joppy

38 ms·

361.
by joppy 8y ago
I fail to see how a category theory perspective is going to help with "grinding out" any interesting theorems about commutative rings, such as: - Every commutative ring has a maximal ideal. - The quotient of a commutative ring by
362.
by joppy 8y ago
Learning group in the abstract, followed quickly by many examples of groups, is in my own opinion the best way to learn about groups. But this isn't quite general -> specific, this is general -> example, example, example. I think
363.
by joppy 8y ago
The consistency with the underlying abelian group could be restated as "multiplication is bilinear, and has a unit", which is the correct perspective to take if you want to "upgrade" from the usual definition to the &quo
364.
by joppy 8y ago
I strongly disagree. From experience teaching category theory to undergraduates, it is totally obtuse before that have a large pool of examples on which to draw. In a very first course, students are still struggling to learn concepts from l
365.
by joppy 8y ago
Of course I'm not recommending learning ring theory without learning the (usual) definition of a ring. This is absolutely rigorous and useful, and immediately after you learn it you can start playing around with rings, and start provin
366.
by joppy 8y ago
I think this is a good point. I find the language of category theory an invaluable tool in my own understanding of abstract algebra, and universal properties are a large part of that. I think that a lot of undergraduate mathematicians could
367.
by joppy 8y ago
Knowing that a ring (in abstract algebra) is equivalently defined as "a monoid object in the category of abelian groups" is not going to help you with your first abstract algebra course. It makes things that are glaringly obvious
368.
by joppy 8y ago
And how many people are going to look through all the raw data you used and try to reproduce your results from it? And it's not even possible from that data to verify that the experimental setup that was producing the data in the first
369.
by joppy 8y ago
It's true that more open-access logbooks might improve things. But even if you had the logbook, you still wouldn't have the custom equipment, experimental apparatus, experimental subjects, and oversight throughout the experiment
370.
by joppy 8y ago
For sure, I would want to. But with how institutions currently asses and pay researchers, it would be detrimental to my career to take the time required to understand the change and update my own work, which might involve dredging up years-
371.
by joppy 8y ago
I don't think that the technical challenges of notifying people are relevant here. The very fact that you would have to update your own research because something you referenced changed is kind of insane to consider. You now not only
372.
by joppy 8y ago
I think the exact tools used are irrelevant to the discussion. If this style of publishing + maintaining older papers became popular, hopefully some better tools would spring up. For what it's worth, I think tools like ShareLaTeX and t
373.
by joppy 8y ago
However, this is an article written by a researcher in a particular field, published on the website of the best-known and most reputable journal in that field, trying to get a message out to members of that same field, about a topic that no
374.
by joppy 8y ago
I'm all for research papers being made more open and available, rather than hidden away through paid-for journals --- this is in my opinion one of the worst parts of how knowledge is shared. However, I'm not sure that making the p
375.
by joppy 8y ago
It’s common practice for scientists to keep logbooks for this exact reason. This is already done.
376.
by joppy 8y ago
This is a bit of a red herring - why would people using Einstein notation write A[i] B[i] instead of writing A⋅B?
377.
by joppy 8y ago
I still feel that the whole expression could be clarified quite easily be writing a \Sum_{a, b} at the front?
378.
by joppy 8y ago
I don't have a problem with using indices for anything, they are fine. Distinguishing upper and lower indices is even better. The exact complaint I have is the implicit sums. For example, a matrix A would be written with one upper and
379.
by joppy 8y ago
It's not actually a new notation though, it's literally just deleting a part of the old notation and then getting the reader to fill that part back in. While this is fine for calculations, I would rather that when equations are ac
380.
by joppy 8y ago
Upper and lower indices are great, but are still unrelated to the convention of dropping the big sigma at the front.
381.
by joppy 8y ago
To the point where writing one large sigma and listing indices under it at the start of each line would significantly slow you down? I found I had to do this mentally during my own relativity class, just to figure out what each expression m
382.
by joppy 8y ago
I've never really understood the point of Einstein notation, as a piece of mathematical notation. Is writing something like A[i, j] * B[j, k] really that much faster than writing something like Sum[j](A[i, j] * B[j, k])? Especially whe
383.
by joppy 8y ago
If you’re already typing in the full address for the server every time, since you don’t have an ssh config file, then is it really so much more work to additionally type the port?
384.
by joppy 8y ago
Hover is not necessarily more hidden UI, but could actually go to making bits of phone UI that currently exists more discoverable. A personal gripe of mine is that press-and-hold on a button is a terrible way of discovering something new, y
385.
by joppy 8y ago
Hilberts list of problems is way less clear-cut than you think. His first and second problems eventually ended up being “solved” only once people figured out what Kurt Gödel was going on about with his incompleteness theorems. But to many p
386.
by joppy 8y ago
The slightly surprising incorrect statement is “each real number has a unique decimal expansion”, which is wrong since 1.00000... = 0.99999... — so when using arguments like this, you need to be careful to always only pick one of these.
387.
by joppy 8y ago
This is an amazing talk, and a transcript does not do it justice in the slightest. If you have the time, listen to the talk!
388.
by joppy 8y ago
What eventually happened is that the proof was wrong, and the community tried not to make a big deal about it, since Atiyah is now very old, and has made many significant contributions to mathematics in the past.
389.
by joppy 8y ago
Most typed programming languages will allow you to form a pair of type (Integer, Integer), and reject programs which try to return something like (Integer, Float). Dependently typed languages might allow you to declare a type (n, m) where n
390.
by joppy 8y ago
Technically the projective coordinate (3,2,1) should be exactly the same as (6,4,2), and every nonzero multiple thereof. So it’s not really correct to say that (x, y, 0) represents a vector, or that adding these projective coordinates is ve

More ›