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Pharaoh RutinTutin

Story Friday August 30, 2019

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8 hours ago, Darth Fluffy said:
16 hours ago, hkmaly said:

Small errors are definitely cumulative ... and they would cumulate to 10 kilometers per day, not decimeters. The goal of navigation accuracy of 15 meters requires the clock on satellites having accuracy of 50 nanoseconds, and the size of that small error between Newton and Einstein is 45 microseconds per day for weaker gravity in it's orbit 20,000 km above the Earth AND 7 microseconds per day for their orbital speed of 14,000 km/hr ... but wait, those actually have opposite direction so the total difference is 38 microseconds per day.

OMG, give yourself a cookie, you found an article with much more accurate numbers than I threw out, but you're still missing the point. In the very article you quoted, it says: "But GPS is an exception" So, go ahead, swallow that camel while straining out the gnat.

Yeah "more accurate". You greatly underestimated the difference. Admit it.

(See later my admission for "camel")

8 hours ago, Darth Fluffy said:

there are competent mathematicians that disagree with you

I'm sure they would agree it has nothing to do with English. And, while there are proofs which hits Gödel or are at least so complicated some mathematicians don't feel satisfied with them, Newton's laws are not one of those. Mainly because they are physics (there is nothing wrong on their math part) and were disproved experimentally.

(Which, sure, is not enough for some mathematicians ; I suspect mathematicians will still insist that the sum of all angles in triangle is 180 degrees even if more experiments prove it's not true :) - although so far it seems to hold.)

8 hours ago, Darth Fluffy said:
16 hours ago, hkmaly said:

From practical, the difference is in most "everyday" cases so small it doesn't matter.

OK, now I would consider the point acknowledged.

Good. I was worried I will need to repeat it after you stated twice I didn't get the point ...

(For reference, yes I got it: majority of people only rarely need to acknowledge the difference ... and practically never need to actually compute it.)

8 hours ago, Darth Fluffy said:
16 hours ago, hkmaly said:

... you need to decide what interest you.

If you mean, you need to choose what context applies, that makes sense.

Well, you don't seem to care about context, but you're right, "you need to decide what interest you in context you need it in" would be correct ... wait, I think in this case your native English would be useful to formulate it correctly.

8 hours ago, Darth Fluffy said:

For the most part, we (big we, all of us, even the astrophysicists drive to work) do not choose; rather, we are born into the milieu; it is the water we swim in, the air we breathe. Our world, our life is Newtonian. The relativistic and quantum effects are imperceptible.

I'm not saying you can't find them if you look for them, just that you won't encounter them unless you do. We are born into a relativistic world, and we are born into a quantum world, neither of which manifest plainly on a daily basis.

Exactly the fact we rarely perceive the relativistic and quantum effect means we should be aware of the possibility, so it wouldn't become TOO big problem when we do.

I remember thing I saw in some sci-fi, but we actually already reached the needed technology: there was a remotely operated flyer and that "remote" line was, by mistake, routed over satellite network instead of directly. When it got near some airship, with passengers, it caught turbulence. The operator tried to compensate, but due to light speed delay over the line, it actually made it worse and he crashed that airship.

8 hours ago, Darth Fluffy said:

So actually, please take it as a complement that I'm willing to respond to you. You bring up good points, you are interesting, and I do not mind a different point of view; I've changed my mind often enough.

Oh. Thanks.

7 hours ago, ijuin said:

GPS is one of the very few things that most people deal with regularly that requires parts-per-trillion precision.

Another one is the computer chip. And the one in smartphone. And I suspect the one in TV as well. However, those devices only need the precision in areas not directly affected by theory of relativity - like, two parts of CPU need to be synced with such precision but they are next to each other and move with same speed so theory of relativity doesn't matter for it.

8 hours ago, Darth Fluffy said:
16 hours ago, hkmaly said:

I don't think the satellites would be able to calibrate often enough.

Meh, you could probably do so and not have enough overhead to really matter, even at a few minute intervals.

For one, the satellites are not "in view" from any of the ground control stations often enough, I suspect. Although there are lot of them, so I'm not entirely sure.

7 hours ago, Don Edwards said:

Even if they have perfect adjustment for relativity, they'd still have to recalibrate the satellites periodically. See, there's this thing called the "three-body problem", and even worse, the "n-body problem". Jupiter, Saturn, passing asteroids, and quite a few other things distort the satellites' orbits a tiny bit through ordinary gravitational effects, and that's a complex problem that hasn't been even theoretically solved - for that matter they don't have a sufficiently complete catalog of the bodies they'd need to adjust for either. And GPS is a VERY-high-precision system.

Of course, and there are also satellite maneuvers, the issue is how often the recalibration is needed. As I said, without adjustment for relativity, it would be necessary to recalibrate all the time.

 

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8 hours ago, Don Edwards said:

Even if they have perfect adjustment for relativity, they'd still have to recalibrate the satellites periodically. See, there's this thing called the "three-body problem", and even worse, the "n-body problem". Jupiter, Saturn, passing asteroids, and quite a few other things distort the satellites' orbits a tiny bit through ordinary gravitational effects, and that's a complex problem that hasn't been even theoretically solved - for that matter they don't have a sufficiently complete catalog of the bodies they'd need to adjust for either. And GPS is a VERY-high-precision system.

Notoriously unsolvable by strictly analytic methods, which feeds back into "proof" and the use of computational hardware. From a practical standpoint, if we throw enough computation at it, we can get close enough (as arbitrarily close as we require).

 

8 hours ago, Don Edwards said:

And GPS is a VERY-high-precision system.

On another tangent, I have the notion that for urban centers, you could do better triangulating off cell towers. IIRC, that was done before cell phones included GPS. GPS works particularly well for the military because you don't have to install it prior to invading. Also, for a satellite, it's pretty high up, and harder to shoot down than your average bear in LEO. Will make a mess of things if that happens, like we need more debris in orbit.

 

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1 hour ago, hkmaly said:

Yeah "more accurate". You greatly underestimated the difference. Admit it.

Yes, but only by several orders of magnitude.

 

1 hour ago, hkmaly said:

I'm sure they would agree it has nothing to do with English. And, while there are proofs which hits Gödel or are at least so complicated some mathematicians don't feel satisfied with them, Newton's laws are not one of those. Mainly because they are physics (there is nothing wrong on their math part) and were disproved experimentally.

(Which, sure, is not enough for some mathematicians ; I suspect mathematicians will still insist that the sum of all angles in triangle is 180 degrees even if more experiments prove it's not true :) - although so far it seems to hold.)

"nothing to do with English" - agreed. English had to do with equating to related but distinct words.

Gödel's Incompleteness Theorem. - I am not aware that this is considered in any sense controversial any more. Nor is the similar Halting Problem. These do not prove nor disprove Newton, they related to the limitations of what you were saying at the time. Something about formal logic, IIRC.

disproved experimentally - I think we are arguing semantics here. You are saying, "Near the speed of light, Newton's laws of motion no longer work, therefore Newton's laws are disproved." Is that a correct summary? I'm saying, "Near the speed of light, Newton's laws of motion no longer give a correct result, use a more refined model in those cases."

sum of all angles in triangle is 180 degrees - It's really weird that you word that the way you do, because you are obviously aware that only works explicitly on a flat surface. In day to day real life, in the process of navigation, the sum of the angles of a triangle exceed 180 degrees. This also rarely affects us; we typically live in a small enough piece of the earth that like relativity and quantum mechanics, we can generally ignore it; the earth isn't flat, but it is huge enough that small pieces of the surface appear flat for practical purposes. And even if you travel long distances in an airplane, as a passenger, you don't need to worry (much) about the nuances of navigation. But the folks we are counting on to get us there better be d@%& sure they know that a triangle's angles exceed 180 degrees.

Your other link - Nice to know the universe at large is flat.

 

1 hour ago, hkmaly said:

(For reference, yes I got it: majority of people only rarely need to acknowledge the difference ... and practically never need to actually compute it.)

I've had to do so for classes only. Then again, I specifically avoided IC design; not because quantum effects are a big player, per se, more having to do with lifespan of employability, but they are not entirely unrelated.

 

1 hour ago, hkmaly said:

Well, you don't seem to care about context, but you're right, "you need to decide what interest you in context you need it in" would be correct ... wait, I think in this case your native English would be useful to formulate it correctly.

Then you haven't been paying attention, all I've been referencing is related to context.

I'm not knocking your English, it's better than my whatever you speak. I can track a bit of Spanish, and I can read some German (and apparently Dutch, which is enough like German that I was able to follow an article I was interested in).

 

1 hour ago, hkmaly said:

Exactly the fact we rarely perceive the relativistic and quantum effect means we should be aware of the possibility, so it wouldn't become TOO big problem when we do.

Well, I don't plan to travel at a significant fraction of the speed of light (in a vacuum) within my lifetime, but you're right, if it happens, I should be aware of the effects. If I worked at CERN, and routinely tossed nuclei around the race track, yes, then I'd be concerned.

 

1 hour ago, hkmaly said:

I remember thing I saw in some sci-fi, but we actually already reached the needed technology: there was a remotely operated flyer and that "remote" line was, by mistake, routed over satellite network instead of directly. When it got near some airship, with passengers, it caught turbulence. The operator tried to compensate, but due to light speed delay over the line, it actually made it worse and he crashed that airship.

That has to do with taking the long path, Newtonian distance, as it were. Yes, the signal is traveling at relativistic speed; no, relativistic effects are not germane to the outcome.

 

1 hour ago, hkmaly said:

For one, the satellites are not "in view" from any of the ground control stations often enough, I suspect. Although there are lot of them, so I'm not entirely sure.

Probably some on other nations soil; I would guess GB and Australia.

 

 

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2 hours ago, hkmaly said:

For one, the satellites are not "in view" from any of the ground control stations often enough, I suspect. Although there are lot of them, so I'm not entirely sure.

The GPS devices typically aren't happy if they are receiving signals from less than three satellites at a time. Maybe in the polar regions there's some difficulty with that, but I'm currently seeing six.

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5 hours ago, Darth Fluffy said:
14 hours ago, Don Edwards said:

Even if they have perfect adjustment for relativity, they'd still have to recalibrate the satellites periodically. See, there's this thing called the "three-body problem", and even worse, the "n-body problem". Jupiter, Saturn, passing asteroids, and quite a few other things distort the satellites' orbits a tiny bit through ordinary gravitational effects, and that's a complex problem that hasn't been even theoretically solved - for that matter they don't have a sufficiently complete catalog of the bodies they'd need to adjust for either. And GPS is a VERY-high-precision system.

Notoriously unsolvable by strictly analytic methods, which feeds back into "proof" and the use of computational hardware. From a practical standpoint, if we throw enough computation at it, we can get close enough (as arbitrarily close as we require).

Yeah, based on the language of the wiki article, I suspect there is proof that no "analytics" (closed-form) solution exists for general case. Of course, from practical standpoint, you are less interested in non-existence of general solution and more interested in what are your options for getting at least rough numerical solution.

Note that this "arbitrary close", while technically true, may be impractical ; in reality, you don't know the exact initial positions of those bodies (with quantum physics, you CAN'T know it, actually) and I suspect that the numerical methods needs recomputation when you get more precise values of those, which might not be true for analytics solution if there would be any.

5 hours ago, Darth Fluffy said:
14 hours ago, Don Edwards said:

And GPS is a VERY-high-precision system.

On another tangent, I have the notion that for urban centers, you could do better triangulating off cell towers. IIRC, that was done before cell phones included GPS. GPS works particularly well for the military because you don't have to install it prior to invading. Also, for a satellite, it's pretty high up, and harder to shoot down than your average bear in LEO. Will make a mess of things if that happens, like we need more debris in orbit.

Technically, yes. Practically, the phone is not configured to communicate with more towers at once than necessary, and the protocol used doesn't contain the set of helpful data GPS does so the triangulating can't be done without communicating.

I'm not sure WHY they can't put data necessary for triangulating in what the cell towers transmit (maybe the towers don't have clock precise enough?) but I think GPS will actually get your position more exact in lot of cases EVEN in cities.

4 hours ago, Darth Fluffy said:

Gödel's Incompleteness Theorem. - I am not aware that this is considered in any sense controversial any more. Nor is the similar Halting Problem.

Neither am I. Those "some mathematicians" were related to proofs which "only" require too much computation to be done by hand. Like four color theorem.

4 hours ago, Darth Fluffy said:

disproved experimentally - I think we are arguing semantics here. You are saying, "Near the speed of light, Newton's laws of motion no longer work, therefore Newton's laws are disproved." Is that a correct summary? I'm saying, "Near the speed of light, Newton's laws of motion no longer give a correct result, use a more refined model in those cases."

Yes we are, of course.

Newton laws of motion basically says that all objects move based on set of equations. Those equations will always give a result, which will be close enough to reality unless something gets close to speed of light, in which case you need more refined model. The laws are however disproved, because they explicitly state that those equations work universally, which is not true.

4 hours ago, Darth Fluffy said:

sum of all angles in triangle is 180 degrees - It's really weird that you word that the way you do, because you are obviously aware that only works explicitly on a flat surface. In day to day real life, in the process of navigation, the sum of the angles of a triangle exceed 180 degrees. This also rarely affects us; we typically live in a small enough piece of the earth that like relativity and quantum mechanics, we can generally ignore it; the earth isn't flat, but it is huge enough that small pieces of the surface appear flat for practical purposes. And even if you travel long distances in an airplane, as a passenger, you don't need to worry (much) about the nuances of navigation. But the folks we are counting on to get us there better be d@%& sure they know that a triangle's angles exceed 180 degrees.

The part about flat surface and Earth not being one is true, but I was not speaking about it (triangle drawn on surface of earth is not really triangle). I was speaking about the fact that it ONLY works in euclidean space. Which is all mathematicians care for.

As a joke (notice the smiling face), I suggested that if it turns out that our universe is NOT euclidean space (which is open problem physicists tries to solve), mathematicians will be made wrong. That only works as joke, because mathematicians are already aware that it only works in euclidean space and just not care about what will the result be in physical world (mostly).

4 hours ago, Darth Fluffy said:
6 hours ago, hkmaly said:

I remember thing I saw in some sci-fi, but we actually already reached the needed technology: there was a remotely operated flyer and that "remote" line was, by mistake, routed over satellite network instead of directly. When it got near some airship, with passengers, it caught turbulence. The operator tried to compensate, but due to light speed delay over the line, it actually made it worse and he crashed that airship.

That has to do with taking the long path, Newtonian distance, as it were. Yes, the signal is traveling at relativistic speed; no, relativistic effects are not germane to the outcome.

Yes, it wasn't directly related to relativistic effects, but it was an example of "you should be aware of your assumptions".

4 hours ago, Darth Fluffy said:
6 hours ago, hkmaly said:

For one, the satellites are not "in view" from any of the ground control stations often enough, I suspect. Although there are lot of them, so I'm not entirely sure.

Probably some on other nations soil; I would guess GB and Australia.

Yes: Hawaii, Kwajalein Atoll, Ascension Island, Diego Garcia, Colorado Springs, Colorado and Cape Canaveral, along with shared NGA monitor stations operated in England, Argentina, Ecuador, Bahrain, Australia and Washington DC.

I just don't want to spend time finding all of those on globe and guessing how much coverage they provide.

3 hours ago, Don Edwards said:

The GPS devices typically aren't happy if they are receiving signals from less than three satellites at a time. Maybe in the polar regions there's some difficulty with that, but I'm currently seeing six.

I'm seeing six and my position is STILL wrong. GPS is not reliable inside buildings. With less than three, you can't get the position correct even theoretically, but usually the phone tries hard to get more because it allows better precision.

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6 hours ago, hkmaly said:

Technically, yes. Practically, the phone is not configured to communicate with more towers at once than necessary, and the protocol used doesn't contain the set of helpful data GPS does so the triangulating can't be done without communicating.

I'm not sure WHY they can't put data necessary for triangulating in what the cell towers transmit (maybe the towers don't have clock precise enough?) but I think GPS will actually get your position more exact in lot of cases EVEN in cities.

GPS was not in cell phones initially. IIRC, it was added in iPhone 1, no? The capability of triangulating off of cell towers could have been added instead, but GPS is more universal; works everywhere.

I had Verizon for a while. In the US, they used an older technology than their competitors, a lower frequency. Much maligned for being archaic, it penetrated buildings better. When we had a storm come through, I'd still have a signal while all my coworkers were bitching out their carriers. I don't know if they still use that, I'm guessing to be competitive with high bandwidth, they've moved on.

 

6 hours ago, hkmaly said:

Neither am I. Those "some mathematicians" were related to proofs which "only" require too much computation to be done by hand. Like four color theorem.

 

That was the example I had in mind.

 

6 hours ago, hkmaly said:

Yes: Hawaii, Kwajalein Atoll, Ascension Island, Diego Garcia, Colorado Springs, Colorado and Cape Canaveral, along with shared NGA monitor stations operated in England, Argentina, Ecuador, Bahrain, Australia and Washington DC.

I just don't want to spend time finding all of those on globe and guessing how much coverage they provide.

East Pacific, West Pacific, East Atlantic, Indian Ocean, Rockies, south Florida. There should be one on the west coast of the US, guessing Vandenberg.

 

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