In 33 Dimensional Space Everyone Can Hear You Scream

Wednesday, January 11th, 2006

The term"my little corner of the world", is often used in a folksy, ironic way to describe one’s modest domain, either professional or domestic. It’s a comforting idea, having a corner the world to one’s self. But realistically, there just aren’t enough corners of the world to go around.

Since we appear to live in three dimensional space, the logical maximum is eight, corresponding to the eight corners of a cube. If we were to locate them on a globe, there would be four in each hemisphere. We might make it easier to address the corners by introducing the directions front/back to go with north/south and east/west.

So we might consider Grand Duke Henri of Luxemburg to be the occupant of the NorthWestFront corner of the world… which leaves just seven more corners to be shared amongst the remaining six billion of us.

Wouldn’t it be nice if everyone really could have a corner of their own, with proper right angles and everything…?

They could, if we lived in 33-dimensional space!

Hyper Earth

On a 33-dimensional world, every one of more than 8 billion people could have their own corner, complete with right angles [more than 500 of them!].

Just to be cute, let’s assume that the diameter of 33D hyper-Earth is exactly 33 metres [a metre is roughly the distance from your armpit to the back of your knee], and that the planet has an evenly distributed population of exactly 8,589,934,592 people [that’s one person occupying every available corner].

Every hyper-citizen would have exactly 33 immediate neighbours, each living about 5 metres away [and yet no two of these would be less than 7 metres apart], and a visit to the farthest person (your antipodean cousin, living on the opposite side of the world) would require a stroll of less than 50 metres.

Does this world sound a little crowded to you? What if I mentioned that if you closed your eyes and took a stroll, the chances of physically bumping into another person are virtually zero? And yet you’ll never be more than 5 metres from another hyper-human. Isn’t that weird?

Hit & Miss

The chance of a falling meteorite actually hitting a person on hyper-earth is so neglible [at less than 1 in 20 billion trillion] that even if there were a million impacts every day, only 1 person would be killed every ten thousand years or so. Calculating such probabilities is purely academic of course, since the chances of hyper-earth being hit by a meteor in the first place are also vanishingly small.

Similarly, firearms would be next to useless on hyper-earth, even given the relatively close quarters, because in 33D there are just so many ways to miss something. The extra 30 dimensions make aiming vastly more difficult, so that beyond the the familiar "left-a-bit" and "up-a-bit" we must imagine a litany of other directions to adjust in, eg: "snerf-a-bit, frite-a-bit, smort-a-bit, blern-a-bit…" etc

Gravity & Mass

It might seem that such a little hyper-planet [just 33 metres in diameter] is unlikely to provide enough gravity keep all those hyper-feet on the ground. But run some numbers and you’ll discover that the volume of hyper-Earth is about 3 hundred billion trillion trillion hyper-cubic metres, probably more than enough hyper-matter to facillitate gravitational attraction.

So anyway, since this is one big messy thought experiment, let’s just assume that gravity on the surface of hyper-Earth is equivalent to regular gravity, causing a downward acceleration of around 10 metres-per-second-squared.

The real difference comes from the 33D equivalent of our inverse-square-law. In 33D this might be called something like inverse-32nd-power-law. In regular space, the strength of a field—be it gravitational, magnetic or electrostatic— is proportional to the inverse square of distance. Which means that if you double the distance from the source, the field strength will be reduced by a factor of 4. In 33D the effect is substantially greater, with a doubling of distance producing a reduction factor of about 4 billion.

What this means for residents of hyper-Earth is that gravity at one metre above sea-level is only 15% of normal. At an altitude of two metres it diminishes to only 2.5%. At 10 metres, the force of gravity will be negligible, less than a millionth of its strength at sea-level.

Sight & Sound

Unfortunately, the inverse-32nd-power-law will also affect energy transmission, severely impacting quality of life on hyper-earth. Small localized light sources, such as hyper-candles, would be either utterly useless or potentially blinding. Night time reading is probably not a great idea, since a light which offers good reading at one metre would leave you in pitch blackness at two, and moving just 50 centimeters closer would probably incinerate you, as the intensity of the light increases 4 billion-fold.

At least in the daytime, light energy from the unbelievably powerful and reasonably distant hyper-sun would allow citizens to see in 32 dimensions.

Carrying on a conversation might be difficult too, since sound energy will obey the same [inverse-32nd-power-]law. In order to attract a neighbour’s attention [5 metres away] even detonating a large thermonuclear device may not be enough, such will be the dramatic attentuation of the shockwave as it expands outwards in all 66 possible directions [each dimension comprises two directions: up/down, left/right, forward/back, smerf/blerf, frite/spleft…. etc ] An explosion which would ionize you at one metre might not even ruffle your hair at five (having less than a billion-trillionth of the destructive power at the latter distance).

Which means the title of this post is actually totally misleading— In fact no one will hear you scream in a 33 dimensional world (although they might just hear you explode should you happen to detonate a nuclear weapon). Communication would still be possible however, with the aid of wires, or even pieces of string, both of which are capable of transmitting energy along a single dimension instead of dissipating it into space.

__________

This post is derived from an old and unfinished article that I found kicking around on my hard-drive, and so I thought I’d post it here to see if anyone reads it closely enough to spot any major holes in my calculations :)

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13 Comments

  1. Tim says:

    Haha, very entertaining. The helpful diagrams make it ;)

  2. dirtymouse says:

    oooh, i love the thought of that, but i fear i would have to move slowly with my candle at arms length. i wonder, what sexual relations would be like?

  3. mark says:

    very difficult I think, for the same “aiming” problem mentioned in the post, it would probably require incredible patience and focus…

  4. Anonymous says:

    I read this under the heading of “Chapter Two” of your ongoing [hopefully] best-selling-novel.
    BTW: I always see your banner as if it’s snowing but then I have to remind myself that little thingies are really stars… they are strars right?

  5. mark says:

    They are indeed stars, although now I am seeing them as snowflakes

    Dare I wonder what “Chapter One” will comprise…?

  6. mark says:

    Oh duh! Don’t answer that, I forgot about previous post titled “Chapter One”

  7. .dan.g. says:

    hi mark

    its great to hear you sounding so much more upbeat than last year when you seemed to be sprialling ever downwards. it certainly makes your musings so much more entertaining.

    best wishes for 2006

    dan

  8. the2bears.com » Hyper Earth says:

    […] Mark Pursey describes a Hyper Earth rather well in this article In 33 Dimensional Space Everyone Can Hear You Scream. Never have I read anything regarding a reality with 33 dimensions, but if I had I cannot imagine it being nearly as entertaining or interesting as this. Plus he has a title that refers to Alien, and any homage paid to Sir Ridley Scott is fine by me. Mark created Drivey, mentioned here, and yes, I’m still waiting (with many others I’m sure) for more. […]

  9. slam says:

    quote: “oooh, i love the thought of that, but i fear i would have to move slowly with my candle at arms length. i wonder, what sexual relations would be like?” ~dirtymouse.

    i think you would have to rule out any candle-light lovin’ as well. while at first i thought that motion itself would require several billion times more enegy to move in all those directions at once, but then i reallized that all human motion is basically linear anyway. motion would, however, get more complex; where before you could either thrust, twist, or swivel to vary any sexual technique, but you would now be able to swank, drifness, ooger, and otherwise wiggle through 29 more new dimensions. dancing should get very interesting.

    on the other hand sex may suffer for many people because of the aiming problem mentioned above. ouch!

    and thanks, mark, for a wonderful laugh!

  10. says:

    Fab! Wonderful to stumble across a fellow multi-dimensional cube fellow! Good food for thought. You might enjoy this:

  11. litreofcola says:

    heh, intriguing stuff.

  12. dirtymouse says:

    and i can’t even dance in 3D! -

    what hope have i got if…

    i have to put my left foot drifness dear and your right foot frite. Now ooger a little babe, now you’re too swanky..

  13. lb says:

    this is the best thing i’ve ever seen on the internets. I gave it a 3.

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