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There Is No Single Instant In Time
tekkieRich writes "Some interesting news from the world of physics. Supposedly, in this paper, the author answers some of the major paradoxes (achilles vs. the turtle and Zeno) concerning our understanding of time. 'Impressed with the work is Princeton physics great, and collaborator of both Albert Einstein and Richard Feynman, John Wheeler, who said he admired Lynds' "boldness," while noting that it had often been individuals Lynds' age that "had pushed the frontiers of physics forward in the past."'"
Public release date: 31-Jul-2003
Contact: Brooke Jones
Brooke.Jones@australia.edu
Independent Communications Consultant
Ground-breaking work in understanding of time
Mechanics, Zeno and Hawking undergo revision
Full size image available through contact
A bold paper which has highly impressed some of the world's top physicists and been published in the August issue of Foundations of Physics Letters, seems set to change the way we think about the nature of time and its relationship to motion and classical and quantum mechanics. Much to the science world's astonishment, the work also appears to provide solutions to Zeno of Elea's famous motion paradoxes, almost 2500 years after they were originally conceived by the ancient Greek philosopher. In doing so, its unlikely author, who originally attended university for just 6 months, is drawing comparisons to Albert Einstein and beginning to field enquiries from some of the world's leading science media. This is contrast to being sniggered at by local physicists when he originally approached them with the work, and once aware it had been accepted for publication, one informing the journal of the author's lack of formal qualification in an attempt to have them reject it.
In the paper, "Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity", Peter Lynds, a 27 year old broadcasting school tutor from Wellington, New Zealand, establishes that there is a necessary trade off of all precisely determined physical values at a time, for their continuity through time, and in doing so, appears to throw age old assumptions about determined instantaneous physical magnitude and time on their heads. A number of other outstanding issues to do with time in physics are also addressed, including cosmology and an argument against the theory of Imaginary time by British theoretical physicist Stephen Hawking.
"Author's work resembles Einstein's 1905 special theory of relativity", said a referee of the paper, while Andrei Khrennikov, Prof. of Applied Mathematics at Vaxjo University in Sweden and Director of ICMM, said, "I find this paper very interesting and important to clarify some fundamental aspects of classical and quantum physical formalisms. I think that the author of the paper did a very important investigation of the role of continuity of time in the standard physical models of dynamical processes." He then invited Lynds to take part in an international conference on the foundations of quantum theory in Sweden.
Another impressed with the work is Princeton physics great, and collaborator of both Albert Einstein and Richard Feynman, John Wheeler, who said he admired Lynds' "boldness", while noting that it had often been individuals Lynds' age that "had pushed the frontiers of physics forward in the past."
In contrast, an earlier referee had a different opinion of the controversial paper. "I have only read the first two sections as it is clear that the author's arguments are based on profound ignorance or misunderstanding of basic analysis and calculus. I'm afraid I am unwilling to waste any time reading further, and recommend terminal rejection."
Lynds' solution to the Achilles and the tortoise paradox, submitted to Philosophy of Science, helped explain the work. A tortoise challenges Achilles, the swift Greek warrior, to a race, gets a 10m head start, and says Achilles can never pass him. When Achilles has run 10m, the tortoise has moved a further metre. When Achilles has covered that metre, the tortoise has moved 10cm...and so on. It is impossible for Achilles to pass him. The paradox is that in reality, Achilles would easily do so. A similar paradox, called the Dichotomy, stipulates that you can never reach your goal, as in order to get there, you must firstly travel half of the distance. But once you've done that, you must still traverse half the remaining distance, and half again, and so on. What's more, you can't even get started, as to travel a certain distance, you must firstly travel half
There Is No Single Instant In Time
Posted by timothy on Sunday August 03, @03:46AM
from the all-is-flux dept.
I've been counting down the seconds until i die and this guy tells me were are no seconds?! geez i dont want to freaking live forever
So, the next paradigm to disappear is the singularity of Black Holes; I never believed in them anyhow...
But, Lynds' is brilliant, if true/not disproofed/widely accepted.
A similar paradox, called the Dichotomy, stipulates that you can never reach your goal, as in order to get there, you must firstly travel half of the distance. But once you've done that, you must still traverse half the remaining distance, and half again, and so on. What's more, you can't even get started, as to travel a certain distance, you must firstly travel half of that distance, and so on.
I always thought the reason you could never get started on the way to your goal was the 'trying to get a woman to go some place when you have been ready and waiting for ages' paradox
Do not try to read the dupe, thats impossible. Instead, only try to realize the truth
What truth?
There is no dupe
when slashcode decided to examine it.
The posting act begins when the submit button is pressed, and ends when the database updates it's article index.
All "events" have a beginning and an end. Some of them have a known duration so the delta is not noted, but it still exists.
I don't know what's so revolutionary about that stance, especially from a practical standpoint, other than maybe the "directionless" nature of time. I think that, however, is an oversimplification that fits into the author's little mental framework he wants to construct. I prefer to think of complex intervals as very small closed sets around the approximate instant. There's nothing wrong or counterintuitive about that.
THIS THING CAN TURN ON A DIME, MACROSSZERO STYLE ALSO FUCK BETA, ~NYORON
The article is either incredibly bad journalism and way over-simplifying the paper, or else it stinks of a hoax.
"Lynds also points out that in all cases a time value represents an interval on time, rather than an instant. "For example, if two separate events are measured to take place at either 1 hour or 10.00 seconds, these two values indicate the events occurred during the time intervals of 1 and 1.99999...hours and 10.00 and 10.0099999...seconds respectively." "
This is stunningly obvious. I learnt the resolution of this, and the tortoise paradox, at age 17 in high school maths classes.
Also, why is the contact for further information an "Independent Communications Consultant"?
OK, I RTFA but i didn't RTFP (paper).
The tortoise vs. Achilles paradox has not really plagued modern physics in that it is not a paradox (anymore - it might have been to the Greeks). The supposed paradox lies in the misconception that an sum with infinite terms will always yield an infinite number. This is obviously not true - As Achilles needs to traverse ever smaller distances he also does that in ever smaller amounts of time.
And the times add nicely up to a finite time - the time when he overtakes the tortoise.
The article claims that this is still a paradox. I think based on the idea in this quote:
> With some thought it should become clear that no matter how small the time
> interval, or how slowly an object moves during that interval, it is still
> in motion and it's position is constantly changing, so it can't have
> a determined relative position at any time, whether during a interval,
> however small, or at an instant. Indeed, if it did, it couldn't be in motion."
Say WHAT?!?
Please tell me why you can't have a well determined position as a function of time and be in motion as well?
He goes on to claim that uncertainties in the values of times is somehow a profound proof that no instant in time exists. Hey, you could say the same thing about the distance the poor fella has to transverse - thus spoiling the whole 'ever smaller distances' thing.
Please enlighten me.
I read about this in the newspaper and thought "wow this sounds exciting". Then I saw the actual paper. It turns out that his ideas are not fleshed out with any mathematics, so its just a philosphical position that he is taking.
I do think that time is a bit of a mystery, and its possible that that his ideas may be roughly right. It might imply that moments or "moment intervals" were some sort of fractal sets, such that a moment can never be finitely splittable (only infinitely splittable). A mathematical model that accomplished this (within the framework of currently accepted/known physics) would be remarkable.
John McTaggart proposed a similar theory in the "Nature of Existence" - written in 1921. Perhaps if physicists payed more attention to philosophy ...
I'm not into the scientific journal "scene", as it were, but I expect that's about as insulting as a review can possibly be. So maybe this guy is onto something profound, but more likely it's smoke and mirrors.
Having been exposed to that "scene", I can tell you that the referees for papers submitted to academic journals are capable of being quite clueless when they want to be. I've known a number of authors who got comments back from referees which made it quite clear the referees hadn't even bothered trying to understand the paper.
Believe it or not, the whole paper-refereeing scene isn't that much different from the Slashdot moderation system. Referees are chosen more or less at random (from within the community of people who are knowledgeable about the paper's subject matter, and who are willing to read and comment on a paper.) And just like Slashdot, some of them won't take the time to read the paper completely, some won't understand what the paper is really saying, and some will let their own personal biases determine how they vote.
TheFrood
If you say "I'll probably get modded down for this..." then I will mod you down.
Zeno's theories are pretty well-established, you know "Man is walking across a road, if you keep on dividing the time intervals, he'll never get there." This Lynds seems to just be restating the theory with some fancy terms.
... you can try and mark an instant in time, but that instant still represents an interval. The more precise your equipment, the smaller the interval, but the interval can get infinitely smaller.
It isn't a theory, rather a paradox. If you keep dividing the time & distance intervals, the two objects never pass each other. They just get infinitely closer. Hence the paradox. The paradox (and most of science for that matter) makes the assumption that time can be measured in finite bits.
What this guy is saying that there are no moments in time (or rather, there is no basic/smallest unit of time), which is why the two objects pass each other.
When you think about it for a little bit, it makes sense. It's kind of like PI
http://philsci-archive.pitt.edu/archive/00001197/0 2/Zeno's_Paradoxes_-_A_Timely_Solution.pdf
/. ed
It may not be the same paper that will be published in Foundation of Physics Letter in August. But it is a complete paper on Peter Lynds' discussion on Zeno's Paradox.
Get it before it's
philsci-archive.pitt.edu/archive/00001197/02/ Zeno's_Paradoxes_-_A_Timely_Solution.pdf
:)
Just in case anyone actually wants to read it before commenting.
Believe it or not, the whole paper-refereeing scene isn't that much different from the Slashdot moderation system.
Has any referee ever sent a paper back and scrawled on it: "J00 f4gg0t! If I ever meet j00 I will kick your ass!"
"This seems to me kind of like how you can't just find pi by measuring the circumference or a circle and dividing it by the diameter. I had always thought of this being because there is no such thing as an exact point in space, but maybe I was just misunderstanding or something."
The only reason you can't determine pi to high level of accuracy by measurement is that in practice there will be inaccuracies in your measurements and in the shape of the circle. measurement issue. In principle, given perfect circle-making and measurement techniques, your accuracy is only limited by the Planck length (1.6 x 10-35m).
In science the burden of proof is on you. If you can't make your case so that you peers can readily understand the evidence your work will most likely be disqualified with comments like those he got from the referee.
You may be 100% right but if your paper is confusing, uses unorthodox terminology and contains crap figures you can bet that the referee is going to disqualify it. This guy should have co-authored the paper with a professional scientist who knows the proper language and the way to present new ideas. And this attitude is not elitism. Science must be ultraconservative to keep the crackpots out. And unlike the crackpots would like to believe, given enough time and attempts to push a new revolutionary theory through (not by one person but by many) it will eventually be accepted as the proof for it accumulates.
BOO! TERRO
The Calculus approach is really a summation of an infinite series. Basically that approach breaks the bits of time into infinitely small pieces -- but they are still broken into pieces. The assumption that time can be broken down into an atomic unit is still there. At least, I think that's the gist of what he's saying.
The brain can't monitor the world continuously so it "samples" it's enviroment every, say, 1/50th of a second. However if something threatening is happening it will sample more often, say every 1/100th of a second. This would be why time seems to slow down in an accident. Conversely it samples less often when it's not threatened, ie when you're enjoying yourself, so time seems to go faster.
I don't remember it saying anything about why boring things seem to take so long, maybe it's just the contrast between the "fun" sampling rate and the "normal" sampling rate.
The journal's site is here, though the August (autumn) issue isn't yet available online.
Some significant red flags here. First and most obvious is the wunderkind's lack of training and (presumed) familiarity with established concepts of physics and contemporary research. This isn't a deal-breaker, of course, but it's worth remembering. I'd love to see untrained theorists challenging - successfully - old-guard physicists with some astounding new insights, but I don't think that's happening here.
Wheeler's one-word endorsement - "boldness" - isn't ringing, and the bit about his age (he's 27) is irrelevant.
From a referee: "I have only read the first two sections as it is clear that the author's arguments are based on profound ignorance or misunderstanding of basic analysis and calculus. I'm afraid I am unwilling to waste any time reading further, and recommend terminal rejection." Ouch with a capital 'O'. There's no maths even referred to in this article, either, which I'd like to see.
"Lynds says that the paradoxes arose because people assumed wrongly that objects in motion had determined positions at any instant in time, thus freezing the bodies motion static at that instant and enabling the impossible situation of the paradoxes to be derived." This hasn't really been a problem since quantum indeterminacy.
From a "prominent Oxford mathematician": "A prominent Oxford mathematician commented, "It's as astonishing, as it is unexpected, but he's right." Unnamed source. HUGE red flag.
Within a quote: "Naturally the parameter and boundary of their respective position and magnitude are naturally determinable up to the limits of possible measurement as stated by the general quantum hypothesis and Heisenberg's uncertainty principle, but this indeterminacy in precise value is not a consequence of quantum uncertainty." He gives no alternative explanation for the origins of this 'indeterminacy.' Up to this point the article's summary has proceeded along basic Planck/Heisenberg lines. There's really nothing new here, except the (in this article) unsupported assertion of a new form of indeterminacy that's not related to quantum effects on measurement.
"Lynds continues that the cosmological proposal of imaginary time also isn't compatible with a consistent physical description, both as a consequence of this, and secondly, "because it's the relative order of events that's relevant, not the direction of time itself, as time doesn't go in any direction." Consequently it's meaningless for the order of a sequence of events to be imaginary, or at right angles, relative to another sequence of events. When approached about Lynds' arguments against his theory, Hawking failed to respond." Ignores Feynman's 'arrow of time' characterization of antimatter as equivalent to matter moving in time-opposite fashion. Also ignores simple observation that time does, in fact, appear to move in one direction. In a layman's article it would be good to mention Lynds' explanation for this, if he has one. If he doesn't, well... And Hawking 'refused to respond' to whom? To Lynds? To the author? On what questions? In what timeframe? A phone call during dinner from Australia? Red flag.
"Although Lynds remembers being frustrated with Grigson, and once standing at a blackboard explaining how simple it was and telling him to "hurry up and get it", Lynds says that, unlike some others, Prof. Grigson was still encouraging and would always make time to talk to him, even taking him into the staff cafeteria so they could continue talking physics." Seriously big red flag. 'Hurry up and get it'? Sounds like high school bong-water theorizing.
"Although still controversial, judging by the response it has already received from some of science's leading lights, Lynds' work seems likely to establish him as a groundbreaking figure in respect to increasing our understanding of time in physics. It a
This article was posted on fark sometime between 0.99999... and 1.0 weeks ago.
(via google cache) http://216.239.37.104/search?q=cache:philsci-archi ve.pitt.edu/archive/00001197/02/Zeno%27s_Paradoxes _-_A_Timely_Solution.pdf
In my reading of his autobiographical, "Surely you are joking Mr Feynman?" I read some implied criticisms of Wheeler. I remember a chapter from this book where Wheeler and Feynman were going to address a small seminar of big brains at the Institute for Advanced Studies, at Princeton, where Einstein was a fellow. This was while Feynman was still a grad student, and Wheeler was his thesis supervisor. IIRC Feynman was nervous about addressing one theoretical aspect of the problem. Wheeler told him to address all the other aspects of the problem, and he would handle the part that made the tricky bit.
When it came time to give the presentation Feynman gives his portion of the presentation, but Wheeler begs off, saying he isn't quite ready, but he expects to complete a paper about it Real Soon Now.
I guess this is the Institute for Advanced Studies equivalent of "the dog ate my homework".
After the seminar Wolfgang Pauli took Feynman aside, and asked him if he could tell him anything about Wheeler's paper. Feynman said he couldn't, that Wheeler hadn't told him anything. IIRC, Pauli said something like, "He hasn't even told his own grad student about his ideas? That paper will never be written."
And it never was.
At least that is how I remember that chapter.
The reason I'm making this post is that I want to point out one thing. Alot of times, when mods, myself included (I metamod about three times a day), come across an article that ranges beyond or above our understanding of a topic, its hard to make a decision as to whether or not something is "informative", like in this article, where I see one post supporting the theory modded informative, and one post criticsing the theory also modded informative. This is physics, people, not YRO. You're either right or wrong in this case. Please do some basic research, please, before modding a post up, just because it sounds intelligent and is well written.
Btw, for all the detractors, this paper was originally published in a European Physics Journal, and most papers submitted to said journals undergo stringent review before being published as fact. This kid is getting supporters in all the right places, and you'll notice that many of his detractors tend to be the type of people who were still arguing the Earth was flat back in the 1800's. Some people just don't want to change, and many of these people are also detractors of Superstring Theory, and are apparently comfortable in dealing with the conflict between quantum mechanics and the theories of general and special relativity.
Another thing I'd like to point out are some of the problems this guy has had getting this paper to light, and receiving the help he deserved from memebers of academia, because of his lack of academic credentials. This is, to a degree, still going on right now. People need to realize that this guy is taking a lot of flak from various experts simply because he doesn't meet their academic pedigree.
Some "experts" need to be reminded that once upon a time someone wrote a very special paper, also widely denounced, also widely refuted for a while. And that person wasn't a department head at a prestigous university, nor was he being funded by wealthy patrons to run his own lab. He worked at a patent office.
Mod Points: Helping you keep your opinion to yourself.
Sounds like "Thief of Time" by Terry Pratchett to me... in that book a guy tries to build a clock that will run on the 'tick' of the universe -- absolute time if you will. However, in building it he manages to stop time short, effectively, as Pratchett puts it, 'sticking an iron bar between the cogs of time'
That hasn't been a paradox in years, not since
people learned how to sum an infinity series.
Say the archilles is running at 1meter per second
and is 1 meter behind the tortoise who is moving at 1/2 a meter per second, then
v = D/T for that total, and for any given length
of time,
D_total = D_1 + D_2 + D_3 + D_4...
T_total = T_1 + T_2 + T_3 + T_4...
D = 1 + 1/2 + 1/4 + 1/8... = 2
T = 1 + 1/2 + 1/4 + 1/8... = 2
So archilles passes the tortois after 2 seconds
just as he should. Of course poor zeno who never
learned to sum series or break out of loops is stuck counting ever smaller freese frames in
an infinite regression, like the famous oozalum bird. But that doesn't bother our athlete or his
slow foe, or nature one iota.
Since my first post which was a joke got moderated troll, i will help the moderators out by posting the quite obvious links one gets when they type the name peter lynds into google.
The source that everyone keeps getting this article from is a self published online journal, meaning noone has read it or reviewed it, the author just submitted it himself.
There is a certain anti intellectualism that runs through slashdot sometimes that i find disturbing.
I will concede that it might, just might be legit, but the markers are all there for a hoax.
N,N-dimethyltryptamine (DMT). Your pineal gland will release it when you're near death. It can also be synthesized and smoked/injected (only *not* - it is now illegal because governments like to control all measures of our freedom, including what substances we put in our bodies, not to mention what we see and hear all the time, what we are lead to percieve as truth... but that's something else entirely), causing the user to transcend space and time...
Thought this would a good thread to post some
x xx.lanl.gov/abs/hep-ph/0307345
other recent physics news...
1. The've just found a pentaquark state.
The rule in quark theory and QCD (the theory of
the 'color' force that binds quarks), is that
quarks always come in triplets or quark anti-quark pairs. Haven't never seen a free quark, theres always been a little nagging doubt that
quark are real. So that fact that they have found
a suprisingly (for QCD resonances) long lived state that can only be make of 5 quarks, the Z+ at 1540Mev, which made of two up quarks, two down quarks and an anti-strange
quark. It was previously predicted by QCD, and is a classic example of the exception proving the rule.
http://xxx.lanl.gov/abs/hep-ex/0307088
http://
Dark Matter, after 10 years of searching theres
finally for faint experiment signals that dark
matter exists. This was been found because two experiments looking for collisions between WIMPs
and cold crystals have found significantly more
signal when at time of the year then the earth
is moving against the motion of the galaxies
spiral arm, than when its moving towards it.
http://xxx.lanl.gov/abs/astro-ph/0307403
It seems pretty clear to me that the zeno paradox is not a paradox at all but just our inability to intuitively solve maths with infinite terms. It reminds me of those visual illusion drawings that cause our brains to make sense of things in a missleading way. Check it out.
At the same time, this does not disprove his paper since the article, is not well writen enough to be useful in determining the validity of this work.
Liberty.
At one point in time Einstein was an unqualified patent clerk. Many years later, he is finally awarded a Nobel prize, because one of his three main discoveries was finally within the certain appraisal of his peers.
Interestingly, at no point in time were Einstein's qualifications equal to his peers'. He managed to pass the Achilles' Academy at a non-instant of time.
I don't understand this concept of indeterminate relationship. It strikes me that his claim boils down to saying that time and motion are not possible unless you regard the set of physical relationships as constituting an uncountable infinity.
But what is the big deal with that? R is uncountable on an open interval, but it still retains a fully ordered relationship.
Zeno's paradox functions because it forces you to analyze time as if it could be mapped onto a countable set (halving interval N).
That said, I don't regard time as a well defined physical quantity. Einstein proved long ago that time does not function as a simple ordering relationship. Yet the only reason I can see that we use the abstraction of time is to suggest that physical ordering relationships exist.
I tend to view physics as having a trinary logic: true, false, and ungrantable. A foundation for physics which was formally non-predictive (lacking a human interpretation of time) would certainly belong to the last bucket, for as long as time remains a proxy of human purpose.
Your post is nonsensical. How can you speak of non-simultaneous observations and at the same time (no pun...) refer to time as a subjective illusion? Are you talking about "the flow of time in one direction"?
There can be no useful distinction between what is "really real" and what models seem to match our sensory data. For example, in string theory you use multi-dimensional membranes where different vibrational harmonics represent different elementary particles. Is this just a practical mathematical model or do these membranes really exist? The question is meaningless. "Das Ding an sich", as postulated by Kant is meaningless.
In quantum mechanics particles and energy can interact over small distances of time (see the Heisenberg uncertainty principle), just as they interact over small distances of space. Also in the theory of relativity time and space are handled almost identically by the equations with the speed of light, c, being just a convertional factor between distances in time and distances in space (almost like converting between meters and feet).
Thus both our best physics models of the world and our subjective understanding of time wants to treat it like a separate real dimension (not a SciFi dimension that you walk through, but a mathematical dimension - a separate orthogonal axis). What further criterions for something "existing" can you have?
The flow of time seems to be purely an illusion though.
Opinions stated are mine and do not reflect those of the Illuminati
Ah, the "academia is really about suppressing the new" conspiracy theory -- the X-Files of the academic world. While there is sometimes an excess of conservatism in "academia", people usually forget how justified caution usually is. For every Einstein-like breakthrough, there are hundreds of crackpot theories. A system is needed to sort through and separate the wheat from the chaff. Oh, wait, we have such a system: peer review and open publication.
This breathless article in EurekAlert has all the hallmarks of a duped science reporter: deep-sounding (but, it seems, semantically null) phrases tossed about with abandon; derision and scorn at the stuffy old guys who just don't get it; and of course the simultaneous disdain for and desparate quoting of authorities. (That is, "most physicists don't agree because they just quote the same old authorities, but look, this Big Name likes my work, which validates it".)
I suppose we'll see how this plays out when the paper is actually published and people get a chance to take a hatchet to it. I'm guessing this will sink like a stone... if it isn't already a hoax.
The Mongrel Dogs Who Teach
Of course, today we know that matter is not infinitely divisable, but that was Zeno's point! You cannot have a continuous function in real life and divide it into discrete segments! In fact, 'poor Zeno' was well ahead of his time, not only arguing against infinitely divisible, but also touching on Relativity! His 'stadium' paradox of two bodies of objects passing each other essencially begs the solution of Special Relatively.
In the archilles paradox, the runner will always have further to go. If time and space can be divided into discrete slices, then the runner will have to transverse an infinite number of slices to get to his destination, which is impossible. Infinity isn't a number, it's a position which is unreachable through finite additions. Therefore, the runner cannot overtake the tortoise, because he has to go through and infinite amount of 'time-slices' to get there. The solution in the article is that time is continuous; there cannot be a discrete slice of time, only a duration of time between two points.
my entire CS Masters was about a program design paradigm with highly esoteric underpinnings and very little mathematical substance - on the other hand it was well funded!
I am on the college committee that controls your funding. I regret to inform you that based on your post I have decided to vote against renewing your project.
Thank you for the information. Have a nice day.
-
- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
You're incorrect. The philosopher who said "You never step in the same river twice" is Heroclitus, a Greek philosopher. Thats why the phrase "Heroclitian flux" refers to the very Heisenburg-esque fact that you change things by interacting with them. Frankly, you sound unfamiliar with the tenets of Zen buddhism, since most of their koans [i.e. meditative stories/poems] are not phrases with actual meaning (such as "you can never step in the same river twice) which can be discovered, but in fact phrases or stories without meaning. The koans are employed by Zen buddhists to become more comfortable with the lack of reason in the universe, and thus come closer to the meditative state of nirvana.
"Stumble before you crawl"
Just quickly scanning it, two things seemed suspicious (apart, obviously, from the content):
bla
then the runner will have to transverse an infinite number of slices to get to his destination, which is impossible
As the other repliers have pointed out, this statement is wrong in the Zeno case. A sum of inifinite series can either converge or diverge. In the Zeno case, the geometric series 1/2^n as n->infinity converges* (thus it doesn't go to infinity to become a paradox in the first place). No fancy new physics is or EVER was necessary to resolve the Zeno paradox, only simple calculus. As with the aether, there is no paradox in the mathematics. The paradox only appears in the (incorrect) human interpretation based on (incorrect) intuition. Galileo said "Without the help of [Mathematics] it is impossible to conceive a single word of it, and without which one wander in vain through a dark labyrinth." *By the ratio test, the limit of the absolute value of Asub(n+1)/Asub(n) is 1/2. Since 1/2 is less than 1, the series converges. See Mathematical Methods in the Physical Sciences, Boas, page 12.
Time is not Quantised.
There, that's a nice, neat summary.
Which if true has all sorts of interesting implications. The argument appears to be that if time was quantised - as all other things, like space, energy etc appear to be - then the Universe could be described by a single n-dimensional vector containing all information. (ie a longgggg list of numbers describing where everything is, but not where it's going as rate-of-change derivatives aren't possible if time is quantised.). It would be "stuck" in this position, if you like. Alternately, if derivatives were allowable, everything would be predictable, with no uncertainty. Heisenberg Uncertainty means continuous unquantised time.
He may be right, he may be wrong, but this is interesting enough either way to be worth study.
Zoe Brain - Rocket Scientist
I think paradox is a misnomer in these cases.
It's actually quite easy to realize why Achilles 'never' catches up to the tortoise: the paradox draws our attention away from the passing of time.
In any given instant, Achilles makes up a certain amount of distance, and the tortoise moves further off by a little bit.
But the trick in the paradox is that at each 'iteration' of the paradox, a shorter amount of time is passing.
Why a shorter amount of time? Because both Achilles and the tortoise are traveling at a constant (but different) speed, and each 'iteration' has Achilles less ground than the iteration before.
If you do the math, the increments of time between each iteration sums up to equal exactly the time when you would expect Achilles to pass the tortoise.
In other words, the paradox is just a trick - break up the time leading up to the fast Achilles passing a slow tortoise into infinite slivers of time, each sliver slightly shorter than the previous one.
The paradox occurs when we assume each sliver of time is the same amount, and that an infinite amount of them results in an infinite amount of time.
Just a trick, nothing more.
My M.S. advisor submitted a paper some years back about using crystal morphology, size, and depth of formation relationships to try and answer some questions about the formation of that particular mineral (dolomite if anyone cares to know...it's very hard to explain how it forms at lower temperatures). One of the referees was also a fellow who also works on dolomite formation, but all work he does involves some fairly high level geochemical analysis. Simply put, the guy just could not understand the paper. This is probably because he didn't *want* to understand a paper using techniques other than the ones he was familiar with. The other two referees loved the paper, but this other guy basically drew a big red X through each page and said it was bullshit.
Well, my advisor didn't take too well to that, so he just pulled it from review for that journal instead of completely re-writing it, and submitted it to another journal that gladly accepted it.
Project Steve
What, you can't infer the meaning of in Soviet Russia, Black Hole eats you! ?
StoneCypher is Full of BS
HERE
For every annoying gentoo user, are three even more annoying anti-gentoo crybabies. Take Yosh from #Gimp for example.