https://www.brianorr.com/blog/2010/01/14/windows-95-easter-e...
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https://www.brianorr.com/blog/2010/01/14/windows-95-easter-e...
Just take a look at the L'Aerophile gazette that started on the late 1800s. Similarly to computers, it's like reading the early editions of Byte magazine. There was a profuse number of people and small businesses from all over the world looking for collaboration with different goals in mind, selling their products and exchanging, stealing and improving on ideas of each other:
https://gallica.bnf.fr/ark:/12148/cb344143803/date https://archive.org/details/larophile08besa
In higher dimensions you get other type of (sometimes weird) operations, related to the Cartan–Dieudonné theorem.
The Telecaster guitar and bass used would be my #1 culprit on introducing noise since pickups are virtually antennas. Mike Oldfield even had added an extra high gain single coil BL pickup to his '66 Tele. If you don't gain stage or ground properly the mics that were used for the acoustic instruments, they could have also captured RF noise easily, even if they had a heavy metal housing that acted like shielding. Some Farfisa organs are also noticeable noisy, although I don't know about their EMI or how banged up was the one used for the album that belonged to David Bedford. The electric piano used was a Rhodes, and those were built like a tank. Finally the tracks were overdubbed over and over. This would in all likelihood have attenuated both the audio and noise, but using a mixer or a tape that is susceptible to interference means that you have more chances of capturing noise at some point in the recording. I guess we will never know for sure.
Anyway, it adds to the mystique of the record.
A human certainly cannot solve a non-computable problem by "playing" computer. However the insight that is created by trying to solve (or invent, in Post's case) something like the PCP, and then the ability to intuit and then prove there cannot be a solution by a non-human, is still an open question. Penrose has his quantic processes inside microtubules explanation which seems a very up your sleeve answer. I don't know if that would be too different to a massively parallel machine with true stochastic non-determinism.
In any case attempting to compare the brain to a computer and calculating the maximum number of states in terms of bits for me is not fair. There are certainly hard physical limits but that pertains the question of consciousness tangentially.
Large scale models prove computers are very good interpolators. They also make evident they lack common sense.
Every time there is a new release of ChatGPT, Copilot, Bard/Gemini, etc. I challenge them with a simple non-computable problem like an example of the PCP. Every time they fail trying to nail down a correct solution. And worse, they try to convince me they can solve the problem and their answer is correct, showing that a computer is still behind pulling the strings.
I once worked in a project that allowed truck drivers to print invoices with a Palm device to printers that needed an IrDA transceiver dongle. What would have been a no-more-than-a-week project in any other sane embedded system turned into a 3 month ordeal. Time was mostly spent troubleshooting and debugging the several layers of the system, from the physical up to the application. Many years after that I worked in BT and BTLE devices and, although I had better tools and software stacks, my experience was exactly the same. Just browse the issues in the BlueZ forum developers face even when attempting to do silly and simple stuff. Imagine trying to use BT hardware and software to do more sophisticated things like synchronizing the audio stream of multiple BT speakers.
In the last years many of the new BT features that are continuously being added to the spec feel like an afterthought. Specially in critical areas like security. Contrast that to a technology like WiFi that was always intended as a typical network communication ecosystem. Things have improved a bit since there is undoubtedly more experience due to all the devices out there with more performant hardware. However the fact that you need to deal with an onion of multiple hardware and software components, each with its own intricacies as a result of the engineer's interpretation of a complex specification - and therefore very difficult to verify and test, explains for me the current situation we are in.
I cannot attest about this particular case, but I can believe that in a similar situation today with all the access to resources through technology we have, the things that capable kids under these conditions could do would be far more reaching than ever.
Audio is a particular good application of this. For example, the old ADPCM algorithms have evolved naturally into their ML counterparts. Some have even less parameters and thus are more computationally efficient because of the advantages of flexible feedback of the training or production models (e.g. RNNs).
It can be argued, since we don't know the ultimate cause of the laws of our universe, that we also rely in abductive reasoning and guide ourselves through models created by correlations based in our experience. But that has happened through millions of years of evolution and we still don't know how to build AI supervisors that can challenge that.
- The Pythagoreans dealt for centuries with the known conundrum of figuring out irrational numbers. I had a computer so I just run a script for measuring the total error with different bisecting rational quantizations (up to 256 IIRC) of note frequencies in the equal-tempered scale within one octave (2^(1/N) splits). Oh, peaks at 12, 19 at 24 on the low side of the counter. That is why they settled on 12 notes, middle eastern has 24 (just double the resolution) and why 19 also sounds good [1]. 12 seems like the minimum acceptable then. Ok, 10 minutes, move on.
- Since we know we can only approximate to irrationals and our brain tries to makes things even, moving through scales with increasing intervals (2^(n/12)) will normally accumulate "tension". Half notes sound spooky. Whole notes are a bit better. Too bad sound perception is logarithmic (= tempered scale) and has non-linear compression on both amplitude and frequency (Fletcher-Munson, etc). Double the frequency is an octave. Perfect fit, brain happy (2^(12/12)). Try to split an octave in half? Again, fitting a peg in the only wrong hole available when using half-note resolution. Welcome to accidentals and the Circle of Fifths. "Try", because of course you can't: 2^(7/12) = 1.498307.... Close to 150%, but no cigar. Close enough for a crippled monkey brain that can only hear up to 20kHz or so. They even named it "Perfect". Moving up: F to C, G to D, A to E...
- Music would be very dull and inadequate if we cannot shift notes up or down. However our brain still recognizes the patterns. We can even play those patterns at the same time, even on different instruments. So that pattern with the same scale on a G sounds good with the other guy playing C (harmonies). What if the guy playing the C wants to play like the guy on the G? Enter modes... Oh yeah, cool Myxolydian tunes. And minor scale too - don't forget that looks THE SAME as an Aeolian.
- Your new singer cannot hit that low notes. What about now moving everything up then? Transpose. We have "physical instruments" like a guitar. Easy, just play the same pattern some frets up. Done. Poor piano player who has a "logical instrument" with notes separated nicely in two different kinds based on half notes and that ugly 1.498307 fraction. Good that he is also good at math. So that C scale becomes a D. He just replaces on the fly some white keys with black keys... F# and C#. But wait a sec. Didn't the Circle of Fifths also moved F to C too? Does it continue like that for all notes? Yes it does! Transposing has the same structure as modes the other way around! So what if instead of moving up we move down, or play the same pattern in the original C scale? For every raised (sharp) accidental we get it's complement lowered (flat) one. Of course, since 7 + 5 = 12! The Circle of Fifth is complete. B to E, A to D, G to C... That G pattern moved down to C? G major scale (aka Ionian) has one accidental: F#. The first flat is Bb. C scale with B lowered to Bb... Yep, Myxolydian indeed!
- We can also use those interval numbers to name chords when we play notes together. We can also name the scales when adding and removing notes, maybe borrowing from other scales. Sounds pentatonic or exotic. The sky is the limit.
- Piano player now teases the guitar player. Now it's her turn to do the math. Looks like "physical" and "logical" instruments are also complementary. What is easy on one needs thinking on the other, and vice-versa. Win-win.
Honestly, that covers like 95% of practical music note theory. Of course there is much more to it (note, rhythm, history, etc). If they have just started explaining it like that without all the mumbo-jumbo it would have made sense since day #1 and I would have saved many years of my life hitting my head in the wall and trying to learn things I forgot within a week. Perhaps the main issue is that not many music teachers are good at math or they would think their students would get scared if they told them it's all math underneath?