What math exactly would you like me to do? 16 bits gives a theoretical maximum range of 96dB while the human ear can hear over 130dB. Good headphones can handle over 100dB signal to noise.
Maybe you should save your grandiose lectures for somebody who doesn't know enough to see through it. There's no reason to assume levels will be at a "reasonable" level and there's no reason to think a high-quality portable music player should only play back 16 bits. That's absurd. Should consumer level music players stop at 16? Sure. I want better than that but if you want to listen to mp3s on your phone nobody's stopping you.
I'm left wondering how much of this anti-Pono talk is shilling on behalf of smartphone manufacturers. I need 24 bit playback in roughly the same way I need a car that does 0-60 in under 3.5 seconds - I like things that are over-engineered so I can geek out on how awesome they are. But thanks to all the killjoys we can't even get excited about the first high quality portable music player because some amateur sound engineers want to show off they once read a blog post on Shannon-Nyquist theory.
24 bits has more information. It's useful for mixing and in cases where things haven't been properly gain-staged, an engineer had an off day, a track hasn't been mastered, etc. Seems pretty basic to me.
I disagree that these things are, in the real world, "solved problems" and I'd rather have an unmastered raw track at 88/24 than a poorly mastered track at 44/16.
I don't disagree that CD quality basically maxes out the ear's natural capabilities, I don't think it's that easy to do.
For a remix I'd rather get a 24-bit stream than a 16-bit stream (that's really 15 bits) and has to be padded up to 24 anyway.
As I ceded in another comment, dithering trades harmonic distortion for noise.
> In order for it to be even theoretically possible to hear the difference between 16-bit and 24-bit audio,
Only for professionally mastered audio which is not a safe assumption in this day and age. If some home engineer recorded a track with too much headroom and you get the 24-bit track you're fine, at 16-bits you have a problem.
I would love a music player where I could play tracks at 88kHz/24-bit because that's what most music is during the mixing process and then an audio engineer can give you the raw version of what they're working with without having to deal with issues of headroom, downsampling and dithering.
24-bit audio doesn't hurt anything other than file size and it has real uses, be it remix culture or just high-quality unmastered music.
Dithering basically raises the noise-floor by trading harmonic distortions for random noise at the cost of the last bit of information (for the uninitiated dithering means you randomly flip the last bit to create a soft truncation.) It's "noise" which isn't technically harmonic distortion but that's kind of splitting hairs isn't it?
I have no patience for articles like this because instead of setting the record straight it just adds more pseudoscience to the mix. Their "experiment" doesn't prove what they claim it proves.
Is 24-bit useful for playback? Yes it is. Do you need it for properly mastered audio? Absolutely not. But there are 10,000 home studios across the country who have music files at 24-bits and a large chunk of those engineers don't know how to master audio. Is a raw 24-bit track better than a poorly mastered 16-bit track? It is to me.
Is 192kHz useful for anything? Probably not. Does it hurt anything? Maybe a little. I would expect a quality music player to go up to 96 anyhow so 192 isn't so bad. Similar reasons as before.
Does this reflect badly on the Pono player? Not really. Over-engineering isn't a bad thing in my book.
When you do experiments you must understand your experimental design enough to understand exactly what you're testing and what conclusions can be drawn from that. If you do A/B testing of 8-bit/16-bit (which is a good idea) you have to understand you're doing the test through your current audio hardware.
The whole point of the Pono player is to have higher quality hardwhere everywhere, including pre-amps and DACs so you have a chance to hear subtle differences.
If you do this test through your laptop speakers you really might not be able to tell the difference. If you'd like to "debunk" the Pono player then do this test through a Pono player pushing music through quality studio headphones.
Making things worse they're using Neil Young's Rockin In The Free World which contains, get this, large amounts of harmonic distortion to begin with. The pre-existing harmonic distortion will only serve to mask any distortion and fidelity loss from truncating to 8-bits.
If you don't own high-fidelity music equipment then this test is like proving high definition television is impossible because you can't tell the difference between a standard and high definition signals on your standard definition TV.
Momentum and Special Relativity don't conflict. Momentum is modified with a Lorentz Factor which for a particle with mass runs to infinity as the speed approaches the speed of light.
For electromagnetic radiation like light the momentum is a function of the energy, not the velocity.
You think what's reckless? The guy who wrote the article has a degree in Electrical Engineering and the article's great.
EMF is not a force and it's not the only thing the word electricity refers to. I've just checked a physics and an electrical engineering textbook and neither refer to electricity or EMF the way you are. I honestly don't know where you're getting these ideas.
In physics there is a fundamental force sosmetimes called The Electromagnetic Force, and in a sense it does describe all of electricity, but it's not the same thing as The Electromotive Force.
> I wonder what the turning point was when people stopped thinking of electricity as magic and instead thought of it as science
Once they could make predictions and those predictions were verified by reality. "When I flip this switch the light will turn on.....When I move this magnet past this wire I can shock my lab assistant...."
I don't know much about D&D but I would venture the guess that electrons are far stranger than mana. I mean, not only do they have a wavelength[0], you can do the Double Slit experiment with them[1], but they also have an intrinsic angular momentum and there are rules of which electron can be where based on this "spin"[2]. That's just for starters.
Calling them "mana" (whatever that is) might not be any more wrong than calling them particles.
To say electricity is roughly the flow of charge looks perfectly fine to me. Opening statement of the wikipedia article on electricity:
> Electricity is the set of physical phenomena associated with the presence and flow of electric charge.
I doubt the article will steer people wrong. The gravity/e-field analogy is accurate, and they're clear to state that Bohr model of the atom is a useful model while providing a link to more info so interested readers could dig in there if they wanted.
> Electricity is the force not the flow...."Electricity"...is always the EMF
Speaking of details the Electromotive Force isn't a force because it doesn't have Newtons for units. EMF times charge does give a force but EMF alone is just Volts. In circuits we may think of it as if it's a force, and it has force in the name, but it's just a potential difference.
Without invoking the maximization of utility we could use game theory and ask if the players were simply minimizing their maximum regret. It was during the qualification rounds, not the finals. It looks like they each preferred taking an advantage or a draw (chosen by their opponent) over playing against a world-class player at a slight disadvantage.
Nakamura's shown that he'll play interesting and sometimes dubious moves because he wants chess to be more entertaining for spectators. He spends a lot of time playing online against weaker players so they can have the memory of that one time they played against one of the best. He's done so much for chess and its popularity that if he takes an early draw once in a while he gets the benefit of the doubt.
> This quote speaks volumes about your own perspective.
Does it? I was pointing out that today there are motives for publicly supporting women in the sciences that didn't exist in 1966. In that quote Feynman pushed things in a progressive direction in a different political atmosphere than we live in today.
> I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up--that is, if you go over each time the same amount when you go up a row, you make a straight line--a deep principle of analytic geometry! It went on. I was rather amazed. I didn't realize the female mind was capable of understanding analytic geometry.
She went on and said, "Suppose you have another line coming in from the other side, and you want to figure out where they are going to intersect. Suppose on one line you go over two to the right for every one you go up, and the other line goes over three to the right for every one that it goes up, and they start twenty steps apart," etc.--I was flabbergasted. She figured out where the intersection was. It turned out that one girl was explaining to the other how to knit argyle socks. I, therefore, did learn a lesson: The female mind is capable of understanding analytic geometry. Those people who have for years been insisting (in the face of all obvious evidence to the contrary) that the male and female are equally capable of rational thought may have something. The difficulty may just be that we have never yet discovered a way to communicate with the female mind. If it is done in the right way, you may be able to get something out of it.
That's almost 60 years ago that he went on record saying that pedagogical issues may be affecting women in mathematics and he had lost faith in the assumption of their inferiority. This wasn't just anybody saying this and this wasn't just any physicist saying this - this was Feynman. This was the guy the other physicists looked at in awe and it was the year after he won his Nobel Prize for Quantum Electrodynamics. Few physicists have ever earned so much respect from their peers.
If that's not convicing then read how he was the one who encouraged his sister Joan to pursue science against the wishes of their mother who thought women lacked the cranial capacity to do science. (http://www.aas.org/cswa/status/2003/JANUARY2003/MyMotherTheS...)
> It wasn’t until her 14th birthday—March 31, 1942—
that her notion of becoming a scientist was revived. Richard presented her with a book called
Astronomy. “It was a college textbook. I’d start reading it, get stuck, and then start over again.
This went on for months, but I kept at it. When I reached page 407, I came across a graph that
changed my life.” My mother shuts her eyes and recites from memory: “‘Relative strengths of the
Mg+ absorption line at 4,481 angstroms . . . from Stellar Atmospheres by Cecilia Payne.’ Cecilia
Payne! It was scientific proof that a woman was capable of writing a book that, in turn, was quoted
in a text. The secret was out, you see.”
Richard was 23 or 24 when he gave her that book. Keep in mind this was the 1940's and it was the same year he received his PhD - so he wasn't just a kid and supporting women in science wasn't the popularity contest it is today. When 24 years later he made the other quote in 1966 he knew women were capable scientists because his sister had already become one.
This is all to say that before you take one chapter from one book out of context and extrapolate across his entire life make sure you get a few more data points to see if the extrapolation makes any sense.
As the blog comments suggest there's a difference between a good self-study book and a good textbook for a class. The book will be accompanied by (at least) what look to be a good set of course notes.
Some googling around suggests his students are quite pleased with him. He has, according to Wikipedia's intro for him, the undisputed king of math blogs. Both of these point to him being at least a good or above average educator.
Out of curiosity, what's the background that lets you be so dismissive of a Fields Medal winner?
At this point I see a blog post written by a well respected mathematician whom I feel comfortable trusting and it's being brushed aside by I don't know who.
For anybody who studies science that isn't an uncomfortable question and it's over century old at this point. The last time the field of science had a high level of certainty that it would solve everything ever was probably the late 1800's.
I dealt with this question in high school physics, it's really no big deal. When you get to a point where all you can do is make a "metaphysical claim with no greater merit than its opposite" you go find something better to do with your time.
For me looking into String Theory's status as scientific/not-scientific is a good way to learn that the Popperian view of falsifiable==scientific is a bit too simplistsic and that classifying things as scientific/not-scientific may not even be a productive activity. It's just not that simple.
A good quote from that thread which may answer your question: "Anyways, my point is that String Theory is not just some whacky idea "what if everything was strings" that exists in a vacuum, but is rather a very natural and conservative extension of Quantum Field Theory to a more general and less arbitrary framework."
It's a good approximation but it misses the mark. String Theory is not verifiable but it's still a scientific theory. Bohmian Mechanics is, some say, by definition not verifiably different from Quantum Mechanics but it's a scientific theory. You might call them "speculative" scientific theories to save the idea but at the end of the day the Popperian [sic?] view of science is a bit too simplistic to be useful.
Is it harder to understand distribution than memorize FOIL? Probably. It's memorizing a process vs. understanding a concept. FOILing won't help you master algebra but if you're in a science class and your teacher needs to get you up to speed on multiplying pairs of binomials then they'll likely just show you FOIL.
I agree with you that FOILing is stupid and might make the student worse off in the long run, but I think depriving them of getting practive with heuristics might be worse. Ideally a student would notice that FOIL isn't a good trick and stop using it, but there are other "tricks" that are extremely useful.
Maybe you should save your grandiose lectures for somebody who doesn't know enough to see through it. There's no reason to assume levels will be at a "reasonable" level and there's no reason to think a high-quality portable music player should only play back 16 bits. That's absurd. Should consumer level music players stop at 16? Sure. I want better than that but if you want to listen to mp3s on your phone nobody's stopping you.
I'm left wondering how much of this anti-Pono talk is shilling on behalf of smartphone manufacturers. I need 24 bit playback in roughly the same way I need a car that does 0-60 in under 3.5 seconds - I like things that are over-engineered so I can geek out on how awesome they are. But thanks to all the killjoys we can't even get excited about the first high quality portable music player because some amateur sound engineers want to show off they once read a blog post on Shannon-Nyquist theory.