Until they fix that weird off-centre trackpad, I'd continue suggesting people go Dell XPS, also the only PC laptop with a trackpad response even approaching that of a Macbook
I will not buy a laptop that doesn't have physical buttons on the touchpad. The reliability of knowing that my clicks are exact, saves me time and frustration. Sadly this is my only reason to not own a Purism.
But if you are considering the Dell XPS, I recommend you instead check out their Latitude 7xxx series. (On the website you find them under "For Work" instead of "For Home"). Like the Dell Latitude 7390 or 7490. Yay for real buttons. And pretty good in other areas as well, such as the keyboard quality, and ports.
It doesn't have touchpoint though. I just want a touchpad with real buttons. There aren't many options for that anymore. Another nice and relatively unknown option is the VAIO (no longer from Sony). https://us.vaio.com
I would LOVE to get a Purism if only it had the buttons.
Not sure. I hate the Lenovo style "the whole clickpad moves so much when you click that you're almost certain to miss" thing. But I also hate the soft "you have no idea if you just clicked or not, do you" thing too. So I really need my buttons and don't remember which variant the XPS has :)
My guess is that it's to keep it center-aligned with the main part of the keyboard. The Librem 15 has a built-in numpad on the right, which pushes the letter and number keys over to the left.
Personally I'd have them just ditch the numpad entirely and center everything, the way they do on the Librem 13. USB numpads are cheap and widely available for those who need them, and typing on an off-center keyboard feels weird.
I have yet to encounter an embedded map that could not have better been
- a static image
- a table of addresses with an external map link
It's not just the idea of wheeling around in some 256x256 box added at the last minute to a Contact Us page, the entire concept of an embeddable map is shit
Their main purpose seems to be to add 1 second to page loads across the web, and feed more clickstream back to the mothership
The main exception to this I can think of right now is Flightaware, but even that does not require such detailed rendering
ELI5: You can turn this problem into finding the best "convolution index", and fourier transforms make computing convolutions cheaper.
ELIUndergrad:
(note that \* means multiplication, there doesnt seem to be a way to escape an asterisk)
Lets start by seeing how this is a convolution. We have the videoSpeech sequence, and the subtitle sequence - each is a vector, indexed by time, of 0's and 1's indicating whether there is speech in that time. We can imagine padding the sequences out on either side with 0's, and consider the alignment task as shifting the subtitle sequence left and right in time until we get the best alignment with the 1's in the videoSpeech sequence. We can express the goodness of alignment as the number of matching 1's, aka the sum over all times t of videoSpeech(t) \* subtitle(t). This is the definition of a convolution: the convolution of two sequences gives a new sequence where the value at index i is this sum above where one of the sequences is shifted by i. Mathematically, conv(videoSpeech, subtitle)(i) = sum( videoSpeech(t)\* subtitle(t-i)). So we can rephrase this problem as, find the index i which maximizes the value of the convolution sequence.
The discrete fourier transform is a function that takes a sequence and gives another sequence. It's relevant here because it "turns convolution into multiplication": fourier(videoSpeech)(i) \* fourier(subtitle)(i) = fourier(conv(videoSpeech, subtitle))(i).
So finally to solve the problem, we get the pointwise product sequence S = fourier(videoSpeech) \* fourier(subtitle), do the inverse fourier transform on it invFourier(S), and maximize invFourier(S)(i) over i.
> ELI5: You can turn this problem into finding the best "convolution index", and fourier transforms make computing convolutions cheaper.
I tried this sentence on my 5-year-old and got a blank stare. He then proceeded to tell me a story about how Darth Vader is so scary and cool and that he's actually Luke's father. YMMV.
ELI5 v2: you can look at the sequences a different way, like tilting your head to look at them from a different angle. and from that angle, we can more easily try every possible way of putting them together, so that we can choose the best way.
I'm writing a program which takes multiple channels of near-periodic audio wav files, and outputs a phase-stable oscilloscope video. This is done by FFT-correlating (a buffer of recent oscilloscope plots) with (the audio signal) (with quite a bit of added complexity for better results). Incidentally I'm also using Python/Numpy/ffmpeg.
It's most useful for "complex" chiptune like FM/SNES/tracker/MIDI music, which are easy to split into monophonic single-note channels. https://github.com/corrscope/corrscope Should I submit this separately (Show HN)?
Ok, use 'x' and write "(note that 'x' means multiplication)" instead of "(note that \* means multiplication, there doesnt seem to be a way to escape an asterisk)". More legible and shorter and 'symbol is already used for the purpose' and..
The problem being solved essentially is: you have two binary strings, and you want to offset one of them so that they match up the best. For each offset, you're taking a dot product of one sequence with the offset version of the other. This is the same as computing the convolution of the two sequences together (https://en.wikipedia.org/wiki/Convolution). Computing this naively would be O(n^2) (doing linear work for each possible offset).
One property of the Fourier transform is that convolution in the time domain corresponds to element-wise multiplication in the frequency domain (https://en.wikipedia.org/wiki/Convolution_theorem), so you can compute the convolution efficiently by taking the FFT of both series, doing element-wise multiplication, and then taking the inverse FFT of the result.
It has nothing to do directly with FFT, which is why it is confusing:
What he is looking for is maximal correlation between two binary series (think "Pearson's r or r-square correlation coefficient"). Now, correlation is just like convolution except one series is flipped around on the time axis. Which means, if you have an efficient way to compute convolutions (and you do, through FFT), you have an efficient way to compute correlations.
(I don't think 5 year olds heard of Pearson's correlation coefficient or convolutions, but ... that's the best I can do).
In many ways, correlation and covariance are more fundamental than convolution - they are closely and directly related to the inner product.
And the only reason to use the FFT here is convenience (i.e., it is fast and simple to compute), but the correlation/convolution property applies to many "transform domains" - Laplace, Z, Cosine, Sine, and a few others (all of which are closely related among themselves, but only a few easy to compute numerically).
I didn't read the Google Cloud part as an assertion of authority, just as a disclosure - if they're talking about competitors (and especially how the choice of competitor negatively impacted GitHub) I appreciate it.
(disclosure - I work for a competitor, not on cloud stuff)
I also appreciate it. Its very common for owners/employees to criticize/attack competitors online anonymously. While the GP wasn't attacking, its just nice to know he works for a competitor.
That wasn’t my intent, quite the opposite actually. I don’t want it to read as “S3 is awfully slow, that’s what the problem was. If they were using GCS then < awesome outcome >”. Knowing that I work at a competing vendor is useful knowledge in this case.
If I know a competitor wrote it, I don't read it as negative. To me, it's a welcome courtesy, but as you say, I couldn't assume it if absent; so I'd probably paint a negative picture of S3 with the same albeit unprefaced sentence.
(Plus, I'm always pleased to see someone not call it a 'disclaimer'!)
Disclosure of Interest should be a common practice across all Industry and web discussions. It provides a lot of additional perspective, most of the places do not adhere to this.
Fortunately HN has kept the culture of disclosure intact.
> Time SRE has at various points had take measures up to and including calling the USAF and telling them their satellites are fucked up
It's another cute anecdote, but Google culture is full of these, always scant on details and always intended to show how big/smart/important/complex/indispensable their engineering is.
"Had to" is a strong term here, it's made to sound like USAF could not possibly have noticed some deviation they were likely to correct of their own accord as a matter of routine as they had been doing for the 20 years of the GPS project prior to Google being founded.
The reality is drift and bad clocks are and always have been a feature of GPS, one explicitly designed for, one an entire staff exists to cope with, and designs depending on the absolute accuracy of a single clock have never been correct
So yes, Google can be very impressed with Google. But I'm not sure that's the issue here.
Is it really surprising that people who have extremely precise time needs and a whole team devoted to solving them would notice issues that other people wouldn't? I think it's a very common pattern that a product has some set of trailblazer users who find issues before the people who make the product.
Also, I think you're over-interpreting. "Had to" here only means that they noticed and reported the issue first because their system depended on GPS time being right. It doesn't preclude the possibility that the USAF would notice and fix the issue eventually, just with a higher latency that Google wanted.
If some condition existed that exceeded GPS intended design, you most certainly wouldn't learn of it first from some random anecdote on HN.. more likely the front page of the BBC as the transportation system instantly collapses
So the anecdote itself is noise, it's intended to show how seriously intractable a problem accurate time is, but it doesn't do that, instead it only demonstrates OP's lack of familiarity with GPS and willingness to regurgitate corporate old wives' tales
A single satellite mildly misbehaving on occasion won't necessarily cause catastrophe. You're normally connected to more than the requisite 3 satellites anyway, so you might notice less accuracy, but not anything terrible.
Most of these systems are designed to work if you lose GPS entirely, so they fail gracefully.
Planes won't actually fall out of the sky if GPS makes mistakes. That's y2k fearmongering.
Why is it hard to believe that a group using GPS for a unique purpose has unique needs and detect unique issues?
Here's an interesting article[1] about how relativity affects GPS satellites. The clock ticks in a GPS satellite need to be accurate to within 20-30 nanoseconds for accuracy, and they tick 38 microseconds/day faster to account for relativity.
GPS is one of the few technologies that have to account for both Special Relativity and General Relativity. The level of engineering that went into the system is just amazing.
Fun fact, GPS satellites use rubidium clocks instead of cesium clocks, and only maintain their accuracy thanks to yet another incredible feat of engineering.
What if all the satellites are off by the same amount?
According to the link posted higher up in the thread, in early 2016 they were all off by 13 microseconds for 12 hours, with no apparent consequences for anything ordinary people use GPS for such as location finding.
To triangulate, I think you need to know (1) where the satellites are, and (2) how far you are from each satellite. I think either absolute distance or relative distance works.
Getting both of these depends on knowing the time. That time comes from the satellites. Let's say they are all off by 1 us. Your time is derived from satellite time. That would mean the time you use to look up/calculate their positions will be off by 1 us from the correct time so you would get the wrong position for the satellites.
A quick Googling says the satellites orbital speed is 14000 km/hr, so using a time off by 1 us to look up/calculate satellite position would give you a position that is about 4 mm off.
The procedure for deriving the time from the satellites would get some extra error from this, but that should be limited to about the time it takes like to travel 4 mm, so we can ignore that. As a result your distance measurements between you and satellites would be off by about 4 mm or less.
The key here is that when all the satellites have the same error, the time you derive has the same error, so your distance calculations should still work, and so you only get an error of about how far satellites move in an interval equal to the time error.
In summary, if all the satellites are off by 1 us, your triangulation seems like it would be about 4 mm more uncertain.
If only one satellite is off, it is going to depend on how the time algorithm works. If the algorithm is such that it ends up with a time much closer to the times of the correct satellites than to the off satellite, then if it calculates the distance from the triangulated position to the expected positions of the satellites, and compares that to the measured distance, it should find that one is off by something on the order of the distance light travels in 1 us, and the others are all pretty close to where they should be. It should then be able to figure out that it has one unreliable satellite it, drop it, and then get the right location.
I have no idea if they actually take those kinds of precautions, though.
The case that would really screw it up would be if several satellites are off, but by different amounts. With enough observation it should be possible in many cases to even straighten that out, but it might be too complicated or too time consuming to be practical. (This is assuming that the error is that the satellites are simply set to the wrong time, but that wrong time is ticking at the right rate).
Precise geolocation relies on extreme time accuracy (the story always being that relativistic time dilation effects with the difference in gravity on the surface vs LEO must be accounted for), so yeah, it wouldn't surprise me one bit that the accuracy required is on the order of much less than a millisecond.
> Is it really surprising that people who have extremely precise time needs and a whole team devoted to solving them would notice issues that other people wouldn't
If GPS timing is bad, a lot of people will notice that their position on the map is incorrect, because that's the whole purpose of the GPS network.
While the speed-of-light propagation is about 300 meters in a microsecond, isn't the final position error possibly much greater? For calculating position on Earth, you can think about a sphere expanding at the speed of light from each satellite. The 1 microsecond error here corresponds to a radius 300m bigger or smaller, which only corresponds to 300m horizontal distance on the ground if the satellite is on the horizon (assuming that Earth is locally a flat plane for simplicity here). For a satellite directly overhead, the 300m error is a vertical distance. Calculating the difference in horizontal position from this error is then finding the length of a leg of a right triangle with other leg length D and hypotenuse length D+300m, where D is the orbital distance from the satellite (according to Wikipedia, 20180km). The final horizontal distance error is then sqrt((D+300)^2 - D^2), or about 110km.
Of course, this is just the effect of a 1us error in a single satellite, I'm sure there's ways to detect and compensate for these errors.
Intuitively this seems wrong to me. If the satellite is overhead, the error would put you 300m into the ground so to speak. I'm not sure why you project that horizontally, and especially why you take the distance to the satellite into account.
As another sanity check, if the error for 1 us is 110 km, the error for 1 ns would be 110 m, and I suspect 1 ns error is not unusual for consumer electronics:
> To reduce this error level to the order of meters would require an atomic clock. However, not only is this impracticable for consumer GPS devices, the GPS satellites are only accurate to about 10 nano seconds (in which time a signal would travel 3m)
> If the satellite is overhead, the error would put you 300m into the ground so to speak.
Right, I was basically calculating where that signal would just be reaching the surface at the same time it was 300m under you. This is a circle around you with a radius of ~110km (again using the approximation of the ground as a flat plane). Thinking about it more, there's not much reason to do this (GPS isn't really tied to the surface of the Earth, it gives you 3-D coordinates). I guess my point was that the 300m of distance from 1us of light propagation should not be thought of as a horizontal distance.
That would be if it were straight overhead, intersecting tangentially with another sphere. Realistically they're not overhead, but if two satellites are 30 degrees apart, the line of intersection between their spheres will move twice the distance one of the spheres moves. The magnifying factor is 1/sin(angle between the satellites from the observer).
If I remember correctly, there was a bug a couple of years back which caused an incorrect time offset between GPS and UTC time to be uploaded to some of the satellites - off by a handful of microseconds. Didn't affect navigation but it did trip a bunch of alerts on systems that relied on precise time. I don't think Google was the one that alerted the USAF to that though, in fact they may not have had sufficiently accurate timekeeping back then.
> Despite the flawed data set, there were no impacts to GPS
positioning and navigation. Furthermore, GPS time (tGPS)
was unaffected. Only a subset of the functions that make
use of the GPS-UTC offset were affected.
GPS is not typically used to confirm a position that is known accurately by other means, and that is not its purpose. Only in those cases where there is a manifest conflict with independent spatial information will the problem be evident.
>GPS is not typically used to confirm a position that is known accurately by other means
I am not so sure about that. The most common use of GPS is in satnav in cars. Satnavs typically show a map, and typically it is very easy to confirm your position on a map. Any inaccuracy by more than the usual few meters would be quickly noticed by the majority of GPS users.
Rarely, if you are navigating at sea or in the air or in the woods... and even on the road, it is not uncommon for my GPS device to be clearly off without justifying the conclusion that there is a fault in a satellite.
Here are some users that have a high chance of noticing visually and in aggregate would probably produce a lot of noise:
* Air and sea port operators and navigators
* Military personal running supply lines
* Military personal on foot in operations and training
* Space-X
* NASA
* River boats
* Fresh water fishermen
* Etc
Out of all the possible users who would notice a 300m deviation just based on visual reconciliation, I personally would not say it would be so rare that the USAF would not find out very quickly. Of course, this is ignoring the equipment that would likely detect the issue way before somebody in the Army started phoning the USAF.
Unless I'm woefully off base here, if the satellites were incorrect, you would basically be permanently 300m off, not just temporarily.
There's not so many GPS satellites out there that you're going to be bouncing around them all the time - even if only one is affected, it would be very noticeable for extended periods of time.
I specifically worded this to be about money not brains. Most readers here can probably imagine how to implement a bounded time service. Most readers here also cannot afford to operate one. That is the point. Operating software reliably at large scale happens to be very expensive. 24x7 coverage with a short time-to-repair costs at a minimum several million dollars per year.
24x7 coverage with a short time-to-repair costs at
a minimum several million dollars per year.
Interesting - what are the constituents of that cost?
What sort of challenges do you face? Do you use PTP grandmaster clocks, or something else? How many sites, and how many clocks per site? Are the support issues mostly hardware failures, configuration problems, or something else? Is 24/7 support needed because the equipment lacks failover support, or is the failover support unreliable or insufficient?
You generally need at least 4-5 SREs for a high availability large (big 5) scale subsystem in a multinational corp just to cover all of the timezones and make sure you're not frantically calling everyone when someone goes on vacation or has to pick up their kid from the nurse. The salary plus benefits and overhead on that is easily in the millions.
I think it was meant that Google has such high costs. I read somewhere that Google operates two atomic clocks in each of its data centers, but I can't find a source for it right now, just this: https://www.wired.com/2012/11/google-spanner-time/
I'm guessing that was a reference to the January 2016 event[1]?
Google wasn't the only company that noticed it, and I have no idea if they discovered it before the USAF, but I can believe that someone from Google would phone up Schriever and ask WTF is going on.
Google also reports software and hardware security vulnerabilities and infrastructure security issues to external companies, organizations, and stakeholders responsible for the the design, operation, and maintenance of external systems. Google isn't the only company that does this - other organizations do too - but at this level expertise is a scarce resource, and we're all in the same boat so it behooves everyone when those capable can and do cooperate and participate in keeping a vigilant watch. This ethos is one if the reason the West dominates.
Turn a profit by pumping crappy tech to the masses?