The article is not actually explaining it, merely obliquely hinting at it.

If you want to look up an IP address and get a server name (i.e. the reverse of a normal DNS lookup where you look up a name and get a DNS record containing an IP address), you do a “reverse” DNS lookup. Since the DNS protocol does not support this operation directly, this is enabled by a somewhat ugly hack, namely the transformation of the IP address into a name, which you can then look up and get a DNS record containing a name.

For example:

foo.example.com. A 192.0.2.3

is a name with an attached DNS record containing an IP address. To do a reverse lookup, we transform the address into the name “3.2.0.192.in-addr.arpa”, and look up not the A record (containing an address) for that name, but the PTR record, containing a name:

3.2.0.192.in-addr.arpa. PTR foo.example.com.

You can think of DNS record types (A/PTR/MX/etc.) as types or classes in a programming language. What data a DNS record can contain, and what that data should mean, is controlled by the record type.

This is the essence of it. There are always various minutiae one could get into, like the fact that IPv6 has a separate procedure to transform addresses into names, and, just as a name can have more than one address, the lookup of one address can result in more than one name.

To directly answer your questions:

• “Timely inversion” is not used as a technical term, it’s just a cute way of referencing the transformation procedure for an IP address into a name able to being looked up in the DNS.

• A “zone” is technically a collection of DNS records, restricted to a particular domain or subdomain. For example, the zone for “example.com” would normally contain all DNS records for not only “example.com”, but also the records for the names “www.example.com” and “foo.example.com”. The purpose of zones is that a zone is the mechanism by which the responsibility to respond to queries about DNS data is delegated to DNS servers. If you want questions about some names to be answered by some special DNS servers, you have to put those names in a separate zone. This is unusual but not unheard of – the other day¹ Cloudflare had problems related to the fact that they have actually delegated “www.cloudflare.com” to separate name servers from the name servers which are authoritative for the “cloudflare.com” zone. I.e. “www.cloudflare.com” is its own zone. Note however that this is unusual. You can tell if something is its own zone by the presence of an SOA record (and NS records) on the name; www.example.com does not have an SOA record, but www.cloudflare.com does.

• “Public” in this context simply means “for use by the public” or “publicly accessible”. And it’s strictly speaking a DNS resolver, not an authoritative DNS server for any specific zone or zones.

• The use of the word “hop” is, I believe, a further indication of the belief by the author in the stack-of-resolvers model, but this is a false belief. What actually happens is that a resolver asks one authoritative server (starting with the root servers), receives as a reply a list of better servers to ask, and the resolver asks those authoritative servers in turn. This is the actual “hop” referred to in reality.

• A “block” of IP addresses is a contiguous span of IP addresses. IP addresses are not allocated to organizations or ISPs around the world randomly or individually, but are instead delegated into as large and as contiguous spans as is possible. This is because the routing tables in routers are composed of lists
of spans of IP addresses, and it is vital to minimize these lists, because if the core routers run out of memory, no more addresses can be routed.

1. https://news.ycombinator.com/item?id=19641155