Ghideon

Unexpected that these beaches look the same at a distance, yet they are different on closer inspection: Top: A beach in northern France covered by pebbles. All* of them are egg shaped. Bottom: A beach in northern Sweden; all* of the stones are flat like "coins". Why are the stones on the Swedish beach flat? Educated guess: *) The vast majority at least; during a short walk no family member observed any flat stone on the French beach or egg shaped stone on the Swedish beach.

Your reply indicates fundamental confusion regarding factors, integers, prime numbers*. Here is an online source that may be suitable: "Gain familiarity with factors and multiples". There are chapters for factors, prime numbers, composite numbers and quiz to test your skills: https://www.khanacademy.org/standards/CCSS.Math/4.OA#4.OA.B *) amongst many other things indicated in the posts; too many to list.

Time is up. The task was: Show, in at least two individual and different ways, why the following statement is false: Answers: 1: Factors of RSA numbers are prime numbers. Prime numbers are integers. The proposed number is not an integer and hence it can't possibly be a factor of any RSA number. 2: An RSA number is a product of two large primes of the same size. Quick head count gives that the primes used in RSA-2048 have approximately 300 decimal digits. The suggested number is tiny and therefore not a factor of RSA-2048.

1: Use the hints already provided: And then new hints: 2: Look at the RSA numbers that have been factored at https://en.wikipedia.org/wiki/RSA_numbers and compare to page 1 in the paper https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf * 3: "Your equations" are just a distraction, they provide no information and can't be used. 4: Unsupported claims are not part of the solutions I think of. *) Basic RSA knowledge

No. Let's express it as a small task intended to approve your critical thinking. Task: Show, in at least two individual and different ways, why the following statement is false: Hint: More hints can be added upon request.

Maybe the "immune system" is a more fitting analogy? The forum can be seen as an organism. When disruptive behavior occurs, the community’s response acts like an immune system, identifying and neutralizing the perceived threat. This protects the forum from the “contagion” of negativity and aims to preserve its overall health, purpose, and constructive spirit.

You are correct. (In my attempt to post something helpful to OP I missed and/or misinterpreted the provided context.)

1: What is your own answer to the question? That could indicate your level of understanding of the answers provided so far; allowing members to provide some clarifications. 2: As an exercise for you: what assumptions have @MigL made about your hardware configuration?

Idea: Use floor*? [math]10^{-\lfloor \frac{n-1}{2} \rfloor }[/math] So that the pairs of numbers are expressed as [math](n, 10^{-\lfloor \frac{n-1}{2} \rfloor }), n \in \mathbb{N}[/math] *) https://en.wikipedia.org/wiki/Floor_and_ceiling_functions#:~:text=In mathematics%2C the floor function,⌋ or floor(x). edit: x-post with @joigus

In your opening post, and in your replies; how much of the content is machine generated? Your newest reference seems older than the cut off point for some well known large language models. Is this a coincidence?

Just got curious; my interpretation; combining explanations already given with some hints in videos. and Assuming there are no hidden pumps or other devices. And the contraptions in the videos need only to work for a short while; just long enough to create a video clip. First video, in opening post: fill the large and wide container with lots of water (in other words, perform work) add a small diameter inlet (I checked one more video and they also seem to have a larger outlet than inlet. In the OP video a hose with smaller diameter seems to be attached to the inlet) open a larger diameter outlet at the bottom While the container is being emptied a smaller amount of water will be flowing in from the inlet due to the lower pressure inside. The large diameter of the tank (compared to the small outlet and even smaller inlet) means it is tricky to see, in a short clip, that the water level is sinking. Guess: By manually filling a tank with lots of water, you can pump up a small amount of water with the help of the potential energy. If the ratios of diameters of inlet, outlet and tank are off then the tank will drain in "bursts", allowing air to flow through the outlet. Similar to a filled water bottle being turned upside down If the device is left for a while tho flow of water into the container will stop and air will enter through the outlet, in "bursts", also similar to a filled water bottle being turned upside down. So, it is just a trick to create a YouTube video. (Or my assumption is wrong and there is a hidden pump )

In traditional propositional logic, truth cannot contradict itself, as a proposition cannot be both true and false simultaneously. Maybe paraconsistent logic* is what you are interested in? In paraconsistent logic it is possible to handle contradictions without rendering the entire logical system meaningless. Managing something that is both true and false in a controlled and meaningful way, allowing for the coexistence of contradictory truths within a logical framework, can have applications in for instance software systems. Disclaimer: I have no deeper knowledge in these matters, and especially not in philosophy; possibly my connection to software does not apply. *)https://en.wikipedia.org/wiki/Paraconsistent_logic

Just curious following the discussion from the sidelines; What is the connection between cosmos, scientific revolution and the linked article? I can't find such a quote in the arXiv paper.

That is, as far as I know, correct. There are some indirect applications in for instance ECC (Elliptic Curve Cryptography) and Elliptic Curve Digital Signature Algorithm (ECDSA). This may be of interest to OP since it is used, maybe on a daily basis, when browsing the internet; Elliptic Curve Cryptography (ECC) is of interest because it offers the same level of security with (much) smaller key sizes than for instance RSA. I did not find an open paper at this time** The following section is an attempt of a summary but it is outside my area of expertise and understanding, maybe @joigus or other experts can contribute: While Wiles' proof itself is not directly related to cryptographic applications, the deeper understanding and advanced techniques developed through his work have influenced fields that use elliptic curves. Without Wiles' Proof the theoretical framework supporting ECC would be less robust. The lack of proof of the Modularity Theorem* could leave gaps in understanding the deep properties of elliptic curves, potentially undermining confidence in their security properties and/or making them more vulnerable to sophisticated mathematical attacks. *) https://en.wikipedia.org/wiki/Modularity_theorem **) This seems interesting but I could only get the abstract: https://link.springer.com/chapter/10.1007/978-981-99-3758-5_5

If that really is a concern that bother you: the ability to catch fish without lead weight seems documented, and we're not likely to run out of rocks and stones: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0257710 (bold by me)

You refer to robotics in different places; is this the same idea as in those other threads?

The experiment in the video you shared demonstrates electromagnetic induction with a moving bar magnet. The video does not show an induction motor (see @Sensei's response for details that may help). (When I studied electromagnetic fields at university we used text books; Google search was not yet invented.)

Do you mean a world where there are all currently paid jobs are performed by robots? So there are robot military, police, doctors, nurses, teachers, politicians, judges, fire fighters, attorneys, robot-repair robots, robot-developing robots etc? This also includes anyone paid to control robots or paid to establish and maintain robot policies (they are also replaced by robots?). In your scenario, what keeps robots from evolving priorities that does not favour human?

A bar magnet is a simple permanent magnet with a north (N) and a south (S) pole. Bar magnets are not used in standard induction motors. (bold by me) Basic designs of induction motors do not contain permanent magnets. (If you wish to discuss other types of electrical motors please specify which design you are referring to)

Generally, that’s not an issue for me.

A bar magnet is a simple permanent magnet with a north (N) and a south (S) pole. Bar magnets are not used in standard induction motors. As far as I know standard induction motors rely on the interaction between the rotating magnetic field generated by the AC supply in the stator and the induced currents in the rotor to produce torque. Permanent magnets, such as bar magnets, are not part of this design because the motor operates based on electromagnetic induction principles, not on permanent magnetism. It seems you are combining technical terms in ways that do not follow textbook definitions or established engineering practices, making it difficult to understand your discussion.

If you quote some specific book we might be able to adress misconceptions or errors. The first phones did not digitize sounds. They transmitted analog signals. If you have a specific question about vintage phones and speakers I may provide some answers and practical insights about the signal chain from the microphone to the speaker. An possibly compare it to noice produced as a byproduct in lights and other electric appliances for additional insights. Are there any specific details you are curious about?

Good question! I did try and found related shapes such as Reuleaux triangle Rounded triangle Epitrochoids Deltoid But not the one I wanted.

This week, thanks to @joigus, I learned about squircles and some associated mathematics. A squircle is a shape intermediate between circle and a square. I got fascinated and then, for reasons unknown, curious about the possibility of a shape that is between a triangle and a circle. I searched and it was easy to find images but not names or mathematical definitions; "triangular squircle" is obviously not a good starting point in a search engine. But the search led me to the cool shapes generated by roulettes** and finally after some experiments the Hypotrochoid: A hypotrochoid is traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. With parameters d=1, r=3, R=9 I get the triangular shape I was looking for: **) https://en.wikipedia.org/wiki/Roulette_(curve)

In which frame of reference is the observer? You seem to forget about relativity in your attempt at explaining relativistic effects.