Eric, You may or may not remember me, I submitted a few "ideas" about higher dimensions to you awhile ago. Anyways I have just started my own home page and wanted to get your permission to add a link on it to your page. You really have a great page! One can't really appreciate a good web page until they've tried to set up their own! You can find it taking up space here:

http://home.pacbell.net/weaslinc/

the only thing of interest right now is the Brain Teaser. Send me your thoughts on it! Plus absolutely ANY advice you may have on starting a web page because I am clueless. Actually, I have a question: I know what "wallpaper" I'd like but have no idea how to get it on my page. Thanks for your time and great web page. -Sal

I have been trying to better conceptualize potential 4 D worlds sporadically for the last couple of years. I have come up with similar 2D representations of a hypercube, (at least the first drawing anyway) and also put together my own 3D representation of a 4 D pyramid. I am not sure whether you have tried this before. This can be done in two parts.

Firstly, construct a normal 3D Trianglular based pyramid, hollow and made of materials of a standard length for each connecting line. (eg. 12 inches per length)

Secondly, After constructing the pyramid, get 4 pieces of string, each of the same length of the above connecting lines. Attach one end of each piece of string to one of the 4 points of the pyramid. At this stage, there should be 4 loose ends, one for each piece of string. Tie them to a point so that point rests inside the pyramid. Some observations.

a. The point (point 5) at which the 4 pieces of string come together will dangle, if the pyramid is held by one if its other points.

b. Take any 3 points from the pyramid and pull point 5 so that the pieces of string for points 1,2,3 and 5 are able to form a tight pyramid (by bringing point 5 to a position where it matches point 4. There should be a total of 4 additional pyramids that can be formed in addition to the main pyramid, by bringing point 5 to points 1, 2, 3 and 4 in turn.

c. 4 a less representative figure, the strings can be shortened to about half their size so that the point does not move.

d. This can be repeated for other figure types such as a hypercube, however the hyper-pyramid is the simplest to simulate.

e. The total cubic area of the 4 D structure should be 5 times greater than that of a 3D structure with the same side lengths.

Please let me know what you think. Best Regard

This is not entirely correct. It's based on the binary system, yes. But the first person puts in 1 ball. That will make the bin have an odd number of balls for all subsequent minutes. With that in mind, at 5:59 it will be off of exactly one half by exactly 1/2 of a ball. I know... technicality. I've enjoyed the puzzles so far though. Very interesting..

This is in regards to the doubler enigma

I believe that the problem with Y2K is that the date is stored in memory as two bytes (as opposed to four). When I first heard of Y2K, this is why I thought it was only a dumb rumor--2 bytes can represent numbers as high as 65537 (unsigned). But they are stored as ASCII numbers. Like "98" for example. So this does present a huge problem. Take a person who was born in 1993. 00 - 93 = -93 = 1000000001011101 in binary, but since the number is unsigned, this person's age is really 32861! Someone who is only 5 years of age is eligible for Social Security. Eric Gumtow

I have a proposed solution for that one: He was hung on Saturday. You see, he was *told* that he would be hung between monday and friday, but the problem never said that he *would* be hanged between Monday and Friday. Or, you can say that Saturday is the day after Friday, and two days after Saturday is Monday, so Saturday *is* between Monday and Friday. Either way, he would be surprised that he wasn't dead on Thursday or Friday, and I doubt he would put a second thought as to whether it would be on saturday. Most likely he would be yelling "I'm alive! I'm alive!" and dancing around his prison cell. Option #3 is that, in the midst of all this dancing, he would slip on the floor and fall on a knife or somethin'. That would be really surprising. For any of those fates, it would still be surprising.

This email is in regards to The unexpected hanging enigma

Eric agrees.

At about 10^-33 cm, space breaks down. You can not physicly travel anywhere between the points that lie on either side of this space, and you can not divide it up any further. Because of this, there is no way to acheive "negative measurement" (although quite a nifty theory) Consequently, this makes movment possible. If space could be divided up infinitly, there would be no movment. Think of the old paradox: to get from one point to another, you have to travel half of the total distance . To get to that point, you have to travel half of THAT distence, and so on.

OK, we all hear stories about UFO's going through maneuvers that would rip the neck off any aircraft pilot. There is a theory about why they're probably able to do this. Gravity distorts the space-time continuum. If you put a gravity field around a body and use it for propulsion, something interesting happens. To an observer, you appear to be travelling rapidly. In actuality, you're traveling at a somewhat normal speed. However, at the same time, you're moving through a very small wormhole you created with the grav. field. Say it takes 5 sec. to get from pt. A to pt. B. You're just taking that 5 sec. and shortening it to about 1 or 2 sec. Get my drift? Yes, this can be considered a form of time travel - but on a very minute scale. It's pretty much negligible. The problem is, you wouldn't want to lose or gain time. We would need some sort of subspace containment field so we wouldn't travel through time against our wishes. Anybody else got any ideas on this?

Gene and I were discussing whether you could see the big bang. Here is what Gene said about "seeing" the big bang by travels so far as to see the light still travling away from it. And so here is what Gene said:

You would not be able to see the Big Bang. It couldn't have happened. If we presuppose that such an explosion did take place, then we would have to consider the sum of all energies existing in the universe as equal to the energy of that first explosion. First Law of thermodynamics. However, the energy that keeps star clusters together, for example, far exceeds the gravitaional energy of the stars themselves. Where does it come from? If that energy is thrown into the equation, then the total sum of all the energies of the "Big Bang" had to be so immense, that the density of the original point out of which that explosion bursted had to be greater than any black hole we know about. Which means that for explosion to actually happen, there had to be energy greater than the density of the original point. Supposing that such an energy is possible, we then would have to look at the universe and calculate not only the forming energies of the stars and galaxies, but the velocities with which they move around their orbits, for those velocities would be a repercussion of the original momentum of the explosion. With that in mind, we would have to presuppose that the velocities of the galaxies located in the same distance range, would have to be proportional to their mass and equal in momentum. However, that just doesn't happen. What we see is that those velocities and those momentums exist in a state of relative disparity in each locale in the universe, however distant. Which tells us that the distribution of energy in the universe is obliging to some different law, not to that of an explosion. That is also a good indicator that the universe is much, much older then what the advocates of the Big Bang are telling us. There is also a possibility that the energies in the universe exist in a variety of states, which alternate, creating a perpetual interchange between those states. What we can see is just one manifestation of one state - material, the way we understand it. I am still trying to figire out how to detect the other ones :) Hope this is not too crazy... :)

Hallo Eric. I like you homepage. May name Sergey Lukantsov. I the engineer from city Tambov in Russia. I work in centre of energy-information medicine. Diagnostic complexes, which I develop, apply in work gravity exsitons. With their help it is possible to fix not only presence microbs or chemical substances in body of the person, but also their "traces" as wave prints. These wave spectra are stored in GRAVITY of connection inside exitons. >From our researches we see, that by the basic carrier of the information in the world spectra are GRAVITY. If it is interesting to you - I can write more in detail. Sorry for my bad English language. I until have of electronic address, but it is possible to write on postmast@tv-polis.tambov.su - my friends there work, they to me will transfer the letter.

Soon will be homepage on geocites.com\CapeCanaveral\1171

By , Sergey..

I tried the Pi calculator and was successful in getting it to run. I found that after about 1000 digits or so it doesn't fit on my screen but it doesn't matter I didn't really need all those numbers anyway!

Quin

Las Vegas Nevada

Eric, If a car is going say 60mph with it's headlights on, we all know that the light travelling from the headlights would not be travelling at c+60. If the same car had a light shining from behind it, we know that the speed of the light behind the car would not be c-60 but, again, just c. Now if the car is travelling at c then what about the light coming from the front headlights? What about the light coming from the back? I would assume, since it is postulated that someone observing an object travelling at the speed of light would see the object as standing still (or getting slower and slower as it accelerated towards c at stop when it reached c), that the light coming from behind the car would also be standing still much like a ball thrown 60mph backwards from a car moving at 60mph would appear to be standing still to an observer. Is this true? It makes "sense" but I was always under the impression that light was constant no matter what (in vacuo). BTW GREAT web page! Keep it up! Thanks. -Salvatore Richichi weaslinc@pacbell.net

I think that in our present universe there are four dimensions, one of which includes time and that the first dimension is time, if they are layered in orders. What I mean by that is that what we think of as the first dimension (a line) is actually the second dimension, because it has time also. That would mean that if we can see in 3d (one being time), we are in 4d, but that does not seem to be able to be proved, because if you cannot see or even measure the fourth dimension, how do you know how it is? Unless we can actually almost see our present dimension, but only through a 3d "lens" so to speak because we have two eyes, one eye would be 3d(one dimension time-you can see things happening). I thought it interesting in one of the theories that I read that if there is a universe consisting of one more dimension than ours than one looking into our dimension would not be connstrained by our dimension or space-time and would be able to see everything and know everything. Hmmmm. That makes it more believable. Jeff Skiles

We consider ourselves to be creatures of the third dimension. Is this bbecause we are aware of time as moving (and therefore time cannot be a another dimension if we are in the fourth dimension) and we cannot figure the exact nature of the fourth dimension?

Interesting site, thank you. Found you via LinkExchange on my own site. Re: FAQ and the fourth dimension containing an infinite number of 3D universes - I recommend that you re-word that to say that it 'may' contain an infinite...until we can actually perceive and analyze it, it may only be a potential and not a fulfilled infinity. E.G., our three dimensional universe is NOT filled with an infinite number of 2D pages. Now I'm going to the rest of the site to explore.

Best,
Cyrano
Gary Hurlbert
hurlbert@earthlink.net
ghurlbert@usa.net
http://www.earthlink.net/~hurlbert/index.html

My Commitment as a Christian: I'm part of the fellowship of the unashamed. I have stepped over the line. The decision has been made. I'm a disciple of Jesus Christ. I won't look back, let up, slow down, back away, or be still. My past is redeemed, my present makes sense, and my future is secure. I'm finished and done with low living, sight walking, small planning, smooth kness, colorless dreams, tamed visions, mundane talking, cheap living, and dwarfed goals. I no longer need preeminence, prosperity, position, promotions, plaudits, or popularity. I don't have to be right, first, tops, recognized, praised, regarded, or rewarded. I now live by faith, lean on His presence, walk by patience, lift by prayer, and labor by power. My face is set, my gait is fast, my goal is heaven, my road is narrow, my way rough, my companions few, my Guide reliable, my mission clear. I cannot be bought, deluded, or delayed. I will not flinch in the face of sacrifice, hesitate in the presence of the adversary, negotiate at the table of the enemy, or meander in the maze of mediocrity. I won't give up, shut up, let up until I have stayed up, stored up, prayed up, paid up, and preached up for the cause of Christ. I am a disciple of Jesus. I must go till He comes, give till I drop, preach till all know, and work till He stops me. And when He comes for His own, He will have no problem recognizing me - my banner will be clear! Prety convicting, huh? To be as committed as this young man requires throwing off any extra baggage the world has dumped on you. Do you truly want to be a disciple of Jesus? Then remain in close fellowship with Him. Get yourself committed. Give you life to the One who gave his life for you. <><

I believe that your proposed answer to Enigma 34 - King's Orders - is incorrect. There are two alternative solutions, depending on the reading of the problem. Each assumes that the servant has NOT "collected" himself. At the first manor, the servant collects one person. At the second manor, he likewise collects ONE (being the total of all those collected so far). At the third manor, two. At the fourth, four. At the fifth, eight. Thus the number collected at manor "n" is two raised to the (n-2) power.(The first manor is an exception to the general rule.) Therefore, at the thirtieth manor, he will collect 2 to the 28th power persons and the total collected (from the formula for the sum of powers of two) is 2 to the 29th minus 1. As an alternative, it may be said that he will collect absolutely NO ONE. As each manor provides soldiers equal to the sum of those collected, the first manor produces NONE. None have been collected so far, so that is the first manor's total. Similarly, the second manor produces none as the total of those collected so far. Each manor thereafter likewise provides NO soldiers in a reductio ad absurdum. Respectfully submitted, The Old Curmudgeon.

I explained that the solution follows this pattern: At the 1st manor= 2^1 then the second: 2^2. At the third manor: 2^3 then 2^4 then 2^5 until 2^30.

Hi, Eric... I think I E-mailed you a week or so ago...but maybe it got lost. There's a home page at where I discuss how the fourth spatial dimension can be there and in Essay #1 I show you an easy way to visualize it. Also there's a pretty interesting discussion going on about the nature of 4D space at . Select the Forum icon and then go the the astronomy venue. In the topic "does light come back?" I'm "the whistler" who's making the argument that it does because the fourth spatial dimension extends the global curvature of a spherical surface into curved space. Regards.. Mike Feltz

I have added these essays since emailing Mike and made a link to his page

Hi my name is Tracy and I am no mathematics or science expert but this is what I think that the fourth dimension could be is our conscious or spirits or universal knowledge or intelligent life that exists in the universe where no matter or three dimensional objects exist at all. The fourth dimension is the invisible dimension. I think time travel will be possible when we learn how to live successfully in the three dimensional world, otherwise we will repeat the same mistakes when we reach the fourth dimension. Tracy price@sia.net.au

It's good that you manage a web page devoted to the fourth dimension; this subject is worth talking about. If nothing else, it combats those who say that such a thing cannot exist. Many of your contributors are trying to "visualize" spaces with more than three dimensions, which is not easy (I myself certainly can't do it). These writers may not know that there are powerful mathematical methods to calculate properties of n-dimensional figures with no visualization necessary. These are covered in the standard sophomore- or junior-level linear algebra courses offered at most colleges; the mathematics is not complicated, but it is quite abstract at times.

Hi there, I am mentionned a couple of times in your enigma winner
list...and I have a small suggestion to you about this very page: why
don't you arrange it differently? Your list is growing week after week,
and soon, it will be much too long to allow any efficient search. You
might want create many small lists of winners for each enigma.  Also,
it'd be nice to have a top 5 rank for the frequency of correct answers
submitted.  While we're at it, use basic HTML coding to let US vote the
difficulty rating of the enigmas (you could give yours and we could
compare it to the public's vote).

I'd like to congratulate you on your page, the enigmas are excellent,
the paradoxes section is picking up (your first 2 are variants of quite
well known paradoxes, but you will get there!). The only vague and
uncertain part of this site is all this somewhat non-scientific (or
personal-opinion-dependant if you may) deliberation on the 4th (spatial)
dimension (alas, the main subject of this site): there's no real
fondation or visceral need to debate the properties of such concept when
you can't even prove its correspondance in reality. Sure, you can work
in 4 dimensional space in mathematics, or even the more generalized
n-Euclidean space for that matter: it is very easy and teached and used
everyday in math, physics, etc.  But the 4 dimensional space is used as
an geometrical analogy of a system of equations (eg: linear algebra).
Can you always establish a link between mathematics and reality? I say
no. We have far more liberty of creation in mathematics than we do in
the real world: in our universe, there are constants (gravitational
constant, Planck constant, vacuum permeability, etc...) that regularize
the allowed fundamental interactions.  Quite a lot of things exist even
when they're extremely unstable (ie: virtual particles created from
quantic vacuum, an atom containing 7000+ nucleons), but not EVERYTHING
can exist (or at least it is thought), such as imaginary speed (complex
number). This makes me think of Plato and his supra-sensorial world
where REAL PERFECT figures (like circle) and concepts really do exist
(and would accessible only by thought)...(sorry, this impulse comes in
part from the influence of a physics history course...hehe) but do not
exist in the real world (try to make an exact circle that would stay
perfect at all scales, even infinitely smaller than the smallest
possible particle, or even the smallest localized iota of anything that
possesses the property of well-defined existance in this universe).

 Here, I do not blindly and arrogantly imply that a 4th spatial
dimension never will be completly accessible to us.  It would prove very
useful in space exploration (for evident reasons).  I have not done
enough general relativity to elaborate on the consequences of the
curvature of space-time in accelerated (or non-) referentials to really
give a quality application for this debate; I am in physics at the
University of Montreal in my very first semester, and have not done any
relativity (or for an extreme short ammount of time) in college.

Eric,

The questions that you are posing on that page are not just intellectual
games to a lot of people.  Contingencies we have to live with take their
toil in our lives and the whole senselessness of our current approach to
the meaning of our  existence is becoming more and more exemplified to
those who want to think.  Mind and Soul as terms of discussion are
gradually escaping the domain of literature and religion into the realm of
science.  What we are seing is a major paradigm shift in human
consciousness.  That which was formerly disregarded as impossible is
gaining astonishing scientific evidence and at this point the very
"probability" as concept is changing its face to reflect the shift in
cognition from proof-based to intuition-based.  The intuition is almost
proven to be a physical substance that exists in the realm of post-quantum
physics.  The theory that we are nothing but scattered organisms inhabiting
a planet as a result of some random exlposion is erroding and erroding very
fast.  The modern thinking acepts the possibility that we are not a
disparate bunch of loosers, not knowing the direction in which we are
going, but, rather, calculated and anticipated SINGLE organism, governed
and directed by laws that lie beyond anything to which we can physically
refer.  The physical reality to which we can attach ourselves is a part of
this organism (I use this term very loosely) and we, each and every one of
us, live in it whether we belive in it or not.  And whether we belive it or
not, the actions that we take affect the rest of us in a way that at this
point we can't even anticipate.  Research the works of Dr. Bohm - you'd be
surprized to learn about his theory.

That is why I am asking you this questions.  It is of crucial importance to
mankind to evolve cognitively and spiritually.  We are the only specie on
this planet that can control our own evolution. Why not do it?

Kind Regards,
GA

I've been looking at various websights that are showing their ideas on what a
hyper cube looks like. My version is similar to the "cube inside a cube"
model. In my version this model is actually 7 cubes, a base cube with six
additional cubes extending from it into the fourth dimension. Since this can
not actually be done the extended squares become distorted and the sides
appear angled. This model, however is still incomplete. 1 additional cube
needs to be added to "cap off" The seven cubes. This is accomplished as
follows. Set the "cap off" cube next to the seven-cubed model. All 6 sides of
the "cap off" cube need to touch all 6 sides of the seven-cubed model.
Imagine the "cap-off" cube is a box. Cut down the corners of the box so it
could lie flat on a table. Next wrap the "cap off" cube around the seven
cubed model in essense turning the "cap off" cube inside out. This "cap off"
cube encircles the seven-cubed model creating my version of the hyper cube.
This may be hard to grasp so if you are interested in my explaination into
this as well as connections this model has to other areas e-mail me at
graycee1@aol.com

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esalts@zoomnet.net

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