The wisdom of seventh graders: A Wrinkle in Time

The recent passing of Madeleine L'Engle reminded me of a quiz seventh grade students were given in order to see whether they were at least paying attention during a reading of a chapter from A Wrinkle in Time. I forget the question exactly, but it asked the students about the mechanism that Mrs Who, Which and Whatsit use to travel through the universe. The correct answer was "The fifth dimension."

One student, who was apparently was paying only part attention during class, wrote "The third dimension."

Let's run down the street. "Woo! I'm travelling through the third dimension!"

1. name required says:

Sorry, but anyone who’s seen Buckaroo Banzai knows the answer to that question.

2. Krenn says:

Only in San Francisco – isn’t the third dimension the Z-axis?

3. Gene says:

So was my class the only one where our teacher read "A Wrinkle In Time" to us in 5th grade? It was NOT boring. She also read "The Lion, The Witch, and The Wardrobe" as well.

It was an Episcopal school, and they put heavy emphasis on learning and morals instead of just being a daytime babysitting service like most schools today.

That changed my life. It awoke my interest in books, especially science fiction, and my desires to "find out all about it" and "do the right thing"

Even today, hearing the name "Charles Wallace" takes me back.

4. Brian says:

I can do better, just sitting here in my chair I’m traveling in the fourth dimension :)

5. Gene says:

isn’t the third dimension the Z-axis?

Well, by convention… since X & Y are usually the coordinates for 2 dimensions.

So you’d have to jump up and down going "Woo! I’m travelling through the third dimension!"

I hate it when I have to correct Raymond! :-)

6. Bahbar says:

What exactly makes the Z axis an up-down axis ?

Say, for example, that your 2 axes are defined by your monitor (or are you not a computer geek ?), Z therefore is the axis your are looking through… Also called depth in most realtime 3D environments. conventions, conventions…

7. ERock says:

Well, axes can defined arbitrarily: they are just a mathematical construct used to make things easier. Ask any intro-to-physics student.

Example, "rolling down an incline" problems are easier to solve when you re-orient your axes so that the incline is your X axis instead of juggling height from a horizontal ground and horizontal distance at the same time.

Personally, I like left hand rule with middle finger being X, index being Z, and thumb being Y. It just seems more natural when mapping 2D things onto 3D space.

8. J says:

Gene,

The simple fact that your body has a height means that any movement includes the 3rd dimension.

9. String theorists would have us moving (and oscillating!) through n dimensions at once, where n seems to be 10, 11 or up to 26:

http://en.wikipedia.org/wiki/String_theory#Number_of_dimensions

Any post intertwingling L’Engle and Banzai is good morning reading in my book.

Perfect Tommy: Emilio Lizardo. Wasn’t he on TV once?

Buckaroo Banzai: You’re thinking of Mr. Wizard.

Reno: Emilio Lizardo is a top scientist, dummkopf.

Perfect Tommy: So was Mr. Wizard.

10. David Walker says:

The Fifth Dimension…

"This is the Dawning of the Age of Aquarius, the Age of Aquariiiuuuuuussssss……"

11. SM says:

Sure I know about the fifth dimension! It’s beyond that which is known to Man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of Man’s fears and the summit of his knowledge.

My buddy Rod told me about it!

12. There are many dimensions besides length/width/height; we deal with them every day.  Time is a dimension; temperature is a dimension; color is several dimensions.  So if you’re sunbathing, you’re moving in at least two dimensions (forward in time, and along one or more color axes)

13. Justin says:

Temperature and color are not dimensions.  Temperature is caused by the vibration of particles in the "regular" dimensions, and color is caused by the varying levels of reflection by a surface for different light wavelengths.  Now if you had said electrical charge was a dimension, I would have a harder time refuting it…(but I don’t think it is).

14. BryanK says:

On electrical charge:  That’s just the number of charged particles.  (Well actually it’s probably the density: the number of charged particles per unit volume, where volume is taken over the normal three dimensions.)

Whether that’s a different "dimension" depends more on your definition of "dimension" than anything else.  If you define "dimension" as "(any single) thing that can be measured", then yes, charge fits that definition.  So do color and temperature, for that matter.  But if you define "dimension" as "an independent thing to measure", then since charge, color, and temperature all depend on where and when you’re measuring in 4-space, they’re not additional dimensions.

(Without the normal 4 dimensions, they would be.  But you have to have something that is a color, or has a temperature, or has a charge, at a certain time — so it’s hard to remove the normal 4 dimensions.)

15. Dewi Morgan says:

Time isn’t a "dimension" in the same way as the three spacial dimensions. Those that call it so are bending English, and physics, past breaking point.

Time’s certainly not a "dimensionless quantity", it’s a metric, and a scalar… it even behaves mathematically a bit like a real spatial dimension in some situations… but that’s where it ends.

A valid alternative meaning of "dimension" is "everything that isn’t a dimensionless quantity" as a dimension. So anything with units, (time, mass, distance, colour, temperature) also become "dimensions".

But in both definitions, the question "how many cm in a minute?" remains no more meaningful than "how many cm in a kilo-per-degree?"

Considering time as a special, one-way spacial dimension is sometimes useful in some models of reality: but it’s foolish to conflate a simplified "time is a dimension" model with reality, and there is no excuse for ravishing English and physics in order to do so.

16. Chris Moorhouse says:

You can’t "ravish" English… she’ll willingly give it up for anyone.

And the "many worlds" idea essentially transforms Time into two dimensions.

Besides, all models are wrong, so all I need to think about is what’s useful.

17. Cooney says:

The correct answer was "The fifth dimension."

Um, tesseract? The exact mechanics are, of course, unknown to us.

18. mccoyn says:

There can be two objects at the same (x,y,z) coordinates at different times.  There can not be two objects at the same (x,y,z) coordinates with different temperatures (assuming we do not consider time).  For this reason, I am inclined to think that temperature is not a dimension in the same sense that time is.  This test should apply equally well to other measurable quantities, such as electric force.

19. BA says:

Z axis is normally the depth axis. X is the horizon, and Y vertical. So running down the street would be a traversal along the Z axis (or traveling in the third dimension).

20. Zanzibar says:

Poor Raymond. He might have to resort to bringing back the nitpicker’s corner after all.

21. Zanzibar says:

Poor Raymond. He might have to resort to bringing back the nitpicker’s corner after all.

22. Quantum Physics Professor says:

The correct answer was "The fifth dimension."

Without specifying which dimension is which, neither the 3rd or the 5th is necessarily correct or wrong. They are both equally ambiguous.

23. Jackal Fizzbin says:

@Quantum Physics Professor: presumably the book referred to the "dimensions" in some particular ordering, and the answer was supposed to be in the context of the book.

24. Puckdropper says:

Dewi Morgan,

You may be messing with Physics and Language, but it sure makes for a good movie line… Something along "The forth dimension is TIME, MARTY!"  (Read that aloud in your best Doc Brown voice.)  :-)

25. Craig says:

Dewi,

Time isn’t a dimension? I’m no expert(!), but I had thought it was. My understanding was that the predictions of general relativity were based on a 4D model of space-time (Minkowski (sp?) space-time, if I remember). I thought the major difference between spacial and temporal dimensions in this model was that time behaved as an imaginary number–making it different from how spatial dimensions work, but still a dimension nonetheless. But the idea isn’t of one "moving" through this dimension, but rather of a static 4D system, right? Interesting thought, though!

26. Iggy says:

Time is a dimension. A dimension is anything that can be measured (obvious from the Latin etymology). The year (time) is 2007. The previous year was 2006, and the next will be 2008. While the mathematics is quite simple, VB developers may think of it as the "dim" keyword.

However, as the physics professor correctly pointed out, which numerical dimension time is is ambiguous without further context (which may or may not have been specified in the book).

27. Haha says:

What is that they say? "A Winkle in Time Saves Nine" is it?

28. Neil says:

Nitpicker’s [That’s one nitpicker, me, although I may or may not be picking nits in more than one other nitpicker’s comment] Corner:

"Let’s run down the street." By this I understand that the street isn’t level, otherwise Raymond would run along the street, rather than down it. Thus, he is travelling through the third dimension (at least, in his reference frame; in my frame in the UK it may only look like one of the other two dimensions!).

29. David Walker says:

E-Harmony.com claims to match people on "29 different dimensions".

I don’t like that terminology, but I have a vision of looking for the closest match between each set of two points in 29-space… with some suitable definition of "close".

Imagine what a processing nightmare that would be, if they really look for the closest match between each male’s "point" with each female’s "point" (assuming heterosexual matches) in 29-space.  For each pair of males and females in their database.

I suspect that the answers aren’t on a continuum; the questions are probably along the lines of "how important to you is blah blah", with 4 or 5 possible answers.

Still, it’s an interesting problem, especialy if you can weight your answers, or answer "I don’t care" to some questions.

Using the word "dimensions" here might be a little bit of hyperbole.

30. Cooney says:

E-Harmony.com claims to match people on "29 different dimensions".

In the problem space, these are dimensions. The issue with finding close matches in 29-space where dimensions are meaningful (you might demand a nonsmoker, so a straight D-function wouldn’t work) are nontrivial but yeah, some method of boxing is probably done.

31. Kay says:

The *mechanism* was a tesseract.

32. Cooney says:

> The *mechanism* was a tesseract.

But it’s unknown how it works. Sure, it operates in 5D space, but how?

33. > some suitable definition of "close".

RMS distance is the accepted definition of "close" in most dimensions… sqrt(x*x + y*y + … );

Even for 29 different variables, this is tractable.  You can use box distance as an optimization.