Ghideon

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.

No. You are mistaken; trivial to see per definition.

The heuristics applied by an expert may appear as bias to a layperson. (I haven't seen the the word heuristics so far in this discussion)

To my limited experience some factors that affects the price and the quality: -Human hair is usually more expensive that synthetic. -If fitting and adjustments are included in price or not. -Some online shops may be more expensive than the cheapest ones but include fitting at a local facility of choice without additional cost. -Breathable, lightweight caps may be more expensive and also comfortable. -Resistance to heat and chemicals; allowing for styling (blow dryers, curling irons ...) Note: a high quality wig may last longer than a cheap one; the average price per year of use may be important in the long run.

That seems to reflect a misconception about how scientists view their profession? Let's say someone discovers and confirms physics beyond relativity theories that could potentially allow for faster than light travel*. My guss is that it would trigger curiosity. A parallel from my profession: there are several fundamental theorems putting constraints on computational models and algorithms. Should one or more of these be shown to be invalid* that discovery would allow for many exiting breakthroughs in areas such as cryptography, communication or machine learning. The new possibilities would be exiting, no matter how much I hold on to the belief that the fundamental theorems are never to be proven** wrong. *) Not likely, just used as an illustration **) I use "proof" rather than "evidence" since for instance P vs NP problem is of mathematical nature.

There are several issues with the first sentence. For instance electrodeionization is, as far as I know, a water treatment technology and not a quantum phenomenon. (Note: If you use downvotes to my posts or other members it does not help you build arguments)

Wrong guess. Mathematics does not seem to be your thing, lets look for something else that may suit your style of conversation. Ok, Lets use emojis. 🍏🌐🎯 🌐🍏❌

Assumption from another thread that you aim for computational models running on currently available computer hardware; Any thoughts on how to get the resources needed to develop and run? Current state of the art machine learning requires quite a lot. Some old numbers from 2020; note that this supercomputer has not resulted in anything resembling AGI as far as I can tell: Reference https://news.microsoft.com/source/features/ai/openai-azure-supercomputer/#:~:text=The supercomputer developed for OpenAI,the top five%2C Microsoft says. That said, running a simple generative AI based software that generates text can be done on a consumer computer. It has nothing to do with developing intelligence but is useful in some contexts.

Ok. For your convenience here is a fe pictures then, illustrating the problem. First picture, what established theories and observations agree upon. On a large enough scale everything is moving away from everything else. The balloon analogy mentioned earlier illustrates this in three dimensions. here is a 2d drawing with earth (blue) in the center. dotted line represents the horizon we can't see beyond; the observable universe. ¨ Second picture; showing your invalid model with the observable universe very far from some large mass. White circle is the observable universe. Third picture let's zoom in on the observable universe, the white circle above: Since we are far away from the mass everything is virtually unaffected and if there is any movement everything move parallel, there is no expansion. and nothing is moving relative to earth so no movement can be observed. Therefore there are no arrows. This is what your (incorrect) model looks like when drawn using the earth frame of reference. Last picture; for your convenience your invalid model superimposed on what we observe. Note the difference. When we look in telescopes we see the movement represented by green dots, not the orange static circles your model suggests. .