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http://www.xkcd.com/687/
Interesting fact: In elliptic geometry, pi is less than arcsine 1. In
hyperbolic geometry, it's more than arcsine 1.
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> http://www.xkcd.com/687/
>
> Interesting fact: In elliptic geometry, pi is less than arcsine 1. In
> hyperbolic geometry, it's more than arcsine 1.
I thought England was already surrounded by water...
did the Chunnel turn it into a peninsula of France?
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Tim Attwood wrote:
> I thought England was already surrounded by water...
> did the Chunnel turn it into a peninsula of France?
I think the idea is that the channel will get *wider* to compensate for
a better Prius (whatever that is).
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> a better Prius (whatever that is).
A car made by Toyota that has much lower CO2 output than most other American
cars :-)
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scott wrote:
>> a better Prius (whatever that is).
>
> A car made by Toyota that has much lower CO2 output than most other
> American cars :-)
...but Toyota is Japanese...?
More importantly, I gather that most American cars are horrifyingly
inefficient, so beating that shouldn't be too hard I'd guess. I don't
really know.
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>> A car made by Toyota that has much lower CO2 output than most other
>> American cars :-)
>
> ...but Toyota is Japanese...?
They sell a lot in America though.
> More importantly, I gather that most American cars are horrifyingly
> inefficient, so beating that shouldn't be too hard I'd guess. I don't
> really know.
I think that's why they sell a lot. The issue in Europe is that you can
just go and buy a small efficient diesel car for half the price of the Prius
and it will have similar CO2 and mpg. So there isn't any reason to get a
Prius.
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scott wrote:
>>> A car made by Toyota that has much lower CO2 output than most other
>>> American cars :-)
>>
>> ...but Toyota is Japanese...?
>
> They sell a lot in America though.
Ah, OK.
>> More importantly, I gather that most American cars are horrifyingly
>> inefficient, so beating that shouldn't be too hard I'd guess. I don't
>> really know.
>
> I think that's why they sell a lot.
Really?
> The issue in Europe is that you can
> just go and buy a small efficient diesel car for half the price of the
> Prius and it will have similar CO2 and mpg. So there isn't any reason
> to get a Prius.
Oh, I see. I thought you meant that American cars sell well because
they're horrifyingly inefficient! :-D
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Invisible wrote:
> Interesting fact: In elliptic geometry, pi is less than arcsine 1.
It's less than arcsine 1 where you're sitting right now. That's why they say
gravity bends space-time.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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Invisible wrote:
> ...but Toyota is Japanese...?
Toyota is *originally* japanese. Like any giant manufacturing company in
industries heavily tariffed, they have plants all over the world, including
the USA.
> More importantly, I gather that most American cars are horrifyingly
> inefficient,
Not especially. They're *bigger* than what you find in downtown london, for
the most part, but the Prius gets something like 40+MPG while still holding
four people plus a bit of luggage.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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>> More importantly, I gather that most American cars are horrifyingly
>> inefficient,
>
> Not especially. They're *bigger* than what you find in downtown london,
> for the most part, but the Prius gets something like 40+MPG while still
> holding four people plus a bit of luggage.
Heck, my Renault Megan holds 5 people and gets roughly 45 MPG.
[Or rather, it did until recently... I haven't figured out why it's
suddenly started rapidly decreasing.]
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> but the Prius gets something like 40+MPG while still holding four people
> plus a bit of luggage.
Cars that get 40+ American MPG (48 UK MPG, 5.9 litres / 100 km) while
holding 5 people and luggage are normal here in Europe - plus they're faster
than the Prius.
One word. Diesel.
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> Cars that get 40+ American MPG (48 UK MPG, 5.9 litres / 100 km) while
> holding 5 people and luggage are normal here in Europe
If Top Gear is to be believed, American cars also can't corner.
> One word. Diesel.
...
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> Heck, my Renault Megan holds 5 people and gets roughly 45 MPG.
My car too holds 5 people plus luggage, gets 55 MPG (if I don't go too fast
on the autobahn!), plus seems to be way faster than a Prius (3 seconds
faster to 60 mph, and 30 mph faster top speed). It's nothing special.
BTW UK MPGs are different to American ones. 40 American MPG = 48 UK MPG
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Invisible wrote:
> http://www.xkcd.com/687/
>
> Interesting fact: In elliptic geometry, pi is less than arcsine 1. In
> hyperbolic geometry, it's more than arcsine 1.
I don't think this is true -- pi is defined in Euclidean space. Read
the first sentence of the Wikipedia article on it.
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scott wrote:
>
> Cars that get 40+ American MPG (48 UK MPG, 5.9 litres / 100 km) while
> holding 5 people and luggage are normal here in Europe - plus they're
> faster than the Prius.
I'll be waiting over 42 American MPG with just enough room for 5 people
and some luggage (OTOH most of the time just me, secondarily me and
Sonic) - even with the warming needed at winter - still having
150bhp/320Nm (upgradeable to 175bhp/370Nm with just a software) with
pretty decent equipment. Sure, it'll be one of the last of it's kind,
but I'm still sure it'll give a good ride for the next 5 years (roughly
300Mm's). Can't wait for next week :).
> One word. Diesel.
Yep. I ordered a Saab 9-3 SC Vector TiDS. Got something like 7ke off
from retail price, since the car is MY09, manufactured just to keep the
factory running while guessing the future.
-Aero
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Invisible wrote:
> Heck, my Renault Megan holds 5 people and gets roughly 45 MPG.
OK, I misremembered. The official numbers are about 50MPG for the Prius, and
that's not even driving conservatively. In contrast, the same measurements
show the "smart twofour coupe" gets about 33 to 40 MPG.
The Megane seems to be a diesel car, which tends to get better mileage
anyway, and almost as good as a Prius running on gasoline.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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Kevin Wampler <wam### [at] u washingtonedu> wrote:
> Invisible wrote:
> > http://www.xkcd.com/687/
> >
> > Interesting fact: In elliptic geometry, pi is less than arcsine 1. In
> > hyperbolic geometry, it's more than arcsine 1.
> I don't think this is true -- pi is defined in Euclidean space. Read
> the first sentence of the Wikipedia article on it.
Yeah. You can't say "pi is xyz" where xyz is something else than 3.1415...
because pi is *defined* as a *constant*, and constants don't change depending
on the situation. The definition of pi implies euclidean geometry.
--
- Warp
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Eero Ahonen wrote:
> - still having
> 150bhp/320Nm (upgradeable to 175bhp/370Nm with just a software) with
Let’s have an argument about the difference between hp and bhp, please. :-P
--
Best Regards,
Stephen
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Warp wrote:
> Kevin Wampler <wam### [at] uwashingtonedu> wrote:
>> Invisible wrote:
>>> http://www.xkcd.com/687/
>>>
>>> Interesting fact: In elliptic geometry, pi is less than arcsine 1. In
>>> hyperbolic geometry, it's more than arcsine 1.
>
>> I don't think this is true -- pi is defined in Euclidean space. Read
>> the first sentence of the Wikipedia article on it.
>
> Yeah. You can't say "pi is xyz" where xyz is something else than 3.1415...
> because pi is *defined* as a *constant*, and constants don't change depending
> on the situation. The definition of pi implies euclidean geometry.
>
What about xyz = the ratio of any circle's circumference to its diameter?
--
Best Regards,
Stephen
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>> Interesting fact: In elliptic geometry, pi is less than arcsine 1. In
>> hyperbolic geometry, it's more than arcsine 1.
>
> I don't think this is true -- pi is defined in Euclidean space.
OK, I rephrase: In non-Euclidian space, the ratio of a circle's
circumfirance to its diameter can be made arbitrarily large or small.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Stephen wrote:
> What about xyz = the ratio of any circle's circumference to its diameter?
Define "circle". Now define "distance". Now we're getting somewhere.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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>> What about xyz = the ratio of any circle's circumference to its diameter?
>
> Define "circle".
The set of all points at distance r from the point c.
> Now define "distance".
I actually can't find a definition for how to do this in a non-Euclidean
space.
> Now we're getting somewhere.
Well, yes... I'm sure somebody somewhere has long since worked all this
out in excruciating detail. ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Darren New wrote:
> Stephen wrote:
>> What about xyz = the ratio of any circle's circumference to its diameter?
>
> Define "circle". Now define "distance".
Why?
> Now we're getting somewhere.
>
No we are here ;)
“Here and Now!” Quoth the mynah bird.
--
Best Regards,
Stephen
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Stephen <mca### [at] aoldotcom> wrote:
> What about xyz = the ratio of any circle's circumference to its diameter?
If it's in Euclidean space, then it's pi, else it isn't.
--
- Warp
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Warp wrote:
> Stephen <mca### [at] aoldotcom> wrote:
>> What about xyz = the ratio of any circle's circumference to its diameter?
>
> If it's in Euclidean space, then it's pi, else it isn't.
>
Would you run that past me again, in English? :-)
--
Best Regards,
Stephen
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Orchid XP v8 wrote:
>>> What about xyz = the ratio of any circle's circumference to its
>>> diameter?
>>
>> Define "circle".
>
> The set of all points at distance r from the point c.
>
>> Now define "distance".
>
> I actually can't find a definition for how to do this in a non-Euclidean
> space.
Oh, I forgot. Now you have to also define the length of a curved line with
no endpoints. :)
> Well, yes... I'm sure somebody somewhere has long since worked all this
> out in excruciating detail. ;-)
Well, yes.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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Stephen wrote:
>
> What about xyz = the ratio of any circle's circumference to its diameter?
>
The main problem here is that xyz is not a constant, but is rather a
function. In spherical and hyperbolic spaces it can be defined as a
function of the radius so you need to say something like:
xyz(r) = the ratio of the circumference to the diameter of a circle of
radius r
If your space doesn't have a constant curvature, then it's a function of
yet more parameters.
The main issue isn't only that pi has a pre-existing meaning, it's that
the value in these non-euclidean spaces isn't even a constant.
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Darren New wrote:
> Now define "distance".
I thought the underlying assumption in this thread was that we're
dealing spaces equipped with a metric tensor, do you automatically get a
definition of distance in the standard manner. How does this require
extra care to define?
I suppose you could argue that circles are a bit trickier to define, but
I think the normal one will work well, and should even be well-behaved
on genus-0 manifolds, or locally on any smooth manifold (like spherical
or hyperbolic spaces).
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Kevin Wampler wrote:
> should even be well-behaved
> on genus-0 manifolds
I take that back, it's obviously not quite well behaved on a sphere
(under some definitions of well-behaved) since there are no circles of
sufficient large radii.
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>> should even be well-behaved on genus-0 manifolds
>
> I take that back, it's obviously not quite well behaved on a sphere
> (under some definitions of well-behaved) since there are no circles of
> sufficient large radii.
Any possible line segment in elliptic geometry can be used as a circle
diammeter. (Since lines that are "too large" to define a circle won't
fit into the space in the first place.)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Kevin Wampler wrote:
> I thought the underlying assumption in this thread was that we're
> dealing spaces equipped with a metric tensor, do you automatically get a
> definition of distance in the standard manner. How does this require
> extra care to define?
>
> I suppose you could argue that circles are a bit trickier to define, but
> I think the normal one will work well, and should even be well-behaved
> on genus-0 manifolds, or locally on any smooth manifold (like spherical
> or hyperbolic spaces).
That's a whole crapload of jargon, right there.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 wrote:
>
> Any possible line segment in elliptic geometry can be used as a circle
> diammeter. (Since lines that are "too large" to define a circle won't
> fit into the space in the first place.)
>
Yes, obviously, so long as you don't define line segments so that a line
is allowed to overlap with itself. But I defined xyz as a function of
the *radius* of a circle, not as a function over line segments.
Defining circles so that they work for all radii under this definition
requires a touch more care (although it is possible).
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Orchid XP v8 wrote:
>
> That's a whole crapload of jargon, right there.
>
Those are all very basic terms for dealing with non-Euclidean spaces.
Since we're talking about non-Euclidean spaces, I don't think it's
uncalled for.
That said, you do have something of a point there, so I'll rephrase:
I thought we were assuming that the spaces we were talking about come
with a pre-defined notion of distance, so why is there a need to
explicitly define it ourselves?
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>> That's a whole crapload of jargon, right there.
>
> Those are all very basic terms for dealing with non-Euclidean spaces.
> Since we're talking about non-Euclidean spaces, I don't think it's
> uncalled for.
Not uncalled for, no. I'm just impressed that there exist people who
actually know WHAT THE HELL THIS STUFF MEANS!
> That said, you do have something of a point there, so I'll rephrase:
>
> I thought we were assuming that the spaces we were talking about come
> with a pre-defined notion of distance, so why is there a need to
> explicitly define it ourselves?
Yeah, that was basically my assumption too.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Kevin Wampler wrote:
> I thought we were assuming that the spaces we were talking about come
> with a pre-defined notion of distance, so why is there a need to
> explicitly define it ourselves?
I think I was more making the point that "distance" isn't a simple
definition when you're talking about space that curves in different
directions in different places.
Indeed, isn't it possible to have spaces where the distance from here to
there is different than the distance from there to here?
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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Darren New wrote:
> I think I was more making the point that "distance" isn't a simple
> definition when you're talking about space that curves in different
> directions in different places.
Sure. I get that.
> Indeed, isn't it possible to have spaces where the distance from here to
> there is different than the distance from there to here?
No. The definition of "metric" demands that it is symmetric (and
reflexive, and transitive).
You can, of course, define a function that represents some sort of
"nearness" which never the less lacks this property...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Darren New wrote:
>
> I think I was more making the point that "distance" isn't a simple
> definition when you're talking about space that curves in different
> directions in different places.
I suppose I normally view distance in Euclidean space from the same
definition that applies to non-Euclidean spaces, rather than the
sqrt(dx^2 + dy^2) form, so I didn't really consider this. You're right
though, if you're starting from the pythorgean theorem view of distance
it does bear some thinking about how it generalizes to the non-Euclidean
space.
That said, I'm not sure it's necessary to actually understand the proper
definition of distance in order to talk about circles in other spaces --
particularly if we limit ourselves to spherical and hyperbolic spaces
which are more or less easy to visualize.
> Indeed, isn't it possible to have spaces where the distance from here to
> there is different than the distance from there to here?
Sure, but the standard interpretation of "non-Euclidean space" that I'm
aware, ie "Riemannian manifold", uses a definition of distance which
doesn't allow such things. All distances are proper distances in that
they obey symmetry, the triangle inequality, etc. I suppose, however,
that you could argue that "non-Eucliean" should be colloquially taken to
include pseudo-Riemannian spaces too (so as to incorporate Minkowski
spaces), but even here you have a pretty nice definition of distance,
although "circles" become a bit nastier to talk about.
It's possible other people mean different things when they say
non-Euclidean space though, so I don't want to pretend that it's the
only way to read that term. Still, that's what had interpreted to be
implicit in the conversation.
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Orchid XP v8 wrote:
>
> and transitive
>
I don't think that's what you intended to say. You probably meant to
say "triangle inequality".
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>> and transitive
>
> I don't think that's what you intended to say. You probably meant to
> say "triangle inequality".
Actually I meant that d(x,y)=0 implies x=y, but even so, that's not the
right term...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 wrote:
>>> What about xyz = the ratio of any circle's circumference to its
>>> diameter?
>>
>> Define "circle".
>
> The set of all points at distance r from the point c.
>
In how many dimensions? Imaginary or real?
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On Tue, 12 Jan 2010 11:09:05 +0000, Invisible wrote:
> ...but Toyota is Japanese...?
>
> More importantly, I gather that most American cars are horrifyingly
> inefficient, so beating that shouldn't be too hard I'd guess. I don't
> really know.
Not much worse than cars in the UK, remember that the US gallon is
smaller, so 34 MPG here (which is about what I get out of my 10 year old
Saturn coupe) is about 7 L/100 KM (or about 40 MPG in UK Gallons if I've
done my math correctly).
The Prius owners I know (a couple) typically get 55-65 MPG (in US
gallons). That'd be 66-78 MPG in UK gallons.
Jim
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Orchid XP v8 wrote:
>>> and transitive
>>
>> I don't think that's what you intended to say. You probably meant to
>> say "triangle inequality".
>
> Actually I meant that d(x,y)=0 implies x=y, but even so, that's not the
> right term...
"identity of indiscernibles" is the phrase you want. And at any rate,
that conflicts more with your use of the term "reflexive", rather than
"transitive". But hey, you got "symmetric"! (and the gist of the
others, I'm just pulling your leg).
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Kevin Wampler wrote:
> Stephen wrote:
>>
>> What about xyz = the ratio of any circle's circumference to its diameter?
>>
>
> The main problem here is that xyz is not a constant, but is rather a
> function. In spherical and hyperbolic spaces it can be defined as a
> function of the radius so you need to say something like:
>
> xyz(r) = the ratio of the circumference to the diameter of a circle of
> radius r
>
> If your space doesn't have a constant curvature, then it's a function of
> yet more parameters.
>
> The main issue isn't only that pi has a pre-existing meaning, it's that
> the value in these non-euclidean spaces isn't even a constant.
Too much information.
La la la la la. ;)
--
Best Regards,
Stephen
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> I'll be waiting over 42 American MPG with just enough room for 5 people
> and some luggage (OTOH most of the time just me, secondarily me and
> Sonic) - even with the warming needed at winter - still having
> 150bhp/320Nm (upgradeable to 175bhp/370Nm with just a software) with
> pretty decent equipment.
Aren't all cars upgradeable with just software nowadays? In my car the
"1.6L", "1.8L", "2.0L" and "2.3L" versions all actually have exactly the
same engine. You are just choosing whether you want the 116, 143, 177 or
204 BHP software installed when you buy it :-) I heard some people got up
to 265 BHP out of that engine, but to me that seems really stupid as all the
other components will not have been reliability tested at that power level.
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Darren New wrote:
> The Megane seems to be a diesel car, which tends to get better mileage
> anyway, and almost as good as a Prius running on gasoline.
My Megane is petrol, although I gather there is a diesel version of most
of these cars now. And yes, diesel has completely different performance
characteristics.
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scott wrote:
> Aren't all cars upgradeable with just software nowadays? In my car the
> "1.6L", "1.8L", "2.0L" and "2.3L" versions all actually have exactly the
> same engine. You are just choosing whether you want the 116, 143, 177
> or 204 BHP software installed when you buy it :-)
Erm... 1.6L means that the engine block has a displacement of 1.6L,
while 2.3L means that the displacement is 2.3L - i.e., the cylinders are
physically bigger.
The Real WTF of course is that displacement is not directly related to
power output in the first place...
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Stephen wrote:
> Would you run that past me again, in English? :-)
Post a reply to this message
Attachments:
Download 'milnerhindley.png' (78 KB)
Preview of image 'milnerhindley.png'
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Invisible wrote:
> Stephen wrote:
>
>> Would you run that past me again, in English? :-)
>
>
> ------------------------------------------------------------------------
>
The bit where it says take away the number you first thought of.
Nice one BTW :D
--
Best Regards,
Stephen
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Stephen wrote:
> Nice one BTW :D
Heh. Somebody had this printed on a T-shirt [as you can probably tell].
I just copied the image file. ;-)
That's apparently the Milner-Hindley type inference algorithm. But whatever.
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Invisible wrote:
> Stephen wrote:
>
>> Nice one BTW :D
>
> Heh. Somebody had this printed on a T-shirt [as you can probably tell].
> I just copied the image file. ;-)
>
> That's apparently the Milner-Hindley type inference algorithm. But
> whatever.
That's what the file name says :D
--
Best Regards,
Stephen
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