One day, you find an unmarked cardboard box sitting on your front porch.
On top of the box is a single note:
“Open me.”
You take the box inside and open it, to find what appears to be a small black laptop nestled between old newspaper clippings. There are no identifying features to the laptop, other than its sleek blackness and small size. When you open the laptop, instead of being greeted with any sort of familiar welcome screen, there is simply text, displayed in white over a black background. The text says the following:
“Welcome to the next stage of the human experiment.
I have have been watching your kind for a while now, and I believe that you are now ready. I have decided to entrust this machine to your care. Do not attempt to figure out how this machine performs its calculations, as uninformed tampering may result in the deletion of your universe.
The item you are now holding is what your mathematicians would call a Universal Turing Machine, similar in many ways to your typical computer. This machine, however, is significantly different from any other currently existent on Earth.
After reading this message, press any button to reveal two input fields stacked on top of each other, and one output field at the bottom. All input fields can be fed any required data from the internet, or can be entered into directly through the keyboard. Input lengths of any finite size are acceptable.
The top input field will accept and is capable of automatically running the intended code of any language or format that is capable of being run on a standard Universal Turing Machine.
That input will then be translated into the necessary binary code to be computable by the internal “black box” computer.
The bottom input field must be fed a finite natural number of any length, which will determine the number of computations per second. Do not worry about exceeding the speed of light, or of going past any other finite limit; the computation itself is performed in a “bubble universe” with different physical laws than your own, and is capable of computing at absolutely any positive finite speed relative to your universe.
The output field will display the output of your calculations, if any exist, after exactly one minute of computation relative to you.
Do with this machine as you will.
Wishing you the best,
God.”
Your finger hovers over the keyboard.
What will you do with this marvelous machine? What can you do?
What happens next is up to you.
>________________________________
NOTE FROM ME, OUTSIDE OF THE STORY: I wrote this trying to work out my thoughts on what might be possible with a machine with unlimited but finite computing power. I was going to continue the story, but found that I honestly couldn't think of all that many interesting things that would be possible to do with such a machine, that couldn't already be done now. As such, I'm turning this question public, hoping that anyone reading this might have some interesting ideas that I haven't thought of.
I really like your first three ideas, and would definitely consider doing that if I was in this position (although now that I'm thinking about it, I wouldn't want to accidentally alert any powerful actors against me so early on in my journey, for fear of getting the laptop confiscated/stolen, so I'd be very careful before doing anything that could potentially be traced back to me online). :)
As for "calculating out how the human body works," I'm not sure it would be that simple to pull off, at least not at first. Taking your statement literally would mean having the laptop simulate an entire human, brain and all, which is discussed later, so for practical purposes I'm assuming what you meant by that is calculating how a typical human cell works; say, a single neuron. You could definitely solve protein folding and probably simulate most chemical interactions fairly trivially, as long as you can express the physics involved as finitely computable functions (which I'm not sure has been proven possible for all of chemistry/quantum mechanics, though I may be mistaken on that). However, in order to figure out how things actually work inside of an entire human cell, you'll not only need to be able to formally express physics and chemistry, but will also need to know what that cell is chemically composed of in the first place (in order to simulate it properly and not just be given fallible guesses by the computer). In order to make this work, you either already have a pretty much complete formal understanding of a human cell, or have figured out a way to specify your goal so precisely that only a manageable number of valid possibilities are given using the known rules of physics, which seems incredibly hard to do, if not totally impossible with our current tools.
More broadly, the same problem comes up when trying to write a program simulating the human brain. The best neurosurgeons in the world are still in the dark about how most of the brain's functions are actually performed, and currently have to make do with incredibly generalized and high-level assumptions. In order to simulate a human brain (rather than "simply" create a generalized non-human AI), you would need a level of knowledge about our own inner workings that is not currently available. Thankfully, you might not need to know the exact workings of an adult human brain to make one, but without that knowledge at the very least you will need to be able to fully simulate the growth of an embryonic brain, and be able to properly "feed" it appropriate outside stimulation, which could plausibly be reduced to the problem of perfectly simulating the working of a single embryonic cell, then letting the simulation proceed smoothly from there.
Regardless, both goals reduce to the general problem that in order to simulate a complex system, we must already have at least some amount of "base knowledge" of that system, or to put it more precisely, we must know at least as much information as is contained in its Kolmogorov complexity. (please correct me if I'm wrong about this btw, I'm fairly confident in saying this, but I may have messed up somewhere due to the complexity (heh) of the issue)
That's what I think makes this hypothetical so interesting to me—the thought that even with unbounded finite computational abilities, some of our most important problems would still require a tremendous amount of physical fieldwork, and would certainly still require thinking intelligently about how to code for the solutions we want.