There are contexts in which multiplying two signals make sense. Others have mentioned electronic mixers like the ones used in radio modulators / demodulators. There are other contexts in which adding makes sense, for example when determining the signal received at a microphone when multiple people are talking. Or the signal received by an antenna when multiple transmitters are transmitting.
Bret describes a "local signal" and a "signal received from a distant source." I think most people (non electrical engineers, anyway) would imagine the local source as someone speaking into a microphone, and the distant source as someone shouting from across the room. In this scenario, we should add the signals, and everything that follows is incorrect.
But to an electrical engineer, the "local signal" could be a local oscillator, and the "distant signal" could be the received signal at the antenna. In this case, we feed both signals into an electronic mixer, and multiplying is the correct way to think about it.
I know Bret is really big on abstractions, but the context actually matters here. You might be able to abstract away some of the physical parts (microphone, antenna, demodulator, etc.), but you can't just skip over additive vs multiplicative contexts.
I 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 and tool systems, with workers spending time improving their tools for improving their tools, leading to accelerating rate of progress," to Papert's brilliant work on the nature of learning and play, ideas that focus my direction and give me joy, I can't help but always remind myself that I may have never learned of these ideas had it not been because of Bret's work. Thank you Bret.
While 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 able to store energy at specific frequency -- a pendulum will swing for a long time, energy slowly decaying. But if the system is excited (imagine a kid on a swing), with each push, we will add some more energy, which will accumulate each time adding to a large response (resonance). The key part is, we need to add energy at the right frequency, push at the right interval, sing with the proper pitch.
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.
So you’re saying the page is simply incorrect and hints at no interesting ideas?
I see the world as composed of interconnected entities which metaphorically influence and resonate with each other, and there is a lesson in the creation of (metaphorical) power by the closer synchronization of these entities.
I extrapolate the implications of this as literally revealing a path leading to world peace.
In sum, I enjoy thought-provoking interpretations way more than thought-restricting interpretations.
It was never my intention to hate or shut out any possible metaphorical ideas.
I first heard of Bret couple times already in a very favourable light and he's on my read todo list.
The thing is that I have one very specific definition of resonance in my mind based on my line of work. Still I do believe it's always good to be open to different interpretations ...
>I see the world as composed of interconnected entities which metaphorically influence and resonate with each other, and there is a lesson in the creation of (metaphorical) power by the closer synchronization of these entities.
Well, half of Sedona residents would agree. But that doesn't describe anything specific of the physical world that a post on physics (as the post appears to intend to be) would cover.
"Resonance occurs when two sources of excitation fall completely in sync, and reinforce one another endlessly."
This is incorrect, even according to the wikipedia article it links to.
Resonance occurs when the excitation frequency matches a natural frequency of the system being excited, causing it to vibrate at larger amplitudes, even perhaps uncontrollably.
It seems that the author misunderstands mixing also - the graph that he presents for the mixed signal seems to be incorrect according to the other wikipedia article he links to.
Yes, the author is describing constructive interference instead of resonance, although the fact that they said multiplication instead of addition indicates that they aren't really speaking correctly about either one.
Imagine an system composed of a mass hanging from a spring, like this [1]. If you pull down the mass and release, the mass will move up and down (oscillate) at a set rate (the system's natural frequency). No matter how far you pull down the mass before release (the amplitude), the system will always oscillate at the same frequency.
Now, imagine you start pushing on the mass (applying forces) while it is in motion. If you were to push up on the mass while it is traveling down, you would decrease the distance the mass would move on subsequent oscillations (damping the amplitude). But if you were to push up on the mass as it travels up, you would be increasing the amplitude of oscillation.
I 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.
Why 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.
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.
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.
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).
I guess he just means sympathetic frequencies or something like that, rather than resonance. As an admirer of Bret's other work, I'm guessing he intended this as a showcase of interactive illustrations of how frequency works in composite. Too bad the terminology is off.
I was hoping this was going to lead into a clear explanation of how a phased-lock loop works. Or a superheterodyne receiver. Or how periodic devices with almost the same frequency and a little coupling fall into synchronization.
I love the visuals, but the problem is in the first sentence: "two sources of excitation." That's not it at all.
If this were remotely true, then when I synced the oscillators on my synthesizer, the volume level would grow uncontrollably. But of course what actually happens is that the amplitude (approximately) doubles.
The problem is that the diagrams do not show what resonance actually is, but only what happens then the frequency of an excitation source matches the resonant frequency of a receiving medium, and in addition when the energy input exceeds the damping effect of the medium.
Nevertheless, it's still a great visual, provided the explanation is corrected.
Hah, 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.
HN commenters have been highly favorable to Bret's work over the years, though it might not feel that way because a small portion of negative comments typically makes a deeper impression than large blocks of praise.
This submission is a special case because there's a controversy around a factual question and the article itself doesn't disambiguate it. No internet forum could resist being triggered in that case. Fortunately it doesn't happen often, and certainly not when discussing Bret Victor articles.
It certainly is a good visualization, but just not for "resonance". It could be good for explaining e.g.
* frequency decomposition
* phase locked loops
* dot products between functions (Hilbert space)
Oftentimes, commenters are aimless cynics - this is especially common in things related to art (where nobody is really more right than anybody else) and business (where anybody who really knows what's going on would be better served by taking action themselves.) When it comes to centuries-old science you're either right or you're wrong, and there's no place for very convincing, very beautiful presentations that are wrong.
This 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 when considering resonance you’re thinking of systems that are approximately linear, or even linear time-invariant systems. Under these approximation, the multiplication happens in the frequency domain which is fundamentally different.
Consider a wine glass and a speaker emitting a sound wave. If the speaker is tuned to the resonant frequency of the sound wave, you can shatter the glass—this is not because the signals are multiplied, but this is just because frequencies near the resonant frequency decay more slowly, so the speaker can keep adding more and more energy to the glass until it breaks.
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
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.
Bret describes a "local signal" and a "signal received from a distant source." I think most people (non electrical engineers, anyway) would imagine the local source as someone speaking into a microphone, and the distant source as someone shouting from across the room. In this scenario, we should add the signals, and everything that follows is incorrect.
But to an electrical engineer, the "local signal" could be a local oscillator, and the "distant signal" could be the received signal at the antenna. In this case, we feed both signals into an electronic mixer, and multiplying is the correct way to think about it.
I know Bret is really big on abstractions, but the context actually matters here. You might be able to abstract away some of the physical parts (microphone, antenna, demodulator, etc.), but you can't just skip over additive vs multiplicative contexts.