tar

barfbag, You are right. People should not fear pills. But my "pride" in not currently being on any medication, does not mean I am not proud, as well, of medical science and our advances in fights against disease and injury. My knees are shot, bone against bone, and I am watching with great interest the advances in ways to get material between the bone that will lubricate and substitute for the cartilidge that was once there. Just can't bear the thought though of having my knee cut off and plastic and metal put in its place. Just can't imagine how all the nerves that worked before, would work after. How will your brain know the position and pressure of everything if the sensors are cut out? Plus I hate pain. Plus I have "faith" in one's body's ability to grow and heal and sense and move. Seems somewhat huberous filled to think a replacement, human designed knee, would be "better", than the one that allowed me to run like the wind when I was 18. I am not ignoring the value of nicotine patches, or methadone, as patches are better than smoking, and methadone seems to be less insidious than heroine. And there is no doubt that unbearable pain is unbearable and pain killers are a blessing and a wonderful gift of science and our knowledge of brain chemistry. I take them when required. My only comment was, I do not finish the bottle. I do not take them, if I can bear the pain. Friend of mine at work had a heart attack many years back. Is on many drugs. Drugs that conteract the effects of the other drugs...and so on. Things he can't eat, things he can't drink, unintended consequences of the mixture of this or that, at inappropriate levels. I am not saying medical science is not wonderful. I just like to not put complete faith in it, and retain some faith in the original equipment we came with. A balance is good. We should not be either completely dependent, nor completely independent on/of each other. We can make mistakes, individually or in groups, and we have tremendously good judgement, individually and in groups. Perhaps its a philosophy, as well as a method, that I am proposing here. Trust each other, trust capability and trustworthiness wherever it is evident, but trust your own judgment as well. And if someone is taking advantage of you, as in a drug dealer, you should allow yourself to step back from a destructive, dependency based relationship with the guy/gal. Don't let draw of the euphoria, take you, where you don't want to go. And never think that someone else, knows better than you, what is good for you...unless you trust them. And its good to NOT trust drug dealers in general, as they do not primarily have your best interests in mind. They just want to sell you chemical happiness, and control you, through your desire for pleasure. My "tapering" method, at its base, is a method to allow yourself the time to see that you can get the dopamine for free, of your own accord, and need not be dependent on any supplier. I now do not have to "make sure" I have a pack of cigarettes within reach. I don't have to think about when I am going to "run out" and when I am going to go to the store and replenish my supply. I do not have a pack in my sock drawer, and another on the top shelf of my closet, and one in a jacket pocket in the hall closet, and three in my car, and one in my pocket and one in my smoking room. I have one cigarette, a "spare", sitting on an entertainment shelf, next to a speaker, behind a little bucket of odd stuff. It has been there for a few years, as a stale old spare, should I ever have been desparate. I can actually see it from here. Smoking it, is not an option. And I am proud that it can sit there, in plain view, and I could go an light it up, but I have judged that that would not be a good thing to do, and it is better, much better that it just sits there, because then I win. Regards, TAR

Barfbag, I understand the value of quitting anyway that works. And I think your method is good, and I understand the workable aspects of the plan. But, and its a bif but, nicotine is insidious. It is easy to underestimate its draw, because it is so powerful and simple a way to "feel good" to feel right. It sings its siren song to us former smokers, and it is important, I think, to not pretend either that you don't want a cigarette, or that you can have a cigarette and then not want another one. In this, Phi's method is bottom line, the best method, to stay a non-smoker. Make smoking not an option. My additional suggestion to Phi's answer is to extend the ban to nicotine itself, as it is the nicotine that is the drug you are craving, at first, and yearning for at second, and missing at third. If you do not remain alert and onguard against the insidious nature of the nicotine, you are likely to collapse to some form of rationalization, that will allow you to yield to the temptation, and thusly make it more possible to yield, again and again, until you are chain smoking, like you said. On the other hand, if your goal is to find natural ways to get endorphines to pleasure your brain, you can just cut nicotine, right out of the equation and just put it on the bad list, of those things you should not do for obvious reasons. If you look at the list of addictive substances, nicotine is right up there, near the top. If you are among the 9 out of 10 people that would want to have nicotine again, after having it once, which you have a 9 out of 10 chance of being, then its best to not have the nicotine in the first place, because you are going to want a repeat performance. Saying "its alright to cheat" plays right into nicotine's hands. It actually is not a very good idea, if being free of nicotine, is your goal. It hurts four ways. It hurts the people you love twice, once because of the deception, and twice, because of the you, you are taking from them in terms of shortening your life and squandering your income. And it hurts you twice, once because you are not being honest with yourself, and twice because you are not taking care of yourself. I stay away from pain killers and only have had them by perscription and the few times I have had them, I have not finished the bottle, and only take them, if I can not bear the pain. I have never had heroin and never will, because I know from what I have been told that it is easy to get "hooked" on it, so I DONT DO IT. I was a big drinker in my youth, and in the Army, and gave it up in Germany, with all that good beer around, after blacking out a few times, considering the expense, the brain cells that I was killing and the possibilty of accident and loss of license, and the fact that I was going for a promotion, and I should be a role model for my subordinates, which being a drinker would not make me. I had wine at my wedding, a farewell drink at a dinner in Japan, and a half a Yeagermeister at conference once, but have put alchohol in the "do not indulge" category. If you look at the list of addictive subtances you will find a few on there that are socially acceptable, like smoking and drinking, but most are really insidious nightmares, that take money, and mind and sense and freedom away from a person. Most leave people messed up mentally, broke, lonely and in poor health physically. So sure, anything you can handle, that the people around you can handle, that makes you feel good, makes you feel right, is acceptable. But the stuff, where there is reason to say no, there is reason to say no. The fact that the stuff itself is telling you to say yes, is even MORE of a reason to say no to it. I doubt my method would work for people addicted to oxycodine or crack cocaine or meth...but hypothethically it might. Its a given that you are going to want to take the stuff, but what if, that first hour on Saturday morning, you put the stuff right within your reach and when your body and mind say to reach for it, you say 'dont reach for it" . If its in your hand, you say "put it down". if its in your mouth, spit it out, put it in the ashtray or in a paper towel and let it burn, let it waste, let it not get in you. For an hour, and notice you don't die, you don't fall apart, nothing bad happens at all, you just don't get the euphoria the drug will give you. But what you do get is an exact understanding of what your relationship with the drug is, and the rest is between you and you. Regards, TAR Never had cocaine or meth or crack or heroine or the powerful pain killers that so many of our youth have gotten addicted to, and switched to the less expensive heroin, but I am really really concerned about the epidemic of meth in W.VA. and the recent epidemic of heroin among the youth of suburban NJ. The W.VA thing has broken a family very close to me. The NJ thing might affect my friends and neighbors, workmates and schools, and maybe someone in my family. Addiction is an obvious potential problem for people. Probably best to solve the thing from the inside out, not the outside in. The illegality of the stuff is only because its so dangerous, not because the people that get hooked are bad. My theory here, is that it is better to help a person find the strength to put the stuff down, than to tell a person they shouldn't do the thing. Its obvious that the decision to say no to the gratification, is up to the person that is going to go without the gratification. The taker is the only person in the world that can say "don't reach for it", "don't put it in your mouth", "don't light it", "don't inhale", "put it in the ashtray, and let it burn". And so what if you have a few shakes and shudders and your body and mind tell you you have to have the stuff. You really don't have to have it. You can live without it, you can feel good without it. Just give yourself a chance to find out what its like to live without the stuff. Things that taste good still will taste good, things that look beautiful will still look beautiful, things that smell good will still smell good, stuff the feels good against your skin, will still feel good against your skin. Completing stuff, winning stuff, straightening stuff, fixing stuff, solving stuff, will still all feel good and right to do. Hugs and kisses will still be sweet and enjoyable. I promise.

Phi, Nice. Your suggestion made me feel good twice. Once, as I remembered a family trip to the Yucatan, and once as I laughed internally at the fact that I don't have a smartphone. (at work, I enjoy taking out my stone age apparatus and pretending to pass it to someone next to me, asking them to show me how to put the business app being presented on the thing). Barfbag, I think that having to smoke regularly, once you smoke later in the day, is an important thing for the "cheater" to remember. Knowing that that will probably happen, once you get your nicotine level back up to post cigarette levels is a good reason not to smoke the cigarette. I found that knowledge was my best friend. That knowledge of my nicotine level being low, reducing the pull or draw of the nicotine in the first place, to the level that you could laugh at, and ignore...and everything would be fine. When you cheated, you had to refight the strong pull situation immediately afterward, as your body was asking to maintain the level (causing a reach and a lightup and an inhale, quite outside your desired condition of being a non-smoker). To this aspect, I would have to agree with your "don't throw in the towel" aspect. Regardless of who knows you cheated or not, the next morning you will be in perfect condition, at a low level of nicotine to go without it, again. If there is anything I am trying to suggest, with my method, it is to give yourself some time to be both a smoker and a non-smoker, so you can notice the almost indistinquishable difference between nicotine induced release of endorphines, and the "imagine sitting on the beach" induced release of endorphines. Once in this position for a week or a month, allowing yourself to experience life at low levels of nicotine, and at high levels of nicotine, not smoking is just as nice a condition to be in as smoking, and then you can easily make the choice to exist in the non-smoking mode, by just not buying another pack, or "borrowing" one from a friend. Then, once in this mode, engage Phi's "not an option" mindset, to avoid getting yourself back into a high nicotine level situation. Was at the pharmacy yesterday looking at the "smoking cessasion" area, right near the waiting area. Nicotine Patches, Nicotine Gum, Nicotine lozengers, and trial doses in this and that form. Really? And what I'm thinking is to just cut out the middleman, and work your way directly toward nicotine cessation. If you quit nicotine, smoking makes no sense anyway. So don't think you are going half way by switching to a different way of getting nicotine. You have not gotten away from nicotine at all. Just found a less smelly way to get it. And you are still paying for the habit. Quit the habit. Give yourself that first hour in the morning nicotine free, to see where you stand, with nicotine. The rest is betweeen you, and you. Regards, TAR

I think there is a huge area of misunderstanding possible, when it comes to "problems". Turing machines and I have never gotton along. I do not ever get the definiton, because they talk as if the machine is doing some sort of problem solving, when the person has just set it up, with all the right definitions and codes and algorithms so that the thing can be "solved". You mention a huge class of problems that turing machines can solve. I suppose the best defintion for that huge class of problems would be that type of problem that turing machines can solve. Regardless, the program still has to be written, the code still has to be designed. The language the machine is going to operate in needs to be known, and the rules upon which the problem will be worded and the solution understood need to be understood. Othewise, you have the monkeys typing out Shakespear situation. They probably can not, and nobody would be there to read it and verify its accuracy anyway, so its a mute point, even if it was possible, which it is not. A machine designed by a human, is endowed with human logic to begin with. It already has a purpose, it already has a goal, it already has a problem that it is solving by its very existence. Perhaps a thought for another thread, perhaps exactly the issue for this one, but I have a tendency to consider the world analogue in nature. Others have a tendency to view it as digital...or a Turing machine, or a simple Ideal Gas Equation. I tend to think of a human being as a focus point, a self, a consciousness that is in and of the world, and has therefore senses and experiences and memories "of and about" the place. Others tend to think that somehow we have gotten it wrong, and are not properly equipped to handle the experience. Really? Like thinking it is impossible to move, and therefore movement is an illusion, is some sort of useful and remarkable idea.

MD65536, But although I did not on purpose propose an incorrect definition so that I could prove it false, such an activity is probably not distant from providing a correct defintion, so you can prove it true. What started this whole discussion, even before this thread, was the fact that I never thought the warrior and the tortoise "problem" was a problem. I never saw the issue. It was just a trick of words, of looking at what would happen to one infinity and inappropriately saying that should have any bearing on another. The warrior would certainly overtake the tortoise, so the question is a non question, the problem has been setup incorrectly, and the "problem" is to figure out where the mistake has been made. It is a GIVEN to me that a mistake has been made or some attribute of reality has been overlooked, because the warrior absolutely overtakes the tortoise. Whether the thing was solved once or a million times makes no difference. Whether I "understand" what makes it a non problem is immaterial. Whether it has been solved or not, 5000 years ago, today or tomorrow, makes no difference. Its not a problem to begin with. Finding a way to solve it, convoluted or simple, machine wise or human wise, language or math, makes no difference if its a strawman argument to begin with. Regards, TAR

barfbag, I think it worked because you learned you could live without the nicotine. One component, that I think is crucial, is that quiting is between you and you. What your friends think, or your family matters completely, but the actual quitting is between you and you. You have to know, that it is alright, not to smoke, that life will still be fine, without the automatic endorphine high that the nicotine will provide. Its sort of like sideways delayed gratification. You get gratified by not allowing yourself to get gratified in the old easy way, and you find out you can get equally gratified or almost as equally gratified, by doing other less problematic things. And then you can easily ignore that "almost" part, because the difference between a nicotine induced release of endorphines and "all the other ways" induced release of endorphines is virtually indistinquishable. As you found out when you didn't sneak out, and instead spent that half hour doing something enjoyable with your family...you "felt" just as good, if not better, than had you gone and smoked one behind the barn. And the "not having to sneak" anymore added some "good feeling" to replace any that the nicotine might have had to offer. Besides, they knew you were sneaking off to smoke. They could smell it in your hair. Before I started my week of tapering I had said to a woman that was usually on the same nicotine cycle as me at work, that I was thinking of stopping, and she said "yeah right". She said if I stopped, she would stop, as her young kids were always on her to stop. During the tapering week I would still go outside, on schedule, but would not smoke. Smoked one I borrowed from another pal around 4 the first day, and smoke on the way home. During the week the important part of the day was the morning. To not smoke that morning cigarette, and to experience life, without the nicotine. I had not yet disallowed the smoking, I would just see what it was like to do without it. I would smoke regularly once I smoked in any given day, but start the next day, not smoking. With no promises, no lies, no challenge, no disappointment, no victory or loss one way or the other. Just found when I bought my "last pack" on Friday, that the concept of it being my last pack was not disturbing. I smoked it and was done...except I found another pack in a jacket, and thought I would stop after I smoked that one up. I finished that pack around 7pm on a Sunday in Early April, and buying another pack is now just not on the agenda. If I bought another pack it would disappoint me, and my daughter and my wife (who still smokes) would not have me as an inspiration to quit, and all the people at work who are proud of me for quitting (including the woman with the kids) would not think as highly of me and "my strength", and I would not be able to report here every week, that the quitting can be successfully achieved...but those things are not reason enough to not smoke. People get disappointed in me all the time, for one reason or another, they would forgive and forget, should I start smoking again. The woman with the kids has not stopped, and I think she had planned to, on her son's birthday, which may have passed, but she is not responsible to me to stop or not. I put no pressure on her, except the pressure of seeing me come out the smoking door and go back in the front door, and not light up. More of an example than an admonishment. She has stopped twice before, once with each pregnancy. She could and probably will stop again, when she wants to. As for my reasons to not light up again, the big one, is I want to breath. Deeply and normally satisfyingly, by myself, for a very long time...until the end of my life. I was getting hints that my smoking might keep me from being able to do that, later on, and I did not like the prospect of sitting somewhere, dying, because I couldn't get enough oxygen into me, knowing that I inflicted the wound on myself, destroyed my own lungs, and could have NOT done such a thing, by simply not taking the nicotine route, to endorphine release. So I look for the 100 other ways to get endorphine released, that a free and natural, cost very little and don't stink and mess up your lungs. Sounds like a win, win. Regards, TAR

Studiot, The circle you drew is only one aspect of an infinite number line. The real number line goes forever in both directions and is as well infinitely divisable. The circle is not infinite in length, its circumference is Pi D. A finite length. If you can not decide on where to start the measurement (first element) and where to end it (same element) then you can be flakey about the infinite choices you have to choose from, but the length is finite, as soon as you choose a unit. The circle is a finite number of those units long. So it is not a good representative of both the first and last member of an infinite set. If you say it is, then anything is. A coastline or a comb or the space between your ears, can be divided imaginarily into any number of slices you desire. An infinite amount. But we are talking about the real number line here. That one that both goes forever in both directions, and has infinite divisions possible of any unit you wish to mark it off with. You can not give be the highest number of units possible, nor can you give me the reciprocal of that number. Because both the length of the line, in units, and the reciprocal of that length as in 1 divided by infinity, are not defined. They therefore cannot either be counted or not counted, depending on a whim or a device or a definition. If something is infinitely large, or infinitely small, you can't find anything larger or smaller than that, cause the last member is not defined. If it was defined, it would be a finite number, which one could then decide was comparable with another number. But since the infinite number line, has no end, and no arbitrary smallest unit, all infinities are exactly like each other, in that the quantity denoted is either infinitely large, or infinitely small. Interesting that Cantor actually argued against infinitesimals, and according to the Wiki article on him was discredited with an erroneous proof against them. So, although I did not ask a direct question in the OP, my question is can we solve paradoxes by talking them through, and seeing where the inappropriate grain size or perspective shift is being made? Or the inappropiate assumption, or the slight of hand switch, or the failure to carry an analogy consistently through. Regards, TAR And yes T is for Thomas A is for Ammon R is for Roth

Thanks iNow, Think I'll go with that. I've tapered off in a week and not entertained any moments of weakness since. Guess I really don't need to report every week, as the quitting is already done. The modified tapering method I used is 100% effective (with a little help from my friends.) Thanks everybody. And if anybody here is trying to quit, or would like to try and quit. Just don't smoke any more. It won't kill you, to stop. Practice living without nicotine for a few hours here and there, and before you know it, you will be able to just not light one up...and it will be OK. I promise. (As long as you take Phi's advice and just stick it in the "not an option" category.) Regards, TAR Just say no to nicotine.

Spyman, Still not smoking, 9 weeks now. But would like to, in an effort to "keep it real" report an other bout of the "mourning the loss", you were talking about. Over the last week, I have on occasion entertained the thought, or lived with the realization, that I will never be able to enjoy a cigarette again. Loss, in the sense of "if your house got washed away in a flood" you could never go into your favorite room, and sit in your favorite chair again, because its gone. What makes quitting difficult for me, is overcoming this obsticle. Not because I can not handle the loss, but because I am the one that has instituted the loss. I had the wrecker destroy my favorite place...so to speak. And they really didn't destroy it, they just changed the street signs so I could not get to the house without going the wrong way on a one way street. If I wanted to, I could still get to my favorite room, and nobody would stop me. I mention this, not to discourage anyone, but to reenforce what you said before, about expecting some continuing battles on certain levels at certain times. And to remind myself, and anybody else that might be in the same boat, that one way street signs are only signs and can be ignored if you want to. But the signs are there for a reason, and one should not disobey them. Could cause an accident, or a death. Regards, TAR

Acme, OK, granted, I am a jack of all trades, master of none, but I am a pretty good troubleshooter. I had a joke saying when we were faced with a tough problem, "it's got to be something." It was a joke, but it always turned out to be true. If something does not work as it was designed to work, then something is wrong. Sometimes with the design, sometimes with the material, sometimes something just fails, or breaks or gets loose or comes up missing. In the case of a paradox, something is wrong, and "its got to be something" that is causing the problem. And not everyone agreed with everyone that ever came up with a good idea. Studiot, Well sure, I would like to know the last member of an infinite set. There is however not a way you could deliver such a thing. The smallest number you could show me could be halved and the largest could be doubled. There was a commerical where the kid was challenged to come up with a number bigger than infinity and the answer was infinity plus one, which was trumped by infinity times infinity. We played that game in math class and the teacher just told us we had the concept wrong, and infinity was not a number, it was a concept. This, we were taught many years after Cantor and aleph and null and all. Set theory and matching stuff up, pairing things off suffers in my imagination from inappropriate grain size shifting. Considering an infinite set an object you can hold in your mind and manipulate and make judgements about. If you say you can do this, and I can't, I will simply call your method inappropriate to the case. You can not provide me with the final member of an infinite set. If you could, it would not be an infinite set. It would be a finite set, with a first, a bunch of others, and a final member. Regards, TAR

Acme, But not having a degree, does not precude one from thinking about stuff. I was following along with Cantor in an attempt to understand how the term cardinality was being used, what was an aleph and what was a null and so on, but there were aspects of pairing up numbers in one set an another, where an understanding of the "complete" set was required. Any infinite quanity is by definition incomplete, as you can not arrive at the last member of the set...ever. If we are to be playing games with infinite sets, concieving of what set of numbers has a companion in the other set, whether there are any extras or duplicates and whether the match is covered in one direction and not in the other, and so on, it would be first required for one to understand the second diagonal argument. As that I thought I understood it, but did not think it was correctly identifying "extra" unaccounted for numbers, the whole argument was not valid in my estimation. I have to get that part squared away, before I can go to more complicated combinations of metamath he is dealing in pretending I understand what aspect of infinity Cantor is suggesting is sizable, when I don;t see it Can't we just talk about the idea of infinity...as in what is its definition, what does it mean to you, without concentrating on the fact that I have not read the book someone wrote. What is interesting to me, or problematic for me, is trying to understand when it is that someone is sufficiently able to write a book. Any tom dick or harry can write a book. And even the best, most well read most agreed upon book is subject to error and the ideas within, open for discussion. The main thought I wished to address with this thread, was that a paradox is usually self induced, as that the universe is not prone to contradicting itself. If one is going merrily along, matching assumptions up with evidence and basing ones next assumptions on what has already been found to work, then everything moves along nicely. If carrying forward two lines of thought, results in a conflict, or impossibility, then something is wrong. Maybe with one idea, maybe with the other, or maybe they are both good, but some aspect or another has not been completely thought out, or tested out, and needs some work. Or maybe the analogy just does not hold all the way through, from concept to reality. Some adjustment needs to be made, some back checking, as to where could we have gone wrong, what is it we need to redefine or look at another way, inorder to have the thing work, with no contradictions or impossible components being required inorder to make it work. You don't like the way I argue. Or perhaps you don't like that I argue, without bringing any quotes to the discussion. But that does not matter. What matters more is if you think I am wrong or right about which parts of my arguments, or if you know the answer to a question I have. Prometheus offered a link, suggesting it gave a good account of our understanding of infinity, which would help in our understanding of the ancient greek paradoxes. I am trying to talk about "our understanding" to get a handle on what that understanding is, and how it is different, better or worse than an understanding we used to have that was somehow defective. Regards, TAR

Acme, I acknowledge that others, many others have and have had superior intellect to mine. I do not say in the least that the ideas and concepts related to the size of a particular infinite set are not possible to have. It was taught to me in school that there were more real numbers, than integers yet they were both infinite in quantity. i, back then, imagined the number line, as containing all the numbers. Every number was on the line, even irrationals and trancendentals had their place on the line. Infinity to me, was the fact that not only did the line extend forever in both directions, but there was no limit to the precision with which you could divide and label any choosen interval on the line. Given the decimal system as a guide, one could easily divide any interval into 10 equal slices by adding a digit. Since the line was infinite, in both scope and precision, there was an infinite number of divisions available between any two numbers. But with this scheme of understanding infinity, the "new" numbers that Cantor said he was making with the second diagonal scheme, were already accounted for. They were not new. Just numbers already on the line in a different place. They were not "new" or additional numbers that one could then consider part of a larger set than the original, infinite one. My question was on the arbitrary nature of the second diagonal of Cantor. I was not suggesting it was impossible for him to think the thing. I was questioning if it made sense and worked out. Regards, TAR Perhaps a topic for another thread but within the set of humans that have been alive in the last 100 years there are subsets such as these. 1. Persons who cannot understand the concept. 2. Persons who can understand the concept but have not yet learned the thing or had the insights required. 3. Persons who can understand the concept, but find it lacking in some regard (purpose, intent, assumptions, rigor, application, scope, meaning, direction, or whatever.) 4. Persons who not only can, but do understand the concepts and agree with them as peers of concept describer. 5. Persons who don't understand the concepts, but agree with them anyway, because they were stated by persons of greater intellect and reviewed by persons of greater intellect and are acceptable on the basis of "trust the experts". I think I am personally in the 2 category, with desires to be in the 4 category, but too lazy and ilinformed to get there. But that does not negate my question. Nor require that my question is not deserving of an answer, simply because I do not see it Cantor's way. There are some basic "hard" questions, related to Zeno, and Hilbert, and infinity and existence and such, that if "we" truely knew the answers to, "we" would not be having this discussion. So, in the context of this thread, I think a direct comment on my "problem" with the second diagonal example, would be better than a link, suggesting that I will find the answer to my question if I read and understood what I read. My question came "while" I was reading a previous link. Regards, TAR

Prometheus, Well thanks for the link. I got a little bogged down with some of the latter more complicated thoughts of Cantor, because I lost him on the second diagonal. I did not agree that the numbers he created by changing the digits found on the diagonal of the first countable list were "new" numbers. They were merely numbers now put out of order from the orignal count. They still could have been in the list already, and therefore not a "new" number. Calling it a new number is implying it had not already been counted, and by my thinking, the "new' number was in the list already in some other position in the count, and thusly by making the transfer of digits, down the whole list, you wind up with exactly the same number of numbers, but you have succeeded only in pairing each up with a new counting number. Breaking its match with the first counting number you associated it with by saying "OK, now this "old" number, which was before in position 6,456,399,049 is now in position 4 in the count. You have not created any "new" number, as that particular sequence of digits was already accounted for. So, permit me to introduce another aspect to this controversy. We cannot say that we have a new and better understanding of numbers, or of infinity, based on the understanding that only a subset of "we" might have. It does not make sense to me that one infinity can be larger than another, because infinity already is at the max of quantity. You cannot beat that, you cannot exceed that, because if you could, your first claim of being at the maximum possible count, would have been incorrect. Regards, TAR Reminds me of a joke/story we used to tell about our plumber/handyman, a Pennsylvania Dutch fellow who proudly exlpained to us how he had helped his son with his math, by explaining infinity to him. "You take a straight line, and you draw it on the page and imagine it still going off the page, out the door, over the field, down the hill, past Sieselsville and keep going and going...all the way to Topton." (a town about 12 miles away)

An interesting "other" situation just occurred to me, that might be helpful, in two ways, in unraveling this "mystery". One in that it deals directly with timing, and two it deals with how a human gets a word out of their mouth. Studdering. I do not know much about studdering, but I remember reading an article in "Discover" that was discussing the "timing" aspect of forming a word, and it is difficult for a studderer to "practice" not studdering...(and this is paraphrasing just what I took from an article read many many months ago, but) because by the time you have done all that it has caused you to studder. So if you can not say a word until after you have planned the whole thing out, in terms of the shape of your mouth and position of your tounge, and the amount of air you are going to force through the chamber and so on, there is no chance that you are going to be able to listen to what you are saying "at the same time". It would be easy to logically consider this situation interms of what has to happen inorder for speech to occur, and through Zeno type reduction ad absurbium decide that it is therefore impossible to utter a clear word. Impossible to think, impossible to formulate a thought, transform the thought to sound, and create the sound, "all at the same time". Therefore speech is impossible. Except we know it is not impossible, and we type out sentences at the exact same time as we are thinking the thoughts. Perhaps we think the thought first and then think about how to put it into words, and then consider how to type it and then type it, but if we were not thinking the thought, while we were typing it, how would the keys be getting pressed in the right order? There is still a chicken and egg type conundrum one faces when logically trying to sort the thing out, where one just can not throw up their hands and say it is impossible, when it so obviously must have a way in which it gets done, and the "timing" aspect that is built into a human moment is a VERY important consideration when attempting to sort the thing out. We have a predictive motor simulator, that "practices" combinations of motor neuron firingings before we actually send the signals. We have "learned" what combinations and timing of said motor nuerons result in what motions, and hence we can walk and catch a moving ball and such, because we unconsiously or subconsciously predict and plan these things out "as" we are doing them. Thus when living in a moment we probably give the moment its whole duration of 2 1/2 seconds to "be" all together considered the same time. So in Zeno, when we hear a phase like "by the time the warrior gets to the tortoise's postion, the tortoise would have moved on" we have given the tortoise a moment to have moved on, that is in actuality a moment already spent by the warrior, and a moment that has already been spent by the tortoise, and we should not give the tortoise "another" moment to spend moving forward. So moment size is crucial in determining what position change can occur within the moment, and we can't be giving the warrior different size moments than the tortoise. We can only be allowing the tortoise to move 1/10 the distance the warrior does, in any given same size moment. So "by the time" the warrior moves 200 yrds, the tortoise would have moved 20 yds, the tortoise would be 120 yds from the starting line, and the warrior would be 200 yds from the starting point, and the warrior would have overtaken the tortoise. You would not even need calculus as an algebra equation would have the warrior overtaking the tortoise. Regards, TAR -funny- firingings-guess there is such thing as finger studder. Fuddering?

Studiot, What happens on the rest of it, is the idea I was trying to loosen up, or let loose, in regards to the OP analogies. I agree with MD65536 that the analogies are not completely right and considering the gears might work, but the spots on the Earth do no completely mirror the "incorrect" setup. The problematic setup, the one that has the warrior never overtaking the tortoise, is not exactly like the two spots on the Earth that will always be the same distance from each other, regardless of the fact that one is moving faster than the other, but attempting to match up such an analogy with the original setup gives one the opportunity to evaluate which and what one is holding constant, and which and what one is allowing to proceed. This is important in considering what functions you are entertaining. Which quanties are increasing or decreasing at what rates, and to what limits. In a video that was posted at some point on one recent thread or another recently related to the Zeno Paradox, a young man was describing a mathematical "proof" of something. He was doing rather well, and came to the rub and then made a switch that I did not follow. Made a switch that was not forced or required or necessary by the lead up. Made a switch that required one already understood the nature of time and space and the overtaking principles under discussion. Like a bait and switch operation. Like he didn't prove a darn thing we didn't already accept as obvious. As if he said "see the piece of candy is getting closer and closer to your mouth as I move it closer and closer to your mouth, but it will not actually ever get into your mouth, unless I decide to give it to you". "There, you can have it now." Regards, TAR

MD65536, I was not, and am not attempting to make the question a non question. It is a good question but deals primarily with a human's understanding of space and time, and as I understand Kant, these things are basic, a priori understandings that we have a grasp of, with no explaination required or possible. As in "what is time?"...well its that thing we all know as past present and future...you know...time. or "What is space"...well its that place where everything is located. Neither space or time are thusly made up of "sub" understandings. They are instead the basic understandings that have no component understandings that one needs to cobble together to reach a composite understanding of some sort. They are instead the starting points upon which all other understandings and judgements and categories of the predicates that we can associate with objects, are built. Everything we can say about an object in general, first relies on the fact that you know what space and time are, and I know what space and time are and we can say something about the way space and time are put together, because of this common a priori understanding. Calculus deals exactly with space and time. So when it comes to describing movement, how it is possible, what it is and what we mean by speed and distance and acceleration, and the change in position of something over time, calculus provides the answers to Zeno's questions. And the convergence understandings take care of the different "kinds" of infinities that Studiot is hinting at. But this can also be handled linquistically because the infinitely many, infinitely small divisions of time, that one must proceed through, to get to the point where the warrior overtakes the tortoise, or the motion starts, or the arrow moves, are actually over in just a few moments, not an infinite amount of moments. The whole infinite set of steps is completed in 10 or 15 seconds, and the warrior is past the tortoise, and the arrow has left the bow, traveled through the air and is sticking in the target. Some part of the debate that caused Zeno to come up with these logical problems had to do with trying to prove the world was one thing, or the world was several. Philosophical and religious differences of opinion on these types of questions are still evident, in the world, and on this board. Immortal, a banned former member here was very much an "illusion" proponent, someone who would say, that there is no movement, that everything is one, and everything is an emination from the one. So the question has been put to me here to show where Zeno's logic is wrong, not that it is wrong. We already know the tortoise will be overtaken. The puzzlement, is how is that possible, when all these infinite divisions of time must be transversed, prior the overtaking moment. Was reading today the Wiki article on Zeno's Paradoxes. It said all the things we are talking about here. It, on the whole is already solved, already understood. Each of the differing explainations of what are the puzzling and meaningfu parts that have been recently expressed on this thread are already in the article. But, the clincher for me, the thing that "proves" what everybody is saying, is that we already know what time and space is and know exactly what can and does happen when the two get together. And therefore anything that would suggest that what is perfectly possible and understandable is impossible, must be sight of hand, and someone has switched the cup the pea is under without noticing the switch. Studiot and I are rather sure all the infinite steps will be completed in a short period of time, because each successive step is a tinier and tinier slice of time, so tiny that you can pack an infinite number of the slices in a very brief amount of time...so the warrior can overtake the tortoise as soon as that brief moment has passed. Regards, TAR

MD65536, I like your breakdown of what it is that I am attempting to do, and not suceeding in doing. There is an "angle" there, that you describe, that of being both puzzling and meaningful, that may be in play here, on a couple of levels. One, why the difference of opinion can cause people distress, as is evidenced by the heat of the debate on a deep level, that seems to be engendered when one fellow/gal takes away, or attempts to take away the other's meaningful puzzlement. And two, in regards, to the nature of a proof or a solution, the question or problem first has to be commonly understood, as to which portion or piece of the situation is the puzzling, and meaningful part. Breaks down on one level to whether or not one "gets the joke". And I think, in the case of Zeno there are different levels involved in the joke. Different levels of puzzlement, and different levels of meaning. Was thinking today about meaning and double meaning and triple meaning, in regards, to this discussion, and was considering how a simple statement like "I went in and back out" can have many different meanings and might have two or three meanings appriopriately understood between two parties at the same time. That is, could be taken to mean you are referring to the room, or the fray, or the job or have some sexual connotation where communication of which and what aspects of meaning are being expressed and understood depend upon context and the next sentence, nods and winks and looks and whether or not the phrasing and word choice and order and such "work" on both or all levels being engaged on. Perhaps the Greek wine, as well has something to do with this discussion. I gave up drinking back when I was in the Army in Germany, during the Iranian crisis...so many years ago. I do not get high, or drunk, and gave up a life-long nicotine addiction two months ago. The only mind altering drug I use now is caffine. In terms of activation theory, I pretty much have to solve the puzzles that are puzzling and meaningful to me. I already "did" the convergence one. I "got it" with the one where the ideal ball bounces halfway up from the drop hieght, and then halfway up from the halfway point, and bounces an infinite number of times, before it comes to rest in a finite period of time. I get that joke. I see how that mathematically works out. The puzzlement it causes me is that I know the actual count of bounces, in a real (not ideal) ball cannot actually be infinity, so I consider what constraints reality would put on the actual test or experiment, that would create an actual finite count, should the test be made with a hypothetical, "actual" ball. That is, there are some other real contraints one can work with, like planck's length and one's definition of a bounce, that would eliminate the requirement or possibility of a next bounce, and thus end the count, before infinity is reached. So, perhaps, in terms of me not yet presenting any solution to the puzzling and meaningful aspects of the paradox in question, perhaps it would be good, at this point, for someone who is puzzled by some aspect of the paradox to state the question or problem or puzzlement, in either words or symbols or both, and I will attempt to answer the puzzlement in words or symbols or both. I have this feeling that there is some aspect of this discussion that is similar to a "strawman" argument, in that a question is posed that is easy to knock down, just for the fun of knocking the thing down. In this regard, we already know the warrior is going to overtake the tortoise, so "duh", you think we might be able to construct a proof to show how that can happen? Regards, TAR But then again, I already presented my solution in the OP. You have to put two gears on a rod and figure that, to properly model the tortoise and the warrior. You can't be putting two dots on a ball and turn the ball expecting to get the one dot to overtake the other. As to reality being an illusion, it can not be an illusion, because then it would have to be somebody's illusion, which would require there to be somebody real to have the illusion. So one can just cut to the chase and be convinced that reality is actual by virtue of there being at least one, but rather evidently 8 billion instances of real entities that can experience the place. This places both the place and the experiencer in the category of "existing".

md65536, Shunning the math is only required in the case where the math comes up with the wrong answer. Where the math says the warrior overtakes the tortoise, then the math has a good chance of not being shunned, but used to describe the situation correctly. There are some logical binds or situations one can get into, that one can think their way out of. When one suceeds in thinking their way out of the bind, so that everything adds up and works and the right analogies and transforms have been applied to the right peices at the right time so that the model reflects the reality, then the problem is solved, and one can say "oh, that makes sense, that is how it works." Nice. I get it. In your post you say that the word never is used in two senses, one in a time duration sense and one in a number of iterations sense. Exactly my point about sorting out where the concepts are linking the warrior and the tortoise and where the math locks a situation in, and where the math is inappropriately applied. I still remember my general thinking in a math class in high school, where the paradox was presented. I was imagining the progression of the warrior getting closer and closer to the position of the tortoise, and every time the warrior took a warrior step the tortoise was not yet completed taking his/her slower and shorter(in distance) tortoise step. It was not many warrior steps, until the warrior had tranversed the intitial head start, and was now negating several tortoise steps with every warrior step, up until the warrior was indeed within a single step of the tortoise, at which point his next step, would place his foot ahead of the spot on the ground that the tortoise's next step was heading. Once this particular warrior step was completed, the warrior would have overtaken the tortoise, regardless of the fact that the tortoise was continually advancing during the overtaking step. So I saw no paradox. Never did. Never will. Because there is no paradox there. The paradox is only in one's mind, if they make a mistake in what is standing for what. Regards, TAR

kristalris. There are a number of paradoxes that I prefer to look at, from a lingual, sensible solution point of view. If something does not add up, or does not work or creates a logical impossibility or contradiction then its a clue to me, that there is work to be done, in rephrasing the question. Putting the two gears on the rod, so to speak, and seeing how that analogy or model works out. In my OP I talked about a situation where the faster moving thing would never overtake the slower moving thing, as that they were "locked" into their relative positions, by the setup of the problem. Any movement of the one, would be exactly linked to the movement of the other and any progress one made was matched proportionately to the progress of the other. In the Zeno paradox such terms as "by the time...the other would have". These words link the two together in such a way, as they can not independantly proceed as a tortoise and a warrior in the real world, would, in an independant fashion, normally proceed. The words of the setup, precude one from considering actual things, like where would the warrior be after running at warrior speed after 1 minute and where would the tortoise be, after 1 min of traveling from his/her "100 meter" head start position at tortoise speed. If the bind up in the situation happens in one's head, whether it is on an analogy level, or a logical level or a mathematical modeling level, then the problem is in ones head, and not on the race track. The useful models that we make in our heads, whether they are lingual or done with symbolic logic or done with mathematical expressions, are, on a base level, only useful, if they have an analogy in reality. If they do not have an analogy in reality, then they are imaginary, and don't require actually fitting or working in reality, as is the case with actual stuff, that operates in a cause and effect, positional manner. As Kant would have said, in regards to his table of Judgements, which cover everything that one can think about an object in general, which equates to everything that can be said about an object in general and hence correlates to his "categories", our judgements are based on our two a priori intuitions, that of space and that of time. Thusly our perception of the world, our judgments of the world and what we can say in general about any object is inherently a "positional" thing. The very neuron firings upon which our perception and judgements and thoughts and language are based, have to happen at a particular place, over time. The chemical environment and connections and pathways of perception and memory and thought being real, actual situations and events that are occuring in the real world in possible, fitting ways, must "make sense" and not be impossible. So we have a solid basis, upon which to build a lingual understanding of a situation. And any symbols that we use, or analogies that we engage, are already sensible, to some degree or another, in that they both mirror reality, and are composed of real positional events and configurations happening over time. We, on a certain level, must already have a feeling for the function and the relationship, the quantity and the quality and the mode, before we write the equation that expresses it. So the meaning comes prior or together with the symbol that stands for the thing. And a lingual solution is just as good and solid as the mathematical one that symbolizes said meaning. And if the meaning is impossible, you can say that it is impossible, in words or symbols, but if the thing is possible, there are probably words we can find to say something understandable about it. And if the warrior will overtake the tortoise, then no symbol system that expresses an inability of the warrior to overtake the tortoise, is correctly put together, or signifying the correct aspects of the situation. And one should rightly rethink the situation and say something meaningful and understandable about the situation, and not get hung up on words or symbols that don't fit together right. Regards, TAR

iNow, Listened to the Stephan Cave thing. Suggested that the four irrational, biased ideas we have, the four stories we tell ourselves when reminded of the fact that we are going to die, are the elixir, the resurrection, the soul and the legacy. Then philosophically suggests that we never experience death, and should not "fear" the void, as that we will not be alive to notice it. Then suggests that ones life is like a book or a story, with a beginning and an end and the thing is, to have a "good story" inbetween. My personal philosophy is similar, as I have mentioned that I figure death will be, for me, much as what it was like, before I was born. And I figure that the goal of life is to live and experience the world and make it possible for others to do the same. But I am not so sure of what the benefit of thinking of these four stories as bias, is. That is, if these four stories are "incorrect", then what would a "good story" be, and who would read it, and who would be the judge? An addendum to my philosphy is that one is remembered, and leaves their "works" in reality. This is the "legacy" story, that Stephan Cave considers a bias. It is not irrational and it is not false, it is actual. We all benefit from the works of dead people, as others that will live in the future will benefit from any good work of ours. We really do achieve something when we die for our country...yet Cave believes that Nationalism is a biased story. I am not quite jiving this understanding of his, with reality. That we would want to be immortal in one way or another, he figures is natural but not rational. What of the ways in which one actually effects life or the world in ways that are not immediately forgotten? Are these not real, and therefore not irrational ways of achieving immortality? A similar argument, toward being "real" can be made for one's genes. That a little piece of Lucy exists in each of us, makes her thusly immortal, and gives rationality and realism to the worship of ones ancestors, and not falseness to the belief that your own "essence" will be felt in the world, even after your death. Plus, you know as well as I do, that many scientists "look" for ways to extend life, and consider what it would take to keep the brain going indefinitely, and the fact that the species has figured a way to get that job done, through language and schools and stories, that give the thoughts of the parents to the children has actually given us a way to carry our spirit, or soul forward. Last week, my wife's cousin's daughter had a baby daughter. Last week my sister's husband's brother died. What lessons and love the world has gained from the life of the one will be gifted to the other. A death and a birth, not completely separate from each other. Something like an actual resurrection. So, I don't think the four stories are only bias and falseness. I think they all have some validity, in metaphorical ways, that mirror actual ways that things happen. Which makes them all four, "good" stories. Regards, TAR

Well, At my record amount of time "not smoking". Think I did this once before. Several other attempts were about a month long. But this time, is different. It is not a challenge to see how long I can go, without smoking. It is a challenge to see how to live without smoking at all. It has been the toughest, just recently, some mental problems, some physical problems, a few outbursts at work, a few repremands in the speculation section and so on, that make one consider going to that sure and easy nicotine high, to feel good, to feel right. But, I do believe I have stumbled upon the right formula, for quiting, and staying quit. Nicotine tapering for a week, to prove to yourself that you can live without nicotine for an hour, or for 8 hours, or 12 hours, without anything bad happening. And then "replacement" of the dopamine rewards that nicotine provides, with the natural dopamine rewards that everything else about life provides. Working on the "list" of things that makes one feel good. And of course, when put to the test, remembering that I have already determined and decided and promised and put into effect, the fact that nicotine, is just not an option. For my health, and so that I might be around for my loved ones, that added time, I just gave myself, by saying no to nicotine. I certainly have not said no to dopamine. That is a good thing. But available for free. With no strings attached. Regards, TAR

Acme, https://www.flickr.com/photos/flickr/galleries/72157644928678005/ Mother nature is looking pretty clever in these pictures. Regards, TAR

Acme, Then, along with Ophiolite you require conscious decisions to be purposeful, and everything else that is not a conscious decision, to be accidental. I was thinking about this distinction yesterday and the distinction was also brought up by Mike a number of posts ago, in terms of "where is one to draw the line" between that done consciously on purpose, and that done accidently with no intent. That we can make a distinction and at least start with conscious human manipulation of the world as "purposeful" and intelligent is proof enough that there is at least in the case of human intelligence and consciousness, something, however small and possibly unique in the universe, that is not accidental. But then, when one looks at the complex human organism, that is so similar in plan and parts and purpose, across 8 billion current examples and however many billion prior examples, one sees a common thread, a pattern that has survived quite independantly of any single instance. An intelligence that supercedes the individual example. That existed prior any of us here being born, and will exist no doubt, after everybody here is dead and gone. Some mitochondria holding the code and plan to pass along, that is itself just unthinking chemicals as was mentioned a few posts ago as all it takes for grass to grow straight away from the center of the Earth. There is some point at which the human race "got smart". Maybe when the first word was spoken and understood. Maybe when the first tool was used as was depicted in 2001 a space odyssey. wjere tje ape throws the stick he/she used in the air and it turns directly into the space craft. But at some point we were natural and accidental, and became natural and purposeful. Where you want to draw the line between the two is inconsequential to the fact of the matter, that there is no objective point at which the human race "fell from grace", ate the apple, and discerned the difference between good and evil, and became purposeful and "unnatural". Ophiolite would like to establish a "difference" between conscious humans and the rest of nature. That we are intelligent and nature is just not very capable or purposeful. Perhaps that we are in some way, because of our imaginations, above nature, better than nature, and a different sort of thing than nature. That is where I say that humans metabolise on purpose, and no one has to think about it. And flowers bloom to draw the bee to pollenate the fruit that houses the seed that passes the pattern of the plant on to the next instance of the plant, and that is mighty smart and purposeful and not a completely different type of thing the plant is doing, than that which the human is doing. Regards, TAR

Acme, You keep telling me to "live with it", like I don't accept it or something. I absolutely accept that the universe has happened and absolutely fits together from bottom to top, from inside out, from outside in, from tiny to huge from huge to tiny, from instant to infinite and from infinite to instant and from top to bottom. Hofstetler and Kant, flowers and great attractors, peanut butter cups and statistical equations are all within the reality we are considering here. All within nature and its processes. What would be your example of "not accidental"? If you have none, then the word accidental has no opposite, no meaning, and you can not sensibly use it. Everything cannot be accidental, if there is anything that is not accidental. I was walking in the woods on Sunday, performing an experiment that Mike suggested in another thread. We coordinated it, so that we were both asking the universe to answer our question, at the same time, so that we could compare our results in an objective, peer reviewed fashion. Initial results were exciting and seemed magical, but I reviewed pictures I took and realized something I thought had happened "magically" had been there prior the experiment. In fact the "answer" I got to my question of the universe, was also there before I asked the question. I had defined the diamond infront of me as the area in which anything subtantial and notable happening would designate a "maybe" answer from the "observers". Anything to the right and up a yes, and to the left and up a no. I asked "Is there a direction orthogonal from here and now, that one can experience?" Nothing happened of note in any of the designated areas. After a minute or two, a moth or bug or something fluttered my left ear, but that was not too notable. I thought the experiment a bust and continued down the path. About 15 feet down the path, right at the base of the diamond I designated to my right, I saw a very interesting "answer". It is the rock, who's picture I have attached. Mike also had an interesting maybe answer to his question. We talked about our experiences and decided there was no magic, no observers, but our minds were not isolated from the universe, and used the universe to think. Left us both in a rather "its all good" state of mind. Its OK to think it not an accident. Its perfectly OK. Regards, TAR

Ophiolite, There must be some rule I am breaking, some "proper" agreement that we have together, to continue to call the place clever, or you would not be at your wits end, trying to understand why we (mike and I) do not see what the problem is, in doing so. Yes this is a science board and not a mystics convention, but, and this is a big but, there is not a way you can call yourself clever, and think the universe had nothing to do with your cleverness. You did not come from "somewhere else", you are part of nature, you are a natural thing, sensing and remembering and modeling the real world. It is not like Mike and I are talking about something magical or impossible. Well we might on occasion, but we look for evidence and proof, same as everyone else on the board. I am aware that somehow I am doing the board a disservice by voicing my opinion about the characteristics of the universe being somewhat "capable"... well not somewhat...absolutely capable, but as Mike said, in reference to Phi's awesomeness comment, we can drop the word clever if it smells of the suggestion of an anthropomorphic god, and just consider the place as a whole has done rather well for itself and we living creatures are a capable lot, doing quite well at reproducing our patterns and surviving in a universe, that otherwise is tending toward greater entropy. And that maybe it is not an accident that things maintain themselves, and that when we see wonderfulness, we can call it wonderful that the world has managed to be as awesome as it is, including us, for so long in the past, in such a big way (8billion wills) at the moment, and is looking like it quite unaccidently will continue to be awesome for the forseeable future. Acme, I am still wondering why it is so important to you that things be considered accidents or purely chance, with no intention or purpose. Not that the universe was intentionally started. That makes no sense either. But given an "unthinking" universe, it is difficult to arrive at a "thinking" natural thing, such as a complex human body/brain/heart group by accident. That is, there has to be a progression from atom to molecule to crystal to bubble to cell to multicell to nervous system to brain to "thinking" thing, that is a natural progression, that takes no magic or god, but is something the universe is capable of doing, by itself. We are in and of nature, We cannot be clever without it. Cleverness had no place other than the universe to come from. That we copy the place, and model the place and remember the place and think about the place, is no accident. We do it quite on purpose. Regards, TAR