
Notes on Resonance - AriaMinaei
http://worrydream.com/NotesOnResonance/
======
ohazi
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.

------
AriaMinaei
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.

~~~
pcmaffey
Do you have recommended reading for Papert's work on constructionism /
learning theory?

~~~
AriaMinaei
Mindstorms was how I was introduced to it. Can't recommend it enough. (PDF
freely available on Bret's site:
[http://worrydream.com/refs/Papert%20-%20Mindstorms%201st%20e...](http://worrydream.com/refs/Papert%20-%20Mindstorms%201st%20ed.pdf))

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mike555
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.

~~~
trevyn
> _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.

~~~
mike555
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?

~~~
trevyn
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.

~~~
mike555
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 ...

------
ubasu
"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.

~~~
whatshisface
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.

------
pitaj
This is resonance:

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.

That is what we call resonance.

[1]:
[https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg](https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg)

------
spiralganglion
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.

------
CGamesPlay
In what physical context do we multiply signals together instead of adding
them?

~~~
lowleveldrone
In a radio, this is done by a mixer circuit, for instance
[https://en.wikipedia.org/wiki/Gilbert_cell](https://en.wikipedia.org/wiki/Gilbert_cell)

------
Strilanc
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.

[1]:
[https://en.wikipedia.org/wiki/Frequency_mixer](https://en.wikipedia.org/wiki/Frequency_mixer)

~~~
elihu
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](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.

------
acobster
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.

------
Animats
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.

But no.

------
richardburton
I have watched this talk from Bret Victor at least once a year to help me
think about what to work on:

Inventing on Principle
[https://vimeo.com/36579366](https://vimeo.com/36579366)

------
teilo
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.

------
burlesona
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.

~~~
typon
I don't think you can be a successful and creative person if you are always at
the whims of random internet commenters.

~~~
whatshisface
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.

------
klodolph
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.

~~~
lisper
>> (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](https://en.wikipedia.org/wiki/Mixing_console)

~~~
gugagore
You are certainly correct in audio applications. "mix" usually means "add".

However in many other signal processing applications, "mix" means "multiply".
[https://en.wikipedia.org/wiki/Frequency_mixer](https://en.wikipedia.org/wiki/Frequency_mixer)

------
carapace
(Small grey sans-serif text means you hate your readers' eyes.)

~~~
jonsen
(That's why it's used for downvoted comments.)

------
tzahola
I 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...

~~~
gugagore
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.

~~~
tzahola
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??

~~~
lpmay
Mixers are physical systems. The precise words for the distinction you are
trying to make is between linear and non linear systems.

