In what physical context do we multiply signals together instead of adding them?
You know AM radio? That's Amplitude Modulation. Modulation here means "multiply your audio signal by a carrier signal".
Notes on Resonance
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Re: Notes on Resonance
#22This is, at best, a misleading presentation on resonance, and my first reaction is that it’s completely and horribly wrong. > The coupling between the two sources is represented by the product of these signals. (Bringing signals into a context for multiplying is called “mixing”.) The parenthetical is technically correct, but when two systems are coupled they only "mix" if there are strong nonlinearities. Normally whe…
>> (Bringing signals into a context for multiplying is called “mixing”.) > The parenthetical is technically correct Not really. In common parlance (e.g. [1]), mixing means adding. If you mixed signals by multiplying, music would sound like noise. [1] https://en.wikipedia.org/wiki/Mixing_console
Yes, the parenthetical is correct. Words like “mix” have different meaning in different technical contexts. In signal processing, “frequency mixer” is a common meaning. https://en.m.wikipedia.org/wiki/Frequency_mixer
Re: Notes on Resonance
#23I don’t know what kind of resonance this post is talking about, but I’ve never heard of time domain signals being multiplied in a physical system...
time domain multiplication is frequency domain convolution.
Which is great if you want to shift the frequency band of some signal. Like if you have 2 songs that you want to play over radio in the same, shared airspace, you shift them to two different frequency bands. This happens electrically/RF-ly as a multiplication.
Re: Notes on Resonance
#24Why are the signals being multiplied together instead of added together? Multiplying them is very unusual. Even the wikipedia article linked by the site, with the text "Bringing the signals into a context for multiplying is called 'mixing' [1]", is talking about adding signals; not about multiplying them. A bit more justification for the math being done would be good. [1]: https://en.wikipedia.org/wiki/Frequency_mixe…
It is not unusual at all to multiply signals. That is how basically any modern radio transmitter and receiver works. It's also how you can convert between the frequency and time domain, which is used in basically any sort of perceptual compression (jpeg, mp3).
Re: Notes on Resonance
#25Why are the signals being multiplied together instead of added together? Multiplying them is very unusual. Even the wikipedia article linked by the site, with the text "Bringing the signals into a context for multiplying is called 'mixing' [1]", is talking about adding signals; not about multiplying them. A bit more justification for the math being done would be good. [1]: https://en.wikipedia.org/wiki/Frequency_mixe…
Actually, the frequency mixer wikipedia page is describing a kind of mixer that multiplies.
The wikipedia page on "electronic mixers" is more informative:
> An electronic mixer is a device that combines two or more electrical or electronic signals into one or two composite output signals. There are two basic circuits that both use the term mixer, but they are very different types of circuits: additive mixers and multiplicative mixers.
https://en.wikipedia.org/wiki/Electronic_mixer
This was news to me; the mixers I'm familiar with are additive. I would call something that multiplies a ring modulator or a heterodyne or something like that. The website could have been a bit more clear that they're talking about a different kind of mixer than how most people understand the term.
Re: Notes on Resonance
#26I strongly suspect that the article is allegorical. That it's describing the resonance between people, using waveforms as a metaphor.
If it were just a technical article, the last step — where you bring the two signals back into phase with each other — would be pointless and redundant. But if the true meaning is outside the mechanistic / technical, then that last step has tremendous purpose.
Bret's background is in electrical engineering. He knows the proper technical meanings of all the terms and concepts in the article. So rather than simply pointing out that he's "misusing" them, perhaps look for reasons that he might have intentionally chosen to do so.
Re: Notes on Resonance
#27While I do like the aesthetics of this, as others have mentioned it is plain wrong. Any explanation of resonance should deal first and foremost with a physical system, not a signal. Having two signals 'resonate with each other' does not make a lot of sense. Not sure what is meant with multiplying because the author then goes to mention integration which in essence, is adding, not multiplying. A physical system is abl…
> it is plain wrong > Not sure what is meant Which is it? :-) As I interpret it, this article is not a scientific description of a particular physical system, but a metaphor. That said, it does make sense in the signal domain. Consider electrical and optical resonance. It gets more interesting when the components are complex-valued.
It's the first one :)
This page is more about constructive interference than it is about resonance. Maybe that's what you are thinking about also?
Re: Notes on Resonance
#28I think you can put together a list, hopefully a long list, of people whose careers would've been very different had they not been exposed to Bret's work. He introduces you to a vast network of ideas, most of which, if you're like me, you only start to appreciate after you've seen a bit of Bret's work. He makes those ideas accessible, beside furthering them on his own. From Engelbart's idea of "aligning human systems…
Do you have recommended reading for Papert's work on constructionism / learning theory?
Mindstorms is probably the best place to start, but there's a list of papers here: http://www.papert.org/works.html
Re: Notes on Resonance
#29I don’t know what kind of resonance this post is talking about, but I’ve never heard of time domain signals being multiplied in a physical system...
time domain multiplication is frequency domain convolution. Which is great if you want to shift the frequency band of some signal. Like if you have 2 songs that you want to play over radio in the same, shared airspace, you shift them to two different frequency bands. This happens electrically/RF-ly as a multiplication.
I know this, but how does it relate to resonance in physical systems?
E.g. imagine a rigid pendulum driven by a sinusoidal torque at its pivot point. Which signals are multiplied here??
Re: Notes on Resonance
#30Hah, when I skimmed this all I thought was "neat visualization." Then I came to the comments... It must be a real high as an author when you see your site is getting a flood of traffic from hacker news - then a hell of a crash when you check it out and all the comments are torching your work.
I don't think you can be a successful and creative person if you are always at the whims of random internet commenters.