Identity in physics can be challenging to find. We’re given a narrow set of labels to choose from, typically theorist or experimentalist, and these can often be time-dependent as we progress in our careers. Throughout my time in the discipline, I’ve worked in experimental labs, theory groups, and more applied settings. Many times I’ve branded myself a theorist, perhaps more out of desire than measure; however, I’ve always wanted a more nuanced way of describing my work, myself, and developmental stage. Short answer: like most things we do, it depends on a clever choice of coordinates.
Three different classification systems (two 2D and one 1D) gathered from leading theorists, compiled. Measures features like preference for mathematical or intuitive tools, goals of analyzing existing models or constructing new ones, reliance on rigor, sophistication of computational tools, etc.
See full post for more, including XKCD-style visuals (because why not):
Recently had to reconcile multiple keys for similar git hosts, and found several posts that were nearly sufficient. Summarized the method that worked for me in terms of namespacing the ssh credentials, hope it’s useful if you find yourself in the same position!
Often in discussions about blackholes, the question arises of observer experience when falling into a blackhole. Due to the extreme tidal forces experienced along such a path, the observer would be stretched out - a process colloquially referred to as spaghettification. This week I would like to look at a happier use for spaghetti near blackholes. If an observer in a stable circular orbit around the supermassive blackhole at the center of our galaxy were to use spaghetti as a tether, how much spaghetti would be required? Restated, the Fermi-Problem question of interest this week is:
> How much spaghetti would be required to form the smallest stable circle around the supermassive blackhole at the center of the Milky Way?
Without giving away the numerical answer, the result is around 3 meals for everyone on Earth!
I first encountered a diagram of algebraic structures at the end of Jeevanjee's second chapter, "Vector Spaces", which elegantly summarizes the high-level differences in structure between sets, vector spaces, and inner product spaces.
I've attempted to augment this map along two dimensions: a structure dimension that aims to measure the number of attributes an algebraic object has, and a specificity dimension that measures the number of constraints placed on each attribute.
This is aimed primarily at mathematical physics, and is intended as a quick reference -- it's obviously incomplete and isn't a substitute for Hungerford, Lang, or [insert favorite algebra book].
I hope you find it as helpful as I did in making it!
I first encountered a diagram of algebraic structures at the end of Jeevanjee's second chapter, "Vector Spaces", which elegantly summarizes the high-level differences in structure between sets, vector spaces, and inner product spaces.
I've attempted to augment this map along two dimensions: a structure dimension that aims to measure the number of attributes an algebraic object has, and a specificity dimension that measures the number of constraints placed on each attribute.
This is aimed primarily at mathematical physics, and is intended as a quick reference -- it's obviously incomplete and isn't a substitute for Hungerford, Lang, or [insert favorite algebra book].
I hope you find it as helpful as I did in making it!
That's not how it's written in the post though. If you just swap out the "inertial mass" at the end and the "rest energy" somewhere in the middle it makes more sense:
> because photons have rest energy (=> kinetic energy) that can be viewed as mass in special relativity
> [...]
> impact the gravitational field despite having no inertial mass (=> rest mass)!
Speaking of "mass" in context of relativity is always a bit tricky. The term "inertial mass" for example is really saying something about how an object behaves under the influence of a force (F = ma), not how it behaves relativistically (that would be "relativistic mass", E = mc2).
Maybe you could write “because photons have energy that can be viewed as (relativistic) mass” then. Or maybe he did really refer to the “rest energy” of photons? That seems weird even for an experimentalist ;-)
I would also be interested in a "math for programmers" approach to deciphering formalism. I've studied a fair amount of linear algebra / differential geometry and could see how Python-definitions might help. I'm less familiar with other areas of mathematics
Slight nit-pick, but matrix multiplication is not exclusively a contraction, but rather a contraction on the tensor product of the two matrices. See the next paragraph for why this is concerning.
I find this notation great for simple applications, but potentially unwieldy for dim > 2. For instance, how would I represent the tensor (or outer) product of two matrices? the inputs would be two circles with two lines attached to each, the result would need to be a single circle with four lines attached. The natural attempt would be something like:
a - o -
/ /
| /
\ |
ab ---o---
| \
/ |
/ /
b - o -
But I suspect the above diagram isn't correct because there are no "open" indices at the end of this. Rather, this diagram seems to represent the contraction of a 4D tensor with 2, 2D tensors.
It seems we we would need a way of connecting circles without implying a contraction of a particular index.
Anyone know how to annotate the outer product of two matrices in this diagrammatic convention?
A tensor product of two matrices is just this, with 4 loose ends:
---A---
---B---
A_ab B_cd = (A⊗B)_acbd. If a,c=1...N then you can think of (ac) as being an index with N^2 possible values, which is what the double line now means... if you like, you may compact it a bit:
But how am I supposed to know that AB is one mathematical object here instead of the 2 separate objects A, B? My point is that there should be a graphical way other than "put them arbitrarily close" to link them together
I prefer your second notation, with the tensor product happening in parenthesis, but it kind of defeats the point of the graphical nature of the notation if we need to explictly write the tensor product I think..
Speaking as someone who uses this tensor notation quite a lot: putting multiple objects into the same diagram is what a tensor product is, and a great thing about the notation is that it reveals that a tensor product of two matrices is not an essential object in itself.
If you wish, you can draw a circle around A and B to "factor out" that part of the diagram as a sub tensor product. Here might be a way to show that matrix multiplication is both "tensor product then contract" and "function composition": https://imgur.com/tcCycYj.png (though I didn't give this gray-circle notation much thought).
Think about this: how is it in a product abcd of plain old numbers am I supposed to see the mathematical object ad without putting them arbitrarily close together? (Well, in standard notation, you do put them close together and write (ad)bc or something.)
The equations satisfied by tensor products are exactly those of drawing things next to each other. Look up Bob Coeckes Kindergarten Quantum Mechanics which was linked elsewhere here.
What you need is two parallel walls where lines can start and end. The rest is all fine.
Good point - I’ll repost without the “show”. I figured that it was a list of texts, each of which can be “tried out”, but if - as you suggest - the criterion really only applies to code, then I’ll change the post
Update: removed the “show” from the title - thanks for the policing (I don’t want to use hacker news improperly, I love this site)
It’s exactly what it says on the can - a list of my favorite texts. You can get the books anywhere, not sure what you’re angry about.
I’m in the process of reviewing each in depth, but haven’t gotten to many yet, though I do own all of them. I will post the individual reviews (the “content” I’m assuming you’re expecting, though I didn’t say was there), so stay tuned for those. Appreciate your feedback
I too am enamored with Hagoromo; however, I wasn't able to get any of the Japanese chalk. I have been using the South Korean produced Hagoromo and find it quite nice. How do you think the Japanese vs. South Korean produced chalks compare?
Good note about the microfiber! I'll have to try that. I've become increasingly frustrated with erasers. When it comes to washing the board, do you use a squeegee at all? I've found a sponge/squeegee combo to make cleaning quick.
A dimension of chalk usage that seems to be missing from your page - what do you think of chucks (holders)? Hagoromo chalk is quite wide (11mm) and it seems that most chalk holders are built for 9mm chalk. I use the Hagoromo branch chalk holders, they seem to have good grip. The other alternative I've found is to look for artist-oriented graphite or pastel holders.
I used to carry a bucket and sponge, then a squeegee, spray bottle, and paper towels. Now I just use a damp detailing towel (not wet enough to drip), and water from the nearest source down the hall. Sometimes one needs to clean the towel and make a second pass to obtain a board that looks newly installed, but generally no squeegee is needed.
Wrong person to ask about holders. I like gripping bare chalk; my hand is too forceful for a holder.
