Superscience is a special TL that is outside the normal GURPS TL scale.
These are technologies that violate our current understanding of physical laws (relativity, conservation of energy, etc.) For this reason any TL assigned to them is arbitrary.
This is why broadcast power has two totally different TLs: TL6^ (Infinite Worlds, Gernsback) and TL10^ (Ultra-Tech).
The problem is the Superscience category didn't exist in 3e and so books like GURPS Steampunk and Steamtech use TL(5+x) rather then TL5^ or TL(5+1)^ making it difficult to figure out just where some of the borderline cases reside.
For example, the Nautilus of 20,000 Leagues Under the Sea (advanced submarine, GURPS Steampunk pg 80) uses cinematic sodium/mercury batteries which it much return to base to recharge. In GURPS 3e advanced submarine was listed TL(5+1) but it is unclear if under GURPS 4e it would still be that TL. Moreover some people have retconned the Nautilus to having nuclear power (TL7) making advanced submarine TL(5+2) or a TL7 oddball. This means that depending on how one view advanced submarine it could be TL5^, TL(5+1), or TL7 (or should that be TL(5+2)^?).
Examples of inconstancies and problemsEdit
Compounding matters is the fact that the superscience category isn't used constantly.
Merlin-1: TL(7+1) magitech (should be TL7^ or TL(7+1)^ due to the magic)
Yrth (GURPS Banestorm) as it fails to explain why that world isn't kicking around TL5-6^ thanks to magic and continual influx of people from Homeline and elsewhere.
Shape metal combined with coal and water could easily produce steam power which would totally change the balance of power. Many other spells could be in this manner to produce TL5-6 items, and you can't hand wave that with the idea that the mages wouldn't allow such tech because it would threaten their power.
Anyone who has looked at the Gilded Age can see how rubbish that idea is as the Robber Barons had great amounts of political power with no magic. Yrth mages would gain even more power so unless they are idiots something else (or someone else) is slowing technological development on Yrth.
Alfheim: TL3+magic rather then TL3^
Azoth-4: China is at TL2^ with everybody else at the TLs they were in 1010.
Azoth-7: TL(4+2) (TL4^ space and weapons). This produces really silly results. Astronomy on the ground is TL(4+2) in Azoth-7 but TL4^ on a space ship which incurs penalties when going from one to the other.
Britannica-5 (GURPS Infinite Worlds-Lost Worlds pg 6) has antimatter bombs but is put at TL5^ rather then the TL10 that the Basic set says such technology is "normally" developed at.
In fact, Britannica-5 shows another aspect of superscience: much earlier development of technology that would "normally" happen far latter. So a TL7 computer that is somehow invented at TL4 would a TL4^ device not TL7. More over its Infinite World description is totally useless at figuring that the TL is: "Britannica-5 is a steampunk reality absorbed into Zone Green a decade ago." (that's it) Per GURPS Steampunk Britannica-5 would likely be called TL(5+1) rather then the TL5^ it did get.
"Falkenstein (Q4, current year 1873), a strange blend of sorcery and TL(5+1) technologies technologies has raised Bavaria to near-great power status; elves, dragons, and other nonhuman races abound. (See GURPS Castle Falkenstein for further details.)" (GURPS Infinite Worlds-Lost Worlds pg 6). Logically the TL should be TL(5+1)^ not just TL(5+1).
Jotunheim (GURPS Infinite Worlds-Lost Worlds pg 10): cosmic energy effectively replaces atomic power and it is called TL7^.
Muspellheim (GURPS Infinite Worlds-Lost Worlds pg 11) is a mixture of TL(6+3) and TL7^ thanks to reverse-engineering of UFO technology.
Roma Arcana (Rome-6) has magic all over the place and yet is TL2 rather then TL2^ or even TL(2+1)
Then there is the technology that didn't go anywhere but worked. For example the heavier than air steam powered flying machine of 1848...though flying would be generous. Hopping might be a better term. A better version appeared in 1874 but that was more a powered glider then what we would consider an aircraft. In 1890 there was another short flight by a steam powered aircraft, the 1894 flight of another steam powered aircraft had a trip of several hundred feet. It would be 1933 before Besler made a steam powered plane that actually flew. So is a heavier than air steam powered flying machine TL5^ or a TL(5+1) invention?