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Posts posted by md65536


Nope.
I seem to be mistaken. There is a good discussion about it here: http://www.physicsfo...ad.php?t=118941
I feel inclined to argue about limits... that 0 times infinity is indeterminate because it uses the "limit as x approaches zero" instead of 0 itself... but I think that is the point. In my example I'd used "infinity" as if it were a number, and that doesn't make sense. I should have said "an arbitrarily large number times 0 is still 0", or I may have gotten away with "an infinitely large number times 0 is still 0". The point is that an infinitely large number is a number (is that valid?) while 'infinity' is not.
So if we want to treat infinity as a number, we have to do so using limits.
That being the case, the question "How many times would I have to take away 0 from some quantity until it is all gone?", might validly be answered with "infinity", meaning "Not any finite number", meaning "No matter how many times you take away 0, it will not be enough to eliminate that quantity."
Your link suggests a clue to the discussion though. The word "indeterminate" seems to indicate a number that can be anything, but it's still a number. "Undefined" seems to indicate the same, but also includes the possibility that the result is not a number at all (or that it's impossible or doesn't make sense).
I'm in over my head, but I googled it and found this: http://mathforum.org....divideby0.html
'Why is 0/0 "indeterminate" and 1/0 "undefined"?'
So I was wrong, but there's some way forward with this. 0/0 appears not to be "undefined".
The solution to "0/x = 0" for x would be indeterminate.
It is the same reasoning that x could be anything in 0 = 0*x, while 1 = 0*x is not true for any number x.
Addendum: I was wrong; 0/0 = 1 is as valid as 0/0 = 0. However I still think that 0*(0/0) might still be 0! Multiplication by 0 doesn't make an undefined thing into 0, but it should make an indeterminate number into 0.
Asking "what is 0/0?" in terms of the example I've been using, is like asking "How many times can I take 0 away from 0 until it is gone?" An answer of "0" works, but so does an answer of "1". Or 10. Or any number. It is indeterminate.
Asking "What is 0*(0/0)?" is like asking "Given the task (of repeatedly taking away 0 from 0 some indeterminate number of times to end up with 0), if I repeated this 0 times, how many times would I have taken away a 0?" Not the best of wording... but the answer is 0.
0 
since 0 doesn't use up any material, I can do it however many times I want without using up anything, but in that instance, don't I define how many times it goes into 0 [...]
I don't think that provides any definition. If I have some quantity, and I ask "How many times can I take away 0 before the quantity is all gone?", there is no answer. It's not any finite number, and it's not infinite either (infinity times 0 is still 0... you could take away nothing forever and the original quantity will remain unchanged).
If you plot 1/x, it approaches infinity as x approaches 0, and +infinity as +x approaches 0. I've always thought of "1/0 is undefined" as meaning that it could be any value from infinity to +infinity... it has no definite value. But the above example suggests that it really means "no possible value".
Edit: Your example, now that I read the whole thing, sounds more like "How many times can I divide 0 into separate piles" or something, and that is more like 0/x, which is defined: it is 0. x is unknown or can be any nonzero value... but I don't think that makes it undefined. Your question is basically "solve for x" where "x has infinitely many solutions."
0/0=1?
I don't see how you could possibly figure that, given that x/0 is undefined.
However, I think it might be possible to try to argue that 0/0 = 0.
If you have x/0 is undefined in the sense that it could be any value and so isn't defined, but you multiply it by 0, the result will be 0 regardless of what x/0 might represent. In a sense, multiplying by 0 can restore definition???
But, given your example above, I'd say 0/0 or 0*x/0 is still undefined. x/0 does not mean "can be any number". I'd say it can better be described as "cannot be defined as a number." Multiplication is not defined for something that is not defined, so 0 * q is not 0 for all possible things q outside of the realm of numbers! Perhaps there is some operation that can be performed on undefined things and result in a number, but basic math operations ain't it. Anything divided by 0 is undefined and any math operation you perform on the result will also be undefined.
Ain't no mathmertician so I reckon someone else'll explain this better.
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??egative world collapsed, i hope anyway, now time to fix the machine and set for a future date?fourth return from the negative world, not much time for web interactions.??ost contact with Jack.?September 6 2011?
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If pushing gravity exerts pressure to keep us pressed against the planet from space, why isn't it affecting us differently indoors? Traditional gravity is a "force", but pushing gravity is just air pressure, which doesn't really add up to that much.
If you have a model (like "pushing gravity") that one says accounts for gravity, then it can only do so by predicting that gravity works as we observe it working. You can discredit the model by finding ways in which the model and observations do not agree. You're not going to get anywhere by assuming the model works differently from gravity (eg that instead of working like gravity, a pushing force would instead work like air pressure). So you can safely assume that any model of gravity is going to work "like gravity" unless it states otherwise. It works through walls. It works in air and in a vacuum. A pushing force vs. a pulling force isn't going to differ there.
Also... gravity does work differently indoors. For regular "pulling" gravity, the walls of a building pull (negligibly) on each other. In a more extreme example of "indoors", the inside of a spherical shell contributes 0 gravitational force everywhere inside the shell (off topic but integration can show this) while to the outside everywhere it contributes a gravitational attraction towards the shell.
Also... with GR you can treat gravitational acceleration as a type of inertial motion through curved spacetime (rough interpretation of http://en.wikipedia.org/wiki/General_relativity#Geometry_of_Newtonian_gravity). You don't need to treat it as a force at all, I believe, in order to model it. So if it is modeled by a force, whether it's pushing or pulling doesn't matter (I am guessing); either should be workable???. I don't think you would need to invent anything new (like an aether) to model it. I think it would be silly to argue either for or against a "pushing force" model by assuming the existence of an aether and/or to assume that it behaves at all like air pressure.
For or against a pushing force, I think it makes more sense to treat gravity behaving like gravity, not like something else that behaves very differently.
0 
Label the circles 1, 2, 3, and the squares A, B, C
Draw them on a rectangle of paper.
Connect 1A, 2B, 3C
then 1B, 2C, all with straight lines.
Connect 2A with a curved line going around B, and then 3A with a curved line going around C.
Connections 1C and 3B are missing.
Connect 1 to the middle of the left edge of the paper.
Connect C to the middle of the right edge of the paper (going up around 3).
Roll the paper into a cylinder, and 1C will be connected.
Connect B to the middle of the top edge.
Connect 3 to the middle of the bottom edge (going around C).
Take the cylinder, and bend it into a donut. 3B is now connected.
On a donutshaped world, this would be possible with utility lines underground and not crossing. But that's not a plane.
In a donutshaped universe, this would be possible with straight lines extending beyond the edges of the flat paper (and thus it's on a plane???).
It may seem unfeasible, but it's not really much harder than making an apple pie from scratch.
0 
How about this variation:
There are 3 doors, only one of them good.
There are 3 guards, and you can ask one of them a question that can be answered with the guard pointing to one door.
One guard always tells the truth.
One guard always lies.
One guard is insane but consistent, and alternatively acts truthful or lies (you don't know which will be first), with each "atomically evaluable" part of your question.
I'm not sure is this variation is consistent. Assume the insane guard would evaluate the "parts" in order that you speak them (or reverse order, would be equivalent, but she wouldn't "optimize" or reorder your expression). Also assume that if the guard is evaluating a part truthfully, she treats any previously evaluated parts as the truth. That is, the guard "acts honest" and conveys the previous lie rather than turning a lie into a truth (which is what the consistent liar does). Assume that if you ask a question that can't properly be answered, the guard will just give you a dirty look and no answer.
What question would you ask?
(If this variation doesn't make sense, I could try to specify exactly how the insane guard is to answer a question.)
0 
That looks like a contradiction
" not to an infinitesimal size is removed."
"Not all the guests can keep being compressed indefinitely."
Why not?
Cuz I says so! Literally, I have chosen (and specified adequately I think) the particular details of the example to arrive at the paradox.
If the guests can't be compressed at all and they entirely fill the finite space of such a hotel, there is no more spatial room for any new guests*.
If they can be compressed indefinitely, then their spatial aspects don't matter at all, and the variation of the hotel is equivalent to the original hotel.
In between is a hotel that can take an infinite number of additional guests one way, but not another way (though a simple change would allow both ways).
I guess it should be noted that these guests by definition are not all the same. Each of the rooms is a different size, and each of the guests fills their starting room so each guest is a different starting size.
* ... of nonzero size. I suppose I should also specify that each guest has a finite size.
Note that a spatially full hotel is full, no matter how small a potential new guest is. If the rooms are sizes 1, 1/2, 1/4, 1/8 etc, and so are the guests, then every guest in the hotel has a nonzero size or volume. The hotel is 2 m^3 and the guests take up exactly 2 m^3 and if you add any nonzero positive fraction to two you get more than two.
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"Suppose each guest can be compressed but not to an infinitesimal size."
Then you can't fill the last room because no guest would fit in it, so there's always a guest left over.
With that stipulation the hotel goes out of business even before you try to add more guests (though I'm not sure if that bankruptcy takes zero time, infinite time or finite time)
Well, there is no last room, but I'd better fix my wording.
To fill each of an infinite number of rooms that take up in total a finite space, it would require that the guests can have infinitesimal size.
I should have simply said "Suppose each guest can be compressed but that there are limits to how much a particular guest can be compressed."
Note that as it's set up (with room n+1 half as big as room n), and allowing guest n to be compressed to fit in room 2n, we must have that an arbitrarily high value of n will allow for an arbitrarily high compression ratio. So we must allow for compression to infinitesimal size.
Please consider the problem with the correction that "but not to an infinitesimal size" is removed.
The paradox still stands. Not all the guests can keep being compressed indefinitely.
Yes, assumptions must be made in any of the Hilbert hotel variations in order to allow them to be possible, but the impossibility of the paradox isn't based on an assumption. You can assume the best case for every assumption. There is no "hidden factor" like money or time. You can assume that an infinite number of people can be checked in in a finite time, for example.
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So, as far as I can tell so far, my whole argument will live or die based upon whether photons that are emitted by a moving emitter are
..."dragged along within the frame of that which emitted them".
No, that's a misleading way of putting it.
If "photons get dragged along with a frame" makes sense at all, then it's not one particular frame it happens to, but all inertial frames. Since this has already caused more confusion than good, I think this explanation should be retracted. What I meant by it was something like how the moon seems to "follow you" when you move. AND it seems to follow each individual who moves. BUT from your perspective, it doesn't seem to follow anyone else who moves independently of you. YET if you imagine someone else's perspective, you should imagine the moon seeming to follow them! If that's too confusing, then certainly my explanation will not be useful.
A similar (but not equivalent) thing happens with light. The difference between the moon and light is that with the moon it's only an illusion due to its great distance; move far enough (say a million killometers) in a straight line and the moon will not stay in the same place in the sky. With light, no matter how far or fast you move, the light will always be moving (not stationary as with the moon example) at the same speed relative to you. With light it's not just an illusion.
A simpler way of reasoning about this is that, instead of imagining light "being dragged along" with moving inertial frames but only from the perspective of observers in such a frame, it is simpler to just realize that any inertial frame is at rest according to observers in that frame. The above explanation tries to explain the same idea, but in a convoluted manner.
This is the root cause of most SR paradoxes: Light signals moves at c in your rest frame, and the same signals move at c according to anyone else's rest frame, even though these frames are not at rest relative to each other.
This is the resolution of most SR paradoxes: Time dilation and length contraction ensure that all of this happens consistently. It's only a matter of how complicated the details are for a given example.
Check out some videos such as this:
They should help visualize the kinds of relativistic effects (namely aberration) that are required to fully explain your paradox.So, again, your paradox might be restated as such: Two objects moving together naively seem to have gravity (and light) from the other "come from behind" (thus slowing the objects) due to the delay in the travel time of gravitons and photons. Yet, in the rest frame of the moving objects, there is no movement at all, and those signals should seem to come from the side, so there must be no forward/backward acceleration. An external observer who sees the the objects moving, will see them subject to aberration, and will not observe signals between the two "coming from behind".
However, complicated details come up when you try to precisely describe the two objects' relative motion while accelerating from one inertial frame into a new one. Aberration (a result of length contraction and time dilation) resolves the paradox, ensuring that the photons we may have thought would seem to "come from behind" according to each object... will not. If we work out the details, we'll find that the 2 synchronized objects will always see each other "directly to the side" while in an inertial frame, consistent with the simpler example of treating them at rest relative to each other (while in an inertial frame).
Why should I not use instantaneous gravity (especially since EVERYONE else is!) when that's the only way I ever get any physical results!!! Please help!
If you use instantaneous gravity you should use instantaneous transmission of light. I would not recommend this route.
If any information is transmitted faster than light, you'll derive all sorts of contradictions that involve violations of causality.
That is to say, the gravitational pull of an object will appear to come from the same place that light from the object appears to come. You will not be "pulled toward an object's current position" while "seeing the object in its past position".
11. In comment #30, md65536 is seems wrong because I don't ever propose that the test masses are moving at nonNewtonian speeds. I don't see how, in this experiment, any lines "appear to bend forward" or how "the other ship appears to be ahead of me" except in time. But, this does not invalidate what he said prior, which seems bangon.
Relativistic effects also happen at Newtonian speeds.
The original paradox involves two objects slowing each other down due to delayed gravitational influence. If they are moving at Newtonian speeds, any angle (off of perpendicular) of incoming gravitons, according to any observer, will be negligible. The angle of aberration (for the same observer) will be correspondingly negligible. You must neglect both, or neither, or you'll derive "small inconsistencies" where there are none.
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I found your analysis pedantic, tedious even, and having missed the point of my premise:
[...]
"Immovable resolve" is quite a judgmental characterization of me. I have been an amateur scientist all my life (since I could think for myself) and I say it as I see it, with the benefit of a hereditary high genius intelligence, as measured by both the SBIS and the WAIS, in case you missed that post.
Well done owl! I'm genuinely impressed. This is how I feel right now:
I gave it my best shot and you sailed through with ease, unable to be confined by my oppressive need for "right thinking" (as I judge it) in others.
I keep getting pulled into your threads because most of the others I'm interested in seem to die (sometimes my fault), while you manage to keep a lively debate going. I was worried I might kill this one, but you quickly proved me wrong. So I'll bow out now, and instead silently cheer you on from now on. I disagree with what you say, but I'll defend to the death of the thread your persistence in saying it.
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You may be a brilliant physicist, but you would have flunked my class on Logic and the Scientific Method.
If you see a flaw in the logic I presented in my last post, by all means specify the flaw. There is no "false dichotomy" in the "either/or" ( or "if/then") conditional (not a syllogism) logic I argued.
Either objects exist and have properties independent of observation and measurement Or they don't. If the latter, then then their existence and properties depend on how they are observed and measured.
Oooof. You would have been fired from my university.
"(A and B) or Not (A and B)" is a tautology and is true.
"Not (A and B) implies not B" is not true in general.
Let A be "Objects exist".
Let B be "Objects have properties independent of observation and measurement".
"If the latter" ("they don't") is equivalent to "Not A and B", which is equivalent to "Not A or Not B".
Not B would mean "Objects don't have properties independent of observation and measurement."
Not A would mean "Objects don't exist", in which case their existence doesn't depend on how they are observed. In this case, your argument is invalid.
Now maybe this is all pedantic and what you meant was what you'd get if you cleaned up the logic and resolved ambiguities with what I think you meant:
"Either (all objects that exist have one or more properties independent of observation and measurement), or not.
Assume: not (all objects that exist have one or more properties independent of observation and measurement).
Then there exists an object that doesn't have any properties independent of observation and measurement.
Then there exists an object that has no properties or has at least one property that is dependent on observation OR measurement."
If this isn't the correct interpretation it can be corrected, but it's not possible to deduce your original conclusion as it is.
If you used proper logic, you'd see the logical problem with your argument. You're basically trying to say that if one property of any object is dependent on observation, then all properties of all objects are. You are leaving out SO MANY possibilities, which cannot fit into your false dichotomy.
Obviously there are "things" beyond science's ability to observe and measure them. (Or would you also disagree with this?) This means that the cosmos with all its properties exists and has intrinsic properties whether we observe and measure them or not. (Repetitive, but it seems necessary.) Do you agree with this or not? If not, then you are an idealist.
Here for example, you jump to "all its properties" with no justification.
I disagree with your statement. But I am not an idealist.
I agree that there are things beyond science's ability to observe and measure. This includes for example things that we can infer the existence of, but aren't practically able to observe, or aren't able to measure (if you want to make any distinction). So I don't even have to limit myself to questioning the existence of things that are not even theoretically possible to observe.
Personally I believe that there are objects that have some properties that are invariant and thus don't matter how they are observed, AND other properties that depend on how they are observed. This means that I believe it is possible that these objects have a real existence outside of my mind. Therefore I am not a subjective idealist, by definition. I do not fit into your false dichotomy.
Hey out of curiosity, why is it that you no longer teach Logic and the Scientific Method?
I'm impressed with your immovable resolve to not give in on any aspects of your arguments. It would be a super useful attribute for a student to have, to reach a point where there is nothing new to learn that makes any difference. Please stop using it to insult others.
1 
This puzzle deals with a variation of Hilbert's infinite hotel... http://en.wikipedia.org/wiki/Hilbert_hotel.
In the simplest example, the hotel can be full but you can make room for another guest by moving every guest one room over.
By induction, you can repeat this infinitely many times, and accommodate an infinite number of new guests.
You can also accommodate a countably infinite number of guests all at once by moving every guest in room n to room 2n, freeing up all the infinitely many odd numbered rooms.
All the above stuff should be clear to anyone familiar with the paradox.
Variation:
A hotel with an infinite number of rooms can take up a finite volume of space. For example, if the first room takes up 1 m^3, and each room n+1 takes up half the volume of room n, then the space of all the infinite hotel rooms is 2 m^3.
Suppose that each guest is exactly as large as their room. In this case, the hotel is full and it doesn't matter if you can find an empty room or not; the hotel spatially is not infinite and cannot fit any additional guests with nonzero volume.
UNLESS... the guests can be compressed! Say each guest in room n can be squished to half their size and fit into room n+1. Then you can free up a room.
So here is my paradox.
Suppose each guest can be compressed but not to an infinitesimal size. Suppose for any guest in room n, they can be compressed only enough to fit into room 2n.
Then, if the hotel starts full but uncompressed, you can free up an infinite number of rooms and accommodate an infinite number of new guests all at once by moving every guest in room n to room 2n.
However, if you had instead freed up rooms one at a time by moving every guest in every room n to room n+1, it is clear you could not do this an infinite number of times.
So how is it that you can accommodate an infinite number of guests arriving all at once, but not if they arrive one at a time?
Is there a flaw in my logic? How do you resolve the paradox?
0 
I would "fit someone" of that description (depending on the specific "aspect" of reality they believe is intrinsic or objective ) into a selective subcategory of idealists who grant reality "independent of our conceptual schemes" to all natural phenomena except, for whatever reason, length/diameter of certain objects and distances between objects in the natural, unmeasured cosmos.
Well that answers my question satisfactorily. It implies that a realist accepts the reality of "all natural phenomena" independent of frame of reference, and any exception makes one an idealist. These are not generally accepted definitions of the words realist and idealist. Just as with "time", you are making up your own definitions for things. I have no problem with that; it's just that I was confused by when you were using words I thought you meant some accepted definition.
(The false dichotomy is either your "all or nothing" separation between realism vs. idealism, or your arbitrary categorization of specific aspects of reality as subjective or objective. I'm not sure which because you haven't explained which, if any, aspects of reality the categorization depends on.)
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most people think of the dimensions simply as a framework of straight lines centered at the centre of the universe with all the matter travelling away from this center.
Some advice I got from this site that I think is applicable is that a paper pretty much needs to have references in order to be taken seriously.
In this case, you make a claim that I disagree with, and there is no reference for me to follow, to see that the claim is backed up with evidence.
Otherwise, you could explain a claim and provide evidence yourself, or omit it if it's not important. Is the above statement necessary?
However, I don't think that you'd find any good references to back up that statement, because I don't think it's true. If gathering references seems like a chore or unnecessary, it might indicate that not enough research was done. In that case you can still write a paper but it's best to avoid making claims or assumptions about what is known and what is out there in existing sources.
The little details are important because probably most serious readers will tend to start losing interest after reading statements that are wrong or hard to understand.
1 
A true TOE would be able to predict the outcome of any experiment. I guess that would include when grandma's tic will act up again.
Would it? By that rationale, wouldn't a "true theory of evolution" be able to predict the outcome of future mutations?
If a TOE includes uncertainty, predicting that a result would be uncertain, would that count as predicting the outcome of an experiment?
I think that if you can prove that the outcome of any experiment corresponds to the predictions made by a TOE, then it would be a true TOE without needing to actually predict the outcome of any experiment. For example, chemical reactions correspond to quantum electrodynamics, and biological processes correspond to chemistry, but you don't have to be able to predict the outcome of a biological process using QE to prove it.
False dilemma. There is also detached skepticism.
Definitely. And plenty of it.
There must be millions of pages of crackpot theory out there. Why should anyone read any particular one of them? If we can get a few people to even start reading our hypothesis, just to have them continue reading we have to make it clear enough to be understood without the reader solving a brain teaser, and we have to make it correct enough throughout that the reader won't become doubtful of what's left, and we have to make it compelling enough to keep the reader's interest. A statements like "Consciousness acts like energy" does not convey a clear enough meaning to be understood, has nothing to convince anyone of correctness, and doesn't convince me to care.
Anyway Approachingavoidance, post away and people will read it, but it's an uphill battle to change the world this way.
0 
You constantly criticize me for lack of supporting evidence. I say that there is a mountain of it for a nearly spherical earth and none for a very oblate earth... a hypothesis with no evidence to support it.
Hahaha. I'm going to feel so stupid one day when I read the headline "Lack of evidence for oblate earth disproves relativity".
Science observes from as errorfree point of view as possible, makes records and so determines things like the shape or earth... which is not in dispute, accept among eccentrics with an unverified theory about length contraction. Seeing things as shaped differently from different points of view does not mean that they actually are shaped differently, depending on how you see them. How many times must I repeat this before you get it.
Probably about as many times as you must repeat "2+2=5" before we "get it".
Repetition doesn't make a wrong statement understood.
owl, where in your false dichotomy would you fit someone who holds the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc., but also believes that length is not such an aspect and is instead observationally dependent?
0 
Then we agree, but you are presenting a false dichotomy.
1) The world is three dimensional and relativity is correct  thus the world is subjective.
2) The world is three dimensional (and objective) and therefore relativity is incorrect
Whenever anyone presents option 3) The world is objective and four dimensional you just respond with 'I think it isn't'.
It is obvious that assuming the model on which relativity is based is incorrect will lead you to finding paradoxes if you assume the results of that model are true.
I think this is the most important unanswered issue here. Even if we ignore "what is real" as owl suggests, and concentrate only on the philosophy, there's still the problem of the false dichotomy. Essentially there is invalid logic being used in the assumption that "if length is not fundamental, then nothing is fundamental but the mind". Ie. "if length contraction is a part of reality, then reality can be described by subjective idealism." (http://en.wikipedia.org/wiki/Subjective_idealism)
It is a false dichotomy because it leaves only two options, where either
1) length is not fundamental and therefore nothing physical is fundamental (which doesn't follow logically), or
2) the only other option is that length and some other arbitrary set of physical attributes are fundamental.
owl, how does length not being fundamental imply that nothing real is fundamental? Does length being objective (as you argue) imply that everything is objective and nothing is subjective? And if not, how do you determine a dividing line between what physical properties are fundamental and which are subjective?
1 
[...] (Tired of the level of quibbling here with dogmatic believers in length contraction.)
[...]
Is earth a very nearly spherical body or is it a severely oblate spheroid, say with diameter through the equator 1/8 th the diameter through the poles, or viceversa, depending on frame of reference?
What is the point of repeatedly objecting to those who accept modern science and relativity's logical necessity of length contraction, and then repeatedly asking if they accept a consequence of length contraction, only to again repeat your objection?
If you want to avoid a discussion of reality as measured by observation, why not just stick to pure philosophy and keep it abstract? As soon as you claim that an idea represents reality, you are forced to deal with the problem that it must correspond to observed reality, and if it doesn't and you can't explain why it doesn't, then your claim cannot be accepted.
I remember being taught that much of the development of logic was done with the goal of proving the existence of god, but they couldn't prove the existence of something real based only on reasoning about abstract concepts. Perhaps it's even been proven that it's impossible to deduce the reality of something based only on abstract logic. Is this true? If so then any progress you make in describing reality will be revolutionary in both science and philosophy. I just don't think that "Imagine a universe where the principle of relativity doesn't hold; seems alright to me; I rest my case" is enough.
1 
Under straight asking (that is, if you were to ask "Which door would you say leads to life?"), he tells the truth. But under this question, he tells a lie. This means that his straight answer would be the door to life, so his answer to the full question could be either of the other doors. I don't think it was specified that he has to act consistently from one time to another, which means that this is a legitimate opportunity.
I think the most useful specification of the rule is that the random guard would have to pick between being truthful or a liar, and be consistent throughout the question. If he could switch halfway through, then any multipart question could probably essentially be given random truth values, and the final answer would probably be random and thus useless. If there's a way to phrase it so that this doesn't matter (I doubt it's possible), that would definitely be Nightmare Mode for this puzzle!
Yup!
[...]
It's so simple it took me a long while to get it. For some reason I'm reminded of NAND gates.
However, given that the random guard could one day answer truthfully and another day answer falsely,
you'd probably have to phrase the question to avoid allowing him to speak of what his answer might be some other time.
Eg. if he's truthful, he may truthfully answer that he could randomly lie if asked a question???
Perhaps, "If I were right now asking which door leads to life, which could you answer with?" resolves the ambiguity?
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When did that become a rule? In every answer so far, the guards can indicate a door. Say in this one, they could indicate up to 2. There IS an answer, and it's super simple.
I think we need to restate the rules for this new variation. The original rule was "You walk up to a guardian and ask him the one question you are allowed and he tells you which door to take." If the guard can give more than one piece of information, why not 3? Why not ask a question that needs to be answered in essay form?
I'd interpret the original rule to mean that a guard can basically indicate a single door in answer to any question. (The precise wording is bad, because if you ask "what door would the other guard tell me to take to avoid death", a valid answer is not the same as the guard telling you which door to take.)
Edit: The rules should be that you can choose whatever door you want based on however the guard answers, however in the case of 3 doors the question would by necessity have to make the guard indicate the good door (not one of the 2 bad doors, which wouldn't give you enough information to choose).
Restated:
1. 3 Guards One always tells the truth, one always lies, and one who tells the truth or lies randomly. Also, by "randomly" I think we mean the guard either answers a full question truthfully or falsely, rather than giving a random answer.
2. there are now 2 death doors and 1 good door
3. You can ask any one guard any question and the guard will indicate a door in response, if it's possible and consistent with rule 1. (Otherwise their head explodes, I think is the standard rule.)
Can it still be done?
(I assume your version is not the same... can you restate it?)
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That looks like an excellent resource, thanks.
After a quick glance at the section it looks like his explanation works with simpler requirements (his works with slowmoving objects but mine requires highspeed oscillation of all masses).
I think I judged these explanations with the wrong criteria. I'd assumed that explanations involving the fewest requirements are superior, because if another explanation requires some other precondition, then the former explanation must be more general and account for a greater range of phenomena.
But I think instead that all that matters is whether or not the required precondition is observed in all cases that the various explanations cover.
In this case, the precondition is the requirement that "all mass must oscillate at the speed of light." So the only question is whether or not that's true, which I think it is (based just on a vague understanding or misunderstanding of matter and energy).
If it's true that all mass oscillates, then an explanation of gravity that makes use of that could actually be simpler or perhaps more intuitive, because it may correspond more closely with reality.
However, correspondence with reality means correspondence with observations and thus also with theories (and their explanations) that correspond well with observations, and the judgment of that is how well the math corresponds. I've been trying to convince myself that this speculation "works", while avoiding figuring out the math, which is probably foolish.
Since we already have equations that correspond well with observations involving gravity, I think the way to turn an idea into a viable explanation is to "massage" the idea and the math to fit each other, while ensuring that one has a reasonable explanation for why each step is being done. Ideally, I'd like to take some already accepted ideas about mass (such as ubiquitous oscillation) and spacetime curvature, and show that existing equations can be derived directly from that.
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If we're talking about the potential, the slope represents the acceleration. [math]F= \nabla{U}[/math] If you divide through by the mass of the object, you are left with the acceleration and the potential
That makes more sense.
If you try to accelerate away from the mass with that force, it will balance gravity and you won't go anywhere.
If you accelerate away with a higher force, you'll move away but it will take infinite time and energy to escape it, until you reach the escape velocity (which will be smaller the farther you are away from the mass, corresponding with decreased gravitational acceleration which can be seen in the video as the slope of gravity wells getting shallower the farther you are from the mass). At escape velocity, your momentum will carry you further from the mass and its diminishing gravitational force will not ever be able to slow you to a stop, and you can escape without any additional energy spent.
Just out of curiosity, would escape velocity instead correspond to the height of the well at any point? Which would also correspond to the integral of the slope of the well wrt. time, along the infinite line of an escape path of an object moving directly away from the mass?
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As we see in this video at 1:00
the moons gravity well is very small, hardly extending towards the Earth. So then how does the moon pull on the Earth?Every mass pulls on every mass (gravity has an infinite range).
The moon's gravity well is not "small" but "shallow", especially at the range of the Earth.
The slope of the well corresponds to escape velocity (I think), ie. how much effort is required to escape from the mass.
If you could accelerate the Earth, it would be much easier to make it fly off from the moon than from the sun.
Or another way to think of it: The Earth's velocity around the sun keeps it in orbit, but it would be fast enough to escape the moon. (We don't escape the moon however, because the earth/moon barycenter also goes around the sun, while the Earth's velocity around that barycenter is relatively much slower).
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I heard a story on coast to Coast about a guy who was driving a car down the road and someone pulled out in front of him. he was doing 90 and had no way of swerving to avoid the other car. the next thing he knew he was on the other side of the car. He looked in his rear view mirror and the guy in the other car was still sitting there looking in the direction in which the first guy came. I know that it is possible for a large macroscopic object to tunnel through a barrier but you would have to wait longer than the lifetime of the universe for such a tunneling to occur.
If there was no chance of it happening then it didn't happen. The chance of something like a grain of sand "tunneling" through a piece of paper is a macroscopic event that is unlikely to occur in the lifetime of the universe (just a guess; can anyone confirm?). A car passing through another would be ridiculously less possible.
A more probable situation is something like this: There was a way of swerving to avoid the car. Possibly the subconscious mind was able to react, and through a combination of quick reaction and luck, the driver was able to squeeze by. Meanwhile his conscious mind may have been in shock or otherwise unable to register or recall what happened in that short amount of time. So it only seemed that it happened too quick to be possible, according to the conscious mind.
The story relies on human perception. It is astronomically more probable that that wasn't so accurate, than it is for a car to tunnel through another. It would also be more probable for the driver's brain to instantly completely spontaneously combust, than for a car to tunnel through another. It would also be less improbable for the driver's memories to be instantly randomly replaced by false memories of an entire alternate life, and to wonder why he'd suddenly teleported into a moving car.
Is it possible that this occurred somehow. Other callers also called in and related stories of driving through other cars in an accident and appearing on the other side. Is anything like this possible or were they all lying? The only way I can see it happening is if the car tunneled or If what I suspect is right and we are in a simulation, they or something simply rewrote physics for that specific event. Also i was registered here and then i was not registered? did they do something to the accounts. because I posted this before and they moved it to pseudo. but then my account got deleted and I don't know what happened.
It sounds like it was a glitch in the matrix.
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Traveling at the speed of light paradox?
in Relativity
Posted · Edited by md65536
Let's consider this in terms of the twin paradox, so that we can synchronize clocks at a single location and make sense out of it.
Suppose you left earth with a velocity that approaches c, and you get bounced back off a mirror one light year away.
The earthbound twin would observe that you reached the mirror after one year, but it would take one year for that observation to return to earth. Over 2 years, the earthbound twin can watch you approach the mirror (assuming we have additional signals to mark your progress, otherwise I think you'd be dimmed and redshifted to invisibility), and then after 2 years, you return at what approaches the same instant that observations of you reaching the mirror reach the earth. The total time is 2 years, the total distance is 2 LY, your speed is measured as approaching c.
The earthbound twin can calculate that "your time comes to a stop" as the Lorentz factor approaches infinity and the elapsed time according to your clock approaches 0. In this case, the earthbound twin has aged 2 years and the traveling twin aged essentially nothing.
Now from your perspective as the traveling twin, as the Lorentz factor approaches infinity the distance to the mirror approaches 0 and the time to reach it (traveling at a speed approaching c) also approaches 0. The return journey is the same. The distance to your destination has lengthcontracted to nothing. You travel essentially no distance in no time. Your time continues passing at the usual rate, but the entire journey happens in an instant. Your speed is c calculated using limits. You'd also calculate that the earthbound twin has aged 2 years in that instant. As usual everybody is in agreement about what happened.
You can only come to a conclusion like "you travel nonzero distance in 0 time" if you mix up frames of reference and use distance from one and time from another, or something like that.
Also, light has no "frame of reference" but we can use "limits as v approaches c" instead of "v = c" to avoid problems.
For example, in the above example at v=c it wouldn't matter if you traveled a rest distance of one m and back, or of a billion LY and back. Calculated using only "distance = 0 and time = 0" for the traveling twin, the rest distance is indeterminate. The earth twin could have aged 2/c seconds, or 2 billion years, or any value.