Unlike the other tests on this website, this one is not so very fully developed. That is because, this field - navigation and rotation in 4 dimensions, is kind of new. So, for example, the chief tool I use in testing, is still under active development.
But let me back up a bit. What is this about 4 dimensions? Is that the same thing as what Einstein said, something about how "time is the 4th dimension"?
No, that is not actually the case. Einstein was aware of the possibility of a 4-dimensional universe but his work on relativity simply said that 3-dimensional space as we know it, and time, are closely linked. Famously positing (correct) things such as, rapid movement through space causes "time dilation."
So that is a whole different topic (and incidentally, if 4-dimensional space is real, as I will briefly explore, then Einstein's work would apply just as well; time and space still relate in much the same way, whether that space is 3- or 4-dimensional).
Right around that same time that Einstein was doing his work (what I'm about to describe both preceded and followed Einstein's most productive years), folks began to speculate and wonder, "What if there were, or actually are, more than the 3 dimensions than we directly perceive?" So for example, in 1884, The Reverend Edwin Abbott Abbot, a theologian and author, wrote the book Flatland - A Romance in Many Dimensions in which beings from worlds of various dimensions converse and interact with beings from other-dimensional worlds. Chiefly a 3-dimensional character interacts with 2-dimensional folk, but - just like in the title - Abbott hints at a 4-dimensional world, or universe. Really I read the book as an allegory and an attempt to get us "3-D bound" folks to consider the possibility of higher dimensions.
The popularity of Abbot's book has waxed and waned in the century-and-a-half since he wrote it, but has never vanished completely from public discourse. It's a wonderful little book that gets you thinking.
In 1943, right during the "golden age of science fiction", authors Henry Kuttner and C. L. Moore, writing under the pseudonym "Lewis Paggett", published a short story titled "Mimsy Were the Borogoves". lt's an engaging story - though it ends dark - about some guy who lives in the future, wants to try out his time machine, and sends one of his kids' toys back in time - presumably back to more or less 1943. The toy, is a simple variant of the "beads on a wire" toy you have probably seen a hundred times and quite likely played with as a small child. But this particular version of the toy, allows children to move the beads around in not just 3 dimensions, but in 4. Therefore the beads take/make strange hops, vanish and reappear, do the things that Kuttner and Moore had figured out, objects would really do. The thrust of the story - and the implication - is that humans can be perfectly able to comprehend, navigate, operate in, and make use of 4-D space. But as little kids we don't get the appropriate stimuli or learning experiences, we have no examples. Give a kid an example (or a learning aid), the story goes, and they will develop 4-D spatial ability and comprehension.
I always used to wish I had a toy like that. But of course such a thing was unavailable.
Until now.
A wonderful gent (well I don't know him personally so I'm just going by what he has provided) named Marc ten Bosch has created the toy - which he calls an "abacus". It's part of his collection of 4-D toys. Of course - at least for the time being - the game isn't a physical, tangible object. What Marc has done, is create a simulation of the 4-D toy described in "Mimsy Were the Borogoves", in game form; it runs on a computer, you're looking at a screen.* The mechanics of the game are (at least to me) interesting; what Marc has done is, program all the various co-ordinate systems and objects into the computer, along with the rules (the math) of 4-Dimensional space, then added the component that "projects" 4-D space onto 3-D space. Just like the 2-dimensional characters in Flatland have to do when they are trying to cope with 3-D projections into 2-D space, we game players have to cope with the various complexities and vagaries of dealing with 4-D space projected into something we're more familiar with.
*He has also "ported" (gotten the game to run) on a VR headset but I have no personal experience with that.
This "fun and games" may all sound fine and good but - as a skeptic may ask/challenge - what good is it?
It turns out that the 4-D toys involve many of the skills discussed in the page about the ORT-3. Such skills as rotation, re-orientation, and navigation (which gets brief incidental mention in academic discussions of spatial ability) are both required, and practiced, in order to work those little beads along those wires, or perform the various tasks the other games enable, feature, support, and/or require. Prediction of what a scene will look like once "rotated" - closely related to the ORT-3 - is woven right into the game, to accomplish much you need this ability, rotation.
There is little else to tell about this test, because:
From the very beginning of my effort I was looking for I.Q. (and more recently, related) tests that are:
The ORT-4 does pretty well, fulfilling those criteria. A big plus at this point is that kids have not been exposed to the "instrument" - the game. It isn't that well-known, yet.
But there is another reason for pursuing the use and administration of this test.
If 4-dimensional toys were only just one more way to assess spatial ability it might make as much sense to just use one of the other instruments. However, as Uttal points out, the process of administering a test is itself educative - a kind of training.
What's being introduced here - and practiced - is a point of view rather different than most people routinely encounter. It could be a valuable point of view, since the possibility exists that significant portions or aspects of the real world that we live in, are best described - or even, "only adequately describable", by 4-dimensional mathematics.
Perhaps the best known examples come from crystallography and mineralogy. Certain regular but baffling features of rocks follow "higher dimensional" mathematical rules. In other words to best understand what's going on you need to posit a world with more than 3 dimensions, and then "project" objects or images thereof, onto our 3-D world. Which sounds, seems, looks, and feels just like the 4-D - to 3-D projection involved in the ORT-4.
Lest the reader think this is all too esoteric to matter, let me quote from the book The Second Kind Of Impossible by Paul J. Steinhardt, a theoretical physicist who got himself deep into geology. He definitely spent time in the real world!*:
[T]he Penrose tiling and other quasiperiodic patterns [found in the real, physical world] are obtained by projections or "shadows" of a higher-dimensional periodic packing of "hypercubes", which are the equivalent of three-dimensional cubes, but in imagined geometries with four or more dimensions of space. Most people cannot visualize how the method works without advanced training, but mathematicians and physicists find the concept very powerful for analyzing the atomic structure of quasicrystals and computing their diffraction properties.
Personally, this evokes something that is familiar to me. Some years ago I ran Young Philosophers workshops, in which children from ages 7-9 and 10-12 discussed philosophical concepts. This went on weekly for years and they did not get tired. Rather, they were very excited to discuss topics such as the nature of reality and existence, virtue ethics, and all the other main branches of philosophy. We never used big words like "ontology", "epistemology", "metaphysics" but we covered those topics, at length and in detail. The kids ate it up and I validated through my own experience, that children, including young children, have a "sensitive period" (as Maria Montessori put it) during which they take to philosophy like a fish takes to water.
Incidentally, I did not invent this practice; I learned about it from a book by Tom Wartenburg titled Big Ideas For Little Kids. He was a recent pioneer of "doing philosophy with children" - he put together supporting materials that made it easy to just follow along, which I did. His work was recent, and though there were other predecessors, Margaret Donaldson, who wrote a book titled Children's Minds, really pioneered this idea - that children can understand what are normally considered, advanced topics.
The connection with intelligence research is, that Donaldson was a protege of Piaget - quite devoted to him, she revered him in fact. But then when she started to do some research on her own she found that his theories (basically, that children lacked capability for abstract thought/reasoning) did not hold up, they were easily falsifiable by experiment. The problem happened because Piaget, when working with children, used bad/flawed test materials, setups, and/or "stimuli."
I believe, and I hope to find, that children really are able to understand and master that 4-D visualization - the skill, outlook, and/or understanding that Steinhardt says, requires "advanced training".
What is the usefulness of this? Steinhardt's a theoretical physicist - how much down-to-earth practicality will result if kids come out of 4-D training, comfortable with the concepts, feeling like "yeah - this is the way the world works; I used to see/do that as a kid"?
20 years ago it may have sounded like a "crank" thing to say, that higher-order mathematics (the mathematics of 4-D space) are required in order to best understand the universe we live in. Which is close to saying "we live in a 4-dimensional world". But from various fields we find this idea creeping in.
In the References section I list some of the many papers now being published that refer either to:
the value and applicability of using 4-D mathematical and geometric concepts in describing the real world, and/or
that at some scales (typically very small) the physical world actually operates in a 4-D manner.
There are more, and they just keep on coming, it's hard to stay current. For now, suffice it to say, there seems to be (possibly great) potential merit in inculcating 4-D thinking, and 4-D spatial visualization ability in high-I.Q youngsters.
*Including an expedition out in the tundra in the Kamchatka area/region of Russia
When I first began thinking about how to inculcate a mastery of - or at least a familiarity with - 4-Dimensional concepts and reality, I thought that I'd have to come up with software on my own. To my surprise I found that plenty of other people had already done good work in this field. Wikipedia provides a list of 4-D games: I haven't looked into them. I have run across another 4-D game called Hypernom which seems to be well-crafted, but though it seems to kind of work on a laptop, it uses a VR headset, which is not useful to me.
How to make a toy, and/or a computer game, into a test? Keeping in mind that we are introducing a new concept, a lot of what goes on is learning. What testing does exist is pretty qualitative, amounting to careful observation. The approach is very much "guide on the side"; besides observation, the administrator prompts as appropriate, to keep test-takers from getting bored, going down dead-end paths, or "cheating" (working not according to their highest potential).
There is a good explanatory video that explains the basics/rudiments of 4D. If the test-taker is amenable and time allows, they can first play the video. Then, get them set up with monitor, mouse, and trackball, show them a few things, set them going, and observe.
I think about the folks (Wecshler and company, I suppose) who came up with the "assemble the elephant" and "assemble the man" tests, back in the day. Presumably they tried out various things, observed, saw how things went. I'm doing much the same - observing the test-takers, "watching the gears turn in their heads", seeing how they respond to various challenges. Also I develop workarounds and/or other "helps" - or "cheats" in game parlance - to avoid, deal with, overcome, or ameliorate dead-end situations. Or just to make things easier.
There is some quantitative measurement involved. The 4D beads-on-a-wire or "abacus" involves moving a bead along a wire from one end to the other, until said bead finally does get to the end. This takes time, which can be measured. Also observable/measurable are the number and kinds of "cheats" the test-taker avails themselves of, and when, how, how often. This gives insight into:
Here are some early samples of what an ORT-4 session looks like:
Uttal DH, Meadow NG, Tipton E, Hand LL, Alden AR, Warren C,
Newcombe NS. The malleability of spatial skills: a meta-analysis
of training studies. Psychol Bull. 2013 Mar;139(2):352-402. doi:
10.1037/a0028446. Epub 2012 Jun 4. PMID: 22663761.
Articles and other material about the reality, value, and/or use
of 4-D thinking, conceptualization, mathematics, and physics:
Thanks to Marc ten Bosch for conceiving and creating the 4-D toys, and for adding a special feature that supports using the toys as a testing instrument.
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