The 128 bit arithmetic part is really interesting. I wonder whether they used libquadmath and whether they needed to implement any extra funcitons beyond what’s available there.
In the process of “shut up and calculate” (SUAC) you often come upon much deeper insights about the involved processes and quantities than you ever could with wordy and “understandable” explanations. Of course simple, explainable models are great, but they have limited ability to describe the world, which is much more complicated. I don’t see how successfully handling this complexity (and getting the successful predictions) could take away from understanding.
It’s not like those SUAC disciplines don’t have simple explainable models. In my opinion It’s just that in order to describe phenomena really accurately or if the described phenomena are complicated enough the only way to get reliable and improvable predictions is via complicated SUAC-type calculations.
I don’t have full explanation of the connection that would be satisfying. However, I think it mainly comes down to symmetry group of the spinors and their 720 degrees symmetry. It is called plate trick for a reason after all: https://en.m.wikipedia.org/wiki/Plate_trick
I find Julia’s Pluto to be reasonably close alternative.
Of course it lacks many features, but plugins systems and overall architecture gives hope for possible extension to include many of the desired features.
This is of course very true but doesn’t take into account invention of computer that is relatively recent.
Since it in principle never makes mistakes (in practice there are of course bugs, but they are usually different in nature than human errors) it changes what is possible and most convenient. You no longer have to optimise for simplicity as heavily for example. On the other hand computers basically can’t deal with ambiguity, so the rules and statements have to be stated very simply and clearly.
EDIT: One example that comes to mind are indexes in functions. Usually they are just additional arguments that are different somehow from the “main” arguments, for example often being non-negative integers. For humans it makes it easier to think and operate about indices separately from the rest of arguments. But for the computer it’s all the same, as all arguments are treated just as argument, (of course it depends on the implementation etc) and there is no need to treat them separately, since every argument is “special”.
I believe computers can change the landscape of what’s best notation. This is an interesting, interdisciplinary topic to explore.
Chess programming is fascinating but it seems for me that it has somewhat stalled in creativity in terms of classical (non DNN) engines. They all seem to use improved versions of min-max/alpha-beta. Which results in computer players that are extremely powerful but also quite dull. This is because they assume that the opponent will play perfect game and will do it at the full strength of the engine.
Basically there is no point playing against the engines at full strength as a human, since it will beat almost any human beyond grandmaster level. And that’s for weaker engines – the medium tier ones will regularly beat grandmasters and the top ones around the stockfish tier will probably not loose 1 game in 100 plays.
That considered I’ve wondered what’s possible dropping the assumptions about perfect play of the opponent. Some probabilistic models of opponent or different way of rating whole tree of moves in the context, instead of position only. For example considering the alternative moves and how difficult it would be to play perfect game for the opponent, it might be better to play combination with a lot of traps with possibility of loosing some position if the opponent plays perfectly. Current engines wouldn’t play such kind of move because they’d assume (via min-max/alpha-beta) that opponent will have perfect answer. Of course, if the opponent is an engine it will, but against humans it would make things much more interesting.
Yes! Those are exactly some of the alternative frameworks I had in mind. Also things like using differential algebra instead of classical epsilon-delta analysis and using Liouville's theorem to calculate integrals gives similar vibes.
Large parts of constructive mathematics seem to also be aligned well with physics and engineering (using only things that can be explicitly constructed) and hopefully could lead to interesting mathematical physics results. Same with, for example, quaternion analysis, which is very rarely used (contrarily to complex analysis), due to difficulties in operating quaternion valued functions, or computable analysis with its surprising result about differentiation of real an complex functions. I get similar feelings about non-classical logics. Somewhat more fringe examples that come to my mind, but are also interesting are for example non-Diophantine arithmetics or Holors theory (tensor generalisations).
Thanks for the "receding shoulders climbing problem" it’s a very nice way to frame the problem. I agree that there is a lot to be done to make shoulder-climbing process faster, easier and more widely available. It should also be possible, to make it more easy by for example storing not only results, but also derivations of many mathematical relations and computations. E.g. nowadays, there is no reason to put only results of integration in the integration tables, but whole derivations should be available as supplementary materials (preferably even in some form of symbolic computing code; this is somewhat realised with RUBI – rule based integration package). Size of the paper book is no longer the problem, so such “interactive derivations catalogues” should be extended to as many possible branches of mathematics, physics and engineering as possible.
I absoultely admire creativity and skills it takes to pursue developement of novel branch/framework of mathematics like this Super Calculus. I think that such original thinking at the fundamentals of mathematical formulations that underlying physical theories is required to overcome at least some difficulties modern physics struggles with. The problem is that it's nearly impossible to tell which one (even combination) is the right one.
The process to create one is so long and difficult, that there often isnt enough time to pursuit and find applications in which these novel mathematics coud prove to be superior over the existing ones. It creates a chicken and egg problem, where there are no arguments strong enough for the physics practicioners to switch these new formulations (as it takes a lot of practice and time with no guarantee of being any better than classical mathematics) and, on the other hand, the creators of these theories dont have enough time/audience/manpower/practice in practical calculations to go as far as where the problems of modern physics lie.
I've been thinking about this problem for some time and I think the right kind of design of the symbolic manipulation and calculation software could be of great help. The design of such software is certainly not an easy task, but hopefully somewhere along the road I, and hopefully others, will find some time and creativity to get started with it.
In Europe this is required in European grants, but also in many country specific funding agencies as well.
In 2018, 11 European research-funding organizations formed what is known as cOAlition S with the primary objective to ensure full, immediate, open access to all publications containing research data obtained in projects funded by its member agencies. The chief premises of cOAlition S were laid down in Plan S, which is scheduled for implementation in June 2020. So nowadays when someone wins grants from these agencies he’s required to publish his results in open access.
It’s not ideal, because many people reserve grant money for open access fees but AFAIK the policy also allows to publish behind paywall as long as you provide publicly available copy in repository (institutional or public like arxiv etc). In my opinion the second option is much better (as it saves money), but not all journals allow to put copy of the article in public repos (sometimes they require that the public version is either before editor’s revisions or puts some time embargo, like a year or 6 months, for publishing final version of the article).
How I wish papers in science and engineering were written in such format (or were created with org-mode source files with code which one could download and play with), where we could preview steps of derivations in some symbolic manipulation program, instead of "after simple transformation we get..."
I’m in similar situation. Didn’t upgrade from Mojave and like my system so far but wondering where to go from here. What competition would you recommend in terms of hardware+system?
The difference is, that there's very advanced mathematics behind string theory and at leas that part can be checked/verified by independent researchers.
But aren’t the shorts for like 140% of the GME stock? That means if everyone holds with prices, sooner or later the shorters will have to buy ALL that stock anyway at nearly any price to cover for the losses and give back shorted stock.
Why wouldn’t it be pursued? Is string theory not pursued by “mainstream science” because (at least for now) it has less predictive power than standard model?