What do we hear when we change the direction of a wire?
mahgister So deep down you are a Russian Mahgister. This is very unexpected and pleasant. I haven't listened to these songs for a long time and once again i note how emphatically all his unique intonations are conveyed in the pre-war 78 recordings. No modern recording can do that way, isn't it strange? Completely outdated shellac beats technological HI-FI in some very important music features. Thank you. |
@millercarbonFascinating. So we got a guy saying the audible differences can only be caused by metaphysical reasons. While at the same time insisting everything be proved with numbers. This is Spock-level raised eyebrow fascinating.No, he does not feel the changes and believes that the bias is to blame for everything. And he is not a person to admit his possible mistakes, now he will write a novel on the subject i'm sure. On a more pleasant note, I believe we are all Russian. This is after all why we call it Mother Russia, is it not? I am puzzled, really. I would never have thought that I would read this on an American forum from local people... Live and learn! Thank you! |
mahgister They say that Vladimir Sofronitsky was the most interesting performer of Scriabin's miniatures, and I think so too. Here are a couple of examples - https://www.backtomusic.ru/19684 track 8 and 9. No less ingeniously did David Oistrakh on his Stradivarius - https://www.backtomusic.ru/19612 tracks 3 and 4. Nocturne just mesmerizes me. These are all 78 pre-war records. |
@dletch2Meanwhile you put forward a second assumption that in a short piece of wire the frequency response can change when the wire is reversed. And It follows from the content that these changes in the frequency response go without the presence of signs of electrical asymmetry of the wire. According to Ohm’s Law, this cannot be. These are exact quotes from the discussion you entered in halfway through: 1 - @cmichaelo: "Due to manufacturing tolerances, a cable isn’t electrically the same from both directions." 2 - @anton_stepichev: "Let’s assume that the speaker wire has an error, but it is microscopic, on the verge of perception and measurement. Then, we will have to agree that the error is common to all the wires. And it turns out that, for example, in a RIAA corrector, the error of the wire going from the MC head to the transformer will be amplified almost 1000 times! .... But we do not observe such errors. So there is no polarity, semi conductivity or any other ELECTRICAL assymetry in a wire." 3 - @dletch2: "Does not work that way. If the error is simply frequency response, the relationship between the perfect and imperfect signal never changes". @dletch2, the meaning of what you said is clear: you claim that when a wire is reversed, an "error is simply frequency response" is possible without the occurrence of "ELECTRICAL assymetry". Now you retract your words, OK, but then again there is the question of amplifying the error by a factor of 1000, which somehow escapes measurement. Why can't your super-accurate instruments measure it? |
Ervin Nyiregyházi in Liszt are.... There is almost no visible Liszt, the performer takes up all the space... Full immersion in music, an amazing person! It reminds me of Oleg Karavaichuk, who could make a symphony out of a waltz https://www.youtube.com/watch?v=SVO956v6wSs Ostad Elahi a musician god also and one of my favorite...On par with the greatest musician god of the century....Menuhim says after listening him that listening him plays was one of the greatest musical event in his life.... After that who will not look for him? he's a hypnotist, technically he doesn't seem to play anything special, but eventually you fall into a kind of meditation. |
ihcho510 posts From the point of view of physics - yes, any wire is ELECTRICALLY symmetric. In any case, no one has yet refuted the example of the absence of an error when it is amplified by 1000 times in RIAA corrector. However, there is a difference by ear. This is actually the question - what is the component that does not relate to electricity, but is felt subjectively? Then, what can cable engineers do to make the cables directional? No one specifically makes the cables directional, they themselves turn out to be so, since the wires have directivity. |
mahgister I've heard about Kozyrev and his bold theory, but I don't know if his ideas can be used in audio. In any case, people like him do inspire the research practitioners that I am, so his influence is obvious. |
@djones51,You both want to jump from kindergarten to college. Let's take it in order, although I doubt it will help. What is there with the semiconductivity of the wire, the question is removed? |
dletch2 Finally, you recognized that, from the point of view of conventional physics, there can be no direction for a wire. This is an important admission, because as an opponent you put all your strength into refuting it. So we agree, there is no secret door or loophole here because the laws of electrical engineering are simple and unambiguous. Now we are in the following situation. You, as a representative of conventional physics, claim that NO ONE can hear the difference in sound when the wire is reversed. In the same way, the difference can not be heard when changing the power cable, you recognized this even earlier. If you are right, then it turns out that a huge number of people can not understand their feelings and are simply biased. However, if you are wrong and there is a subjective difference, then obviously you should look for it not in conventional electrical engineering and acoustics (we found out that there can be no difference within their framework), but somewhere else. Nevertheless, you persist in suggesting the use of blind tests developed by conventional physics to determine changes in the same conventional framework. How can such tests give the correct answer in our situation? |
djones51 thank you for drawing attention to the grammar error, I hope it will be clearer to you now: "choosing the position of the plug in the socket in which the music sounds better" Is the question settled? You read it again. You simply dismiss bias by waving your hand. In my opinion, it is you who constantly dismiss the essence of the matter, find fault with grammar and other irrelevant things. We'll get to the bias later, this is undoubtedly a difficult question, but it is not solved by the blunt methods that you suggest.. Now please go up three posts and answer the question I asked dletch2 about the blind test. |
dletch2 To each of your similar statements, I responded with direct quotes and comments, to which you had NOTHING to object. Now you decided to accuse me of juggling of facts. Write down all four cases with accurate quotes and point at where and what exactly I have "twisted". Then we'll see what your words are worth. |
Gentlemen materialists, you have not yet answered the question about the reliability of blind tests. Let me remind you that at the moment we have found out that when the wire is reversed, there are absolutely no changes in the electrical signal occur. Thus, according to the laws of conventional physics, these changes are not present in the acoustic signal and we can not hear them. Next thing is all known subjective tests including blind tests are designed to detect audible differences in the acoustic signal, but we already know that these differences do not exist. So what else can we prove with blind tests in our situation? |
djones51Next thing is all known subjective tests including blind tests are designed to detect audible differences in the acoustic signal, but we already know that these differences do not existIf they don't exist then I guess you have your answer. I wouldn't ask if I have the answer. Do you find a mistake in my logic? |
dletch2 Well well well.. Out of the four, there are already two left. I hope you understand that until you show where and how exactly i changed the meaning of your words, the accusation remain nothing more than libel. I'm waiting for proof. |
djones51 djones51, your colleague has already switched to a placebo, and you're still offering blind tests. They can't give the right answer, don't you understand the logic? "Let me remind you that at the moment we have found out that when the wire is reversed, there are absolutely no changes in the electrical signal occur. Thus, according to the laws of conventional physics, these changes are not present in the acoustic signal and we can not hear them. Next thing is all known subjective tests including blind tests are designed to detect audible differences in the acoustic signal, but we already know that these differences do not exist. So what else can we prove with blind tests in our situation?" |
djones51 Yes, you quoted the conclusion, not the logical chain that led to that conclusion and I was not asking you to believe it. I was asking about a possible error in the logic that leads to this conclusion. starting with the audibility of a particular effect according to electrical engineering. Where exactly can there be a possible mistake? |
djones51You need to go into politics, they appreciate people who, instead of answering a question, confidently say something out of place with a smart look. It is also obvious that you do not understand electronics and are afraid to express your opinion about it. This is my conclusion. |
djones51 Wait. I gave a specific, logical reason why it is impossible to rely on a blind test in such a situation, and not just stated that "we have to leave out basic science like blind listening tests". I expected you to criticize the logic, not just say, "The answer is, it doesn't exist." |
djones51 I'm not trying to convince you of anything, I know perfectly well that it's impossible. Read again the question of the topic, it is not about convincing those who do not hear, but about how you can explain audio anomalies to those who hear them and successfully use the knowledge in their systems. For me and for many others, the direction of the wire is as commonplace as its absence is for you. Despite this, I believe that the ability to reason in educated, unbiased people should be the same. I hope you have an imagination, assume that you have been dealing with the direction of the wire for many years, show it to friends and acquaintances, discover interesting patterns related to the direction, these patterns are successfully used by other people in their audio projects. All doubts about the reality of the phenomenon and many similar anomalous effects in audio have long disappeared. The only question left is, why do we hear (feel) something that isn't in the signal? Naturally, I still don't know what it is, but logically, it can't be related to electricity, thus it can't be measured by electrical appliances and evaluated by blind tests. So the question is: are there any errors in my logical chain (that I have already posted several times) if there is no doubt that when the wire is reversed, not only is it audible, but its sertain direction is fundamentally important for a more natural reproduction (perception) of music? |
djones51 Not hearing, but feeling. In my opinion, this is the only possible explanation if you definitely feel changes where they can not be according to the physics (changing a power cable, reverse a wire or fuse) . This is just logic and apparently you can't say anything sensible about this. |
Dletch2Neither you nor djones51 answered the question, you just expressed your humble opinion about the audibility of the wires (bias and placebo = BS). You are not asked to talk about these rather trivial things, but you are plugging your ears and repeating your bias mantra non-stop in every post. I want to remind you that you accused me of libel and said that you proved it. I am waiting for your proof, or do you not care about your reputation? |
Interestingly, the changes in the sound associated with the replacement and orientation of the wires can be recorded and played back. After digitizing, the difference will not be heard as clearly as in live, but the nature of several consecutive changes will already be recognizable and based on the recordings, you can track how much you have progressed in setting up your system or, conversely, how much you have been led away somewhere. The recording allows you to repeatedly return to the evaluation of the results and eliminates the influence of momentary deviations in perception related to mood, health, fatigue, etc. Serious changes in the recording system, when you orient every wire, including the mains wiring in the room and select every detail of the system by ear, lead to a fairly noticeable difference in sound. For example, the violin, the most sensitive instrument to recording and playback errors, becomes more flexible, begins to SING more expressively, and the intelligibility of the individual instruments in the group improves. Here I can give a lot of examples, for instance, Grappelli's violin in its usual form sounds sharp, Django's guitar is lost in its background. https://www.youtube.com/watch?v=h-zSlE5ZgOA The 78 record gives us a completely different impression - the violin sings and at the same time does not obscure the guitar, which, as it turns out, can also sing if it is in the brilliant hands of Django. https://www.backtomusic.ru/19652 The frequency response in the recordings is quite different and this is the first thing that catches your ears. If you listen to the recording for at least 30 seconds, this difference ceases to interfere with the evaluation of the musical properties of the recordings. When tuning up a system for digitization, almost always subjectively positive changes in the sound occur against the background of deterioration in technical characteristics caused by the rejection of the negative feedback, the use of imperfect homemade radio components (capacitors, resistors and coils), ancient triodes, and so on. As a result, we have a completely illogical situation: the most important moments for the perception of music are improved, while the technical characteristics of the system are deteriorated. A question I've been asking myself for years - how can this be, if the technical (electrical) characteristics determine everything? |
wolf_garcia I don't think it makes sense to redo the cable if it's going to be used in a subwoofer. Usually in complex systems with multi-band speakers and subwoofers, the directivity of the individual wires is not as important as in simple tube amplifiers used with two-band speakers. The sub itself badly affects the playback of acoustical music to a much greater extent than a cable - in exchange for a better bass, you get worse plasticity of acoustic instruments and some other artifacts in middle range. So my opinion is if the system is configured to listen to classical music, it is better to just get rid of the subwoofer along with its cables, and if you listen to electronical music, then the direction of sub's wire will not matter much. But no one can say with certainty how important the direction of a single wire is in your system and specifically for you. This should be tried. |
I received an interesting email yesterday: Hello Anton! I don’t have Windows too, but I have a laptop with Linux and Wine that are used to run Windows programs under Linux. I installed the player and optimized some mp3 files. It definitely works! I would say that optimized files sound more airy and openly. It’s like you’re turning a wire in the right direction. This is very strange, I have never seen a computer program that makes a file sound more natural and it is free and easy to compare. After all this is the perfect example how two equal digital files can sound different. Specially for biased naysayers. |
djones51 Tastes may differ, and this is normal, the main thing here is that you can feel the difference. If you do such experiments often enough, you will eventually get rid of your grains of salt. |
@eagleeye7 First of all, I have to thank you for such an interesting example! No laughing at all, because I definitely know that the direction of the wire used as the radio antenna is just as important as the direction of the wire in the signal chain. This can be easily checked on any receiver, or better on an old tube radio, where the difference is more obvious. You can even see it on the TV if you use an old-style aerial antenna instead of a modern digital cable signal. The difference here will be noticed not only by ear, but also by eye, in case you care the difference between the image of old movies and modern digital ones. But unfortunately this example can not prove the wire direction audibility in signal chain. The antenna picks up the RF signal, the meter also responds to the fluctuations of RF signal together with the level of rectified audible signal. There are a lot of extraneous interference in the RF signal, which change both in time and from the slightest deviation of the antenna from the initial position, this is the weak point of the receiver meter based proof. Wires definitely has preferable direction, but each attempt to explain it by means of difference in electricity signal is easily challenged if you know the ropes of radio engineering. I still cant imagine how wire direction can be explained withing physics. With respect. |
eagleeye7 I can’t try it right now, have no appropriate tuner. Anyway I do not argue with the efficacy of your method, it certainly deserves attention. I only noticed that it is impossible to locate the exact reason of the directivity with its help. We can’t directly hear the RF signals, and even if we could, speakers can’t play them back. So we need to look for the real reason not in the RF area, that’s what I meant. But may be we can somehow feel the RF right from the wires and other parts? Probably.. But here we are already going beyond conventional science. |
@invalid The difference in SQ is obviously exist but it can't be measured by electrical measurement device. All metals are electrically symmetrical and remain so regardless of the mechanical deformation they receive during the manufacturing process. You can turn them all in any direction you want, and nothing will change in its electrical behavior. That's the whole mystery. |
@mijostyn You will not find anything useful with the microphone, because when you reverse the wire, there is no change in the electrical signal at the speaker terminals. As for linearity, its value is greatly exaggerated. There is absolutely no need to make the linearity of the system with an accuracy of 0.3 db, much less 0.1 db. If it was so important for perception, we would not be able to enjoy listening to cassette recorders, receivers, and so on. By our nature we automatically adapt to changes in the frequency response within a wide range, this is how our perception works. Adaptation to changes takes a few tens of seconds, after that we get used to the new reality and the new frequency response becomes "transparent" for us, it does not interfere and does not help us to perceive music, it just becomes a kind of reference point, relative to which we perceive sounds.. This statement is easy to verify, if you have timbre controls in the system, turn the controls a bit, spend 10 minutes listening calmly and analyzing impressions, make a conclusion. And do not forget that the linearity of our hearing changes depending on the volume - https://en.wikipedia.org/wiki/Loudness. Why do you set up a system with an accuracy of 0.1 db if with a small enough change in system volume, the linearity of your hearing changes by several DB? Isn't it stupid? |
eagleeye No doubt. I would add the digital cables Directionality here. The method that I outlined provides Documentation that a specific Cable Design exhibits or does not exhibit such Directionality to RF Signals. I think because of relative complexity of the method in comparison with this simple schematics, it probably lack the sensibility, otherwise it would be obvious, that each wire has directivity together with certain unique coloraition. Think about all of the harmonics & sub harmonics of the 60 HZ line frequency that is all around audio equipment. It's likely that some cables pick up this noise, which is then further amplified in downstream amplification stages & may well be heard, with some Cable designs. I know the fenomenon and some similar ones, for instance the difference in SQ arising from different methods of mounting radio components of the amplifier - a modern one when radio components lying on a circuit board and outdated point to point wiring where the components do not touch the board and each other. The point-to-point sounds more openly and naturally. But it can't be be related to RF unless we somehow feel the RF directly from environment. Speakers can't reproduce RF signals, and the indirect influence of RF in well designed amps is much less than we can hear. |
thyname You are mistaken. We do not have to diagnose all possible diseases of an audio system. On the contrary, to avoid significant complication of the matter we should regard an amp and all its wiring as a black box with just input and output. The measurement devices allow us to analyze the difference between electric signals of the input and the output with precision that exceed our hearing possibilities quite a lot. With proper measurement we can be sure that on the output (on the speaker terminals) there are no RF signals or audible signal distortion and all the more that nothing is changed when we reverse a single wire (see article by Douglas Self). After that, we can say with confidence that the acoustic signal will also not have any interference associated with wires and cables coloration and directivity. As a result we face the paradoxical situation when we hear what is not presented in the signal. IMO there are two possible ways of thinking about it: 1 - Psychoacoustics and medics are wrong about hearing sensibility. But here we contradict thoroughly checked scientific data derived from the best organised subjective tests ever. And we contradict logic, because wires/cables audibility is perseived against the background of relatively loud noises. Why white noise at -50db level does not mask the microsounds that presumably occur at -100db level? There is no logical answer to this. 2 - Simultaneously with an acoustic signal we perceive some still unknown type of information using sixth sense. No matter how crazy it sounds, this is the only logical explanation for the phenomenon so far. And by the way, the many references about inconsistencies in scientific theories of hearing that Mahgister provided us make this assumption not as crazy as it seems at first. It would be nice if you suggest another logical explanation of the matter for a change. |
@manueljenkin1, It's a pity that Eric Juaneda from Junilabs ignores the questions. My friend asked him to explain the principles of file optimization or just say something about this interesting thing. He didn't answer. In the meantime, I became convinced that there must be some non-physical explanation for the change in sound that we feel. It is strange but the only thing the optimization program does is load the file into memory, wait for a while, and write it back to the hard disk. At least that's what the programmer told me when he de-compiled the file and analyzed the code. Why this changes the sound of the file is unclear. I've done some research on how people feel about the difference in optimized files. There is no repeatability here, some prefer original files, some - optimized, some non-audiophiles do not even feel the difference at all. However, here we certainly have another confirmation that digital audio is far from perfection and audiophiles feel the difference in the sound of files with the same checksum. And there going to be some more then just conventional physics to explain this phenomenon. |
@manueljenkin, I see you are a pro in digital, a lot of special information, thanks. I wonder how it can help us. You know, no matter how complicated the situation in hardware and software are, if we going to play two files with similar checksum on the same computer, they should sound identical. But in our case they don’t. So may be they are somehow not identical? Can you check the sameness of the files? Your opinion is quite interesting. |
@manueljenkinI can't quite understand it. IMO if the noise and charge distribution somehow affect the integrity of the file, then this should affect the checksum. Conversely, no matter what noise and interference may occur on our hard disk or anywhere else, if the checksums of the files are equal in the end, then any previous interference does not matter, since they do not affect the final result. To find out that there is no negative impact of noise and charge, you can simply copy the file about ten times, and if the checksum of the last copy does not change, you can be sure that the hard disk, software or anything else on this computer does not cause digital errors. Therefore, copies of files on this computer should sound exactly the same. But this is not the case. For example, the file will sound different if you copy it to a second hard drive or USB flash drive and play it from there. At the same time, if we copy the file back to the hard disk and check its integrity, we will not find any errors. All this looks more than strange for a theoretically perfect digital sound, doesn't it? |
@manueljenkin Wait. I know about thresholds, error correction and about various difficulties of reading from damaged storage media cells. All this should not concern us, since when copying and reading a file in a working computer, after all the background correction operations we get either an identical copy or a read/write error. We have no errors while copying and playing back files, therefore the noises, the charges etc. are within normal limits. Moreover, even if we hypothetically assume that some latent digital error occurs, it is not clear where exactly it occurs so that it cannot be detected. Do you have any ideas on this? Another question - can you explain how the file sound optimizer can affect the noise, charge or any other ANALOG properties of a HDD for the better? |
@manueljenkin You tend to complicate things, and with this approach it is almost impossible to understand the problem, because, as you correctly noted, we have a lot of areas in the computer where we can suspect problems. However, you forget that we can logically exclude the vast majority of these suspicions. daс can be easily influenced by noise in the data, clock and especially ground lines When we compare the sound of two identical files recorded on the same medium, when the player switches from one file to another, none of the above interference in the computer changes, that is, these interferences do not prevent us from making the correct conclusion about the sound of the compared files, all other thing being equal. On the other hand, we can easily make sure that the intended noises do not affect the sound the way we hear it in our audio examples. To do this, it is enough during listening, for example, to insert and remove a USB flash drive from the computer, connect/disconnect the PSU in the laptop, start background hi-res video playback via Internet or any power consuming software, etc. If desired, you can come up with a lot of actions that will simulate serious changes in the level of noise and interference of the computer and conduct a simple but effective study of how your DAC reacts to heavy changes in the level and spectrum of interference emitted by it. Have you conducted such experiments? To go into exact details of the modes in which the write environment affects the access noise profile, it'll require a deeper understanding into the actual physical characterization of the floating gate cells used (and most of this is proprietary and not visible to general consumers, includes me) Here again, it is enough to simply analyze the situation, and not go into deep technical details. What do we have - the program loads a file into memory, presumably does something with it (in fact, nothing physically happens with the data) and writes the file back to disk. At the same time: - This program does not work "at low level", that is, it cannot select a certain "low-noise" place on the disk and write the improved copy of the file to this place, since the physical location of files and folders on the disk is completely determined by OS. - There is no code in the program that would analyze the disk surface for noise or anything else. - Suppose different cells of the disk "sound" differently, then it is still unclear how the program, when repeatedly overwriting a file, makes similar changes in the sound (improvements or deterioration-it does not matter) for each copy. In theory, we should get an unpredictable result with each rewrite - either an improvement or a deterioration or non at all, and as a result, something indefinite in the end. In my opinion, it is quite enough to stop clogging your head with noises and charges and start thinking of something else. |
@manueljenkin Yes, and noticed a lot of improvements. I have tried a lot of system level tweaks, even went to the extent of taking a custom minimal commandline linux distro for audio (again sounded better than the familiar gui systems), and have also explored custom tools in windows that optimize a lot of the internal system processes.... Everything from even changing the buffer size changes the sound. (Includes all types of buffer, either in dac or in system). I agree, simple structures, schemes and programs sound better to me either. In my experience the more lower noise system gets (lower system activity), any further improvement is far easier to hear than with a stock system configuration... ... My friend has successfully done AB-X on other computer audio tweaks I mentioned in earlier paragraph, his network streamers and signal regenerators. I don’t think there’s anything wrong with my approach. Nothing wrong, of course, if you are just looking for a better sound. The problem is it will not help us understand the reasons for what is happening, and I would like to understand it. The influence of noise is just your assumption, so far you have not given a single description of the experiment confirming the specific influence of noise and not any other causes that occur during the tweaks. At the same time, in the previous message, I gave proof that the work of the program is in no way related to changes in noise or other analog properties of the media. You have not refuted or confirmed the correctness of this proof, instead you wrote: I am looking deeper into the intrinsics of the drives (the physical manifestation) since it has an impact that is uncorrelated from the rest of your guesses (doesn’t do defragging, cannot check optimal areas in disk if there was ever one since it is out of control of even the OS, it’s the controller that handles it). Please explain, hypothetically, what can be found in the filling of the HDD so that it indicates the influence of noise (or whatever) on the sound of the file processed by the program? |
@manueljenkin Can you just answer my previous question: @anton_stepichev Please explain, hypothetically, what can be found in the filling of the HDD so that it indicates the influence of noise (or whatever) on the sound of the file processed by the program? Keep in mind that: - nothing physically happens with the file |
@andy2 Yes, if you play copies of files from the same HDD, everything is PHYSICALLY the same, all the things being equal. If you really want to down that path ... to the nth degree then anything is possible. A preliminary logical analysis of a task is not at all an n-th degree, but the first thing anyone should do before starting to delve into technical details. The preliminary analysis tells us that there is no physical or material cause-and-effect relationship in the situation with optimizing the sound of audio files (as well as with changing the direction of wires and some other things). Therefore the cause, the effect or both are beyond the scope of conventional physics, isn't it obvious? |
If you're talking about different file optimization, then sure it would have effects on the soundI'm talking about exact digital copies of files that sound different after optimization with the Junilabs player http://www.junilabs.com/fr/products/audioplayer.html. |
Andy2, there are no contradictions, I’m trying to explain to you a simple thing that is understandable even to a schoolboy. This is getting ridiculous, by God. You wrote: Of course if optimized then it may sound different. During playback, the audio file has to be "decompressed" or if you will "processed" by the CPU. Therefore it will have its own digital interference signature which will affect the DAC clock. OK. Imagine that we have an original file (A), an optimized file (B) that is PHYSICALLY identical to A, and an ordinary digital copy of the file (C) that is PHYSICALLY identical to A, all located on the same disk. Then: By the sound: A ≈ C ≠ B. In the digit: A = C = B At the same time, you claim that A sounds different from B because A is not physically equal to B since the files have "its own digital interference signature". This in itself is nonsense, but let’s assume that it is. Then answer the question: Why then is the sound A ≈ C? In other words, how can normal copying differ from optimization if in both cases we always have files with the same checksum at the output? Keep in mind that if we do re-optimization (B1, B2, B3...) and re-copying (C1, C2, C3...), we have: By sound: A ≈ C ≈ C1 ≈ C3 ≈ Cn ≠ B ≠ B1 ≠ B2 ≠ B3 ≠ Bn In digit: A = C = C1 = C2 = C3 = Cn = B = B1 = B2 = B3 = Bn So answer the question please, then we’ll see who is schizophrenic and who is just stupid. |
