More on Infinity

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Julio]: It seems plausible on the infinitely large, but how is it posible on the infitely small? Shouldn't there be a limit?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

In chapter one, in the section on Zeno's extended paradox for matter, I list the "paradoxes" or logical dilemmas that occur if a smallest particle exists. What answers do you envision to those points? -|Tom|-

Hello, my name is Enrico and I graduate student at University of Rome in Philosophy and Cosmology program.

I want to starting a new to topic but read this one and is similar to my questioning. I have read Dark Matter book I found in library and question the context Zeno's paradox is used in the book. I asked my professor for my thesis and he answered his opinion the paradox used in wrong context. We make a study of the book and professor believes the paradox used to justifying small scales of particles in existense. The problems seems that many people dont know Zeno's paradox was formulated to support Monism theory of Zeno teacher Parmenides. Paradox is used in the wrong context in the book. This says if space infinite divisible no motion can start at all because there is infinite emtpy space between infinite divisions. Some think motion start but never end but this is wrong Zeno's original paradox. Zeno and Parmenides know motion exists but the paradox is question of the medium of motion and not motion. Best to say Zeno's paradox support Atomism of Democritus but some believe the opposite because dont understood the paradox. Very not many people understand the paradox. When we speak with American philosopher we see they dont understand the paradox.

Meta model say scale is infinite then motion cannot happen if no perfect medium present for motion. This is Zeno's paradox. My professor says Meta Model has logical problem. If infinite scale then no motion if not some medium present. How Meta model solbe this problem?

Enrico

Yikes! Enrico, I like most of what you say, but the English is tortured. May I straighten it out? Neil

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Meta Model say scale is infinite; then motion cannot happen if no perfect medium present for motion. This is Zeno's paradox. My professor says Meta Model has logical problem. If infinite scale then no motion if not some medium present. How Meta model solbe this problem?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Those who "understand" Zeno's original eight paradoxes (and the ninth one introduced in <i>Dark Matter</i>) appreciate that the paradoxes are called paradoxes because they cut both ways: Whether space and time (and matter) are infinitely divisible, or whether there is a smallest possible unit, a logical problem exists.

You and your teacher merely repeat half the original argument. Your objection, as it is usually stated, is that one cannot cross the street if space is infinitely divisible because, when one has crossed half way, half remains; and when crossing half that, 1/4 remains; and so on forever, with always a fraction remaining. The argument is that one cannot take an infinite number of steps in a finite time, and therefore motion in an infinitely divisible space is impossible.

There are two problems with this; and your failure to mention either entitles me to claim your side "doesn't understand the paradox" too. Many books have been written on both sides of this debate. But such claims and counter-claims will get us nowhere. We must use logic and reasoning to solve this "paradox".

In <i>Dark Matter</i>, I list many of the problems that occur if there is a smallest possible unit of space. I won't repeat all those arguments here. But it is important to see, as argued in the text, that they have no possible solution without violating one or more principles of physics. So the first problem with your position is that you have not solved all the problems that arise if your "solution" is adopted. Would you care to try?

The second problem is that you ignore, or perhaps did not understand, the solution offerred in <i>Dark Matter</i> to the paradoxes: If and only if time, space, and matter are all infinitely divisible, then the technique popularized by Gamow of "one-to-one correspondences" allows us to prove that the sum of an infinite series can be finite. In particular, in the example above, the steps match one-to-one the terms in the infinite series 1/2 + 1/4 + 1/8 + 1/16 + ..., for which the sum is exactly 1.0.

Put another way, the limit of the ratio of delta-x over delta-t as delta-t approaches zero, which is the definition of velocity, is finite. In MM, you can't even argue there is an "infinite distance" between points because every point is occupied at some infinitesimal scale so there is no "empty space"; and because every scale, no matter how small, looks the same as our scale in overall character.

These are difficult concepts to deal with, no matter what the correct solution. If you hope to contribute to the solution instead of adding to the problem, these matters must be addressed. I refer again to the text for a fuller exposition. -|Tom|-

Tom

Thank you for answering. I will try better English. If you come to Italian messages I will not complain if you speak not perfect Italian.

Gamow's argument is illogical and brings up Socrates paradox of the wheels. A one-to-one correspondence is a very old problem for another paradox. I think you use the paradox in a "preferred sense". Again no crossing can even start, this is the point not understood by those using the paradox. The paradox is not about getting to some place but about the medium of motion. I tried to explain this. If motion starts then there is convergence if infinite sum principle is used with infinite divisible. But this is not the solution as you say. You assuming motion. This is not the original paradox and not many understand this. Again, if motion starts at all, then motion finishes if there is no limit of smallest scale and series converge. The paradox is if you think of scale infinite. Then no motion can start. This is hard for people to understand and claim other people dont understand. Speed make sense if motion starts. If there is not speed it makes no sense. If Meta Model has no empty space then Zeno's paradox says no motion can start at all because you do not know where to go as you divide there is no half-way point to start with. Half way of infinity is infinity.

Analyzing paradox is the job of a lot of people at the Philosophy department here. I asked two more professors and said the same thing. Maybe you are thinking of other paradox but Zeno's paradox is about motion starting and finishing. You only talk about finishing. This is not a problem and is solved many years ago but not by Gamow. Gamow is wrong logically and physically. You may try to see if in Meta Model motion can start at all. I think no. This is Zeno's paradox.

Thank you

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Tom, Thank you for answering. I will try better English. If you come to Italian messages I will not complain if you speak not perfect Italian.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The comment about your English was from Neil DeRosa, not from me. Neil has Moderator privileges on this MB, and I recommend that you allow him to make minor changes to your messages, if needed, to improve their readability. He will be careful not to change your meaning. This will allow more people to follow this discussion. If you wish, you may send him email and perhaps preview or review any changes he suggests. Just click on his name to see his email address.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Gamow's argument is illogical and brings up Socrates paradox of the wheels. A one-to-one correspondence is a very old problem for another paradox. I think you use the paradox in a "preferred sense".<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Declarations, even if shouted, have no weight in a logical argument. Many thousands have been persuaded of the reasonableness of Gamow's argument, which is why his book on infinity is famous and still in print half-a-century later. If you have found a flaw, please state it. If you do not understand Gamow's argument, that is okay -- many people don't. But in the absence of a counter-argument, you should read descriptions by other teachers or authors until you understand the argument the way others do, right or wrong. (Of course, if this changes your mind, you might need to pass your present course before letting your teacher know you disagree with him. <img src=icon_smile_evil.gif border=0 align=middle>)

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Analyzing paradox is the job of a lot of people at the Philosophy department here. I asked two more professors and said the same thing.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Appeals to authority are something else that is invalid if used to prevail in a discussion in science. It does not matter if every authority in the world agrees about something. If it violates logic or experiment, it is wrong. The side with the better scientific reasons, not the side with the greater authority, wins.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Again no crossing can even start, this is the point not understood by those using the paradox. The paradox is not about getting to some place but about the medium of motion. I tried to explain this. If motion starts then there is convergence if infinite sum principle is used with infinite divisible. But this is not the solution as you say. You assuming motion. This is not the original paradox and not many understand this. Again, if motion starts at all, then motion finishes if there is no limit of smallest scale and series converge. The paradox is if you think of scale infinite. Then no motion can start. This is hard for people to understand and claim other people dont understand. Speed make sense if motion starts. If there is not speed it makes no sense. If Meta Model has no empty space then Zeno's paradox says no motion can start at all because you do not know where to go as you divide there is no half-way point to start with. Half way of infinity is infinity.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

This still ignores both the validity of the Gamow argument and the impossibility of the "smallest possible particle" position. You cannot say that MM should make a different choice until both these matters are addressed. But nonetheless, let's address your one point by itself.

How can motion be initiated? MM's answer will obviously surprise you. It cannot be initiated. Your question has a built-in assumption of absolute space. MM differs from all other cosmologies in not allowing that or any other assumption. We just make deductions from first principles and see what the outcome is.

Let me explain (but not from first principles; see <i>Dark Matter</i> for that). MM shows that substance cannot cease to exist. It can decompose or explode, but only into smaller entities (particles and waves), which can later reassemble into larger ones again. And if it cannot pass out of existence, then it follows that it cannot come into existence in the past. Later in MM, we see that substance and existence are synonymous -- What exists is occupied at some scale, and what is occupied exists.

A similar thing is true of motion. Consider an object at our scale in motion. Suppose it runs into another similar object head-on at very high relative speed. Both objects may fragment or explode; but the motion (momentum) of the original objects is 100% preserved in its fragments. If the collision is at non-destructive speeds, the motion (momentum) is still preserved in the rebound. Or if the objects are able to absorb motion, it is preserved in the form of heat, which is increased speed of the molecules inside the body. But motion is like matter, and cannot pass out of existence. So it follows that in the past, it cannot come into existence either.

So how does the motion of the universe arise? If there is no absolute space, who is to say that anything is really "in motion"? Substance simply has existence. There is no absolute rest. Different substances have their own standards for rest. As that is altered by collisions, they acquire new standards for rest. The change itself is what we call "time", and the continual relative relocation of substances in all the directions in which they have extent defines what we call "space".

So my answer is, whatever the momentum state of the universe is at any instant, that is what it always has been and always will be. Momentum cannot pass out of or come into existence.

And that answers your question about the origin of motion in a definite way. The maintainance of motion is then addressed by Gamow's one-to-one correspondences.

(Once again, I must stress that convincing you and convincing your teacher are two very different matters. I do not know your teacher, even his name. But a typical man in that position who has been teaching a certain thing as fact for many years would find himself in a very difficult position if asked to consider that the position he has been teaching might be wrong. Vested interests overwhelm reason for most persons, unless they have learned and implemented the "controls" feature in scientific method. The purpose of controls is to separate the outcome of any problem from the biases of the scientist overseeing the matter. Anyone not accustomed to that procedure will have many areas in his/her life where the person is absolutely and unmoveably convinced of something because of the inevitable confirmation of one's biases without controls. Yet in science, this absolute conviction cannot be given any credit because the world is filled with people having absolute convictions about diametrically opposite positions.) -|Tom|-