abstrakraft

Just because the event is true doesn't mean it's presented with the correct statistical context. For example, if, hypothetically, 2 people developed complications from the vaccine out of a treated population of 20 million, a front page headline exclaiming "Covid Vaccine Causing Complications" would be technically true, but also propaganda.

The linked article is about a town in Antarctica, not Alaska.

I'd add to that: How do we keep stereotypes from reinforcing themselves?

If you go through life looking to be offended, guess what? You're going to get offended.

The whole point of this thread is that Apple is telling us to not rely on dead simple devices (camera covers, tape, etc.), and instead to trust their internal mechanism that they claim can't be beat. If people take them at face value, but the mechanism is in fact complex enough to admit an exploitable vulnerability, that's a net loss of security, and is a step in the wrong direction.

They also claim that if you add a (MFI-compliant) case to the iPad, and close it, that this similarly disconnects the microphone. The simplest mechanism to do this sounds complicated enough that it reduces my confidence in the mechanism. The point of half the comments in this thread is that a hardware interlock mechanism needs to be dead simple. This sounds like a step in the wrong direction.

A capacitor would also mean that you could quickly switch the camera on and off without triggering the light.

And what sort of hardware switch is it that guarantees the 3 second minimum?

Taking a selfie requires no preparation. We've all got cameras on our phones, so it's easy enough to do. I'm not really a selfie person, per se, but in the right place and context, I might snap one for posterity.

A tourist walking around with their phone in a selfie stick has put preparation and forethought into the endeavor. Before leaving their hotel to see some wonder of the world, they consciously thought, "I'm going to take a bunch of selfies today so I can post them on social media and gain influence because I'm somebody." This attitude represents everything many people blame for giving rise to the modern overcrowded tourist destination experience.

I'm sure there exceptions, and some people just like pictures with themselves in them, but this is the impression it gives off. You asked why people hate selfie sticks, and this is a likely reason.

They can and they do. I've paid Georgia Tech athletic fees while attending remote campuses with no amenities.

I agree, the sanity check is not sufficient. It confirms the concept that as pressure decreases, area increases, but is not sufficient to confirm a linear relationship. In the limit, the area clearly does not become infinite when pressure drops to 0.

For the case you suggested above, this is essentially how run-flat tires work. Of course, the sidewall of the tire isn't as stiff as the support ring, but they do provide some support.

This method doesn't account for the support of the tire itself through the sidewalls, as opposed to the pressure contained within it.

You should be able to estimate this contribution by fitting to the curve of area vs pressure at lower pressures. For example, the linear F=PA relationship clearly breaks down at 0 pressure, as F>0 and A>0 when P=0.

Yes. Most of the time, the reason is that there is a general form for computing derivatives of products ((xy)' = x'y + xy') and composite functions (chain rule) while no such general rules exist for integrals.

Any comments on the cheaper, earlier edition printed by Dover as "The Nature of Light and Colour in the Open Air"? Is the later edition worth the higher price?

Winner Take All

Not with a planar or linear array. I'm skeptical, but prepared to learn something: what sort of array can generate a square beam?

Even lasers spread. This guy agrees with me: https://www.quora.com/Is-the-light-from-lasers-reduced-by-th...

The inverse square law totally applies in the case of phased array beamforming, you just have a much higher gain to start with.

Of course it can. Any rotating frame has Coriolis forces.

According to https://en.wikipedia.org/wiki/United_States_emission_standar..., https://en.wikipedia.org/wiki/List_of_U.S._states_and_territ..., and some arithmetic, about 36% of the US population lives in CARB states.

In my experience, those who grew up with Papoulis, 2nd edition loved it. I grew up with Papoulis, 3rd edition, and find the layout and typesetting to be among the worst of any book I've ever read, bad enough to significantly affect usability and ability to quickly find things.

One has to wonder why only numbers for suspected, rather than confirmed, magnet ingestion are reported.

10 years ago, I would have argued the same about the gov't just arbitrarily expanding asset seizure laws, but here we are.

Civil cases categorically cannot directly result in incarceration.

Concerning the difference between our definitions of measurement, I was referring to the prior probability of making a measurement given the true state, which is P(z|x), or, if you prefer, f(z,x) = P(Z=z|X=x). This PDF is Normal(Hx, R). The distribution you refer to is that of the image of the true state in measurement space (Hx), which is Normal(z, R).

Concerning the general question of dimensionality and numbers vs. functions, I'm afraid I still don't understand the fundamental issue. I agree that probability notation isn't the best, but each of those terms can be replaced with a Gaussian (or in the case of the denominator, an integral of the product of two Gaussians). You end up with a function in terms of x_k and the sequence of z's. You can then choose which variables are free or bound and evaluate the function as your application requires. If all variables are bound (the case that you know the measurement z_k, and are evaluating the posterior probability of the state at a given point), all the terms are numbers (yes, densities), and there are no dimensional issues. If you leave x_k free, you end up with two functions in the numerator, and a number in the denominator. Those two functions are Mahalanobis distances (which are scalars) in an exponent, and again, no dimensional issues. In general, such operations with PDFs represent various combinations and manipulations of event spaces that need not be commensurate. Computing the PDF of a coin flip given the distribution of all of the positions and velocities of the molecules of air through which the coin flies requires comparing a two-state PMF to a virtually infinite dimensional PDF. Notationally speaking, no problem.

Probability notation generally works best for the people who already understand the concept in question. Let me take a crack at your question.

The equation in question is P(A|B) = P(B|A) P(A) / P(B). In modern Kalman filter literature, this would be stated as something like: P(x_k | z_k) = P(z_k | x_k) P(x_k) / P(z_k). It is generally left as implicit in these sorts of equations that everything is also conditioned on the sequence z_1 to z_{k-1}. In this equation, x_k is a free variable in the state space (possibly multi-dimensional, so a vector), while z_k is the measurement, which is a realization of the random variable distributed as N(H(x_k), R_k). The result is a PDF over the free variable x_k.

So let's tackle the terms one by one:

1. P(z_k | x_k) - this is the probability that we measured z_k, given that the true object is at x_k. This is the aforementioned normal distribution N(H(x_k), R_k).

2. P(x_k) - this is the prior probability of the state estimate, generally after propagation through the motion model from P(x_{k-1} | x_{k-1}). In the Kalman filter, this is also Gaussian, and conveniently has the same mean as the term above (see note below).

3. P(z_k) - this is the denominator that someone else mentioned earlier can be effectively ignored, which is right - you only need it to normalize the numerator. If you must compute it, it can be factored as the integral over the entire state space of P(z_k|x_k)*p(x_k). Given z_k, this is a number, not a function.

4. P(x_k | z_k) - The result, which is a Gaussian PDF. You can arrive at it numerically by plugging in specific values for x_k, in which case (1) and (2) are numbers. Or symbolically, in which case (1) and (2) are functions, and you'll end up with the form of a Gaussian PDF.

Note: The original article quotes a distribution for the product of two Gaussians with arbitrary means. It does not state that this is an approximation, which is exact only in the case of equal means. This is why unbiased measurements are one of the Kalman assumptions.

The article takes as given that it's easy to generate such a magic random input: it's simply a stream representing 0.5.

A natural noise process (e.g. thermal) with a variable threshold could do it. PRNGs spend a lot of effort on statistical properties that may not matter for this use case. You absolutely must, however, guarantee the correct bias, so such a noise process would need to be tightly controlled, likely temperature controlled.

That there's confusion between the various concepts speaks to their similarities.

Copyright and patent are both intended to encourage innovation by providing the originator with a temporary monopoly on the use of works/processes/etc. Both are frequently discussed here in the context of large corporations/publishers using them to stifle the innovation they were designed to encourage.

Trademarks are often used in tandem with copyrights to protect a body of work in different ways - while "Steamboat Willy"s copyright will eventually expire (if it hasn't already), the trademark of the Mickey Mouse character will last indefinitely (so long as Disney protects it).

Distinctive trademarks are also commonly protected by design patents. Yes, they protect the work in different ways, but the two are related in their use and concept.

If you're so against collective terms, I hereby insist that you no longer refer to the "United States", or "European" culture. But I digress.

Ugh, this argument is tired and dumb. Thank you for bestowing upon us all the sacred knowledge that there are different kinds of IP, but we all already knew that, and choose to continue to refer to them, collectively, as IP, because they actually are similar in a lot of ways.

"pi-calculus" would be a better term to use in the title, since the glyph used for pi looks like "n"