Letters to the editor: philosophy by numbers

  • These letters to the editor will be the final pair published until such a time that the threat of the coronavirus is behind us and we are permitted to freely roam the streets once again.

    David H. writes…

    Hi John,

    I wanted to say a quick hello, and offer appreciation for your recent episode, where you discussed expertise and the way we shift perspectives — and how difficult that can be.

    I’m a philosophy professor in Denver and I specialize on pragmatism; this school of thought saw Darwinian evolution as profoundly influential even for philosophical theory. William James gave a good overall account of the battle pragmatist theory itself was facing by setting it in the larger framework you described in your episode. In his articles and in his book Pragmatism, James writes,

    “I fully expect to see the pragmatist view of truth run through the classic stages of a theory’s career. First, you know, a new theory is attacked as absurd; then it is admitted to be true, but obvious and insignificant; finally it is seen to be so important that its adversaries claim that they themselves discovered it.” (from his book)

    As someone who researches pragmatism and also aesthetics and experience — but who’s just getting fully into audio now (at a higher level than before) — I find it so interesting to hear those with expertise in a non-philosophical area get philosophical. As a pragmatist, my M.O. is to reach beyond theory into arenas of practical and aesthetics life where there is something I can learn; to read (or hear) someone from that arena reaching back toward philosophy is a treat. I’ve recently heard the Currawong guy do this about objectivity/subjectivity and also Andrew Robinson, a bit.

    So — that’s it. I appreciate the effort and difficulty involved in trying to say something at such a general level. Many who look to you for gear reviews may have a different reaction, but I loved it and wanted to tell you.


    David H.
    Professor and Chair, Philosophy
    University of Colorado Denver, USA

    A long-form email for one Mathias P. …

    Hi John,

    I hope you don’t mind if I call you John. First of all, I’d like to say, that I really enjoy your Youtube channel. I’m watching almost all of your videos, even if the gear that you present is of minor interest for me. But the way you present it is always entertaining and that makes a good channel. Big fan 😉

    It seems, that you’re struggling to explain why digital audio matters and why it’s not just ones and zeros. It seems that there’s also a big part of the community still doubting that digital can make a difference, even if a simple listening test would prove the opposite. But some people obviously trust what they’ve been told more than what they hear. But that’s another story…

    In the media, they always talk about jitter and noise and the importance of power supplies, clocks, galvanic isolation. They are right, but they never comprehensibly explain why that makes a difference.

    So, here’s my attempt that might explain why digital signals matter:

    First of all, we have to understand that there is a difference between signal and information.
    To make things clearer, I’d like to use the expressions transmission, signal and information.

    So what does that mean?

    Let’s start with an analog transmission where the information is „hard coupled“ to the signal. The signal IS the information, so to say. When we send a perfect 1kHz sine at a certain level to a speaker, it will reproduce a perfect 1kHz sine wave at this level. When this signal picks up noise or it is distorted or damped, your speaker will reproduce the distortion, the noise and the level will be slightly lower. So the information you hear is one to one the signal that your speaker receives.

    No surprise so far. Right?

    So now let’s look at a digital transmission. Here things a bit different. Now the signal is decoupled from the information because the information is quantized. The information is just represented by the signal. Let’s say we’re sending a perfect square wave to a receiver and on its way the signal is distorted. This won’t affect the information, because the receiving IC doesn’t simply „reproduce” but interpret the signal. If the voltage level exceeds a certain threshold within a certain time window, it will switch on and you have a logical one. If not, it stays off and you have a logical zero. So within each time voltage window (for one / for zero) the signal can have infinite states that still represent the right/same information.

    So your signal can be distorted, as long as it fulfils the requirements for a correct „interpretation“ of the receiving IC without affecting the information and that’s the reason why you can transmit digital data over long distances without any information loss, even if the signal is distorted.

    So far, nothing new. Just a slightly different way of seeing it.

    Now things are getting interesting 😉

    When we listen to digital audio, the digital information (the ones and zeros) from your hard drive will be transferred from your streamer into a digital signal (a square wave) and this square wave will be modulated from your DAC into an analog signal. At this point, the information is no longer decoupled from the signal! It is really important to understand that the digital signal is transferred into an analog signal. Not the digital information! That means that all the distortion that you have on your digital signal will be transferred to the analog signal! Now the information is „hard coupled“ to the digital signal and therefore all the benefits discussed before are lost.

    To make things a bit clearer, let’s look at an example. Let’s take DSD.

    In most DAC chips the conversion is made via DSD. Technically it uses (PDM) Pulse Density Modulation. So you have a square wave at a very high frequency and the density of these pulses lead to a certain level on the analog side. That signal can be seen as a digital signal. High voltage is one, low voltage is zero and that’s the way native DSD files are stored. An array of ones and zeros and the density of the ones represent the level.

    To convert this digital signal into an anlog signal you need nothing more than a low pass filter. A small capacitor and resistor can do the job. But that also means that all distortions of this digital signal are passing the low pass filter.

    Let’s say the voltage is not perfectly constant due to a poor power supply. These overlaid voltage fluctuations (different heights of the pulses) will pass the filter.

    Let’s say you have jitter and the blocks of your square wave are not equally wide. That would result in a density fluctuation and lead to level fluctuation of your analog signal.

    Let’s say the blocks are not perfectly square and they look more like a saw tooth. This will affect the density and therefore the analog signal.

    Noise is very often claimed to be a big problem in digital audio. Just think what happens when high-frequency noise interferes with a high frequency-digital signal. You’ll probably get beats* when the noise frequency is close to the signal frequency which will probably lead to a tremolo in the audio band.

    * check Wikipedia: beat (acoustics)

    To summarize:

    As long as we transmit digital information, signal and information are decoupled, we have no losses, the world is alright. But when we want to reproduce music, the information is coupled to the signal and all the problems we have with analog audio appear again.

    This is actually just a very rough look at this topic. We actually have to understand, how the distortion on the digital side will be modulated to the analog side. DSD is actually a very simple example. That’s why I have chosen it. For PCM and ladder DACs the modulation is completely different. For simplicity, I’ve also ignored reading errors.

    I hope my explanations are comprehensible and maybe they help.

    If something is unclear or if you have any questions, please don’t hesitate to contact me.

    Best regards from Munich


    Written by John

    John currently lives in Berlin where he creates videos and podcasts for Darko.Audio. He has previously contributed to 6moons, TONEAudio, AudioStream and Stereophile.

    Darko.Audio is a member of EISA.

    Follow John on YouTube or Instagram

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