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Great Schrodenger's cat!
Posted: Mon Oct 06, 2003 5:45 am
by XMEN Gambit
<!--EZCODE AUTOLINK START--><a href="
http://www.nature.com/nsu/030929/030929 ... <!--EZCODE AUTOLINK END--><br><br>A proposed experiment where a bacterium-sized mirror can be in two places at once, due to some quantum-level photon fiddling. Oh, and a vacuum chamber at near absolute zero, too.<br><br>The cat would be SO dead in this scenario. <!--EZCODE EMOTICON START :lol --><img src=
http://www.ezboard.com/images/emoticons/laugh.gif ALT=":lol"><!--EZCODE EMOTICON END--> <p><!--EZCODE IMAGE START--><img src="
http://www.xmenclan.org/xmengambit.gif"/><!--EZCODE IMAGE END--><br>XMEN member<br>Card-carrying DTM<br>OKL Fish-napper<br><br>Though a program be but three lines long, someday it will have to be maintained.<br><!--EZCODE ITALIC START--><em> The Tao of Programming</em><!--EZCODE ITALIC END--></p><i></i>
Re: Great Schrodenger's cat!
Posted: Mon Oct 06, 2003 1:42 pm
by XMEN Ashaman DTM
Gambit:<br><br>You ever hear of the term "state machine" ??<br><br>If so, and you know what it means, do you think the universe is like that?<br><br>What drives the states then?<br><br>You can't say some fluctuation of the universe itself, because that's a circular argument. <!--EZCODE EMOTICON START ;) --><img src=
http://www.ezboard.com/images/emoticons/wink.gif ALT=";)"><!--EZCODE EMOTICON END--> <br><br><br>I've thought about this for a while. I am starting to think that it's not. And that our perception of the progress of time is an illusion. My reasoning stems from thought about what the universe is like for a single photon; it travels at lightspeed, has no mass, and it's entire existence is in an erily silent universe (there is no progression of time at lightspeed). So I've been thinking that the progression is an illusion. The only problem is in reconciling the fact that the photon CAN'T be a particle in its universe... it has to be a line since there is no change in its state, yet we perceive it to travel. This means that the line is predetermined. But how does the line "know" the route it takes? And by line, I mean that the photon itself is spread out over its entire route; only we see certain parts of it as it travels. The photon only sees what's in a line in the direction it's going (blue shifted, of course), and in the direction of where it has been (red shifted, of course).<br><br>It's like I can almost visualize the whole process, but it's like it's on the tip of my tongue. I've been looking at different mathematics to describe this. But so far, the closest thing is the relationship between discrete and continuous math. <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Mon Oct 06, 2003 7:12 pm
by XMEN Gambit
Welcome to quantum mind-bending. <!--EZCODE EMOTICON START :) --><img src=
http://www.ezboard.com/images/emoticons/smile.gif ALT=":)"><!--EZCODE EMOTICON END--> Let's see what kind of brainstorming we can do here.<br><br>A photon doesn't have to be a particle, or a wave. I think it's just a planck unit of energy whose effect is determined by a probability curve which can interfere with itself. (gotta remember that slit-lamp experiment, and stranger ones!)<br><br>A photon has to be massless. If a photon was matter at all, then according to Einstein it must have infinite mass (since it's moving at <!--EZCODE ITALIC START--><em>c</em><!--EZCODE ITALIC END-->). Since that's obviously not the case, the thing has to be massless. Or there are some problems with his theory.<br><br>If you were traveling at <!--EZCODE ITALIC START--><em>c</em><!--EZCODE ITALIC END-->, like a photon does, you couldn't see behind you at all - what could catch up? Your view to the front might not be much better, probably just a point-source. <br><br>As you say, because it's traveling that fast, a photon doesn't "age," time doesn't pass for it. So, from it's "view", it is released at location A and then absorbed at location B in the same moment. An instantaneous transfer of energy.<br><br> <p><!--EZCODE IMAGE START--><img src="
http://www.xmenclan.org/xmengambit.gif"/><!--EZCODE IMAGE END--><br>XMEN member<br>Card-carrying DTM<br>OKL Fish-napper<br><br>Though a program be but three lines long, someday it will have to be maintained.<br><!--EZCODE ITALIC START--><em> The Tao of Programming</em><!--EZCODE ITALIC END--></p><i></i>
Re: Great Schrodenger's cat!
Posted: Mon Oct 06, 2003 9:41 pm
by XMEN Ravok99
This stuff fascinates, and confuses me, no end. <!--EZCODE EMOTICON START :D --><img src=
http://www.ezboard.com/images/emoticons/happy.gif ALT=":D"><!--EZCODE EMOTICON END--> <p>"Patience is a virtue ... for other people." -Ravok</p><i></i>
Re: Great Schrodenger's cat!
Posted: Tue Oct 07, 2003 10:04 am
by XMEN Ashaman DTM
<!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>A photon doesn't have to be a particle, or a wave. I think it's just a planck unit of energy whose effect is determined by a probability curve which can interfere with itself. (gotta remember that slit-lamp experiment, and stranger ones!)<br><hr></blockquote><!--EZCODE QUOTE END--><br>I fully comprehend the wave-particle experiments and have applied the ideas to gas dynamics. What I'm getting at is what is the fundamental nature of the photon. We can say it is pure energy, has no mass, and all that. But what IS it? What element of the universe's fabric is it an aspect of? Some people think of the universe as a seething pot of virtual particles; and it probably is. But that still doesn't give me an idea of <!--EZCODE ITALIC START--><em>what</em><!--EZCODE ITALIC END--> the stuff the universe is made of.<br><br><br><!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>If you were traveling at c, like a photon does, you couldn't see behind you at all - what could catch up? Your view to the front might not be much better, probably just a point-source. <br><hr></blockquote><!--EZCODE QUOTE END--><br><br>Not quite.<br><br>You'd see an extremely blue-shifted point source in front of you, but an extremely red-shifted point source behind you. With the rest of the universe fading to black as you pan your view to 90 degrees to your sides. (Because at the sides, almost nothing can get to you... unless you count the stray particle hitting you at just the right point.)<br>Even though the information never catches up to you, you still see the effects of moving away from information travelling with any perpendicular path to you. That's a result of Einstein's equations.<br><br><br><!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>As you say, because it's traveling that fast, a photon doesn't "age," time doesn't pass for it. So, from it's "view", it is released at location A and then absorbed at location B in the same moment. An instantaneous transfer of energy.<hr></blockquote><!--EZCODE QUOTE END--><br><br>Not exactly. There are no instants when there is a progression of time in the photon's universe. So to say it's an instantaneous transfer of energy is an erroneous thought. From its point of view, there can be no "existence, and then no existence". And since there is no progression of time, the photon can never move in its reference frame. It's stuck. This is the crux of the problem. You can't dictate a change in momentum (energy) unless there is time. But in the photon's world, there is no time, so there can't be any such thing as momentum.<br><br>In essence, without time, you can't have an instant of no object, then an object. There is no time for a transition. Quantum mechanics says that you can have infinitely small slices of time. What we see in the physical world says that there is a strong possibility that there is a limit to the size of your time step (planck time).<br><br><br><br>Which leads back to my original question. Is the universe a state machine? Can it be?<br> <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Tue Oct 07, 2003 11:07 am
by XMEN Gambit
But it's NOT an object!<br><br>I said, from the photon's perspective, it is released/generated at the same moment that it is absorbed by the target. Though a photon really can't have a "point of view" because time doesn't pass for it, as we've both said over and over. It doesn't have anything we could call an existence or lifespan. <br><br>A photon just a model we use for moving energy from point A to B. The energy itself doesn't change ("it's stuck"), but the emitter and absorber do. What is it really? I dunno. What's gravity? Though we can postulate the existence of "gravitons", they're just a model for explaining effects we can measure, as are photons.<br><br><br>I still don't think you'd see anything from behind while moving at lightspeed. <!--EZCODE EMOTICON START :) --><img src=
http://www.ezboard.com/images/emoticons/smile.gif ALT=":)"><!--EZCODE EMOTICON END--> <br><br><br><br>If the universe IS a state machine, I'd hate to model it. Can it be? Sure, but as you said, you then have to postulate something outside. God, a metaverse, whatever.<br> <p><!--EZCODE IMAGE START--><img src="
http://www.xmenclan.org/xmengambit.gif"/><!--EZCODE IMAGE END--><br>XMEN member<br>Card-carrying DTM<br>OKL Fish-napper<br><br>Though a program be but three lines long, someday it will have to be maintained.<br><!--EZCODE ITALIC START--><em> The Tao of Programming</em><!--EZCODE ITALIC END--></p><i></i>
Re: Great Schrodenger's cat!
Posted: Tue Oct 07, 2003 6:31 pm
by XMEN Ashaman DTM
<!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr>But it's NOT an object!<br><br>I said, from the photon's perspective, it is released/generated at the same moment that it is absorbed by the target. Though a photon really can't have a "point of view" because time doesn't pass for it, as we've both said over and over. It doesn't have anything we could call an existence or lifespan. <br><hr></blockquote><!--EZCODE QUOTE END--><br><br>Okay... two things here:<br><br>First, photons ARE objects. They do impart momentum to things they interact with, and they can change the energy states of atoms, molecules and particles. They are more than a mathematical description or energy packet. They physically exist.<br><br>Second. The second part is <!--EZCODE ITALIC START--><em>exactly</em><!--EZCODE ITALIC END--> the quandry that I am describing.<br><br><br>Say a photon is generated in our reference frame, then passes a black hole so its path changes (and it's momentum). Now, in the photon's world, it doesn't "know" about the black hole until it encounters it. To it everything remains the same. BUT, because it passed the black hole, it now ends up in a different direction than if it did not pass the black hole.<br><br>Now, what if two photons were generated and sent on the exact same path. Only the two are entangled, and one of them passes the black hole. The one photon will change to relfect the change in momentum of the other. Now, what I am getting at with this is:<br>If the black-hole-encountering photon was entangled with the other photon. The pair will reorganize themselves to reflect the encounter with the black hole by the one photon. (Because there was a change in momentum... apply heisenberg's uncertainty principle, and the result is that the momentum is fixed by the black hole's "observation" of the particle.) The other photon will reflect that change with its momentum. But we've already established that the photon never changes due to the zero delta_t in the photon's reference frame. But there is a change in momentum... where is the transition?<br><br>With that thought in mind, here is the question:<br><br>If a photon travels and encounters something to change its momentum, then the photon should reflect this, correct? From our point of view, the photon changes. We would call it a "change in path" or whatever. Now the question is: since we observe a change, how is this reflected in the structure of the photon from the photon's point of view?<br><br>Also, if the photon's interaction causes the photon to transfer energy to the collidee (thus destroying itself), then a new photon is created because the collidee has excess energy (as is the case thought by particle physicists), then that would point to the interaction being similar to a state machine. BUT, how you can you have a <!--EZCODE ITALIC START--><em>true</em><!--EZCODE ITALIC END--> state machine (one that has no transition between states), with a real system? A system where the instantaneous transition between states would require an ENORMOUS amount of energy?<br><br><br>I'll post more, but I have to recollect my thoughts. <!--EZCODE EMOTICON START :D --><img src=
http://www.ezboard.com/images/emoticons/happy.gif ALT=":D"><!--EZCODE EMOTICON END--> <br><br><br><br>I am trying to picture things that we observe in our reference frame, as they would appear from the photon's point of view. <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Wed Oct 08, 2003 12:31 am
by Scorch
<!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr>I said, from the photon's perspective, it is released/generated at the same moment that it is absorbed by the target. Though a photon really can't have a "point of view" because time doesn't pass for it, as we've both said over and over. It doesn't have anything we could call an existence or lifespan. <hr></blockquote><!--EZCODE QUOTE END--><br><br>Uhh... I thought it worked like this.<br><br>from the PHOTONS point of view time would pass, however there would be no distance between where it started and where it ended up.<br><br>Form OUR point of view, the photon travels a distance, but it would not age.<br><br> <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Wed Oct 08, 2003 8:47 am
by XMEN Ashaman DTM
<!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr>from the PHOTONS point of view time would pass, however there would be no distance between where it started and where it ended up.<hr></blockquote><!--EZCODE QUOTE END--><br><br>Nope. If you have an instantaneous change in position like that, your acceleration and velocity must be infinite. Both of which can't happen.<br><br>If you do a Lorentz transformation on the photon to be in its reference frame, your time approaches zero as you approach c. (Take the limit as v -> c in the Lorentz transformations.)<br> <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Wed Oct 08, 2003 6:41 pm
by Scorch
Asha, time, distance and mass are all effected by high speed travel.<br><br>If I remember from Astronomy correctly they effected by the formula, <br><br>i = 1 / sqrt(1 - ( velocity^2 / Speed of light^2 ))<br><br>Where if you sent a spaceship flying at 50% the speed of light to a star 5 light years away and came right back...<br><br>at 50% the speed of light i = 1/sqrt(1-( .5^2/ 1^2) = 1/sqrt(1-(.25)) = 1/sqrt(.75) = 1.1547<br><br>Distance<br>The total distance would be 10 light years. from Earths point of view. But if you asked the spaceship how far it was going travel, <br><br>Distance(new) = Distance(old) * (1 / i) = 10 * .8660 = 8.660ly.<br><br>Time <br>Well if the space ship left, to the star and came back Earth expects the ship back in 20 years (distance 10 divided by speed .5 = 20)<br><br>However the Spaceship expects to be back in 8.660/.5 = 17.320 years.<br><br>So who is correct? they both are<br><br>From Earths prespective time expands for objects traveling at high rates of speed. That is to say 1 second takes longer on the spaceship.<br><br>Time(earth) = Time(spaceship) * i = 17.3205 * 1.1547 = 20<br><br>or<br><br>Time(spaceship) = Time (earth)* (1/i) = 20 * .8660 = 17.3205<br><br>Mass<br>Mass is being ignored right now as it really doesn't matter to the probelm.<br><br><br>back to your probelm.<br><br>A photon travels at c, or the speed of light, if you plug that into i, you run into probelms because you are trying to find out the square root of 1/0 and 1/0 has no real answer however if we look at the graph y = 1/sqrt(1/1-x^2) from 0 to 1 we see as x increases y decreases towards 0<br><br>if we look at the graph of y = 1/(1/sqrt(1/(1-x^2)) from 0 to 1 we see that as x approachs 1, y approachs infinity.<br><br>So what do we have from this? well we see from the spaceship probelm that distance is changed by 1/i which is the second graph we looked at. thus at 1 there is no real answer however the limit of it is 0, therefore the distance must be 0.<br><br>As for time, as I said, from our prespective the time would stop for the photon because each second would take an infinently long time, however FROM THE PHOTONS POINT OF VIEW, NOT OURS, time would run normally, It just has 0 distance to cover therefore it is whereever it gets as soon as it leaves.<br><br>Thus it is the perspective as to what happens.<br><br>From the photons point of view It travels at the speed of light, however as distances are 0 it will get to where its going as soon as it leaves.<br><br>When we look at it we think it hasn't aged it had to travel a great distance.<br><br>However because time and distance are both effected by i by the same amount, it keeps realities in sync with each other as whatever is messed up in distance gets fixed in time. <br><br>If we sent the photon to a star 5 LY away and it came back,<br><br>The distance is 10 according to earth, but it is 0 according to the photon<br><br>Earth expects the light back in 10 years<br><br>However the photon has 0 distance to cover and expects to be back instantly. However the photon experiences the time as normal, but since its wherever it is sent instantly, we percieve that time doesn't pass for it <p></p><i>Edited by: <A HREF=
http://pub141.ezboard.com/bxmenclan.sho ... >Scorch</A> at: 10/8/03 8:09 pm<br></i>
Re: Great Schrodenger's cat!
Posted: Wed Oct 08, 2003 7:35 pm
by XMEN Ashaman DTM
<!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>A photon travels at c, or the speed of light, if you plug that into i, you run into probelms because you are trying to find out the square root of 1/0 and 1/0 has no real answer however if we look at the graph y = 1/sqrt(1/1-x^2) from 0 to 1 we see as x increases y decreases towards 0<br><br>if we look at the graph of y = 1/(1/sqrt(1/(1-x^2)) from 0 to 1 we see that as x approachs 1, y approachs infinity.<br><br>So what do we have from this? well we see from the spaceship probelm that distance is changed by 1/i which is the second graph we looked at. thus at 1 there is no real answer however the limit of it is 0, therefore the distance must be 0.<br><hr></blockquote><!--EZCODE QUOTE END--><br><br>Thus I said to take the <!--EZCODE ITALIC START--><em>limit</em><!--EZCODE ITALIC END--> as v -> c. That would mean that at c, time does not exist. There is no delta time, no derivative of time, nothing. There are no problems mathematically... you just look at the limit.<br><br>From the same Lorentz tranformations, only with respect to distance, your length does decrease as v -> c. So that would imply that what you said here:<br><br><!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>As for time, as I said, from our prespective the time would stop for the photon because each second would take an infinently long time, however FROM THE PHOTONS POINT OF VIEW, NOT OURS, time would run normally, It just has 0 distance to cover therefore it is whereever it gets as soon as it leaves.<br><hr></blockquote><!--EZCODE QUOTE END--><br><br>is indeed correct in that sense. What I am getting at is causality related.<br><br>We know that the speed of an electromagnetic wave can be faster or slower than the speed of light.* The <!--EZCODE ITALIC START--><em><!--EZCODE BOLD START--><strong>information</strong><!--EZCODE BOLD END--></em><!--EZCODE ITALIC END--> contained in that wave is constrained to travel at the speed of light. Thus, we can never (with known physics) send information across vast distances in an instant.<br>*If you need a reference for what was said in this paragraph, look up the terms "group velocity", "wave number", and "frequency" and how they relate to electromagnetic waves.<br><br>So, the question is still: how does the photon know its path? And WHY does the photon's point of view (which is invariant) have no bearing on what happens at non-luminal velocities? Why does a time-invariant system, which has to exist in order to satisfy the way we think electromagnetic energy works, exist if there is such a thing as a state-machine-type universe (which is what our universe is according to quantum mechanics)?<br>(This is just rephrasing the same questions that I asked from the beginning.)<br><br><!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>Thus it is the perspective as to what happens.<br><br>From the photons point of view It travels at the speed of light, however as distances are 0 it will get to where its going as soon as it leaves.<br><br>When we look at it we think it hasn't aged it had to travel a great distance.<br><br>However because time and distance are both effected by i by the same amount, it keeps realities in sync with each other as whatever is messed up in distance gets fixed in time.<br><hr></blockquote><!--EZCODE QUOTE END--><br><br>That should be the case according to the equations. The problem is... there has to be a transition between reference frames. I know it's intuitive for me what is going on in reference frames that have signicantly different velocities. It's the transition that is the kicker. The other thing is to try and visualize everything that you see and experience in the photon's reference frame... you can't... which is why I am wondering about this whole thing from this point of view:<br><br>If time does not exist, then what is the transition between existence and no existence (for the photon), or the transition between states (for say... an electron)? If there is no transition, then the energy needed to change the state of either the photon or should correlate with the energy needed to instantaneously: alter space-time such that a particle could exist, make the particle exist, and instantaneously alter space-time again to make the particle exist in a different way or make it disappear alltogether. That would mean that for each instantaneous change in state of a particle (even if it's in a unit of time of planck-time), there is an energy associated with that. And the particle will always change state unless there are no accelerations acting upon it or no interactions with other particles. Thus the thought that maybe there <!--EZCODE ITALIC START--><em>is</em><!--EZCODE ITALIC END--> a transition between states, only we don't recognize it yet. <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Wed Oct 08, 2003 10:06 pm
by Ambush Bug
<!--EZCODE QUOTE START--><blockquote><strong><em>Quote:</em></strong><hr><br>Thus the thought that maybe there is a transition between states, only we don't recognize it yet. <br><hr></blockquote><!--EZCODE QUOTE END--><br><br>And that, friends and neighbors, is why Nature made peyote. <!--EZCODE EMOTICON START ;) --><img src=
http://www.ezboard.com/images/emoticons/wink.gif ALT=";)"><!--EZCODE EMOTICON END--> <br><br>Sorry, I couldn't resist.<br><br>I don't think I got far enough in physics to know what a 'state machine' is--could any of you provide a definition and purpose of such a machine? With that piece of info, I might be able to contribute to the discussion. (This whole bit on <!--EZCODE ITALIC START--><em>c</em><!--EZCODE ITALIC END--> made me remember a definition of 'dimension' I once heard--the space within the Universe, centered on you, that's exactly the same number of light-years in diameter as the age of the Big Bang. Mind-boggling. Assuming an infinite Universe, o'course, which we can't observe anyway.) <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Thu Oct 09, 2003 1:07 am
by XMEN Ashaman DTM
<!--EZCODE EMOTICON START :lol --><img src=
http://www.ezboard.com/images/emoticons/laugh.gif ALT=":lol"><!--EZCODE EMOTICON END--> @ AB<br><br><br>A state-machine is a machine with distinctly different "states".<br><br>Think of it like this:<br><br>you have a machine that can store 1s or 0s in three different "slots".<br><br>One such order would be this:<br>slot 1: 0<br>slot 2: 0<br>slot 3: 0<br><br>Okay... now say that there is something that causes a change in the system. Say someone puts a 1 in one of the slots. So the new order would be:<br><br>slot 1: 0<br>slot 2: 0<br>slot 3: 1<br><br><br>Now, if we look at all the possible arrangement, then it becomes clear that each arrangement corresponds to a different "state" of the system. When you account for all the possible combinations of the constituents of the system, then you know all the states of the system.<br><br><br>Now, a state-machine is a system that can change between different states. For a computer, this is the case. There are millions upon millions of different states a computer system can be in (the different ways that 1s and 0s can be arranged throughout the entire hardware). The thing that gives the ability for the computer to have different states is the clock generator... this allows for a "time step" to be implemented which allows for an ordered progression between states. The other thing that allows for an ordered progression between states is that computers are basically an assembly of different logic gates (AND, OR, XOR, NOT, XAND, etc.). It is the arrangement of the different possibilities of the logic gates' states, that allows for computations to take place.<br><br>Think of it like this:<br>step 1: take data block 1<br>step 2: take data block 2 and add it to data block 1 (An AND operation)<br>step 3: read output of AND operation in step 2<br><br><br>The data can only progress through the system because there is a clock generator somewhere sending out pulses that everything in the entire computer uses to signal a change.<br><br><br><br><br>Here's something else:<br>Even though every computer is technically a state machine, the more complex ones are not thought of as state-machines. I have to think of the computer hardware I work with as a state-machine so I can account for all the possibilities for the states and write software accordingly. You can get around the state-machine idea by using higher level logic like "add data 1 and data 2" instead of the more detailed and lower level :"feed bit n into data channel 1 of AND gate, feed bit m into data channel 2 of AND gate... (recieve impulse from clock to start change to new state)... output bit p from AND gate, while simultaneously feeding bits n+1 and m+1 into AND gate channels 1 and 2, respectively... and so on.<br> <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Thu Oct 09, 2003 5:55 am
by Variable
<!--EZCODE EMOTICON START :eek2 --><img src=
http://www.thzclan.com/forums/images/smilies/eek2.gif ALT=":eek2"><!--EZCODE EMOTICON END--> <br><br><br>Well thanks guys. I have to go find a sponge now to sop up whats left of my brain after it came oozing out of my ears about 3 posts ago. <p></p><i></i>
Re: Great Schrodenger's cat!
Posted: Thu Oct 09, 2003 6:22 am
by XMEN Gambit
ROFL @ Var <!--EZCODE EMOTICON START :) --><img src=
http://www.ezboard.com/images/emoticons/smile.gif ALT=":)"><!--EZCODE EMOTICON END--> <br><br>Asha, why aren't computers "considered" state machines? Seems to me they're perfect examples. Very complex ones, but eminently demonstrable as such. Any brief tour of assembly code should make it QUITE apparent. <p></p><i></i>