal with it.
TL/DR The standard for digital phone lines is (was) 7 bit samples multiplied at 8,000 samples per second.

7 * 8000 = 56,000 = 56k

Had ISDN in Europe at home in the late 90s.

How common was it in the US and elsewhere?

So you are from Germany? :) nobody else invested in ISDN. Whats more US ISDN was incompatible and incumbent telcos fought hard against implementing anything allowing users faster speeds without bigger bills https://yarchive.net/phone/isdn_politics.html
Nope: Portugal B-)

Back in the day, our incumbent telco was quite cutting edge technologically.