The Land of No Shadows

That really made me smile a lot!

I think I need a better grasp of the hypothetical Twod world before extrapolating further. In Twod world you say there are no shadows, but that light from the 2D star enters Mr. Flat's house through breaks in the diagram. If there are no shadows, then how do the parts of Mr. Flat's house that do not receive light appear?

I guess you got me right there on that one. I think I 'splained and assumed too much in the first description of the experiment. Actually, there is no house, because Mr.Flat has no 3D object with which to draw the lines. He can't saw flat boards, because that would be 3D as well.(confusing isn't it?).

Let's go back and say there are no shadows in TwoD world because it requires a third dimension. Forget the part about his star and his house for now. If Twod world had shadows that could exist, would they just be uni-dimensional projections?

The real question: What does a shadow from the Fourth dimension appear to be in the world we know as ThreeD? Since we "normally" see shadows as a 2D projection of a 3D object, would the 4D object project a shadow that is 3D?

You beat me to it. I found that book quite interesting.

Man, you went and let the cat out of the polygon!

Polygonticians will be all over this!

My next question: In Flatland (Twod world), how do they read and write, since any mark (as we interpret it) seems to be a barrier to cross, except they cannot cross it, as that might involve a classical object tunneling through an energy barrier (as do quantum objects when conditions are appropriate).

The initial queston remains: Can a 4D object project any shadow onto 3D world that is a 3D projection, or does it lose two dimensions during projection? Is the 4D shadow something more like a movie projecting on a screen, i.e.- two dimensional plus time?

Or is Twod world truly a land without shadows? Remember that Twod world is not a sheet of paper, but is more like a spatial membrane, a plane in two-dimensional space. Also, we can later allow for the flexure of Twod world such that it might be allowed to fold over onto itself, thus mapping point (A,t) to point (B,t'), or (x,y) to (x',y') while apparently holding t constant.

GA.

One of my favorite books

There must be shadows... if the light can't enter some parts... the lack of light is a shadow.
Del

If one considers that surfaces in Twod world may consist only of lines, and those lines are constructed by the connection of two points in the membrane, the lines are infinitesimal in thickness, and I cannot assure anyone that light would reflect from or be absorbed by them in the least. The entire construct of a Twod star seems implausible, so I am not sure at all that their light source (if they have one), originates within the constraints of their ordinal dimension.

Perhaps a 2-dimensional world may not have stars, solar systems, and galaxies as does our 4-dimensional universe (adding time as the fourth dimension, and also allowing Twod world to experience time as the 3rd dimension seems allowable).

If this is the case, then apparently, we are back to (1) a land of no shadows, and (2) no ability to distinguish actually the source of light projecting onto their dimension. It sort of makes no sense, because there is no "up" or "down" for them to look to.

I suspect that you would not be looking for shadows. You would be looking for unexplained lack of shadows, that is, a location which should be in shadow, but is actually lit from a source not present in your 2D or 3D world. Possible example, a movie scene where the couple sits on either side of a candle flame which is the only light source. You see both are strongly lit from the left side, but they can't seem to see it.

HA!

Now there you go!

Light is an electromagnetic wave,

Light is dual nature of physics, because light is also a particle and has been proven. With the essential theory that evolved from electromagnetics into quantum mechanics.

proven with the inference experiment.

OK, maybe then light can only interact with Twod world in the form of particles being stopped, or passing through the plane. Maybe they have two-dimensional gardens?

How can any living cell ever be two-dimensional? Ain't gonna happen.

Apparently we think along similar lines, no pun intended. I posted an almost exact same thought before I saw this post of your (made previously), well done indeed.

If light has anything to do with Twod world, it MUST come from off-plane. Se still know, however that in "our" world, even the most microscopic interaction with light is still by definition three dimensional, thus the entire discussion boils down to this:

Could an untrained observer in Flatland (Lubbock, Tx) discover (1) his/her world is not flat, although still three-dimensional since he/she has the property of height, houses, trees, vehicles, etc. also have height? It depends on what the observations are, and in which directions these are made, does it not?

Never put the bong down , reality sucks.

And there can be a shadow in Flatland. Problem is a sun would appear as a line which would have one hell of a penumbra shadow from an object.

What about refraction, does that also take place in Twod world?

I really was not using a bong when I came up with this idea for a question...

What about refraction, does that also take place in Twod world?

Sure but it would have to be going thru two different mediums.

I am still having another issue with light propagation through Twod world space.

Maxwell's equation is strictly three-dimensional, with the E field perpendicular to the H field, and both perpendicular to propagation direction. If this "test" world were strictly 2D, then light cannot propagate at all in that plane. Therefore, any reference to light, shadow, or refraction, or reflection is pointless, and irrelevant.

Residents of Twod world must be dead, since there is no known energy source for them, and second of all, if they were not dead, they would be blind as a cave rat.

I agree, but really, I put the bong down long, long ago, in a place far, far away.

Again, I respect you, but SolarEagle posted a pic of your bong on another post, here.

Here it is :

Not sure how he got that pic, but you know the bird, he can find any pic, looks like that is made to share with a friend.

Wow a 3 globe wofen poofer, those are rare....

I salute you with the back of my left hand raised. Thumb and pinkie finger folded, now read between the lines, amigo. I don't own an F bomb, or a bong.

I am trying to contemplate the universe, as has been mankind's pastime through the ages, since we became beings that were self-aware.

Suppose here we are in 3D world, seeing what we view as a near spherical universe (or something ellipsoidal perhaps), and this is the flat field view of the universe.

If however, space is not rectilinear, and is in fact, curved, such that one could conceivably travel throughout space (of an expanding universe) in a single path, we could arrive back at the starting point without changing "direction", then that would prove the curvature of space, unfortunately there is not enough time in the universe to complete such a trip.

Wow. Just plain old wow.

<unsubscribe>

Wow, I was just funning with you. Sorry you can't take it. Obviously what you are trying to contemplate is too deep for me. Seeing as I can not contribute to a 2D shadow world discussion, and you are offended by my kidding about it, I respectfully unsubscribe..

BTW I really don't think you have a bong, but peace!!!

Sorry, if I gave you the impression I was ticked off by your joke in the least. I knew you were joking. I have an odd way of playing along with jokes.

I think I am with your w.r.t Twod world Threed world, and Fourd world.

Interesting the way a dog tilts his head sideways when I am explaining something technical to him.

[FIRST: with regard to "^{_{...since we became beings that were self-aware"...}}]

contrary-to the bold-&-impudent arrogance spewed in endless streams by the likes of Dawkins, Hitchins, etc...WE WERE CREATED THAT WAY (^{_{I know that you know better}}).

And, there are plenty of good folk around this globe onto which we were placed {scientists ("then and now"), theoretical physicists, theologians, and Nobel Laureates} who would defend that truth with far greater eloquence than these poor fingers can produce, in this tiny space.

NOW : While I agree that "thought experiments" can be fun and interesting, there are "times and places" ... as well as LIMITS to any-and-all "foolishness"... {and, that is NOT to suggest that all such inquiries are 'foolish or whimsical'. Each must determine for himself, in many cases, what is and what isn't.}

If a person chooses to believe [[either]] that :

(A) everything-that-there-is <^{_{detectable by man or not}}> just "made itself". And (^{_{still 'A'}}) since [man] MUST be "smarter" than stuff that can simply "make itself", it is necessary to "catalog" any and every "thing" that comes-along, including ideas, as "fundamental knowledge"... or...

(B) that "no God" (if there is one?) could possibly have made a universe so 'confounding' to us that we can't figure-it-all-out...

... then, they shall inevitably be bound to push the limits of human imagination, and sell those imaginations as "Good Science" to every sucker that scans those bookracks... because (as stated more eloquently than I would muster):

"You don't have to 'prove anything' in your book, because nobody can EVER prove you to be wrong!"

It was John Polkinghorne, KBE, FRS who once said: "the nearest analogy in the physical world [to God] would be ... the Quantum Vacuum."

... and so (at this point) I'll "reference-back" to a couple posts that I had made on 'Dark Matter' previously, both HERE, and HERE....

My Dad {^_ref} had a little "sign-post" on his desk {I may have posted previously} that said:

"Great minds discuss IDEAS. Average minds discuss events. Small minds discuss people."

I also recall him asking me on several occasions...when I had my face in the 'boob-tube'.... "Are you watching science, or science fiction?"...

It IS good to know the difference.....

Sure, and no argument. Suppose if we ever found the curve of space, God might be just around the bend.

[ ^{_{"though the vipers may spit yet again..."}}] Re: "God might be just around the bend"

He *IS* everywhere (^_omnipresent)...... no exceptions, no question.

and our lives are nothing more than a shadow, or a breath-or-wisp, or a vapor...

||^{_{always-and-forever, whether one believes in Him, or not...}}||

It is usually when we turn around that God is visible holding us up.

..then we must all be a piece of God and a component of mass consciousness?

My girlfriend who has an interest in Edgar Cayce (an interesting character imo) where Edgar Cayce referred to it as we all are 'one', which is part of what you described.

One in the spirit (with the body of believers), not one with all bodies, or even one with all minds. Who would want to be "one" with someone criminally insane, cruel?

Who would want to be "one" with someone criminally insane, cruel?

James, of all people, I'm surprise that this came from you... I believe in god, but, I'm don't consider myself a religious man. I'm sure you know the parable of the rich bon vivant glutton and poor Lazarus at the temple door.

Being compassionate on someone who is ill, and rendering aid to them has nothing to do with being "one" (i.e.- having a single-minded purpose in coherence with them).

Hey, in this picture you just painted, I relate far more to Lazarus than to the rich bon vivant glutton, although I could lose a few pounds, alright.l

Interesting coincidence, Lazarus was the first to be resurrected from the dead (directly by Jesus).

I never said, "Go out and harm people you do not relate to, or whom you find repulsive." Those people may be more in need of your (and my) help, than their victims. Sometimes the best way to help a violent criminal, return them to the maker, but only when the victim's family agrees, or there is no time to decide.

Sometimes the attacker makes the decision for everyone, and the would-be next victim has to simply stop them dead in their tracks, like a rabid dog.

Being compassionate on someone who is ill, and rendering aid to them has nothing to do with being "one" (i.e.- having a single-minded purpose in coherence with them).

Ok,... who was Jesus crucified with on the mount? What was their background?

hint: Luke 23:32-43

here's a piece of my experience,... I'm a Lutheran, raise and still am,... and the holy rollers in our congregation, were the biggest sinners.

I never said, don't associate with sinners. If you did that, you would have nothing to do with me, I assure you.

As to the crucifixion: Jesus was reportedly between two sinners, one a thief, and the other apparently a murderer. One was repentant, the other was cynical, so no wonder which one Jesus told would be with Him in paradise.

There are clearly those that are way past salvation, even though it is also crystal clear it was being offered, and is still offered by the authorities, and by the Church.

I have nothing within myself worthy of redeeming, it is only the mercy of God that allows me to live each day.

Hmmmm....(^{_{being uncertain as to your exact meaning/intent}})...

"then we must all be a piece of God and a component of mass consciousness?"

"In a sense, yes" . . . and/but (contrary to the "Will" Provine school-of-thought):

most affirmatively endowed with 'free will'...(!)

There is a verse in the Bible that goes something like this:

In Him we live and move and have our being.

"In Him we live and move..." Acts 17:28 ... (^{_{tis a cinch, to retrieve phorgotten memories, these days}})

Slartibartfast once said that the likelihood that he would actually find out what's going on is so close to zero that his response was to just get on with things. When asked if that made him happy, the reply was "No."

I think that b uy a 2D perspective all things would simply translate as varying shades and depths of the combination of colors present in that reality.

You only get two options for the physical perspective in that world. Either looking at a flat sheet of paper from the thin side so that everything is just a shaded infinitely thin line with height and depth or from the other 90 degree perspective where the whole view of everything is presented all at once in a height and depth perspective.

As for us 3D beings we perceive the (as we can define it so far) 4th dimension as time which for your 2D world they too would need a time dimension as well for anyting to interact with anything else regardless of whether their perceptions are in 'line view' or panoramic 'flat face' view orientation.

Is this another: "Young's Modulus of Pinto Beans" thread?

Not really, I am seriously interested if we can have a philosophical discussion about my question, and if it relates to how we perceive and understand the universe around us. Is that of any particular interest to you?

" how we perceive and understand the universe around us." -
Perhaps we perceive and understand the universe around us based on a projected content that is undefinable to us; not too unlike the shadows projected into the minds of the residents in Plato's Cave.

This whole thread is hilarious, if not un-parsable.

"Is this another: 'Young's Modulus of Pinto Beans' thread?"

No, Lyn, that's the thread for Tequila and lime junkies.

https://web.stanford.edu/class/ihum40/cave.pdf

I spent time drinking beer and viewing a phenomenon know as the Paulding light. Shadow people were part of the discussion..

Maybe 3D shadows are the answer. Maybe shadow people are from the 4th dimension?!

Q? How would a 2d being be aware of a shadow?

How many dimensions are we dealing with again?

There could never be a 2-dimensional world, it's impossible, at best your third dimension would be very narrow...

That little blue man is sure staying busy killing the shadow people...

How can a dimension be restricted as to scope?

I agree it is impossible, especially for us to consider it as such. Even if spatial dimension was limited to 2D, there is still the third dimension of time to consider.

Answer me this riddle: Can a 4D object have a 3D shadow in our "normal" world?

"^{_{Can a 4D object have a 3D shadow in our "normal" world}}"

I'll admit it : my brain hurts reading such "speculative" things, especially when the various 'aspects' of the discussion are not adequately defined/described/delineated (in layperson's terminology).

i.e./e.g. ~ what exactly IS the 4th dimension to which you refer...? (a friend loaned me his Fabric of the Cosmos, in which Brian Greene left me utterly bewildered and unsatisfied with regard to there being 10 or even 11 dimensions).

I am just fine with this being "Newton's" wonderful universe, and, with there being a Spiritual realm throughout (that is far more real than anything that we can perceive in this ethereal existence).

Can anybody here, in clear/concise non-obfuscating language, explain the "flatness" of this universe (as opposed to the massive "curvature" that it supposedly ought to exhibit).....? I would really appreciate getting a real grasp on THAT for starters.....

If I knew, brother, I am not so sure I would be asking such questions. I am curious, but we know what that did to the cat on the wire.

I am pondering if what we think is dark matter/dark energy is really a projection onto our plane of reality from a higher order dimension? I have no data, nothing to suggest really that this is the case. It is a question for sharper, younger minds than mine.

I too, am happy (or at least I was happy) with Newton's world, and God's world existing in some harmony. I don't think we can ever truly grasp the world laid up in store for all humanity at the end of our era. I don't beg for that day to come, because life as we know it, is so very beautiful and precious.

No reason to have trepidation, however, as the long sleep comes first, and no man is aware of what goes on outside his dreams.

I agree we need some definitions. Without them, I find understanding the discussion is all going over my head. Which I guess in a twod world would not be possible - so would I be invincible if no one could get one over me...

Since no one has any weight in Twod world, no one could shove you around either, without some cooperation.

I think I failed to see several of the issues with Twod world, so I should have made it ThreeD with a severe restriction on the third (up/down) dimension.

Thus Lim(x)->∞; Lim(y)->∞; and Lim(z)=0.01 (non-zero, but definitely not ∞)

Yes now you have asked an interesting question....What is the true nature of a dimension? I submit for your perusal the possibility that we are 2D and the third dimension is movement....after all have you ever seen anything not moving in this universe? So possibly we are 2 dimensional creatures moving through space/time creating the illusion of a 3rd dimension....

in that case, what is thickness caused by? Momentum induced dimensional drag?

What would the thickness be caused by? Are you sure you want to know....the answer may cause madness....In any case, if that is the case, I don't want to know, and since I would have to find out to tell you, well there you are....

ROFLMBO, since in Twod world no thickness.

Yes, except our motion has all degrees of freedom. Not stuck in one place in 2D.

Certainly, we are in motion, whether the motion is relative to nearby objects we observe or not.

That gets off into deeper and deeper quagmires of thought.

..."Can a 4D object have a 3D shadow in our "normal" world?"...

I don't think so, dimensions by their very nature are undetectable from each other....Now it's true that an intelligent creature could manifest a presence in multiple dimensions but would have no physical qualities, therefore undetectable except by observed influence...How this would be done is well beyond my understanding...and I think beyond my capability to understand...

The 4D creature when intersecting our "plane" would reveal his D-1 projection would he/she not? For example, a spherically symmetric (ball) creature in 3D could only project either a point (at intersection tangent), or a circle, hollow or not, onto the Twod world. A 4D "sphere", would it have a 4D "volume" of 5/4(π)(r)⁴ ? And would its projection exhibit a volume (3D) of 4/3 (π) r³ , and present itself as a spherical shadow (projection), just as a ball projects a 2D shadow. The concept of 4D "volume" makes no sense in our dimensions. I am pretty sure, no one has actually named such a "solid", maybe just maybe some mathematician I am unaware of??

I am sure also this is beyond my capability to understand, since I cannot "imagine" it as anything I could possibly be familiar with.

While this may seem to be matter-of-factly true, we must consider the ability to cloak ones existence may also exist...

Fascinating! Illogical? but fascinating.

If you panned your perspective of the attached graphic 90 degrees left or right, up or down, in a truly 2D world everything would vanish, right? Since there's no z axis? I guess the question is could things interact with each other in only 2 dimensions? Like running on blocks, etc? If things can or can't interact in 2D only, does that necessarily mean that type of "world" couldn't exist?

I think there was a Star Trek TNG episode where they discovered 2D beings... I forget how they approached it, though.

I think there was a Star Trek TNG episode where they discovered 2D beings...

Yes:

https://en.wikipedia.org/wiki/The_Loss

methinks they approached it (the 2D beings) lightly to as not to make a bad impression.

In this two dimensional reality, would an individual be able to see anything?

Really?

If we accept the answer as yes, then would you not see, simply, a line from the 'floor' extending to whatever the tallest visible item is?

Care to explain that one a bit further? I am not "seeing" it.

Suppose in Twod world, instead of forward/back, right/left, we have up/down, right/left.

Would everyone be a "bottom-dweller"? What would they see up there in their slice of heaven?

Could a "tree" grow "up", and could yew make a bow from it? The spreading chestnut tree only gets to spread right and left. Mr. Flat could now have height and breadth, just no depth. There would be no stepping over water, except left or right.

I suppose objects could sink in water, so they could have boat-like objects as well. The ocean could be deep, but not wide at least not in both ordinal directions.

With flat eyes, could they actually focus anything, and how would they rotate their noggins to look up? Very confusing. Very confusing indeed.

Life after the break up of 'The Blue Man Group'?

I think in your analogy, the 3D being needs to be pressing on the plane of the 2D world, distorting it with a dimple so that where there had been some straight lines, they now look bent to Mr Flat. He can tell his space is not right, but since he can't see the dimple - other than by noticing bent lines - he can't explain what has happened to his space. Also, to his view, the dimple affects the space he lives in, but is not a part of it.

Now we are getting somewhere? I think you are about to tie this in with Special Relativity and Gravitation. Spatial distortion induced by gravitation.

Let's forget shadows and other such, and extrapolate the concept of 2D-3D-4D; these are all spatial dimensions, not space-time. Take a table top as the 2D world; as 3D beings we can reach inside a closed polygon without breaking the boundary and make a change. Our cross section to the 2D being would be an irregular sorta roundish object. Now imagine that God is a 4D being. He could reach inside our 3D world without breaking the boundaries and do, for example, repairs. Another name for repairs might be healing. He could also do other things, call them miracles, by inserting or deleting something via the 4th dimension.

Then what about a stacked dimension scenario where the smallest thing we can see is the largest thing they can see, and the largest thing we can see is the smallest thing the next dimension can see...This could go on forever as far as we know...and the worlds could be as different as the scale...and the physics unique to each dimension...

James! Come to dinner....

....Mother I've got my spinning fire wheel working....once we scale it up it will power the world....

OK,,,but can't it wait till tomorrow, your dinner's getting cold.....?

Where exactly did you obtain that picture of me in High School? I immediately recognized the beard, and the cigarette drooping from my mouth as I held the fire wheel in my nicotine-stained finger tips.

Sounds like wifey is not calling me to dinner so much as asking, "where is my Grilled Market Salad with Avocado Lime Ranch dressing from Chik-fil-A?"

Whereupon I reply to her, just when I got the timey windy firey thing working, only to have to have lie it down on my work bench, "I suppose I have not transported it from hither to yon, in your time frame of reference. Would you like it to appear before or after the next commercial, after all, I am your Android, a Robot for Bhudda."

I pondered the world of scaled dimensional perception when I was about 10-12 years of age, and came to the conclusion that the universe is an organism with parasites. The cautionary part being that the tail of the dog has fleas, with dogs on them of microscopic dimensions (probably water bears), and the dogs have fleas on them as well...ad infinitum.

I thought it was turtles all the way down...?

Since we cannot see the 4th dimension, they could be bears, water bears, dogs, fleas, and/or turtles. OK, then it's turtles. If space-time is curved in our 4D world where time is one of the dimensions, what do things look like in 5D (time is one of the five)?

turtles. ninja turtles I tell you.

Turtles all the way down. But are they boy turtles or girl turtles?

Boys, the girls are busy with other issues.

Yes James Stewart; I believe the Mangod might be a Ninja Turtle.

Whatever the brew is, it wants sharing!

LOL - Killian's Red all around, I suppose.

Fantasy is still fantasy.

Sometimes muscles work ever so much more comfortably for the stretching that took place prior to the walk.

Personally I always hated stretching before a workout. To me it was just wasting valuable stored energy resources my body would need soon.

Same with a 'cooldown run' after a hard workout. Stupid wastes of time and energy in my books.

I just know that walking hurts when I fail to stretch my legs first.

When you're right you're right, and you're right.

I thought Carl Sagan explained it very well:

https://www.youtube.com/watch?v=N0WjV6MmCyM

More on the Tesseract:

Totally mind expanding, right?

...Or Carl's protegé Neil deGrasse Tyson

https://www.youtube.com/watch?v=lM_HPAXwJFw

Here's an interesting thought:

In a 3D world, a light source behind the viewer casts a 2D projection of darkness onto a surface in front of the viewer.

Now, the general consensus is that time is the 4th dimension.

Picture that some unknown "light source" in the 4th dimension is essentially behind us (i.e. in the past), casting a 3D "shadow" over the 4th dimension in front of us (the future).

Just as in our 3D world, despite the 2D shadow, we understand that the other spatial dimensions are there, we just cannot see them. Similarly, we understand that time will continue passing into the future, we just cannot see what is there.

No idea what the unknown light source would be in this thought though. Some divine being? Black holes? 42?

Maybe the light source is a single discontinuous event. The further you look, the deeper this gets.

Certainly, in life, it seems at times, that events in the past shape the future in ways we can and simultaneously cannot predict. Choice makes all the difference, along with determination. For example, if you saw Beethoven's projection as a boy, would you have seen Beethoven the composer?

Please clarify how can there be any real light sources in a world of only two dimensions ? ...

A sufficiently complete, detailed, and labelled, 2/3-D diagram could be a starting place...

Mr. Solid, from 3-D Earth, could not have any height in in 2-d Twod Land to cast a shadow, although he might be the source of some other form of (electromagnetic ?) energy that would be projectable outside of Twods' 2 dimensions, but would that qualify as ''light'' in Twod Land? ...

TV characters are in a 2D world, although I feel this is just an echo of their true existence....

...but now cartoon characters are indeed 2 D....how do they manage?

...no still 2D....just better shading...

...nope

DOh!! That is gonna leave a mark!

We were at a library sale today, and came up with the book "Flatland, A Romance of Many Dimensions" by Edwin A. Abbott. Interesting with the topic we are discussing! It is only 83 pages. This was mentioned by Rixter in #5.

https://books.google.com/books/about/Flatland.html?id=HKackp-vG-YC&printsec=frontcover&source=kp_read_button#v=onepage&q&f=false