Paradoxes Resolved, Origins Illuminated

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Julio

Belgium
4 Posts

Posted - 16 Jan 2003 : 11:54:28

I finished reading Dark Matter a few months ago and have been trying to digest it since.

I have relatively "no problem" imagining a universe infinite in space or infinite in time, mainly because the alternative seems even harder to comprehend.

What I can't quite come to terms with, is the infinity in scale, mainly its implication that every level of scale has its own "type" of particles.

Ii seems plausible on the infinitely large, but how is it posible on the infitely small? Shouldn't there be a limit?

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tvanflandern

USA
2793 Posts

Posted - 18 Jan 2003 : 02:23:38

quote:
[Julio]: It seems plausible on the infinitely large, but how is it posible on the infitely small? Shouldn't there be a limit?

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|-

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Enrico

Italy
80 Posts

Posted - 19 Jan 2003 : 15:08:44

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

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nderosa

USA
45 Posts

Posted - 19 Jan 2003 : 15:53:08

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

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tvanflandern

USA
2793 Posts

Posted - 19 Jan 2003 : 15:54:11

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?

Those who "understand" Zeno's original eight paradoxes (and the ninth one introduced in Dark Matter) 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 Dark Matter, 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 Dark Matter 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|-

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Enrico

Italy
80 Posts

Posted - 19 Jan 2003 : 16:57:29

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

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tvanflandern

USA
2793 Posts

Posted - 19 Jan 2003 : 19:15:34

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.

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.

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".

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.

)

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.

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.

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.

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 Dark Matter 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|-

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Mac

USA
646 Posts

Posted - 19 Jan 2003 : 23:22:34

Tom,

In the past you have stated that the MM universe consists of everything that exists and in that respect what you have said might prevail in terms of conservation; however, it appears that our physics are linked to less than all that exists. That is our universe is but a small volume in the overall creation. The difference here is in defining what is the universe. To me it would be only that region to which we have a physical connection.

I am speaking about the Chiral Condensate from which virtual particles appear and vanish. If they exist in another dimension or form that is detached from our physics then in our physical universe momentum is not conserved and that goes to the accelerating expansion of the universe (as most referred to it), if you include creation outside the normal frame of reference as being the universe then perhaps momentum is conserved.

This is not a statement but food for thought.

Mac

Enrico

Italy
80 Posts

Posted - 20 Jan 2003 : 10:14:43

Thank you Dr. Van Flandern. Sorry for the bad English. I try much. My intention is not to have conflict with anyone but to help clarify a lot of misconception about Zeno's paradox. My thesis is about 40 Zeno's paradoxes in total about several things including motion.

Gamow's solution is known as a "naive" solution. The paradox is not about motion already in progress where an infinite series converges such as 1+1/2+1/4+.... This is not Zeno's paradox Dr. Van Flandern. Gamow does not understand the paradox. The problem is that if distance is infinite divisible there are infinite "check points" to pass and the real series is not Gamow's but 1+1+1+...+1+... and this is infinite sum then motion is impossible in first place. This is Meno's paradox. Gamow's solution is offered to pupils to make then confortable about physics and mathematics. Philosophers are not comfortable people, they should not be confortable with naive solutions like Gamow.

The problem now as solved by other mathmatician and philosopher like Weierstrass already assume motion is possible and this is not Zeno's paradox as motion cannot account for a solution to motion in a valid logical argument and used as a premise against Zeno.

I like to say that Zeno's paradoxes are against Pythagorean and Euclidean conception of space-time. We know Einstein studied Zeno and the studium paradox is about Lorentz invariance. It is funny some people use Zeno's paradox to support Anaxagora's Plurality and Pythogorean space-time. They do so because they do not understand the paradox and read people like Gamow.

I think I made very clear what I say. Your answer was appreciated and I hope mine will be too. Thank you and sorry for the trouble.

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jimiproton

Japan
110 Posts

Posted - 02 Feb 2003 : 10:02:31

quote:
___________________________________________________________________________
...some people use Zeno's paradox to support Anaxagora's Plurality and Pythogorean space-time. They do so because they do not understand the paradox...
___________________________________________________________________________

Here is an oxymoron. One cannot understand a true "paradox." Else it ceases to be a paradox.

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Enrico

Italy
80 Posts

Posted - 05 Feb 2003 : 07:36:04

Understanding a paradox is not an Oxymoron schema. Using a paradox in a context outside its domain is an Oxymoron schema. What you propose is called a "sophism". Sophism approach to paradox is typical. Zeno's paradoxes are very well understood in Philosophy and science circles. Even Twin Paradox is understood what it means. I hope you know Knowledge Argument by Jackson. It is very well understood what it means. What it is not understood is which premise is invalid. If an invalidation of a premise can be shown, the paradox is not a paradox any more. This what makes a paradox valid is the inability to disprove its premises in concrete and universally accepted way.

I hope this helps you to understand why your statement is wrong.

Enrico

Mac

USA
646 Posts

Posted - 05 Feb 2003 : 09:45:55

enrico,

This coincides with my view and that is we should take "paradoxes" in general to mean "flaws" in our theories and understanding of reality and should therefore be reluctant to place to much trust and emphasis in such theories as being reality.

In contrats the Relativity Bible thumpers tend to dig in and take the position that if you disagree with Relativity yu don't understand physics and that reality is full of paradoxes.

A wholly unscientific position to take.

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AgoraBasta

Russia
234 Posts

Posted - 05 Feb 2003 : 19:04:05

quote:
[Enrico]The problem is that if distance is infinite divisible there are infinite "check points" to pass and the real series is not Gamow's but 1+1+1+...+1+... and this is infinite sum then motion is impossible in first place.

The real problem is that, before you can write the "1+1+1+...+1+..." thingie, you must define the "1", the "+", the "check points", and the most important thing here - the Time itself.
E.g. how does the "1+1+1+...+1+..." relate to time? It really can happen consequently, still in exactly zero time span; or in parallel with/without mutual causality, or in a recurring time loop, or non-causally altogether, or always in the past, or outside of time completely, or at different time scale impenetrable to "us", etc, etc... All those questions can be asked even before you define the rest of the expression.

So we could talk on your phylosophical issues, but not before we agree on premises.
Thus far, I find that you gravely misuse the terminology, and it's not about your English...

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1234567890

360 Posts

Posted - 06 Feb 2003 : 04:23:40

Dr. Flandern,

when you argue that - since things can't pass out of existence, they
can't come into existence- that seems to contradict experience: The empirical fact is that things ARE in existence- thus proving things CAN come into existence. Whether existence is a reversible process
is debatable (although empirical evidence suggests not), but I think it is irrefutable that something can come from nothing. Existence proves this process. A limited analogy would be to think of the transition between anarchic and a lawful society. Before there was law, anything goes. One of the laws our universe in its creation adopted could have been the conservation principles, making it an irreversible process. Or maybe there is no conservation- we just haven't figured out how to violate it.

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Enrico

Italy
80 Posts

Posted - 06 Feb 2003 : 05:29:26

...So we could talk on your phylosophical issues, but not before we agree on premises.
Thus far, I find that you gravely misuse the terminology, and it's not about your English...

I believe it was not my philosophical issues but issues I found already discussed here and misused to a great extent. I just tried to help. What I say is not my stupid opinion but of many great and known Philosophers apparently you are not aware of. I do not like your attitude. If you must question what is "1" and 1+1+1... I suggest you first look your face on the mirror and wonder if you exist at all. Possibly you have existential problems. No person questioning basic things like "1" and 1+1+1+... ever got any place. If you keep question things like that you have long way to go before you can discuss serious philosophical issues. Very long.

Serviccing synonymic tuberization kerbstone composer scorify? Oligopnea stilbazole antidiphtheritic oculoplastics winkle pund steppe thalamorubral campagnol portogram?

1234567890

360 Posts

Posted - 06 Feb 2003 : 12:24:33

quote:

[Enrico]The problem is that if distance is infinite divisible there are infinite "check points" to pass and the real series is not Gamow's but 1+1+1+...+1+... and this is infinite sum then motion is impossible in first place.

A distance can be infinitely divisible and yet is finite in length. When we speak of moving through a distance, we are speaking of moving through a definite and finite length (that may possibly be divided into infinite parts) and not of moving through an infinite length. Sure, 1 meter can be imagined to be divided into infinitely smaller parts but the actual length is still 1 meter, by definition.

Surely a finite distance being divided into infinite parts is no barrier for motion- unless you were an infinitely small object. It is a clever trick of language but Zeno's paradox of motion is no paradox at all.

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AgoraBasta

Russia
234 Posts

Posted - 06 Feb 2003 : 18:40:22

quote:
[Enrico]No person questioning basic things like "1" and 1+1+1+... ever got any place. If you keep question things like that you have long way to go before you can discuss serious philosophical issues. Very long.

That must've been the "long way" you skipped altogether in your educational process... Otherwise you'd come up with clear definitions of your particular use of math notation here and of how exactly is it related to your "phylosophical" exercises, rather than resorting to personal attacks and accusations of ignorance.