Read "From word to sentence. A computational algebraic approach to grammar" by J. Lambek. Your university library should have a copy, if not press the issue to your librarian.
Start though with Smullyan's "To mock a mockingbird".
These suggestions reflect my taste. Art is a language, so understand how language is studied and use it to approach art.
If you're serious about the art part, make sure you make art, or at least dissect art you like using the formal tools you're introduced to.
Don't really understand the technique, but would like your thoughts on if it's possible to give a Penrose tile set as a seed and see if aperiodic order is generated.
I'm not sure, but I think that Penrose tilesets are what I call "easy": you can't run into a situation where you can't place a new tile. It would be great if someone here could confirm or deny this.
So if this is the case, then Penrose tilesets are not interesting to WFC, because you can produce arbitrary tilings with much simpler algorithms.
Right now though WFC is only working with square tiles, but it's not hard to generalize it to arbitrary shapes. Paul F. Harrison made a tiling program that supports hex tiles: http://logarithmic.net/pfh/ghost-diagrams See also the relevant paragraph in the readme (just search the word "easy").
Penrose tiles are "easy" on an unbounded canvas, but I'm pretty sure they're a 100%-probable "contradiction" (because they're aperiodic) on a bounded toroidal canvas.
I think you're right about Penrose tiles being easy. One could, however, potentially use this with polygonal tiles to find their Heesch numbers and maybe even make some advancements in solving some of the many unsolved problems associated with Heesch tiling.
Maybe it could be interesting to place Penrose tiles with the simple algorithm, but color them with your algorithm just like you're currently coloring squares.
Oracle claims that one of their CPUs is equivalent to two vCPUs. If this is true, then their rack rate is a little less than EC2 per instance hour, and block storage looks like it's half the cost.
But with Amazon, all my instances are either reserved or spot, so I'm paying far less than rack rate.
It all comes down to price per performance. You can't tell anything from these headline numbers. But since we're prohibited from disclosing results of any performance testing, there's no easy way to know.
> I'm really fascinated by the idea that physics might be completed in my lifetime.
That's an unfortunate thought to be fascinated by. You should study some physics, instead of reading popular articles about it, or even what pre-eminent physicists say about their work.
I can simply illustrate the situation by saying if a question Q eventually provides answer A, the a new question Q' arises: why A?
You can tell yourself "it doesn't matter" but quite frankly, at the human scale, physics is already a done deal.
Which only further illustrates why your thought is a bit naïve.
I certainly could read more, but I do have a degree in physics and philosophy.
Certainly there will always be questions like: why something rather than nothing?
However, if you have a (relatively) simple set of rules, like the standard model, which work in every context and (in principle) predicts all observable phenomena, it does seem like you've crossed some kind of threshold. An intellectual threshold - as you say it has limited practical implications. It would be a watershed like observing alien bacteria. You're not going to do much with it, but it seems to put you in touch with the cosmic.
There might still be lots of emergent phenomena we don't fully understand, but we could still be confident that the underlying physics is totally understood. An example of this might be the Navier–Stokes equation - we don't fully understand it, but I don't think many people think that a complete understanding of why nature obeys this law will lead to any fundamentally new physics.
It's certainly possible it's just questions all the way down, perhaps smaller and smaller structures will be observable at higher energies, but it's an open question.
Another option is that we're close to bottoming out all of the complexity - and that's the possibility I find fascinating.
I'm not envisioning a time when every possible question has been answered, instead I'm thinking of a time when any questions about fundamental physics will either have been answered or we can be satisfied that no empirical evidence will answer them.
QM may already have hit this knowledge barrier. We know from Bell inequities there are no hidden variables, there is simply no empirical way to predict with certainty the state of a quantum system. We've hit the edge of the knowable.
"Whereof one cannot speak, thereof one must be silent" - as Wittgenstein might have said about the situation.
In defence of throwaway000002, when I talk with physicists about the idea that physics might be completed they mostly don't think it's likely. I don't think they subscribe to the questions all the way down model, instead they think we have a long way to go yet - though I think most researchers don't have clearly formed views on the subject.
"An example of this might be the Navier–Stokes equation - we don't fully understand it"
We don't fully understand the flow of fluids, whether or not the NS equation is a good model for them. That the theory of elementary particles is more "fundamental" than the theory of turbulence is one point of view, not unreasonable. But another way to look at it is: the science of fluid flows has its own fundamentals, that are true whether or not a particular fluid is made of particles.
I guess what I should have realized, and is my mistake, is that the idea of physics being completed is actually a philosophical issue, and given different philosophical bases you can arrive at different conclusions.
Ultimately, however, it's up to physicists to determine when their work is done, and as you say, they don't think it likely ever will be.
For me things like turbulence and critical phenomena are the more interesting questions out there, because they're still very much human-scale, and our only excuse is that we can't compute at the scale required to verify results, the calculations are just too fantastically large.
I'm sorry I know nothing about core.logic. However, if you are familiar with Prolog, and sufficiently motivated to work through cited references, this paper is a good place to start. [1]
Never met a whole -3 pizzas, nor a whole 0 pizzas for that matter.
That should be enough for you to deduce what I believe whole numbers are.
I should add, for a mathematical audience, I'd be careful, because of possible confusion, and insist on saying positive integers, and non-negative integers in the case of what I'd call the natural numbers.
Pragmatically I believe you are correct. I think negative whole numbers and zero are also a subset of "whole numbers" along with positive whole numbers.
He comments on the video linking to two papers on arXiv which relate to the material in the lecture: https://arxiv.org/abs/1608.08225 and https://arxiv.org/abs/1606.06737