That is a whole 'nother subject. Before going there, maybe we can agree that Kosko's point about fuzzyness is not bivalently false?
It is bivalently true in quantum physics, as theorized by Schrödinger. I do not know if it has value in other domains.
Some theoretical physicists are not so sure Schrödinger's model is the final word. Highly complex deterministic behavior can appear to be statistical. According to some people, we won't know until we understand nature at Plank Scale. IIRC probing the corresponding energy level would require an accelerator larger than 10 times the size of the sun. Maybe take a Kardashev Scale type III civilization to do that.
https://thedebrief.org/what-would-a...implies that the required,the size of the Sun.
https://kardashev.fandom.com/wiki/Category:Kardashev_Scale
When did that become a given? Striking coincidence it maps so well to the physical world if so.
Okay. Maybe 'discovered' by man would be a better description? ...Epistemology has long history with various disagreements along the way. Some of math comes from that sort of historical roots.
OTOH, I know a guy with a PhD in abstract algebras. There is no practical application for his exact area of expertise. He makes a living doing other things. Maybe his specialty area is an invention? At least unless and until someone finds a practical use for it.
EDIT: Still, if there were never any men in the universe, would math as we know it still exist. That's not to say the universe is without any order, its just to say that man's models are not the final word.
Also, have seen some people who say things like an apple falls from a tree because the law of gravity demands it. Not exactly. IMHO its more like the law of gravity is a logical model invented by man to predict the effects of gravity.
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I was going to respond that Georg Cantor understands completely and transfinite numbers may be a candidate for invented math but a quick search suggests potential applications in high energy physics.
Okay, but which came first, the math for its own sake, or was it motivated by search for a model to help with physics? Is god or some alien force causing man to invent what he needs to know before he knows he needs it?
Maybe it goes both ways, but it's interesting how much (originally) "pure" math has ended up being useful in some way. The basic functions of digital electronics were invented/discovered by George Boole, who had no clue that the idea would ever be useful for anything.
https://en.wikipedia.org/wiki/Pure_mathematics
https://en.wikipedia.org/wiki/Pure_mathematics
Well OK. My point is that complex numbers are a reliable design tool, not that they circumvent the laws of physics.
Capacitors have resistance and inductance (and a resonant frequency). Some capacitors are nonlinear with respect to voltage.
Resistors have capacitance and inductance. Inductors have resistance and capacitance. Transistor junctions have a nonlinear base-emitter and collector-base capacitance. Etc, etc, etc.
In spite of that, I still use complex numbers to obtain useful design parameters in a fuzzy world.
I expect "soundstage" is related to phase shifts. I worked in commercial video
for 45 years. In analog video we would measure "differential gain" looking for
amplitude changes of a high frequency (3.58 MHz subcarrier) riding on a low
frequency ramp (15.7 KHz line rate). This is exactly the same as I.M. distortion
in audio.. In video we also checked differential phase. The color subcarrier in NTSC
encodes the phase as HUE and the amplitude as SATURATION so the phase is even
more important than the amplitude.
Does anybody even measure the possible differential phase shifts in an audio
amplifier? It might be an interesting experiment.
G²
Steve Deckert uses imagery to describe soundstage and sound in general.
https://www.decwareproducts.com/papers/paper017
https://www.decwareproducts.com/papers/paper018
https://www.decwareproducts.com/papers/paper017
https://www.decwareproducts.com/papers/paper018
All that illustrates to me is that psychology is a work in progress at a very early level, and has a long way to do. Ever seen stats on repeatability of psychology studies?
That's because they are asked a question by a politician or similar, who wants an answer that's yes or no, and won't listen if given a full answer.
All education is like that, as billshurv said. At each level what is taught is expanded. But at no point in my education in science was I taught the sort of binary absolutes you allude to.
It seems - in those quotes, which may not represent his argument well - that Kosko is setting up straw people...
So what. Even if there were people who could hear a pin drop in Tokyo while drinking coffee in San Francisco it does not make sighted subjective listening more objective. Hypothesis alone does not carry far in science. Eventually you need to provide objective evidence as well.
The only things that should be measured are the room acoustic anomalies. Everything that addresses those anomalies must be auditioned by ear. And the placement of the speakers needs to be determined by ear, no matter which method you use for speaker placement. The room anomalies can be mapped out using a SPL meter and one or more test tones. 315 Hz, for example. Room anomalies include slap echo, first and second reflections, standing waves, other anomalous speaker produced regions of high sound pressure, for example on wall between speakers, etc. I look for sound pressure levels higher than say, 6 dB above the average sound pressure in the room.
There is an army of acoustic solutions, including but not limited to acoustic panels, echo tunes, tube traps, constrained layer dampers for walls and windows, Helmholtz resonators, Mpingo discs, diffusers, tiny little bowl acoustic resonators, crystals. I once constructed a 9 foot long folded S shaped Helmholtz resonator from PVC pipe, purple primer and PVC cement to address a nasty 75 Hz standing wave.
I almost forgot, one more thing, as a progress treating the boatload of acoustic anomalies you should check your speaker placement periodically because things change the better the room sounds the more accurately you can determine speaker locations.
There is an army of acoustic solutions, including but not limited to acoustic panels, echo tunes, tube traps, constrained layer dampers for walls and windows, Helmholtz resonators, Mpingo discs, diffusers, tiny little bowl acoustic resonators, crystals. I once constructed a 9 foot long folded S shaped Helmholtz resonator from PVC pipe, purple primer and PVC cement to address a nasty 75 Hz standing wave.
I almost forgot, one more thing, as a progress treating the boatload of acoustic anomalies you should check your speaker placement periodically because things change the better the room sounds the more accurately you can determine speaker locations.
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Of course the message of a whole book cannot be captured in a few brief quotes. If you read it and want to understand it you can, or you can go in with a mind to find any excuse to dismiss the whole thing. Its certainly a thing people sometimes do, decide what they think and reject an idea before ever understanding properly.
IMHO, what Kosko is trying to explain about science was the valence of his intuition about science versus math. How does one explain that intuition other than by telling a story that gives a sense of what the intuition felt like. It doesn't mean every word of the story is strictly, literally, mathematically true. Again iMHO, its purpose is to share a sense of the intuition that led Kosko in the direction of fuzzy logic and fuzzy thinking. I think if you read the book you will see what it is he is trying to explain.
Changing the subject a bit, fuzzy logic in particular was deemed a threat to science by some scientists as it runs somewhat counter to the precision of logical positivism. However, logical positivism had already been on the decline for some time.
Quoting from near the end of the logical positivism article at Wikipedia:
By the late 1960s, logical positivism had become exhausted.[50] In 1976, A. J. Ayer quipped that "the most important" defect of logical positivism "was that nearly all of it was false", though he maintained "it was true in spirit."[51][52] Although logical positivism tends to be recalled as a pillar of scientism,[53] Carl Hempel was key in establishing the philosophy subdiscipline philosophy of science[16] where Thomas Kuhn and Karl Popper brought in the era of postpositivism.[48] John Passmore found logical positivism to be "dead, or as dead as a philosophical movement ever becomes".[51]
https://en.wikipedia.org/wiki/Logical_positivism
https://en.wikipedia.org/wiki/Postpositivism
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