## 2073: "Kilogram"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

SuicideJunkie
Posts: 423
Joined: Sun Feb 22, 2015 2:40 pm UTC

### Re: 2073: "Kilogram"

Quizatzhaderac wrote:The phrase "all four dimensions" is meaningless without a coordinate system; there're not a finite number of dimensions, so the only way you can have all of them is within a specific context.
...The three well-known Space-Like dimension, plus the single well-known Time-Like dimension; the ones everyone is familiar with.
Which dimensions did you think I was referring to?

WriteBrainedJR
Posts: 158
Joined: Tue Apr 16, 2013 3:08 pm UTC
Location: Right Behind You
Contact:

### Re: 2073: "Kilogram"

SuicideJunkie wrote:
Quizatzhaderac wrote:The phrase "all four dimensions" is meaningless without a coordinate system; there're not a finite number of dimensions, so the only way you can have all of them is within a specific context.
...The three well-known Space-Like dimension, plus the single well-known Time-Like dimension; the ones everyone is familiar with.
Which dimensions did you think I was referring to?

Assuming Animorphs references are acceptable here (and I feel this is a reasonable assumption), it must be four of the other six dimensions that are curled up into themselves.

Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

### Re: 2073: "Kilogram"

SuicideJunkie wrote:Which dimensions did you think I was referring to?

Even if you stick with Cartesian coordinates for the space definition, look at your chosen X, Y and Z for space-coordinates. Choose a line from the origin that is none of these (you have a doubly-infinitely free choice), choose a second line that is perpendicular to that (only a singularly infinite choice) and then a third to be perpendicular to the plane the first two formed (two choices, unless you have a Handedness-Rule already in mind).

Then you can instead work with cylindrical or spherical coordinates (polar on a plane with an extra perpendicular cartesian dimension, either direction, and polar on the plane with polar rise, ditto), the latter being mapping best to the lat/lon/alt cordinate trio, except for the the oblate spheroid distortion factors and other fine details of distortion that your system ought to plug in.

And that's assuming you anchor it to the Earth (presumably a net zero drift across all tectonic plate movements, and your choice of axis (rotational, magnetic, etc) and zero meridian. And which hemisphere is positive (north) and your convention w.r.t. East/West. All of which are extra decisions still to make if you don't go for a completely geocentric origin. Astronomically you can tie a geo-originated set of dimensions to the rotation of the 'firmament', but there's probably a similar problem to that of continental drift if you want to work across epochs of time, but beyond Earth a helio-/galacto-centric origin, before you start thinking at bigger levels of scope.

And all that's without considering time in the whole space-time system. Frames of reference, Minkowski diagrams, etc. Before considering distortons, the implications of a wrap-around dimensionality to the cosmos (finite but unbounded) and if/how you measure it all from the starting/ending singularity.

Which is probably more complex than you need to go with GPS, but a dimension in space-time can be anything, so long as it is perpendicular (linearly or circularly or... any other relation I've forgotten might apply to 4D) to all other dimensions in that space-time. (All before you consider the 'wrapped up small' ones that we don't notice.)

orthogon
Posts: 3075
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

### Re: 2073: "Kilogram"

I think that to the best of our knowledge there are a finite number of dimensions, be it 4, 10 or 26. Sure there are an infinite number of coordinate systems, but only (let's say) 4 coordinates are required to specify an "event" (4D point) and these can be converted to any other coordinate system. So it's fine to say that GPS gives you "all four dimensions". We don't live in a Hilbert space...

In practice, I think the system has more and less well matched coordinates, because the accuracy of a fix is better in the plane of the ground (i.e. latitude and longitude) than it is in altitude. The visible constellation at any given point is better distributed laterally than vertically, so the determination of altitude is less well conditioned.
xtifr wrote:... and orthogon merely sounds undecided.

DavidSh
Posts: 211
Joined: Thu Feb 25, 2016 6:09 pm UTC

### Re: 2073: "Kilogram"

Quizatzhaderac wrote:Correct, the raw satellite signal differences don't require a specific coordinate system. The raw satellite signals are also not GPS; GPS is a system for global positioning, which includes standards to systemically derive a position on the globe from those signals.

The phrase "all four dimensions" is meaningless without a coordinate system; there're not a finite number of dimensions, so the only way you can have all of them is within a specific context.

There are published standards for the satellite signals, which include current standard orbital elements of the satellites. relative to the earth's axis and the intersection points of the equator and the ecliptic, things like eccentricity, inclination, longitude of ascending node, argument of perigee, semi-major axis, and so forth (well, that's most of them).

I don't know of any published standards for the computation by consumer client devices -- a natural way would be to first determine position in rectilinear coordinates centered at Earth's center of mass, one axis due north, one at the intersection of equator and ecliptic "First point of Ares", before converting to lat-long-altitude coordinates corresponding to any of a small number of standard geoids. (Sea level isn't a sphere, or even, at this level of accuracy, an ellipsoid.) I suppose there are other ways, but this seems most flexible, given that the user may want to select the geoid used.

(Latitude and longitude depend directly on the orientation of measured vertical, which can vary from what you would expect from pure geometry, because of density variations in the earth .)

Old Bruce
Posts: 215
Joined: Tue Jun 28, 2016 2:27 pm UTC

### Re: 2073: "Kilogram"

ijuin wrote:America is a country where the normal serving size for beer is neither one glass nor one bottle, but rather the pack of bottles in which they are sold. Drinking six to twelve bottles or tins at once is quite common among enthusiasts.

But it is American beer and thus your 'enthusiasts' are mere amateurs. [some sort of sneer (which is actually ironic because I don't drink anymore ) emoticon]

Pfhorrest
Posts: 5439
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

### Re: 2073: "Kilogram"

Better to drink weak, pissy-tasting beer than warm, beery-tasting piss.

(Who am I kidding, all beer is piss).
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

Posts: 1798
Joined: Sun Oct 19, 2008 5:28 pm UTC
Location: Space Florida

### Re: 2073: "Kilogram"

DavidSh wrote:[
I don't know of any published standards for the computation by consumer client devices --
The reference coordinate system is WGA 84, which is spherical coordinates on an oblate spheroid with some corrections for altitude based on local conditions.

I don't think it's a fiat standard or anything, but if somebody says "GPS coordinates" they likely mean this system or (at least) something very similar.
The thing about recursion problems is that they tend to contain other recursion problems.

dtilque
Posts: 150
Joined: Sat Oct 11, 2008 5:53 am UTC
Location: Nogero

### Re: 2073: "Kilogram"

DavidSh wrote:
Pfhorrest wrote:Are these oz as in 1/16lb, or floz? And are floz standardized between US and imperial systems? (e.g. is a US pint exactly 4/5ths an imperial pint?)

These are fluid ounces. The US fluid ounce is about 4% larger than the Imperial fluid ounce. The Imperial fluid volume system is based on the volume of a standard weight of water at some standard temperature and pressure. The US fluid volume system is based on cubic inches.

Specifically, the Imperial gallon was defined as the volume of 10 lbs of water at 62 degrees F. As far as I know, pressure was not specified, but this was 1820-something, so maybe they didn't realise it was an issue. At the same time, the Imperial pint was set to 20 floz, so if the US gallon was exactly 8 lbs of water, the two fluid ounces would be the same. But the 8lbs/gallon is only approximate. The US gallon's original definition was 231 cubic inches, so a US gallon of water is somewhere around 8.3 lbs.

Conclusion: that "pint's a pound, the world around" aphorism is not even true in the US, much less the rest of the world.
“This world is a strange madhouse. Currently, every coachman and every waiter is debating whether relativity theory is correct. Belief in this matter depends on political party affiliation.”
-- Albert Einstein, 12 September 1920

commodorejohn
Posts: 1180
Joined: Thu Dec 10, 2009 6:21 pm UTC
Location: Placerville, CA
Contact:

### Re: 2073: "Kilogram"

Old Bruce wrote:
ijuin wrote:America is a country where the normal serving size for beer is neither one glass nor one bottle, but rather the pack of bottles in which they are sold. Drinking six to twelve bottles or tins at once is quite common among enthusiasts.

But it is American beer and thus your 'enthusiasts' are mere amateurs. [some sort of sneer (which is actually ironic because I don't drink anymore ) emoticon]

Now, now, sir! There is plenty of good beer in the U.S. It's just not any of the major megacorporate megabrands that get all the marketing and are (I assume) the majority of what gets exported to foreign countries.
"'Legacy code' often differs from its suggested alternative by actually working and scaling."
- Bjarne Stroustrup
www.commodorejohn.com - in case you were wondering, which you probably weren't.

Eebster the Great
Posts: 3460
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

### Re: 2073: "Kilogram"

ijuin wrote:America is a country where the normal serving size for beer is neither one glass nor one bottle, but rather the pack of bottles in which they are sold. Drinking six to twelve bottles or tins at once is quite common among enthusiasts.

No real American would drink twelve tins at once, or even a single tin of beer, because we don't sell beer in tins. We sell it in cans. It is only acceptable to confuse tin and aluminum in the case of foil, not beverage cans.

That said, it's true that many beers in the U.S. are drunk in large quantities, but that's bound to be true in the U.K. as well, since their beer is just as weak. In a place like Belgium that has much stronger beers, it wouldn't be realistic to just down a twelve-pack like it's nothing. Because some people enjoy the experience of drinking lots of beer, light beers get a lot of sales and the most popular beers are pilsners with light color and taste. Now that craft beers have exploded onto the scene, with strong and diverse flavors, some people still want beers that they can drink in quantity. So they sell "session" beers with lower alcohol content (but not necessarily lower price) for that purpose. These are similar in strength to British beers traditionally drunk in sessions (3-4%, or sometimes a bit higher) but with whatever flavor (often a pale ale). In all cases, the standard size for a beer is 12 fl oz, but larger sizes are also somewhat common, up to a max of about 24 oz for a traditional beer and 40 oz for a malt liquor.

In a bar, people don't buy packs of beer (obviously), but the old staples like Budweiser are still very popular. (Many people, particularly younger people, can't stand that flavor, but plenty still like it.) Most draft beer servings are 16-24 oz, though 16 is sort of a standard. Beers larger than about 21 oz are sometimes called "tall" or "tall boys." Expensive or very strong beers are sold on draft in lower quantities, as low as 8 oz for very strong porters and the like. Beer in the bottle might also be sold in "buckets" during special events like football games, where a "bucket" typically is a literal bucket with 4 or 5 bottles of beer in it, sometimes on ice. The idea is to get 4 or 5 beers at a slight discount compared to their usual (already low) price.

At a party, beer may be pumped from a keg. Parties featuring beer kegs are called "keggers" and are particularly popular in college fraternities. You can look up the standard keg sizes on Wikipedia (can't remember exactly), but usually people get a half keg or pony keg rather than a full keg, since that can be hard to finish in a single party and frustrating to transport. Bars that are large enough will use full size kegs for their draft beers, and bars with less space will get smaller kegs.

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

### Re: 2073: "Kilogram"

orthogon wrote:So it's fine to say that GPS gives you "all four dimensions". We don't live in a Hilbert space...

Technically, we do, but GPS is not precise enough to care.

Eebster the Great
Posts: 3460
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

### Re: 2073: "Kilogram"

Phase space can be infinite-dimensional, but each particle still has just three degrees of translational freedom. We don't "live in" an infinite-dimensional Hilbert space.

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

### Re: 2073: "Kilogram"

"Each particle" is already an approximation. There is no such thing as "each particle" in the world that has number-phase uncertainty.

Eebster the Great
Posts: 3460
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

### Re: 2073: "Kilogram"

Fine. Configuration space can be infinite-dimensional, but spacetime is still four-dimensional at all observed scales. Maybe I'm using the wrong vocabulary, but I don't think the claim that we are not living in a Hilbert space is particularly controversial.

edo
Posts: 436
Joined: Thu Mar 28, 2013 7:05 pm UTC
Location: ~TrApPeD iN mY PhOnE~

### Re: 2073: "Kilogram"

scarletmanuka wrote:
Soupspoon wrote:Which SF novel is it where they hack up a handheld "pimeter" to check suspicions about an alien artefact-ship when they suspect that something is odd with the entrance? Something Rama-like, but I'm also fairly sure it wasn't in the Rama series itself. I never quite knew if that was supposed to be spacial distortion or mathematical 'truth' being tested.

Eon, by Greg Bear. And it was pretty clearly spacial distortion; there's a massive spacial distortion (the "flaw") running down the whole length of the seventh chamber. The whole, very long length of the seventh chamber...

The novel where testing the mathematical version comes into play is Contact.

kaloo wrote:I've honestly always been annoyed that kg is the SI unit for mass. Shouldn't the Gram be the unit we're defining with our arbitrary nonsense?

The cgs system was tried for a while, but that of course has the same problem with centimetre. As normal human activities go, m and kg fit a wider range of activities than cm and g, so here we are.

A meter for length, a liter for volume… how about a keter for mass?
Co-proprietor of a Mome and Pope Shope

Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

### Re: 2073: "Kilogram"

Metre, litre and ketre.

(Actually, make that "let(er|re)". Or go the other way, but bishops might get confused.)

da Doctah
Posts: 983
Joined: Fri Feb 03, 2012 6:27 am UTC

### Re: 2073: "Kilogram"

If the base unit of mass is the kilogram, surely my vitamin supplements should be labelled in microkilograms (or nanokilograms for the trace nutrients).

Or if you'd rather use centimeters for length, how many hectokilocentimeters is it from here to New York?