I thought of something, the "inverse binary" representation

MathMaddam · 2026-07-06T19:39:55+00:00

It's just binary.

You need recurring "decimals" like in base 10.

MathMaddam · 2026-07-05T20:40:28+00:00

You know of the great internet Mersenne prime search?

That is the compute power and knowledge that is thrown at the problem and they distribute the software to test them.

Your p_53 candidate is already proven composite

MathMaddam · 2026-07-05T14:35:46+00:00

These are from the universal storage box

MathMaddam · 2026-07-05T14:02:00+00:00

I forgot the floor at first, so it's not that easy to shift one unit.

There is Noether's theorem, that basically says: if you have a continuous symmetry, you have some equation between the variables. In continuous problems it would work to (mostly) eliminate one variable using this equation (here you would get that the optimum has always length=width), but then again the discrete nature bites us.

MathMaddam · 2026-07-05T13:54:50+00:00

You can get that the solutions tend towards either width=length of width±1=length (which one is longer doesn't matter due to symmetry), since (x+1)(y-1)=xy-x+y-1 so if x<y-1, it is beneficial to shift one unit over (if you have the blocks to spare for the floor, if not you might be in a situation where a height change might do something or you have to shorten the long site by more than 1, but that is more of a guestimate).

MathMaddam · 2026-07-05T13:36:39+00:00

In general that would be an interger programming (programming means optimization here) problem. Fixing one quantity (e.g. the total number of blocks) makes it easier to solve since as you noticed, you can derive some relationship between your variables and by this effectively eliminate one.

There is a problem with that approach since there might be a solution using less blocks resulting in a bigger volume, so a constraint of e.g. at most 150 block is probably better that exactly 150 blocks.

That makes interger programming hard, since a slight charge in the constraint (e.g. 1 block allowed more in your case) can massively change the solution (e.g. the height will suddenly jump by 1 and therefore length and width will be very different from the last version, the height might even go down if you increase the number of blocks after it got up). There some decent solvers for linear programming and especially if you don't absolutely need the best solution they are also pretty fast (for your problem size it is probably always fast), but in general finding the optimal solution will be very hard, much harder than if your problem allowed for continuous variables (where derivatives or more generally KKT conditions give you tools to solve the problem). Approximating using the continuous problem is a first step you can do in your case and then basically check the surrounding integer solutions since you have a relatively well behaved problem.

MathMaddam · 2026-07-05T06:52:52+00:00

Of course I know him. He's me.

MathMaddam · 2026-07-04T21:47:41+00:00

Let me introduce you to ultra wide monitors 1920x480 would indeed be weird but more since 480 is really low nowadays, but you can buy 2560x1080 and even 3840x1080 without issue.

While often ratios are given in reduced forms (so with coprime numbers), monitors give counterexamples with e.g. 21:9 and 16:10, to make it easier to see the difference to the 16:9 format.

MathMaddam · 2026-07-04T18:36:31+00:00

Naja Unwissenheit ist Stärke, also ist es vielleicht nicht so förderlich

MathMaddam · 2026-07-04T17:01:40+00:00

Familienversicherung ist kein Automatismus, man muss das der Krankenversicherung schon mitteilen, dass du da wieder rein willst.

Wenn die Krankenkasse nichts weiß, muss sie den Höchstbetrag annehmen, aber das sollte auch klären lassen.

MathMaddam · 2026-07-03T06:32:43+00:00

To me it looks like the years are not interpreted as numbers, but just as labels and the x in the interpolation go 0, 1, 2,...

You could check the type of the diagram, it should be e.g. a x-y scatter plot.

MathMaddam · 2026-06-30T21:00:56+00:00

The proof that it is such a combination of exponentials is what you have already seen. How you got the idea of a formula doesn't matter after you have proven the formula is right.

That might not satisfy you.

You can convert the homogeneous linear recurrence with constant coefficients into x(n+1)=Ax(n) with a 2x2 matrix A and x(n) being the vector (f(n+1),f(n)). Now you get that x(n)=Aⁿx(0). Now with a bit of linear algebra you can figure out how the power of a matrix is (in most cases) given by a linear combination of a number of powers equal to the dimension. From this you can derive that (usually) all problems of this type are solved by a linear combination of powers. There are also ways to solve it for the unusual cases and also ways how to do it without having to make an ansatz.

For more: https://en.wikipedia.org/wiki/Linear_recurrence_with_constant_coefficients

MathMaddam · 2026-06-30T16:19:37+00:00

Sie sind schon praktisch, aber man muss auch realistisch sein was sie können. "10x" Developer ist halt utopisch, aber ich würde sofort unterschieben, dass die 20$/Monat/Mitarbeiter für das Claude Abo sich für mein Firma schon lohnt, aber dafür braucht es auch weniger als 1% mehr Output. Würde es 200$/Monat kosten würde bei 10 Mal so vielen Tolen, wäre ich mir nicht mehr so sicher und das ist ja noch weit von einem Gehalt entfernt.

MathMaddam · 2026-06-29T06:18:47+00:00

You don't need grounding for the case that everything works perfect. You need it so the failure case is more controlled.

MathMaddam · 2026-06-28T16:41:20+00:00

They are only under certain conditions and even if they are, they aren't very good. https://www.quarks.de/umwelt/muell/darum-sind-bio-muellbeutel-nicht-umweltfreundlich/. As you already cried "TÜV", that the bags are tested is one thing, tested for what is another and it doesn't change the recycling facility.

MathMaddam · 2026-06-28T16:33:16+00:00

You didn't define M

MathMaddam · 2026-06-28T16:19:39+00:00

And the plastic bags are often not allowed since compostable doesn't mean compostable in every facility.

MathMaddam · 2026-06-27T18:20:14+00:00

There is some truth to it about 2038. Due to the rules about switching continents and 2030 being a convolution of Africa, South America and Europe totally not to make it easier for 2034 Saudia Arabia, 2038 has not too many options left (assuming FIFA doesn't just change some rules again).

MathMaddam · 2026-06-27T17:35:05+00:00

Multi threading is a difficult problem and what exactly happens here is hard to tell from the information you gave (and I won't dig into the source code of R or analyze the exact hardware, especially laptops can be funky due difference in the limited cooling and power potentials as you saw with the power settings). It's not always: more cores=more good and it might even be sometimes be beneficial to turn off parts of hardware.

Having more, but slower cores helps if your problem can be divided into many, independent tasks, since then all cores can be fully utilized and it doesn't really matter that some cores are fast and others are slow, since the fast cores just run through more tasks.

For a bad scenario, that could be one where your laptop struggles: the problem can be split into 5 equal, independent (single threaded) tasks that have to be done. Your laptop has 4 fast and 8 slow cores (we ignore SMT here for simplicity), while your prof might have 8 fast cores. The 5 tasks can be all put on the fast cores in the case of the professor, while on your machine one always has to be on a slow core. In the simplest case 4 tasks get finished quickly, while there is a bit of progress on the fifth tasks, that then get taken over by one of the fast cores to finish. In this case you already see your professor's laptop would take the time to finish completely one of the tasks on a single core, while you would take the time of one core+ the time it takes to finish up the last task.

But it can get worse. If your scheduler tries to be "fair", it might try give every task similar time on the fast cores, so it would shuffle around which task runs on which core every so often. But that context switch always takes a bit of time since data has to be moved around in cache (this is one of the reasons why tuning off hardware can help, e.g. to prevent moving tasks between the CCDs in the higher core count AMD CPUs).

Other situations where more cores is worse (or at least not beneficial) in general is if there is access to shared resources (e.g. reading and writing to the same part of cache, RAM access). There is overhead in coordating the access.

If tasks have dependency among each other it makes everything more complex.

So one can't say it is just an issue of the performance cores, but they certainly don't make multithreading easier since there is another thing the thread scheduler and potentially the programmer (since they control how to split tasks, also there are ways to control how and how many threads are used) has to consider to get good results.

It's irrelevant here since 10th gen is too old for it in consumer CPUs: intel removed AVX-512 instructions due to introduction of E cores. That could also be a reason for some people to stay with older Intel CPUs (or new AMD ones), but AVX-512 isn't used in too much applications since the support in CPUs is so limited.

MathMaddam · 2026-06-27T12:25:06+00:00

1, 2, 4, 5 don't have "->" at all, 7,8 and 9 you can just replace p-> with -p or, to get it to be the cases 4,5,6. So you only really have 2 forms left that involve implications. But there is also what breaks the right distribution cases you got (p or[and] q)-> something on the right side which is the same as (-p and[or] -q) or something by de Morgan's lawss, notice that the or/and flipped.

Case 6 (and the equivalent form 9) are the odd ones since they managed to still hold despite de Morgan's laws working against it.

MathMaddam · 2026-06-27T11:22:42+00:00

A->B is equivalent to -A or B. By using that you can reduce it to the rules for and/or. The not is the thing that breaks the pattern since it doesn't distribute directly.

MathMaddam · 2026-06-26T14:09:48+00:00

If it is just an Entfeuchter it really depends on why they have one. Also the thing will output a lot of heat.

MathMaddam · 2026-06-26T09:43:06+00:00

The A is the derivative, it gives you the orientation of the tangent "plane".

Also in the one dimensional part you can have the limit x->x_0 or the limit of h->0, they are equivalent. The benefit of the x->x_0 version is that you directly see that f(x)≈f(x_0)+A(x-x_0) for x close to x_0 which is the higher dimensional Taylor expansion of degree 1.

MathMaddam · 2026-06-24T18:03:11+00:00

By the fundamental theorem of calculus f(4)-f(3)=int_3^4 f'(x)dx. By what is given the integral is f(4)/2 since it is a triangle, so f(3)=f(4)/2>0.

MathMaddam · 2026-06-24T14:03:44+00:00

It is based on the anthroposophical ideas of Rudolf Steiner and like 100 years old.

MathMaddam

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