Could someone explain in Simple terms what exactly is flatland Analogy and what does it mean to put...

please...

waiting for a response...


bye!

*sniff sniff* do i smell homework?:bugeye: :D ;)

Flatland is an imaginary two-dimensional world. Looking at the differences there would be between life in a 2D world and life in our familiar 3D world can give us insight into the differences between a 4D world and a 3D world. This is useful because we can't directly visualise a 4D world, just as a Flatlander can't directly visualise a 3D world.

The point of view of a Flatlander looking at the 3rd dimension is therefore analogous to our viewpoint looking at the 4th dimension.

Flatland was a book written by Edwin A. Abbott in 1884.

Click here for the Flatland story in it's entirety. (http://www.alcyone.com/max/lit/flatland/)

kinds regards
Paul

<i>sniff sniff* do i smell homework?</i>

Umm...nope.I am a C.S engg Student IIIrd year.I dont have Physics as a subject.But i am interested in Physics a lot.I was reading this stuff about this Flatland and I got confused.My confusion was:

as to how and what will happen when a sphere will pass to this 2D world.How it is perceived as a point first by the people and then a circle and what are the Primary points etc.


bye!

:) very cool, then. good luck to you! bye.:)

zion,

A sphere passing through Flatland would be seen as a point which lengthens
to a line the diameter of the sphere, then returns to a point and disappears.

What would make it different for a Flatlander is that were he to walk around it
at any particular moment, the 'line' would remain the same length rather than
shrinking to a point before returning to it's initial length during that particular
moment.

:cool:

Chagur, replace the word "line" with the word "circle" in your statement, and then it will be correct

Sorry, it is correct as it stands.

Only seen from 3D would the 'hole', if you would, in
the two dimentional plane appear to be a circle.

For the Flatlander 'circle' can only be conceptualized
as a line of constant length regardless of orientation.

:cool:

first of all, there is no "seeing" in 2 dimensions. electromagnetism simply does not exist in 2 dimensions, so there will be no light.

secondly, even if there were light, a pure sphere doesn t block light, it s just a mathematical surface. so there is no reason why i shouldn t be able to see the "hole" in the middle where the interior of the sphere intersects the 2d plane that i live in. the light from the "hole" will come to my eyes, and i will see it in my 2d world.

thirdly, even if the sphere intersecting my 2d world is opaque, so that i cannot see the "hole" in the middle, it is true that it might "look" like a line segment, since i have no 3 dimensional perspective with which to see the interior, then i would only see the profile. yes, the profile of a circle is a line segment, but there are still ways of measuring that it is a circle. for example, a bunch of area that i could walk through before is now blocked off by the introduction of a circle. a circles satisfy the jordan curve theorem line segments do not. that means that a circle divides this 2d world into two parts, an interior and an exterior. a line segment does not.

since in fact light cannot exist in 2 dimensions, the profile argument holds no weight. since i can make such topological measurements as the truth of the jordan curve theorem completely independently of the existence of light, therefore i can know whether what i am looking at is a circle or a line. they are very different.

Abbott knew this, zion knows it, and i know, so i don t know why you don t, Chagur.

zion:

to explain why the 2d creature sees first a point, then an increasing circle, then a decreasing circle, then a point, then it disappears, is quite simple. just imagine a sphere passing through a plane. since the 2d creature can only see within her two dimensions, she will only see the intersection of the sphere with her 2d world. at first, the sphere is tangent, and the intersection is a single point. as the sphere passes through, the locus of the intersection will be a circle of increasing radius, until it is the equator of the sphere, then the radius of the circle of intersection will begin to decrease, until it is a point again, and then the sphere will pass out of the 2d world into the higher dimensional realm, and she will no longer be able to see it.

Oh ye of little imagination and less understanding!

In Flatland there be 'light', of whatever sort, else how would
you, a Flatlander, find the entrance to your house?

What sphere is there for you to 'see', Flatlander? All you are
aware of is that it is different from the wall of your house in
that 1) It is curved; and, 2) There is no entrance! Oh yes, you
have two eyes ... Therefore binocular 'vision' ... and can see
'depth' ... How else would you not walk into things?

Not a circle, a curved 'line' which, if you attempt to walk
around, brings you back to your starting point. If you're very
curious and have a way to measure, you will discover that
there is such a thing as a 'circle' ... That strange word the
Spaceman used ... It exists, and lines are not always straight.

Circles and lines, and squares and triangles, are not the same, or
any other figure for that matter my two eyed Flatlander, and you
will have become a mathematician in the never-never world of
Flatland.

:cool:

Originally posted by Chagur
Oh ye of little imagination and less understanding!

In Flatland there be 'light', of whatever sort, else how would
you, a Flatlander, find the entrance to your house?

What sphere is there for you to 'see', Flatlander? All you are
aware of is that it is different from the wall of your house in
that 1) It is curved; and, 2) There is no entrance! Oh yes, you
have two eyes ... Therefore binocular 'vision' ... and can see
'depth' ... How else would you not walk into things?

Not a circle, a curved 'line' which, if you attempt to walk
around, brings you back to your starting point. If you're very
curious and have a way to measure, you will discover that
there is such a thing as a 'circle' ... That strange word the
Spaceman used ... It exists, and lines are not always straight.

Circles and lines, and squares and triangles, are not the same, or
any other figure for that matter my two eyed Flatlander, and you
will have become a mathematician in the never-never world of
Flatland.

:cool:

right. um. so we agree that circles exist, and that they are not the same as lines. so tell me again why the sphere intersects my plane in a line?

'We' agree that circles exist, but Freddie Flatlander only sees a
'line'! A curved one, but a line, not a circle. Part of his world, for
the time being has been displaced by the odd thing you (and I)
call a 'sphere' and he can't 'see' around it, let alone 'look over'
it.

And, your sphere doesn't 'intersect' the plane of his world; it, as
I said, displaces it. His world doesn't exist within your sphere,
whether solid or hollow.

Night now :cool:

Chagur, i'm afraid i'd have to disagree with, because i believe in the Flatland story, the soc. status of a 'person' was determened by the # of side the had, therefore, the flatlanders had a way of seeing al the side of a person otherwise they would all be just lines, so the could see a circle, so a sphere movin through flatland would me like a circle that magicly appears 'out of nowhere', changes size, and dissapears...

Sol-Man,

If the 'person' you're looking at has four facets, or lobes, you
would know that the individual is an eighth level personage
in that he/she is symmetrical and seeing the 'side' toward you
is sufficient. Ex. Seeing a 3D person from the side you only
see one arm and one leg but know, more likely than not, that
the person has two arms and two legs (body symmetry).

I'll say it one more time: Freddie Flatlander cannot see a circle!

Dependant on the size of the sphere displacing 'his' plane of
existence, he may see anything from a slightly curved line to
a tightly curved (almost, to us, half-circle) line; so tightly, he
can almost see around it ex. the difference between standing
before a sapling and standing before a mature tree.

:cool:

Chagur,
By displacement you mean the sphere makes a hole in flatland which it fills which it's own presense?

Sal-man has already given you the correct answer.

Rotation is the key. All Freddie need do is rotate (or move around) any object and he can discern what it is by careful observation. Assuming he can't just go up to the objects and touch them!

In Flatland everything looks like a line from edge on, however, if they are lines they will appear to shrink to nothing should you see them head on, because lines are 1-dimensional.

A circle however, would look like a line that never changes size whatever position you see it from.

This is different for semi-circles, triangles, squares, pentagons, hexagons, etc etc. oblongs, rhomboids, etc etc. If you rotate any of these they will appear to grow to a certain size and then shrink down to a certain size. You would be able to obtain their shape by measuring how much they appear to change in size with the frequency of the change in relation to one rotation.

Freddie Flatland can see/detect circles. In fact, they are by far the easiest to detect. Easier than lines because they can disappear. No math is needed to recognise a circle. All the others require painstaking measurement.

But I guess Flatlanders would have evolved to the point where this is common practice and they can recognise someones shape immediately (although it would get increasingly hard the more sides anyone has or more odd their shape).

kind regards

§lîñk€¥™,

No, it does not 'make a hole'; it displaces the plane in which Freddie lives.
As it continues through the plane, the plane closes back up ('heals'). Hmm
... Think of it as passing the sphere through a soap film; the soap film being,
in this case, Freddie's 2D world.

I already replied to Sal-Man; his 'answer' was not correct.

Already addressed Freddie moving around something. And yes, the 'line'
created by the sphere, were Freddie to move around it, would not change
size ... But only if the sphere is not moving through the plane of Freddie's
World at the moment he moves around it (can't really use 'walks' around it).

Just Freddie's binocular vision should be all that is necessary to identify
various shapes. Remember, with binocular vision he has depth perception.

Freddie can detect, deduce, a circle ... But he cannot 'see' it (already
addressed).

Consider how subtle the clues we utilize to 'recognize' someone, particularly
a baby, visually.

Best :cool:

Chagur posted...
Already addressed Freddie moving around something. And yes, the 'line' created by the sphere, were Freddie to move around it, would not change size ... But only if the sphere is not moving through the plane of Freddie's World at the moment he moves around it (can't really use 'walks' around it).
Just Freddie's binocular vision should be all that is necessary to identify various shapes. Remember, with binocular vision he has depth perception. Ah, that will teach me not to read the whole thread. :o

I didn't take into account binocular vision either, which would mean if FF saw a line head on he might mistake it for a very short-based triangle sharp-end on. Of course, he could look sideways at it thus narrowing the distance between his eyes, but he would have to go to the other end of the line (or triangle) to be sure of which.

In the case of the moving sphere, this is an interesting one. First it might seem to be a very short line. Not quite a point, but short enough that he might miss it head on. Then it would grow. It would reach a maximum, and then begin to shrink, eventually disappearing. This would be consistent with a short line rotating.

However, if the line grew very big, FF might wonder why he hadn't spotted it earlier.

Freddie can detect, deduce, a circle ... But he cannot 'see' it (already addressed).Well, he does in fact see a circle. But he doesn't know for sure unless he moves around it and finds that it never changes size.

Consider how subtle the clues we utilize to 'recognize' someone, particularly a baby, visually.I'd like to, but you'd have to tell me what they are first. :)

kind regards

"I'd like to, but you'd have to tell me what they are first."

You're pulling my leg, are you not, §lîñk€¥™?

Best :cool:

I undersand what you are saying, Chagur, but it seems to be semantics as far as I'm concerned.


Seeing a circle in Flatland is like seeing a sphere here. No matter which direction I approach the sphere, I only see a circle. All the same, I still say I'm seeing a sphere.


While I do claim I see a sphere based on other clues--that the circle doesn't change as I move my head from side to side, that light reflects off it in a certain way--it's commonly agreed that I still see it.


I think it's silly to make a distinction between the visual image by itself and all the clues we use to add to our image of it. It's an easy reduction to the absurd--without these clues I don't even see a circle, I just see points of light.


A good rule of thumb might be that if Freddie does not have to consciously deduce or detect that it's a circle, then he sees the circle.




And as for the soap bubble thingy--why would Freddie detect anything at all? Wouldn't a displacement like that effect whatever methods he uses to see--i.e. the light of Flatland would bend?

In relativity, when space is bent or streched or whatever, it is only apparent to an outside observer. Wouldn't a sphere passing through Flatland as worst cause Freddie to think some other part of space was getting all funky, but not wherever he was? And if he was far enough away to be an outside observer of the event, it wouldn't look like a circle at all, but like time sped up in the area around where the sphere was going through.

welcome to sciforums, tarrou.

b]Chagur[/b] posted ....
You're pulling my leg, are you not, §lîñk€¥™?Well, yes and no. I have some ideas of what involves face recognition but I am not a cognitive psychologist or similar, so really anything I would say on that score would be a pure guess. :)

kind regards

Flatland was a social comentary. It had nothing to do with physics or mathematics in any way, but some people (esp. high school honors teachers) like to pretend that interesting things can be learned from the book that couldn't be learned much more thoroughly from a mathematics textbook.

Not quite, tarrou.

Seeing a sphere in 3D requires visual clues to differentiate it from a well
rendered 2D picture (an optical illusion) in that your left eye does not see
the exact same image that your right eye sees ... If the picture is not a part
of a background, and you are not free to move about, you would not be
able to tell which was the sphere and which was the picture of a sphere (a
circle).

Try this: Cut out a paper circle and a strip of paper whose length is the
same as the diameter of the circle. Make a dual 'pinhole' viewer and place
it so that you can only view the edge of the table on which someone else
places both the circle and the strip so you are only able to see their edges.
Only if you are able to move the viewer from side to side will you be able
to determine which is which without raising the viewer.

Although the light bending is an interesting thought, it is not addressed in
Flatland and is therefore, AFAIAC, extraneous to the discussion.

Take care and welcome to Sciforums :cool:

§lîñk€¥™ Although I have a bachelor's in psychology, my master's is
in Criminal Justice. Couldn't handle the psychology of the time (late
'50's) ... And not too much of the CJ. But what the hell, Uncle Sam
was willing to pick up the tab to 'professionalize' Corrections and I
enjoyed the late '60's, early '70's campus scene.

So, if you can accept my just being a curious cuss, I'll offer my ideas
with the proviso that we start a new thread over in Human Science
(more appropriate) and you can then offer yours. Deal?

Best :cool:

White Knight,

Suggest you go back to the James R's post at the beginning of the
thread and read what he had to say. I can't say it any better.

Take care :rolleyes:

Chagur posted...
Although I have a bachelor's in psychology, my master's is in Criminal Justice. Couldn't handle the psychology of the time late '50's)Hehe, didn't like the LSD eh? ;)

... And not too much of the CJ. But what the hell, Uncle Sam was willing to pick up the tab to 'professionalize' Corrections and I enjoyed the late '60's, early '70's campus scene.Why look a gift horse in the mouth? No one would rightly blame you for feathering your nest when given the opportunity, or of excessing in par-tay. :)

So, if you can accept my just being a curious cuss, I'll offer my ideas with the proviso that we start a new thread over in Human Science (more appropriate) and you can then offer yours. Deal?Much as I appreciate you laying down a friendly gauntlet, so to speak, I'm not sure if what I have to say has any depth or would be worthy of much more than a passing glance and dismissal.

I'll make a deal. Seeing as you're the one being curious :D, if you start the thread over there and post me a link to it, I'll take a read and throw in my two cents. How's that? :)

kind regards

The acid was great until they started tossing in other junk, §lîñk€¥™ :D

Ah yes, Boone's Farm and Tantric Yoga on a city roof top. Great times, those.

Anyway, before starting the thread discussed, I grunched a bit and realized
that my thoughts were rather superficial at best and decided to do a bit of
Googling to see what was new and exciting ... Nada! It was like stepping
back two score years and thinking 'the old neighborhood hasn't changed all
that much'.

The thing that I found most interesting was that I didn't find a single paper that
addressed the old 'they all look the same to me' aspect of recognition. An aspect
which, whether applied to our species or any other is progressive. As though the
initial observation creates a rough template that is increasingly refined through
repetitive observation/viewing thanks to a hard-wired mechanism that is most
evident in the 'imprinting' by chicks, but is not totally lacking in our species. Or
present, but too 'animal-like' to be seriously considered (except by someone like
Desmond Morris, a zoologist).

Enough rambling. Sorry.

Best :cool:

Flat surface - with no thickness. Even if we assume (for the sake of imagination/visualisation) it to be a billionth of a billionth of 1 nanometer it is sufficient to slice thro the sub-atomic nuclear particles... Matter does not exist in flat-land !? May be patches of fields of varying strength and type..!!..

Pl rebuke gently..!!!... if wrong .!

Since Flatland exists only in one's imagination, assume it to have zero thickness ...
That being the case, 'matter' exists in Flatland ... In the same sense that it exists
in 'thought'.

Don't know what else to reply, everneo :cool:

Originally posted by everneo
Flat surface - with no thickness. Even if we assume (for the sake of imagination/visualisation) it to be a billionth of a billionth of 1 nanometer it is sufficient to slice thro the sub-atomic nuclear particles... Matter does not exist in flat-land !? May be patches of fields of varying strength and type..!!..

Pl rebuke gently..!!!... if wrong .!

according to our current theories about what matter is, well, it is a point particle. you can have a point existing in 1, 2,3 or any dimensional space you want. of course, some of the properties of matter depend on the dimensionality. for example, the gravitational force is 1/r^2 dependent in three dimensions. in two dimensions graviation force would be 1/r dependent. for some particular reasons, classical electromagnetism as we currently understand it, just wouldn t be there at all...

the zero thickness of two dimensional space is no more a problem for particles in a 2-dimensinoal universe than the zero 4-dimensional depth of our 3 dimensional universe is for the real particles in our 3dimensional universe

Thanks, lethe. It almost makes sense to me now :D

:cool:

Good book to read is:

Geometry, Relativity and the 4th dimension. R. Rucker.

That'll sort things out.