Meanwhile over in the mechanical engineering department, someone is complaining that they have to learn physics when they just wanted to build cool cars.
I took engineering for a year before I realized it had nothing to do with trains.
Yeah that’s why you go into physical training. That physically has trains… Right?
I wonder how many in that class will ever need to think about multitape Turing machines ever again.
Never used a Turing machine, but I have a project that generates NFAs and converts them to DFAs so they run faster.
The point of these lectures is mostly not to teach how to work with Turing machines, it is to understand the theoretical limits of computers. The Turing machine is just a simple to describe and well-studied tool used to explore that.
For example, are there things there that cannot be computed on a computer, no matter for how long it computes? What about if the computer is able to make guesses along the way, can it compute more? Because of this comic, no — it would only be a lot faster.
Arguably, many programmers can do their job even without knowing any of that. But it certainly helps with seeing the big picture.
Arguably, a much more important thing for the students to learn is the limits of humans. The limits of the computer will never be a problem for 99% of these students or they’ll just learn on the job the types of problems they’re good at solving and the ones that aren’t.
The limits of computers would be the same as the limits for humans. We have no reason to think the human brain has a stronger computation power than a Turing machine.
So, in a way, learning about the limits of computers is the exact same as learning the limits of humans.
But also, learning what the limits of computers are is absolutely relevant. You get asked to create an algorithm for a problem and its useful to be able to figure out whether it actually is solvable, or how fast it theoretically can be. Avoids wasting everyone’s time trying to build an infinite loop detector.
Two govt spooks are hunting a dangerous fugitive who is also a humanities graduate. He escapes into a sprawling maze of tunnels. “It’s hopeless,” one of the spooks says. But the other simply says, “Watch.” then proclaims loudly, “studying linear algebra is important because of its use in stochastic processes and image manipulation.” Before he finishes the sentence, the fugitive emerges back out the tunnel and shouts, “but what’s even more important --” and is immediately knocked unconscious and taken for questioning
I didn’t go to university, because I wanted to learn useful stuff, but because I’m curiousity driven. There is so much cool stuff and it’s very cool to learn it. That’s the point of university that it prepares you for a scientific career where the ultimate goal is knowledge not profit maximisation (super idealistically).
Talking about Turing Machines it’s such a fun concept. People use this to build computers out of everything - like really - it became a Sport by this point. When the last Zelda was Released the first question for many was, if they can build a computer inside it.
Does it serve a practical purpose? At the end of the day 99% of the time the answer will be no, we have computing machines built from transistors that are the fastest we know of, lets just use these.
But 1% of the time people recognize something useful… hey we now found out in principle one can build computers from quantum particles… we found an algorithm that could beat classical computers in a certain task… we found a way to actually do this in reality, but it’s more proof of concept (15 = 5×3)… and so on
Ram is literally just the tape. Modern computers are just multitape turing machines, albeit the tape ends at some point.
4 years later: “this button is the wrong color. fix it ASAP”
Since when were Turing machines ever nondeterministic?
Wait till you hear about oracle machines. They can solve any problem, even the halting problem.
(It’s just another mathematical construct that you can do cool things with to prove certain things)
Thanks for the fun rabbit hole. They can’t really solve the halting problem though, you can make an oracle solve the halting problem for a turning machine but not for itself. Then of course you can make another oracle machine that solves the halting problem for that oracle machine, and so on and so forth, but an oracle machine can never solve its own halting problem.
Nondeterministic turing machines are the same kind of impossible theoretical automaton as an NFA. They can theoretically solve NP problems.
It’s been a long long time since I touched this but I’m still almost positive deterministic machines can solve everything in NP already.
