Have you noticed Abbot's original title page of Flatland? A cloud (of unknowing) with multiple gateways of dimensions tucked here and there, fourth, fifth, sixth rising toward... ten dimensions. Published in 1884!
I also love Michio Kaku's Hyperspace, accessible to us dreamy and distractable liberal arts types. I read it aloud to my youngest son years and years ago. He wasn't such a good reader so we made it through together at his insistence.
For groups, there's an animated DVD, Flatland, with a book, and voices by Martin Sheen and Michael York. Multiple dimensions is such a basic and important concept for people of faith. Thank you!
I loved the decaying fruit! Perfect!
It's no wonder we only perceive shards of Reality. Like Isaiah's three dimensional description of seraphim - six wings, eyes all over...
Thank you, again.
S.G.

I read an article this morning about a theory that explains why the speed of objects in our universe seems to be increasing instead of slowing down, ad physicists would expect: http://www.dailygalaxy.com/my_weblog/2009/09/is-time-slowly-disappearin....

The answer: time is slowing down, only we can't perceive it from our place within said time and space. Only someone outside our time and space could observe it.

Sounds familiar. Wow.

Like you, I love straining my liberal arts education to try to grasp 20th century physicis. Have you ever read The Elegant Universe by Brian Greene? If not, you really should. Greene is a world class physicist that did both a Nova series and wrote this book trying to explain the rudiments of string theory to people like you and I. To get there, he has to spend 1/2 of the book explaining first general relativity and then special relativity. All of it fascinating. I have read the book five times and each time, I understand a little more. (I will give you a sneak preview - if string theory is proven correct - there are actually anywhere from 6 to 23 (I believe) additional dimensions - but all but the familiar four are incredibly, incredibly small. It is the strings exploring these additional dimensions that give all matter and energy the observable characterisits in the 3 dimensional world.)

For what it is worth, I can somewhat grasp the fourth dimension by thinking of it in terms of coordinates. Pretend that you are just about to throw a football. To reach the wide receiver who is running as fast as he can, you have to calculate vertical placement (up/down), horizontal placement (right/left), distance AND at what time will the receiver arrive where I throw it. In other words, to know precisely where something is (either in the past or future), you have to add a time coordinate.

You wrote, "the fruit exists in all of its temporal stages at once." I do not understand the insertion of the words "at once". This implies time does not move in someway. Thus, I think my understanding is not consistent with your understanding - but in science many times two peoples' perceptions that appear at odds turns out to be in sync - just viewed from a different angle.

Dave

Okay, so I majored in physics precisely because of these kinds of conversations (and because I had read Flatland, along with a lot of science fiction, and popularizations...) I figured I would probably quit and switch to an English major whenever I got to the point where it was just too hard, but ended up sticking with it through my PhD -- which was in optics, in the end, not cosmology or anything cool like that.

But they never talk about this stuff in physics classes. What they teach you is math, tecniques for solving homework problems and predicting the results of experiments, and the interpretation is up to you. So beware -- any physicist talking about what the math actually *means*, including me, is just giving his or her own opinion.

That said, I think that you're absolutely right about what it means to think of time as a fourth dimension. You know, a cone is a circle that is different sizes at different points in space. In the same way, you can imagine a human being, who starts out as a tiny baby and grows to adulthood, as an object which is different sizes at different points in time. We can even picture it, sort of, by stacking a bunch of cut-out, flattened images of the child one after another, so that we can see the change in time as a change in space instead -- the child would look sort of like a cone with a funny human-shaped outline. (This kind of diagram, in which a spatial dimension is replaced with time on one axis of a graph, is actually a very popular tool in physics).

I picture us all as long, tapering tubes in spacetime -- we start at a single point (a point in spacetime is called "an event") and then grow and wind around and around as we go to school and work and back and across the country to visit relatives, until I suppose, we die, and our atoms begin to disperse throughout the universe... Physically, the tube becomes a cloud.

(By the by, I also get a kick out of thinking about what the physical difference between "alive" and "dead" is in this way: while you're alive, you lose atoms and gain them but a pattern persists, like gas molecules blowing into and out of the great red spot on Jupiter, a storm which has existed for hundreds of years. But when we die, the pattern falls apart, like a storm dispersing. Our bodies then lose atoms slowly as we decay but have lost the ability to replace them...)

I am no longer religious, in the sense of believing in the supernatural, but I believe that the natural world is quite miraculous enough... And I am not terribly bothered by the idea of mortality, because I think the past is just "over there" somewhere (points in the negative "t" direction). So I'm not infinite in the time dimension... I'm not infinitely tall or infinitely wide either. If I someday cease to exist, it means that I don't exist *at that time* -- but it doesn't negate my existence at other times. I'm a tapering tube...

Strangely enough, when I was a child who loved to read and wondered if I myself might not be a fictional character in a book, I found comfort from a related idea -- that even when I was finished with a book, the book was still there. I could dip back into an early chapter and the characters I loved would still be doing just what they were doing the first time I read that chapter. Though when I am reading a novel the story unfold one event at a time, once I am finished I realize that the whole story really exists at once. Cinderella is not *now* scrubbing floors or going to the ball -- the story's time is separate from our time, and for us the whole story exists at once.

It's occured to me that if I think of time as one of those tapestries that illustrates a story, showing events unfolding from left to right, it maries this idea nicely... Time on a tapestry really is a dimension -- left is the past, right is the future. So convenient that my literary and physics-based metaphors marry so nicely together... It probably just means I'm inclined to look at time this way and would regardless of whether I'd ever learned any physics.

Of course, the problem with this sort of "time is a dimension" stuff is that it tempts one to think of the future as equally fixed, determined, static. I don't want to get too deep into the free will problem in this comment, which is already more than long enough, but I will say that the tension between this model of time as a dimension and the fact that the future is (according to quantum mechanics) truly unknowable in some aspects -- this tension exists in physics, mathematically, too. Some physicists are much more deterministic than others. There is a lot of work out there on randomness, statistical mechanics, and why things fall apart on their own but rarely put themselves together -- why causes always precede effects, why the "arrow of time" points in one direction, while there is no similar "arrow of length"...

It's a complicated subject, but I'm satisfied, for now, with a fairly simplistic answer. Just as what is happening on the left side of a tapestry does not determine what happens on the right side, what has happened in the past does not necessarily determine what will happen in the future. And just as the right and the left sides of the tapestry are equally real, so too are the past and the future.

Whew. That was a lot of typing.

-Mary (mks.mary -at- gmail.com)

Huh? I was signed in. Well - "Dave" is me.

Michio Kaku has another book, Parallel Worlds, that is outstanding. He does a similar thought experiment, only works from the idea in string theory that there are more dimensions something like 10 or 20?) He points out that hypothetically a 3D person could act on a 2D person in ways that would appear totally supernatural. The 2D person could perhaps interact in some small ways with the 3D person, but would seem so incredibly limited. So if we exist in 4 dimensions, what if there is a 5th dimension, say the "spiritual" dimension, which acts on us? It would be beyond space and time as we know it and the one(s) who occupy it would at least appear to us to be omniscient and omnipotent.

I've used something like this to describe God so many times, and every time I or someone I know ventures back into the area of "well, if this means this, then this could mean THIS..." I get terribly excited about it all.

For me, this kind of thinking started when I first read A Wrinkle in Time. I've always wondered how many folks working in theoretical physics and/or string theory were inspired by L'Engle, and if they knew of her deep faith.

I don't really have anything dramatic to add here, Gordon - I'm just happy I had enough brain cells left today to comprehend a little of what you and others have to say on the topic. :-)

Grace & peace,
Scott

Dietrich Bonhoeffer: "It is only by living completely in this world that one learns to believe. One must abandon every attempt to make something of oneself, whether it be a saint, a converted sinner, a churchman, a righteous man, or an unrighteous one...

-
This is real meat to me, RLP. It's awesome that you're going down this road. (For me, anyway.)

I recall an incredibly fascinating YouTube video by Carl Sagan, wherein he describes, very plainly, what the people in Flatland would experience when, say, an apple took a trip through their dimension, viewing only 2-D slices of the apple as it passed through their plane of existence. He used that analogy to bring the viewer along on a further explanation of higher dimensions.

We can see a cube, since it's a 3-D shape, but all a Flatlander could ever see would be some sort of two dimensional representation OF that shape. So what he did was hold up a clear, plastic cube to a light source so that the shadow of a cube was visible on the wall. Given enough changes in perspective of the shadow of the cube, one can begin to grasp the higher dimesionality of the object under scrutiny. The shadow is not the thing, but the shadow gives you insight into the thing in the higher dimension.

He then took it one step further and introduced the tesseract. The tesseract is, ostensiby, a three dimensional representation (or shadow, keeping with Sagan's analogy) of a four dimensional object. From viewing the tesseract, we can get a sort of glimpse (like the slowly rotting fruit) of an object in the fourth dimension.

Wikipedia has a short page on the object, and there's a fascinating animation of it that's very hypnotic if you look at it for any length of time and try to figure out just how that works.

http://en.wikipedia.org/wiki/Tesseract

I would link to the Sagan video on YouTube as well, but it's blocked at work (dang it!) and all I can do is suggest a search for it.

Mary picks up on what perplexes me (as a person with small philosophy and less math and physics knowledge): the implications for human free will if time is a dimension we live in, and if all moments in time, hence, exist simultaneously.

The argument you all are developing seems compatible with Calvinism. This is a scary thought for a liberal Presbyterian like me. We dispensed with the doctrine of predestination some 100 years ago.

Putting it on a more personal level, the question is: Do I have any control over my moral choices? Do I have any hope of learning a better way of living? If I do "improve" my way of living or inter-relating or working or whatever, is this just something that was going to happen anyway?

Humbling is one word for this train of thought; another word might be "self-annihilating."

I call the metaphor I use to understand this idea "The Cosmic Brick". The metaphor starts with a You Tube Video. You know that little slider at the bottom of a you tube video? You can pause the video and slide the slider back and fourth. Whenever you stop moving the slider you get a picture. A normal two dimensional picture like you take with a still camera. We could print out each of these pictures and bind them together like a book. If we trimmed off all the margins we would end up with a three dimensional shape, a brick, where one of the dimensions corresponds to time. If we took a slice of the book through each of the pictures we would see neat swirly patterns in the two dimensional representation of a three dimensional image, but we can't easily perceive what is going on when we look at it that way.

Now imagine God's you tube video of the history of the universe. Of course the images in God's "pictures" are three dimensional. So the "brick" is four dimensional. Each picture is an instant in time. Each molecule, atom, and sub-atomic particle in the universe frozen in it's place. Motion is created by the relationship of one "picture" to the "pictures" around it.

What am I in the cosmic brick? I am some sort of four dimensional blob. There is a point in time where I come into existence, for a period of time and over a certain area I have various levels of agency and influence, and then I am no more.

What is consciousness and why is it so bound up in time? I'm trapped in this wafer thin instant, "now", that is sliding through the cosmic brick at the speed of light. Even though the hyper plane that represents "now" extends from one side of the brick to the other my senses and awareness can only perceive what happens very close to me. The rest of "now" is as unknown to me as what came before me and what will come after me. I am so small.

Psalm 144 v 3

3 O LORD, what is man that you care for him,
the son of man that you think of him?

But he does think of me. In fact, that may be the best definition of what I am; an idea in the mind of God. A very very large God.

Not really. We don't experience it as a whole, we just experience the moving time front that our senses can perceive. We can do as we please. The fact that a being who is not time-limited sees all of what we will do and have done does not imply that we are predestined. That being is not time-limited. There's no "now" for him, no future and no past. He sees everything whole, all at once. For us, there's a past, which we cannot change, a "now" where we live, and a future we can change. It isn't predestined what we will do, or can do. It's just that he, not being time-bound, isn't tied to past, present, future. It's all one piece to him. So he sees the result of our choices, and the actions of our past, and the experience of our present all at once.

It's not Calvinistic. Or any other theology with which I am familiar. It does sound sorta like Calvinball, though.

Chuck Nolan

There are two separate questions here

A) Is the future determined by *the past*?

If Newton's laws were strictly true, the answer would be yes. If you knew the present position and velocity of every particle in the universe, you'd know all of their future histories. So scientists for a long time thought the universe was "deterministic" in this sense. Relativity is completely consistent with this idea, and furthermore, treats time as a dimension in the sense that we're discussing here, so relativity made scientists if anything more deterministic. But then along comes quantum mechanics, which insists that some events are truly random -- even if you know everything there is to know about a particular atom of Uranium, you can't predict when or if it will radioactively decay (statistical predictions are still allowed -- you know what fraction of uranium atoms in a large sample will decay in a given amount of time.) And randomness isn't the same thing as free will either, of course...

B) Is the future determined by *God*?

This is a different kind of determinism than the scientific kind, in which the machinery of the universe, once set in motion, cannot deviate from its programmed task. If God is all knowing and all powerful and etc then he knows and controls the future the way and author knows and controls the plot in a novel. The events of the last pages of the novel are not predictable from the events in the first pages, so the novel is not deterministic in the scientific sense, but it's hard to argue that the characters have "free will" (though in a *good* novel, the author may find that they have to do things other than what he or she had planned, in order to remain consistent characters..)

I'd argue that these two kind of determinism have nothing to do with one another. One can be true and not the other, very easily.

I've heard physicist-types argue that because in physics everything is either deterministic or random, physics leaves no room for free will. I disagree. But the kind of free will I believe in -- the ability of a human being to create patterns in randomness that are individually *theirs* -- also applies to plants and storms and solar systems and any other self-sustaining pattern. Tornados and mushrooms have "free will" according to my definition. What we, or a tornado, does with the random inputs we get from the universe -- a ball flying our way, perhaps -- is deterimined not only by the laws of physics but by the shape of our particular patterns, by the details of our insides -- windspeeds and temperature gradients and vortex shapes, for the tornado -- and in the case of humans our psychologies, our minds, and I dare say our "wills"...

But this is still all just my personal philosophizing, not scientific "fact." Plenty of physicists would diagree with me.

Very interesting post, RLP! I'm still grooving on the concept of kairos that you introduced me to with a previous post. This post triggered a couple of thoughts I hope you find entertaining:

In the 2D example, I personally enjoyed Mary's example that a linear reading of a book, the unfolding of the story from our POV, doesn't change the fact that the book (and its story) exists in its entirety at once. I found it to be harmonious with your example of fruit existing simultaneously in all states at once, though our personal experience of the fruit may be more like a flipping through a book of those states at a measured, relative pace.

But what really struck me was this:

We experience chronos time as if it was an ordered, universal constant. And yet we have discovered it is in fact relative.

We experience kairos time as a disordered, personal variable. And yet the closest universal concept I have of "the right time" or "the season of ..." is God's Will, which if anything could be absolute, foreknown, this is it.

So I experience the relative as absolute and the absolute as relative. Based on this I can only conclude that there are some serious limitations with my instruments that are making the measurements. This is the stuff humility comes from. :)

many years ago when experimenting with some hallucinogenics, i went back and forth between being "blissed out" and being absolutely terrified. the blissed out part came from an experience of a very long and slow inhalation, and having the sensation of expanding out into the whole world, the whole universe, becoming one with everything, etc.

the terrified part came with being drawn back into the nitty gritty of my surroundings. i realized as i was coming down from my trip that the blissed out part was associated with slowing down the experience of time. in other words, if the subjective experience of the time it takes to inhale changes from the "normal" 5 seconds or so to a much, much longer time, then you are no longer just filling your lungs with oxygen and exhaling, you are experiencing the sensation of inhaling forever, and ballooning out into eternity. imagine what it would feel like to breathe in and never have to stop breathing in.

so a glimpse of t=0 (for me) equaled some kind of closer connection with the divine. gives some new meaning to: "be still and know that I am God", "stop and smell the roses", "chop wood, carry water" ... do what you can to slow down your perception of time, and you are getting closer to God.

BTW i am not recommending hallucinogenics. during my trip i also felt a loving presence that told me to stop experimenting -- that although i was being given a deeper view into reality, drugs were not the right path to "get there"

Hey RLP, I'm no physicist but your analogies with the fruit sounds fine to me. ;)

Have you read Grendel by John Gardner? (Retelling of the Beowulf from the monster's point of view.) The chapter where Grendel talks to the dragon (who is omniscient) about time and causality sounds like it's right up your alley. :) It certainly made my brain do some intricate dances...

To Mary and Closet Pent. and others grappling with free will issues.

I get what you're saying. But I think once we enter the realm of talking about time as a 4th dimension, a dimension we cannot even perceive, it feels like going backwards to start talking about whether or not this changes our free will.

Sort of like dragging our three-dimensional thinking with us into a fantasy land of 4 dimensions. I don't know, intuitively it seems to me that the question of free will becomes...obsolete or irrelevant. We're talking about a state of being that we cannot understand, so philosophical questions related to implications of that state of being seem like they don't have enough groundwork for a meaningful conversation.

Off the top of my head. Or maybe I'm just tired. I LOVE these conversations in the comments. But often I've spent so many hours with the essay that I don't have as much energy as you guys. THANKS for the great thoughts and ideas.

Chuck, always nice to here from Eeyore. ;-)

Terry Pratchett is one of my favourite authors. He often mingles mind bending concepts into his very funny engaging worlds.

One of the best concepts from one of his Discworld novels is this that of the fourth dimension. The personification of Death (grim reaper, scythe and all) sees things in their fourth dimension, and so sees a cat as something like a carrot - every stage of it's growing life, from a tiny kitten all the way to it's large and flabby old age...

I love that idea.

None of my physics-for-laymen reading changes my position in relation to a belief in God. My feeling of awe doesn't prompt me to take another step toward belief. But to quote Richard Feynman, one of the most brilliant physicists of this or any other time, "I don't have to know an answer."

I think the two-dimension creature would see the dot turn into a line, wouldn't it? Not into a circle. A three-dimensional creature looking down at the plane of the two-dimensional creature would see the circle. (Or a two dimensional-creature on a different plane who's figured out how to communicate between planes--but now we're into multiverses.)

Have you subscribed to RADIOLAB? It's everything wonderful about this stuff.

That was me--and disregard the title. I decided to delete the book recommendation because it's always obnoxious when people do that.

closet pentecostalist

Okay, I'm lost. I can't follow the physics here. And I admit that after puzzling over the free-will thing for a bit, I cannot even sustain that bewildered questioning of whether I possess any agency.

I'm just wondering about a possible scriptural tie-in. Think of Moses asking to see God in Exodus 33. (I've been reading the High Calling Daily devotion.) God, so the story goes, grants him a little peek, but only from behind: "My face will not be seen." Is this a symbolic way of presenting Moses' growing understanding of what God is like, an understanding he acquires by talking with God through time? Is it a way of saying Moses looks back retrospectively on his communion with God, and catches a glimpse of Who God is?

This is a subject which interests me very much. I'm not a scientist but enjoy reading and learning about it, and have done since I was a child. So I have a couple of reading suggestions, which are very different to each other and so might seem silly, but they are the things I have read which I've enjoyed most, so far.

1) children's books by russell stannard (a professor of physics at the Open University, which is a great institution to allow anyone to do a degree) - I particularly like _Uncle Albert and the Quantum Quest_ and _World of 1001 Mysteries_
These are definitely children's books, which I first read aged about 10, but it doesn't make the ideas seem any less exciting. Russell Stannard has also written books for adults and writes extensively on the intersection of science and religion.

2) George Ellis, _Science in faith and hope: an interaction_: Ellis is a south african cosmologist and a quaker, and this is a lecture he wrote. If you can't find a copy, a similar lecture is available in pdf from the website of Australia Yearly Meeting (sorry I can't post a link, but if you google Australia Yearly Meeting, click Publications then Backhouse Lectures, it is the 2008 link)

Do you have recommendations to make? I would like to hear them.

Marie

Oh dear. I love it when people recommend books - sorry if it felt obnoxious, Keith.

Marie

I will throw in a couple:

"Fantasia Mathematica", edited by Clifton Fadiman, contains the Robert Heinlein story recommended above -- "And He Built a Crooked House." It's about an architect who designs a house in the shape of an 3-D "unfolded" tesseract... It also has a story called something like "The Captured Cross Section" which is about a four dimensional being whose cross section in our world looks like a sphere, and the attempts of the hero to capture it. And there's a story about Klein bottles (the 3D equivalent of the Moebius strip -- it requires a "twist" through the fourt dimension). And a bunch of other mind warping stuff, some of it very literary.

George Gamow's "Mr Thompkins" books are famous (and short) little fantasies set in worlds where the effects of relativity and quantum mechanics are much more obvious than they are in ours. Not so much about the fourth dimension, but fun plays on the ideas of modern physics, by one of the physicists who worked on them.

I am still enjoying this post! I hope it doesn't slide right out of my 3 dimensional brain.....

It brings home "....through a glass darkly, then face to face.." (poorly paraphrased I'm sure) from scripture.

Gives new light to deja vu (we're not really seeing it again. We're sensing it's presence further on in time)

Explains what extra sensory perceivers are perceiving. And opens up all kinds of cool new advertising slogan possibilities for psychics.
;-)

I have no problem with the issue of free-will. We still have free-will even though it's already happened. I cannot say today what I am going to choose tomorrow. I get to choose it tomorrow. Just because it's already happened doesn't mean I don't get to choose. It scares me a little that I understand this.

Very very very cool stuff.

Presbyterian Gal

RLP, I wish to give voice to a sentiment I've been mulling over. I am uncomfortable with emphasizing wonder at the universe as the source of Christian worship. Of course it's a proper religious sentiment (for Christians as for others), but it seems to me that the primary wonder should be salvation. Even before Christ, God does make it pretty clear that we should see how awesome the world is, but when he's getting down to business with the Israelites it's "I am the LORD your God who brought you out of the land of Egypt, out of the house of slavery", not "...who made the world". I love wrapping my head around the kookier bits of physics, but any impulse to worship that comes out of that seems overly impersonal for a faith centered around a personal God.

i like to imagine that people walking toward me are actually just the sub atomic particles whirling around - and if i was careful enough i could actually walk through them. i can visualise in my head the idea of a strong clump of swirling electrons for their brains and the rest of them is connected by flashes of light and clumps of lights. I am probably insane.

RLP, thanks so much for this post, and for encouraging the subsequent conversation. as the child of two scientists, i was lucky enough to grow up hearing about these sorts of brain-exploding concepts -- like your girls. so i do want to point out that i believe you have hit on a very key part of parenting: stretching your kids' brains. and also letting those stretchy little brains explore in their style. my poor physics dad and chemistry mom probably are slightly disappointed that i actually ended up with a huge aversion to all that concrete-ness of math and science and went flinging myself pell-mell down the humanities path...but they never told me as a kid that the stories i was devouring were "too old for me" or that the understanding i was gaining from them was somehow "less true" than if i knew all the laws of thermodynamics.
and that's the theme i see here: we have these giant heady concepts of quantum physics intersecting with the beauty of human story and imagination. people are recommending books AND talking about Newton's law. some may understand more through the fantastic worlds of L'Engle; others through Greene's writing on string theory. and what's exciting is that no matter if you try to approach the mysteries of existence through myth or algorithm, there is still a sense of wonder. i think whether that wonder is at the natural world, the gift of salvation, or even of the miracle of a child's love is less important than cultivating the attitude that welcomes such joy in the intrinsically non-graspable: if perfect love casts out fear, then having joy and wonder in the face of understanding how small and how much is unknown -- and not collapsing in terror -- is truly a manifestation of God's love.

and yes, download and listen to every podcast of WNYC's Radiolab. please. it's an incredible show and does marvelous brain-twisty wonder-inducing things in the most creative ways. like this thread, it is a delicious interaction of science and the human story.
just go to radiolab (dot) org or get it through iTunes.

the new dimension is already here. People do not speak of it for fear of being crazy. Some can see it already. It is in Faith that one sees all. It is another vision.