As someone with a high energy theory background but has only read titles/headlines about this time crystal business, can you give a precise TL;DR on what a time crystal is?
Let me know if my synopsis above helps, or if you have any specific questions from a high-energy theory point of view. Given your background, you might appreciate that we ran many simulations, to characterize the sample, understand our early results, and build our echo sequence.
Love the idea - looks like a well-thought-out and much needed abstraction. The way I’d pitch it is that it allows one to create UI in a completely declarative and stateless manner.
To each their own, but I’d hate the firefox-style scrolling tabs UI suggested by the article.
1. I don’t want to be surprised to find some old tab hidden by the scroll.
2. Id like to be able to close tabs without first scrolling to it.
3. If I control tab past the last tab does it scroll to the first tab? Id then have to scroll back to find my latest tabs?
4. Again, personal preference, but if I had 50 tabs open and wanted to go back to the 24th one, id rather navigate to it through a search engine or bookmarks, rather than trying to locate that particular tab.
You can see all open Firefox tabs, including titles, with a button to the right of the tabs.
You can move a tab to the right with ctrl-tab and back to the left with ctrl-shift-tab. If you go too far, just ctrl-shift-tab.
How would you go to the 24th tab in Chrome, if no title is visible? With Firefox, you can use the button to the right of the tabs to view a list of all tabs, with titles, and find your tab from there.
Another useful tool is onetab. When you have too many tabs, send them into onetab and reopen them as you need them.
Regarding point 3, you do know that holding shift allows you to go back when ctrl tabbing, right?
I've never had an issue with old tabs being hidden. Although in general I rarely have more than 8 or so open in a window since I'll generally have multiple windows open across several workspaces
This is excellent. Amazing (equation + picture)/text ratio.
Complaint: you don't define your notion of "space". In chapter 1 it's some informal notion that you use to motivate the definition of a set (??), in 1.3 and 1.4 it becomes clear by space you mean "set". Then later you start talking about dimension of spaces, implying not only do they come with a topology now they have a well defined dimension, so a locally Euclidean Hausdorff space or something - but maybe you just mean R^n.
Comment for other commentators in this thread: not all expositions is tailored for the masses. A piece of pedagogical literature that does not appeal to your background doesn't mean it's not good. There's a very clear need for exposition on basic structures in probability theory and this fits there.
It's like the definition of set defined here should really be a subset, and the definition of space should be a set. Maybe just say a set is any collection of objects?
- It's not clear to me what distinguishes your picture for a convolution layer from any other tensor of the same shape. Would be nice to visualize the filters/kernels somehow.
Here's a generalization that yields an infinite family of similar observations.
Step 1. Take any "torus knot with n marked points": which for our purposes will mean homeomorphism classes of embeddings from a circle with n marked points, to the torus.
Step 2. Draw it on paper.
In the case of the Coltrane drawing, n = (5 octaves * 13 notes per octive) = 65. The author exhibited 3 non-homeomrphic embeddings of this circle into the torus in the three images below the protractor picture. In particular these are embeddings generated by iterated Dehn twists on the unknot. You can classify them by winding number.
The image right below the aforementioned ones also shows an embedding of a circle with marked points into the torus if we choose to identify the 2 'c's. This time there's only 13 marked points. This suggests the following. To a circle with marked points, one can associate a canonical family, labelled by integers, of circles with marked points as follows: take any covering map of the circle, and declare the union of the fibers over the marked points to be the new marked points. In the case of the music scale analogy, we take the circle with 13 marked points, and this in particular gives a family of circles with 13 * k marked points for any positive integer k, and the musical interpretation is that k is how many octave one chooses to have. In the images mentioned above k = 3 and k = 1 are exhibited.
There's a simple further generalization of all this: we can replace the torus with any topological space. For example, doing this on a higher genus surface or a non-orientable surface would both yield probably interesting-looking diagrams.
