1524: "Dimensions"

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Re: 1524: "Dimensions"

Postby Quercus » Wed May 13, 2015 10:09 pm UTC

orthogon wrote:No, it's toward your panther's partner's genitals. (Predictive text made that particularly surreal and disturbing)

We've been through this before. It's a perfectly average sized house cat who is definitely not a panther :)

azule wrote:
ggh wrote:
Spoiler:
area wrote:
bachaddict wrote:Why am I getting deja vu reading the comic? I feel like I've seen one of the concepts before, like time travel or something.


I have definitely read or heard this text before, and I can't remember where. It's driving me sufficiently nuts that I dusted off this forum account in the hopes of someone putting me out of my misery.

Frame 9 of 20

This is what she linked to: Image,
same (full size) image in a spoiler:
Spoiler:
Image


ggh is the man! I also had a small feeling a familiarity with this comic's concept, but to find out that it's exact-FUCKING-ly the same???!!! Well, thanks for drawing a picture for it, Randall! hah!! Now get on to including some Beanish into a new comic as you contemplated doing long ago! Exclamation points!!!!1

I'm guessing that Randall found an old note with the comic idea and forgot that he'd already used it.

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Re: 1524: "Dimensions"

Postby rmsgrey » Wed May 13, 2015 10:21 pm UTC

Heimhenge wrote:
mikrit wrote:Aren't there plenty more dimensions in dimensional analysis, like luminosity per mass-length and whatnot? But maybe they only have the name (that is: the family name, Dimension) in common with the four that became famous.

I tried to understand why dimensional analysis works, once. Didn't succeed, though.

PS: remarkable memory you got there, ggh.


The first time I ran into dimensional analysis I was amazed that worked as well as it did. Of course, you need to be sure you have included all the possibly relevant parameters. That can sometimes be tricky. If you're looking to derive the formula for how long it takes water to empty from a container with a hole in the bottom (my first attempt) that's pretty easy to do. But I'm not sure it would be of much value for a truly non-trivial question. And either way, then you've got to run an actual experiment to measure the proportionality constant.

[EDIT: Just realized I never answered the question.] I'm pretty sure dimensional analysis works because it's based on the definitions built into SI, and that's a rigorously crafted and internally consistent system.

Dimensional analysis can prove that a formula is wrong - or at least incomplete - by showing that the dimensions are inconsistent. If you have a pretty good idea roughly what the formula should be then eliminating a lot of wrong possibilities leaves you with relatively few candidates for the right answer.

It doesn't prove that the formula you end up with is (a constant multiple of) a correct one, but it does give you a much better chance of being right...

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Re: 1524: "Dimensions"

Postby Abelard » Thu May 14, 2015 1:44 am UTC

Envelope Generator wrote:May I ask you if you've considered all the possibilities that "down" might offer you?


Holy Zarquon, I can't believe no one else wants to see the basement, the microfiles, or the heating system...

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Re: 1524: "Dimensions"

Postby mikrit » Thu May 14, 2015 8:04 am UTC

What I find weird about dimensional analysis is that one is allowed to multiply apples and oranges to get appleoranges, or divide them to get apples per orange, but never ever add them. Why is multiplication more flexible than addition? And am I allowed to raise an apple to the orangeth power?

Back to four famous dimensions: in my country there is a rhyme to tell your fortune by noting from which direction you hear the cuckoo.

North cuckoo is sorrow cuckoo,
East cuckoo is solace cuckoo,
South cuckoo is death cuckoo,
West cuckoo is best cuckoo.
(It rhymes better in Swedish).

At the current state of the art in fortune telling, it is unknown what it means to hear a cuckoo from above, below, the past, or the future.
However, other bird auguries are found here: http://www.smbc-comics.com/?id=3622
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Re: 1524: "Dimensions"

Postby Copper Bezel » Thu May 14, 2015 8:29 am UTC

mikrit wrote:What I find weird about dimensional analysis is that one is allowed to multiply apples and oranges to get appleoranges, or divide them to get apples per orange, but never ever add them. Why is multiplication more flexible than addition? And am I allowed to raise an apple to the orangeth power?

Maybe I'm not following here.

Let's take two dimensions of space. Now we'll divide them by time. We now have area per unit time, which I can use to mow my lawn. What would subtracting mass from this expression even mean, and how does it help me mow my lawn?
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Re: 1524: "Dimensions"

Postby Kit. » Thu May 14, 2015 9:24 am UTC

It could mean, for example, that there is a theory that postulates that the peak performance of an ideal lawnmower is directly proportional to its mass.

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Re: 1524: "Dimensions"

Postby mikrit » Thu May 14, 2015 9:30 am UTC

It is just that I feel somehow that I understand dimensional analysis only halfway, and that there is some further level of understanding that is possible to achieve, if I had the right insight. But I can't explain very well what I feel is missing.

That's not very sensible, I suppose. Nothing to see here, move along (in a timelike or spacelike direction).
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Re: 1524: "Dimensions"

Postby orthogon » Thu May 14, 2015 10:06 am UTC

Kit. wrote:It could mean, for example, that there is a theory that postulates that the peak performance of an ideal lawnmower is directly proportional to its mass.

Such a theory would involve a constant of proportionality, which would have dimensions of area per unit time per unit mass.

mikrit wrote:What I find weird about dimensional analysis is that one is allowed to multiply apples and oranges to get appleoranges, or divide them to get apples per orange, but never ever add them. Why is multiplication more flexible than addition? And am I allowed to raise an apple to the orangeth power?


One idea that might help is that units are fundamentally multiplicative. When you say "2m" you really are multiplying the dimensionless number 2 by the unit "metre". 4m is twice 2m, i.e. 2x2xm. 4m2 is 2m x 2m = 2 x 2 x m x m. We don't normally write the times sign in there, but it's in there implicitly. Similarly, you sometimes see plots in which some quantity is divided by a unit to give a dimensionless number to plot on the axis: for example you might see an axis labelled "height/m".

If you start adding quantities that have different units, you have something like 2m+2kg; we tend to say that this simply isn't meaningful, but it's more the case that it's not particularly useful because those two terms will remain forever separate. It could still be useful: you might have 2m of licorice and 2kg of chocolate: if there are 10 of you you each have (2m+2kg)/10=20cm+200g. But note how careful you have to be to keep the units as a multiplicative factor in their respective terms.

On the other hand, if the units have the same dimensions, you can work with them: if I have 2m+6in, I can note that in=0.0254m, so I have 2m+6x0.0254m=2.1524m. Note how the normal rules of multiplication apply.

Also, just because things have the same units or dimensions doesn't mean that adding them up is meaningful. Having 2kg of chocolate and 2kg of sand is different to having 4kg of gold; if you want to know whether you're over your baggage allowance it's ok to add, but if you want to know what it's worth at today's prices, you need to factor in the price per unit mass before you add.

In terms of raising to a power, my hunch is that it's unlikely that you could ever have a meaningful formula in which the exponent had dimensions, but I'll need to think about it further!

[EDIT: s/your/you're/]
Last edited by orthogon on Thu May 14, 2015 5:17 pm UTC, edited 1 time in total.
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Re: 1524: "Dimensions"

Postby Kit. » Thu May 14, 2015 10:58 am UTC

orthogon wrote:
Kit. wrote:It could mean, for example, that there is a theory that postulates that the peak performance of an ideal lawnmower is directly proportional to its mass.

Such a theory would involve a constant of proportionality, which would have dimensions of area per unit time per unit mass.

The constant of proportionality (which, frankly, is no different in its idea from the constants we use to convert Gaussian electromagnetic units to SI ones, and just slightly different from those constants we use to convert imperial units to metric ones). It would also allow us to measure lawn areas in such convenient units as mower-pound-minutes, like now we can measure interstellar distances in light-years.

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Re: 1524: "Dimensions"

Postby HES » Thu May 14, 2015 11:54 am UTC

orthogon wrote:Also, just because things have the same units or dimensions doesn't mean that adding them up is meaningful. Having 2kg of chocolate and 2kg of sand is different to having 4kg of gold; if you want to know whether your over your baggage allowance it's ok to add, but if you want to know what it's worth at today's prices, you need to factor in the price per unit mass before you add.

I would argue that kg(chocolate) and kg(sand) are different units. In the case of baggage allowance, they happen to be equivalent.
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Re: 1524: "Dimensions"

Postby Valarya » Thu May 14, 2015 12:20 pm UTC

Gwydion wrote:
mattcoz wrote:
Envelope Generator wrote:May I ask you if you've considered all the possibilities that "down" might offer you?

What is "down" in terms of dimensions?

Toward the enemy's gate, of course.


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Re: 1524: "Dimensions"

Postby gmalivuk » Thu May 14, 2015 12:47 pm UTC

Heimhenge wrote:[EDIT: Just realized I never answered the question.] I'm pretty sure dimensional analysis works because it's based on the definitions built into SI, and that's a rigorously crafted and internally consistent system.
It's convenient that SI has a lot of conversion factors equal to 1, but in principle dimensional analysis doesn't require any particular set of units.
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Re: 1524: "Dimensions"

Postby mathmannix » Thu May 14, 2015 1:05 pm UTC

niauropsaka wrote:Do other dimensions even have names?

Yes. The Bible names the four directional dimensions as breadth, length, height, and depth:
Spoiler:
Paul, in Ephesians 3 wrote:17and that Christ may dwell in your hearts through faith; that you, being rooted and grounded in love,
18may have power to comprehend with all the saints what is the breadth and length and height and depth,
19and to know the love of Christ which surpasses knowledge, that you may be filled with all the fulness of God.

That is, God can give us the insight to see the fourth directional dimension.

Or (as an alternative source, or to rebut the arguments to this notion), note this conversation between A. Square and the visiting sphere:
Edwin A. Abbott wrote:I. Space, my Lord, is height and breadth indefinitely prolonged.

Stranger. Exactly: you see you do not even know what Space is. You think it is of Two Dimensions only; but I have come to announce to you a Third - height, breadth, and length.

I. Your Lordship is pleased to be merry. We also speak of length and height, or breadth and thickness, thus denoting Two Dimensions by four names.

Stranger. But I mean not only three names, but Three Dimensions.
So, another naming convention would be breadth, length, height, and thickness.
Last edited by mathmannix on Thu May 14, 2015 1:08 pm UTC, edited 3 times in total.
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Re: 1524: "Dimensions"

Postby PM 2Ring » Thu May 14, 2015 1:06 pm UTC

CharlieP wrote:(Veering off-topic)

Several years ago I tried "inventing" a variant on noughts-and-crosses, played in four dimensions. From (hazy) memory it had a 3x3 grid of the usual 3x3 grid, so "lines" could be completed horizontally, vertically or diagonally on a single grid, by using the same cell position in grids in a horizontal, vertical or diagonal line, or (I think) a combination of both. So if putting a cross in the centre cell of the grids in the top row could be considered analogous to completing a "vertical" line, it follows that putting a cross in the centre cell of the grids in the left column would be a fourth dimension.

I tried running it past a friend.

"But the fourth dimension is time!"

"No, in this particular game there are four dimensions, drawn in 2D".

"But the fourth dimension is time!"

"Popularly, yes. But in the context of this game I'm using four directional dimensions, to make it more interesting".

"But the fourth dimension is time!"

I gave up on the concept.


Although calling time the fourth dimension is popular, it's more sensible IMHO to call it the zeroth dimension. Then it doesn't get in the way when you want to do stuff in systems with more than 3 spatial dimensions. FWIW, this is the usual convention in relativity; see Four-vector.

But to get back to higher-dimensional noughts-and-crosses (or tic-tac-toe for our American friends), it can be fun, but as rmsgrey points out it's a trivial win for the first player in dimensions > 2 on an order 3 board. However, the order 4 game isn't too bad in 3 or 4 dimensions. I introduced the 4x4x4x4 game to my classmates in high school, using a similar layout to yours - a 4x4 grid of 4x4 grids, and it became quite popular for a while.

For more fun, try "wild" noughts-and-crosses: both players can play either a nought or a cross on each of their turns, the winner being the first person to make a complete line of either symbol.
Another variant is misère noughts-and-crosses (aka reverse noughts-and-crosses, or toe-tac-tic): the first person to make a complete line of their symbol loses.
And of course, to really get your brain going, you can combine both of those variants. Weird as it might sound, wild misère noughts-and-crosses seems more natural than either variant on its own.

You can play those variants on a standard 2D 3x3 grid, but you have to adopt the additional rule that the centre square is out of bounds on the first move; such restrictions aren't required for games on order 4 boards.

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Re: 1524: "Dimensions"

Postby orthogon » Thu May 14, 2015 1:22 pm UTC

PM 2Ring wrote:[...]noughts-and-crosses (or tic-tac-toe for our American friends), [...]

Oh yes. "Tic-tac-toe" was what we used to call "rock-paper-scissors": we'd chant those three syllables as we shook our fists, with "toe" coinciding with the instant at which the weapon was revealed. Anyone else? Or was that a hyper-local thing?

ETA: why is noughts-and-crosses called tic-tac-toe, anyway?
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Re: 1524: "Dimensions"

Postby gmalivuk » Thu May 14, 2015 6:54 pm UTC

mathmannix wrote:Yes. The Bible names the four directional dimensions as breadth, length, height, and depth:
But height and depth are not different dimensions. They go along the same axis, just in opposite directions.

mathmannix wrote:So, another naming convention would be breadth, length, height, and thickness.
And "thickness" is also not a distinct dimension, but rather something you could use to describe the thinnest of the other three.
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Re: 1524: "Dimensions"

Postby rmsgrey » Thu May 14, 2015 7:07 pm UTC

orthogon wrote:ETA: why is noughts-and-crosses called tic-tac-toe, anyway?


Apparently it's an onomatopoeia originally used for a game involving tossing a wooden baton onto a marked grid, that got adopted for a different game using a marked grid...

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Re: 1524: "Dimensions"

Postby mikrit » Thu May 14, 2015 7:34 pm UTC

orthogon wrote:One idea that might help is that units are fundamentally multiplicative. When you say "2m" you really are multiplying the dimensionless number 2 by the unit "metre".

Yeah, I think that helped. Thank you! And I liked the licorice + chocolate example, too. As it happens, my wife loves licorice while I love chocolate, so it is comforting that dimensional analysis does not rule out that our marriage can work...

About etymology,
Wikipedia wrote:"Tic-tac-toe" may also derive from "tick-tack", the name of an old version of backgammon first described in 1558. The U.S. renaming of Noughts and crosses as Tic-tac-toe occurred in the 20th century.
But that theory raises the questions why you would name noughts-and-crosses after backgammon, and why backgammon would be called tick-tack.
Personally, I always thought the three syllables represented the three movable pieces that each player has got (in that version of the game). Is that Three men's morris? And chess ought to be called "White king, white queen, white bishop, other white bishop...".
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Re: 1524: "Dimensions"

Postby 5th Earth » Fri May 15, 2015 1:53 am UTC

For those of you who don't like the distinction between space-like and time-like dimensions, I recommend the Orthogonal Trilogy by Greg Egan, which takes place in a universe with only space-like dimensions. All the physics (and the odd results) are worked out in great detail, plus it's a good story.

http://gregegan.customer.netspace.net.a ... GONAL.html
It seemed like a good idea at the time.

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Re: 1524: "Dimensions"

Postby Thorbard9 » Fri May 15, 2015 12:52 pm UTC

cellocgw wrote:
Pfhorrest wrote:Z dimension, or forward-backward: the dimension of your motion vector
Y dimension, or up-down: the dimension your motion vector is curving in
X dimension, or left-right: the dimension perpendicular to the plane of the other two


True for optics; false for aircraft (where X is the direction of motion, strangely enough. Guess they wanted Z to be parallel to gravity)


I work in 3 CAD packages which are all from the same supplier, each handling XYZ differently.

In one, for 2D drawing, XY is a flat plane, normally implying the ground plane with Z elevation above it (ie parallel to gravity) - alternately for "elevation" drawings, X is horizontal and Y vertical.
The two for 3D drawing make it complicated, one assumes XY is ground with Z elevation, the other insists XY is a vertical plane (X horizontal, Y vertical) with Z being towards the viewer or away.

It gets rather confusing when switching between the two.

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Re: 1524: "Dimensions"

Postby duckshirt » Sat May 16, 2015 9:52 pm UTC

SpaceDetective wrote:
area wrote:I have definitely read or heard this text before, and I can't remember where. It's driving me sufficiently nuts that I dusted off this forum account in the hopes of someone putting me out of my misery.


I've seen this exact text before in a deleted 2012 tweet by BeeStapler.

I can't post links here yet, but there's bit more info on this comic's reddit thread in /r/xkcd.

Yeah, that's still weirding me out. Tweet copied verbatim and it's strangely deleted. Maybe BeeStapler is Randall in disguise? He tweeted a joke about terrible Boston roads earlier.
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Re: 1524: "Dimensions"

Postby Angelastic » Sat May 16, 2015 10:17 pm UTC

I'm tempted to follow BeeStapler now, except that my follow count is 1337 and their follower count is 1337, so it would ruin it for both of us.

(Incidentally, Bee Stapler is followed by 6 people I follow who have met or collaborated with Randall, so it's a plausible hypothesis.)

Bee Stapler's lists are amusing:

Blocked
Float On stuck in head
Honeybee die-off suspects
Parks & Rec Cast/Crew
Final Shortlist
O-negative organ donors
Probable Animorphs
Ahead in line for throne
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Re: 1524: "Dimensions"

Postby gmalivuk » Sat May 16, 2015 10:59 pm UTC

duckshirt wrote:Maybe BeeStapler is Randall in disguise?
That would be my guess, honestly.
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Re: 1524: "Dimensions"

Postby philipquarles » Sun May 17, 2015 7:04 am UTC

I'm being inexorably pushed down towards the earth, but since the earth doesn't move, it's only noticeable when I try to struggle against it.

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Re: 1524: "Dimensions"

Postby Carlington » Sun May 17, 2015 12:54 pm UTC

gmalivuk wrote:
mathmannix wrote:Yes. The Bible names the four directional dimensions as breadth, length, height, and depth:
But height and depth are not different dimensions. They go along the same axis, just in opposite directions.

Unless you're talking about depth as in depth perception, then it's used to measure the distance along your line of sight.
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Re: 1524: "Dimensions"

Postby x7eggert » Sun May 17, 2015 5:39 pm UTC

The Moomin wrote:During my maths degree, one of the tutors mentioned "the nth dimension of porridge".

I can't decide whether being pushed through porridge would be soothing or horrific.


I think it would be too hot or too cold.

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Re: 1524: "Dimensions"

Postby x7eggert » Sun May 17, 2015 6:02 pm UTC

mikrit wrote:What I find weird about dimensional analysis is that one is allowed to multiply apples and oranges to get appleoranges, or divide them to get apples per orange, but never ever add them. Why is multiplication more flexible than addition? And am I allowed to raise an apple to the orangeth power?


Multiplication allows you to create an area (orthogonal), adding allows you to go ahead (straight).

If you have 20 applesoranges and want to divide it among two apples, each one has a share of 10 oranges. If you have 20 manhours of work and two men, each one has to do 10 hours of work.

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Re: 1524: "Dimensions"

Postby mathmannix » Mon May 18, 2015 8:18 pm UTC

gmalivuk wrote:
duckshirt wrote:Maybe BeeStapler is Randall in disguise?
That would be my guess, honestly.

(Preface: I don't really use twitter; I don't know the right terminology.)
But... there's already a twit, @xkcd, "Randall Munroe", with 23.8K followers. Which has apparently never tweeted? Would he have a second one? Is that allowed?
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Re: 1524: "Dimensions"

Postby Angelastic » Mon May 18, 2015 8:25 pm UTC

mathmannix wrote:
gmalivuk wrote:
duckshirt wrote:Maybe BeeStapler is Randall in disguise?
That would be my guess, honestly.

(Preface: I don't really use twitter; I don't know the right terminology.)
But... there's already a twit, @xkcd, "Randall Munroe", with 23.8K followers. Which has apparently never tweeted? Would he have a second one? Is that allowed?

You can have as many Twitter accounts as you have email addresses. He might well want somewhere where he can tweet things without legions of xkcd fans critiquing them or judging them differently because he's the Great Lord Randall.
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Re: 1524: "Dimensions"

Postby gmalivuk » Mon May 18, 2015 8:32 pm UTC

One other of his that's public knowledge is @whatifnumbers or something like that, where for a while he posted random interesting numerical facts he came across while researching the what-if articles.
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Re: 1524: "Dimensions"

Postby david.windsor » Tue May 19, 2015 9:08 pm UTC

I like Left, I think you would get farther being pushed Left rather than Time
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Re: 1524: "Dimensions"

Postby ps.02 » Tue May 19, 2015 11:44 pm UTC

david.windsor wrote:I like Left, I think you would get farther being pushed Left rather than Time

Yes but is it meaningful to Wait for it?

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Re: 1524: "Dimensions"

Postby Echo244 » Wed May 20, 2015 9:53 am UTC

Waiting for something that's already Left sounds... suboptimal. ;-P

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Re: 1524: "Dimensions"

Postby Kit. » Wed May 20, 2015 3:30 pm UTC

Some might claim that you would get farther being Taken rather than Left.

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Flumble
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Re: 1524: "Dimensions"

Postby Flumble » Wed May 20, 2015 3:58 pm UTC

Anyway it's best to go left, unless you want london to turn into a nuclear wasteland and great britain to turn into a labour camp.

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Re: 1524: "Dimensions"

Postby Mikeski » Wed May 20, 2015 9:08 pm UTC

Echo244 wrote:Waiting for something that's already Left sounds... suboptimal. ;-P

People do that all the time, for everything from buses to lovers to deities. Many things that have Left will come back again.

Waiting for something that's still Right here, that's the suboptimal strategy...

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Re: 1524: "Dimensions"

Postby Echo244 » Thu May 21, 2015 8:10 am UTC

Mikeski wrote:
Echo244 wrote:Waiting for something that's already Left sounds... suboptimal. ;-P

People do that all the time, for everything from buses to lovers to deities. Many things that have Left will come back again.


So... a dimension that comes back on itself?
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Re: 1524: "Dimensions"

Postby Copper Bezel » Thu May 21, 2015 8:14 am UTC

Left is one of the little curled-up ones, then?
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

she / her / her

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Re: 1524: "Dimensions"

Postby Angelastic » Thu May 21, 2015 1:40 pm UTC

Echo244 wrote:
Mikeski wrote:
Echo244 wrote:Waiting for something that's already Left sounds... suboptimal. ;-P

People do that all the time, for everything from buses to lovers to deities. Many things that have Left will come back again.


So... a dimension that comes back on itself?
No, it just turns out that at high enough energy, left and back unify to a single dimension.
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Re: 1524: "Dimensions"

Postby emok » Sat May 23, 2015 11:09 pm UTC

A curled-up dimension seems useful.

If I had to pick a direction other than the future to be inexorably pushed in, I'd switch to spherical coordinates and pick the azimuthal angular coordinate. That way I'd just spin or go in circles. Assuming I retain control over the radial, polar coordinates it seems I could go pretty much anywhere (though not choose which way I'd look) and with some control over the temporal coordinate also stay for a while or return soon enough.

Is the stretch from dimensions to coordinates cheating? Are Cartesian coordinates more fundamental than spherical? Are angular coordinates space-like although they are not lengths?


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