md65536

Do you think that Earth might be flattened, as per SR theory (length contraction), or do you know that it is close to spherical? The latter is true by the best Earth science of direct observation. Take your pick. A flattened Earth is simply nonsense, based on a very stupid theory that objects have no shape on their own but rather depend, for their shape, on how they are observed. Think about it and decide for yourself.

Very similar to:

Btw, before I take off for the weekend (or while I am gone) will you please answer the following, now posed for the third time... very relevant to the "length contraction" part of relativity theory:

"Do you really, truly deny that "...the distance to the Sun (remains) around 93 million miles, regardless of who is flying by at whatever speed measuring it?"...

or that a squished nearly flat shape of Earth is equally valid with the well established nearly spherical shape?

Very similar to:

I'm gone for a long weekend after checking in tomorrow morning, so I want to ask an important question before go, just to simplify the issue presented in this thread, and I will post this before reading anymore replies from this afternoon. (Tired of the level of quibbling here with dogmatic believers in length contraction.)

 

[...] let me ask the forum a sincere question:

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 vice-versa, depending on frame of reference?

Very similar to:

I asked (again) recently if anyone actually believes that earth's diameter or earth-sun distance actually varies with different frames of reference from which they are measured. Apparently no one wants to look foolish enough to affirm contraction/expansion of that diameter or the one AU distance, but relativity's "length contraction" insists on their variability.

You ask this question over and over but you don't accept any of the answers that people give.

Philosophy (ontology) asks what it is. Science asks how it works,without asking what it is. Call "it" anything, and make it a part of the math equation. Don't even ask what it is. Ontology asks what it is.

Both philosophy and science are concerned with the answers to questions. You do not seem concerned with answers. Are you sure what you're doing is philosophy?

You've mentioned that philosophy of science is interested in knowing how we know what we know. But you don't seem concerned with even knowing what questions can be answered. You'll ask questions over and over again regardless.

I might consider it some form of meditation to repeat unanswerable questions over and over, but your posts seem to me more about the statements than about contemplating questions.

I still don't know what your goal is. Are you "enlightening us" with questions but no answers? Or are you waiting for someone to come along and say "You were right all along and Einstein and everyone after him were wrong!", and then for that elusive genius to give definitive answers to all the meaningless questions you incessantly ask ("What is IT that curves?")? These are questions for which you've never provided a lead in to a discussion of any answers.

Science does fine without your questions. It has its own questions and it actually works toward answering them. What is the goal of the questions you ask? Have you even begun to figure out how one would go about answering them, let alone actually tried to answer them? You ignore answers, and then ask again. Is there any progress being made?

Feynman--"Philosophy is bullshit"....

Not always!

But plenty of evidence in this thread for how it can be.

I read a few articles, and I already know how fractals themselves work, but I don't get how I'd write a formula for them or make them on paper. Basically all I know about them mathematically is that in a Julia set it just repeats a function over and over again, and a Mandelbrot set uses imaginary numbers, and the initial points don't escape to infinity.

What's been discussed here so far involves iterating over a grid of pixels and using a function to evaluate a color for each pixel.

To draw fractals on paper you'd probably want to do it a different way.

If you take a shape or a line segment, and modify it in some way to create additional (smaller) shapes or line segments, and then modify each of those segments in a similar way, and keep going until the details are small enough, you should end up with a fractal.

Some easy fractals to start with:

Mountain:

Start with two horizontal points at either end of the page.

For each set of two adjacent points, find the midpoint and then raise it or lower it randomly by some factor that is proportional to the horizontal distance between the points (so that the random offset gets smaller as the points get closer together), and add a point there.

When the points are close enough to not be worth subdividing further, connect them with a line.

Tree:

Start with one vertical branch from top to bottom of the page.

For each branch, add some specific formulation of child branches. Eg. split each branch into thirds, and add a "twig" 1/3rd along the branch, pointing 60deg to the left, with length 2/3rd of the branch, and add another twig 2/3rd along the branch pointing to the right with length 1/3rd of the branch. This particular formula will give you a lopsided looking tree.

Repeat for all new twigs/branches that are big enough.

If you do this and look at what you've drawn, you'll see that each branch on its own looks exactly like the full tree, only smaller.

Lame-looking snowflake:

Draw an equilateral triangle.

For each line segment, divide it into 3 sections and draw an equilateral triangle jutting out of the middle section. Repeat.

These are just 3 simple examples off the top of my head. There are probably much cooler, interesting ones out there, with instructions. It's not hard to come up with your own variations. If you look at simpler computer-generated fractals, you may be able to detect a pattern that can be used to draw each smaller iteration, based on a bigger iteration.

Thanks again for having a go at this! I hope it's been some fun for you. I am not convinced by the reasoning of removing elements from one set but not the other. I think there must be an error because I think we can show that the formula is wrong by looking at the simple case X=Y=T, i.e. my two subsets are the whole set. In this case, it doesn't matter what N is, the probability has to be 1, because whatever element(s) you pick from one subset are bound to be in the other. But your formula for P2 gives 0 if Y=T, so the final probability also comes out to be 0.

 

As I said, I will try the N=1 case or some other simplification. It's obviously a bit too ambitious to have a go at the general case yet.

Well, it's an interesting puzzle and I think I must have OCD.

In the case that X=Y=T, the probability that N elements in X match exclusively with N elements in Y is 1 iff N = X, otherwise the probability is 0. I think it's okay for the formulae to fail in impossible cases, and usually you exclude impossible cases in the description of the problem (because we'll already know that it's impossible if N is too low relative to T, etc).

The reasoning is that "This formula only works when there is enough of the T elements to be split up among A and B so that after the N elements are matched, there are still enough unique elements to fill out A and B." Otherwise if it's impossible to do so the probability is 0. So we can say "For X-N+Y-N > T-N, the probability is 0, otherwise it's... (some formula)".

But I must have been on crack in trying to figure out the "P2" part in my last post. So I'll give it another go!

Basically, in the P1 part we match the first (in an arbitrarily chosen order) N elements in A with elements in B. We can remove this subset C of matching elements from A, B, and the full set with T elements. We're left with 3 smaller sets and we want to find the probability that none of the elements of the first are in the second, where both sets are subsets of the 3rd.

So let's look only at the P2 part with some new names. Let's call the sets E, F, and G, with size e,f,g respectively, where E = A \ C, F = B \ C, and G = {the full set with T elements} \ C.

We want the probability that no members of E are in F. I tried to do it one way above and the math didn't come out nice.

But I realized that the problem is equivalent to finding the probability that all the members of E are in the remainder of G after removing F. That is, if all members in E are in G \ F, then no members of E can be in F.

So like with figuring out P1, the chance that the first element in E is in G \ F is: (g-f)/g

And for the next element is (g-f-1)/(g-1)

etc for all e members... with a product of P2 = (g-f)!/(g-f-e)! / (g!/(g-e)!)

I just checked an example in a spreadsheet and I get the same value as the convoluted math of my last post!

Note that e=X-N, f=Y-N, g=T-N

So I think the P1*P2*(_XC_N) formula is now something manageable, when it's all put together!

I think I may try a less general case first, such as N=1 or X=Y, and see if I can work out the formula for that, and hope that it will help me see the general problem in the right way. The second part will have to be done in some such way as the one you suggest, but I haven't found a way to think about that yet.

So, out of curiosity I tried working through the first part and I get the same answer you did.

I should warn you that I'm not a mathemagician!

ALSO NOTE: At the end of writing this I ran into a problem that puts the math for "P2" below in doubt. If you can follow my reasoning below you might be able to figure out if it's okay or if not, maybe you can see the right way to do it. I'll probably look at this again later and see if I can figure out the problem, but it might be beyond me!!!

First part:

Consider the first N elements of set A. The chance that the first element is in Y is: Y / T. The second (Y-1)/(T-1), etc.

The product of all N is: P1 = Y!/(Y-N)! / [T!/(T-N)!]

This is the same answer that you came up with.

So while we were doing this we removed matching elements from B and the set that had T elements so that they didn't affect the probability of matching subsequent elements.

We're left with (X-N) elements that we want to make sure are not in a set of (Y-N) elements, which can be chosen randomly from a set of (T-N) elements.

Sorry for the mess of notation but let's call C the matching subset with N members.

The chance that the first element in (A \ C) IS in (B \ C) would be: (Y-N)/(T-N)

So the chance that it's not is 1 - (Y-N)/(T-N)

Now, we don't have to remove any elements from (B \ C), because we didn't match any!

I'm not so sure if we should remove it from the "main set" that has (T-N) elements left in it. But I think that we should!

So the chance that the second element in (A \ C) is NOT in (B \ C) is 1 - (Y-N)/(T-N-1)

We do this for all (X-N) elements...

... exceeding my math abilities...

We get the product P2 = [1 - (Y-N)/(T-N)][1 - (Y-N)/(T-N-1)] ... [1 - (Y-N)/(T-N-(X-N-1)]

I don't know how to simplify that. There's gotta be a simpler expression!

Finally X C N = X! / (N! (X-N)!)

Then the final answer would be P1*P2*(X C N)

Note: If (X-N)+(Y-N) > (T-N) then P2 must be 0, because there is no way to divide the "leftover" elements of the full set between sets A and B, with no overlap between them.

If we allow such a case, then one of the products in P2 should be 0, but you could also end up dividing by 0.

Hrm.....................

Atheism in general isn't specific enough to exclude either a belief in the non-existence of deities, or a lack of belief. I think both sides in this thread have used the word atheism in an over-specific way to exclude one or the other.

See: http://en.wikipedia.org/wiki/Atheism#Implicit_vs._explicit, and more-so http://en.wikipedia.org/wiki/Atheism#Positive_vs._negative

If you want to exclude one side or the other, use more specific terminology.

So either my formula is wrong or the extension you suggested is wrong. I need to get my head round that!

I think that using the number of combinations and simply multiplying by that, assumes that only one possible combination can work. Otherwise, the probability of one combination working can overlap with the probability of another combination working, so you can't just add their probabilities together.

As an example, say that X = Y = T = 10, and we choose N = 5.

Obviously, all 10 members in your chosen set (A) match all 10 members in the other's chosen set (B). Probability is 1.

Any subset of 5 that we choose will also match (but not exclusively; the remaining 5 will also match).

10 C 5 is 252, so if we just add up the probabilities that each possible set of 5 matches, then we get a probability of 252, which is wrong.

My formula is wrong for doing it this way. If your formula is right, mine won't work with it.

However, with the original question of matching only exactly 5, if say X = Y = 10 but T = 100, and say that the intersection of X and Y has 5 members... then there is only 1 possible combination of 5 members from X that matches exclusively with 5 members of Y. The chance that one combination matches excludes the chance that some other combination also matches.

I haven't wrapped my head around the first part of the puzzle enough to know whether either of our methods seems right or not.

That is... my strategy is to find the probability that some specific (but generic) set of size N will match exclusively, and then multiply by all the possible ways you can choose that set. If you can find the probability that any set of size N will match exclusively, then you don't have to worry about the number of ways you can choose such a set.

Btw, before I take off for the weekend (or while I am gone) will you please answer the following, now posed for the third time... very relevant to the "length contraction" part of relativity theory:

"Do you really, truly deny that "...the distance to the Sun (remains) around 93 million miles, regardless of who is flying by at whatever speed measuring it?"...

or that a squished nearly flat shape of Earth is equally valid with the well established nearly spherical shape?

Folks, owl has been kind enough to provide some discussion material to keep us going while he is away and there is no one to tend his thread, and we haven't even managed a half-decent answer to this thrice-asked question yet.

I myself don't feel qualified to answer, having already given unaccepted answers to same question when it was asked in the form of "Do you honestly think that..." and "No seriously, do you really really really think that... (really?!)"

He'll be back soon and it would be quite embarrassing if we didn't have an answer this time that's at least better than the pitiful sets of replies we gave last two times around.

I was wondering if there have been any neutrino bursts which have reached us a few years before the observance of a super nova? Surely we could've detected something like this by now. If not, are there any groups checking the data to see if we have observed this?

SN1987a is 168000 LY away. A burst of neutrinos was detected at 3 separate observatories about 3 hours before visible light was detected. http://en.wikipedia.org/wiki/SN_1987A These two observations can fairly confidently be correlated.

With OPERA's 60 ns "faster than light" speed, neutrinos (of another flavor I guess) might be expected 4.1 years in advance. With an estimated error of 10 ns, that translates to +/- 0.69 years. So that's over a year's worth of possible observations of a neutrino burst that could be connected with SN1987a.

I can only answer your question with more questions:

- Are there any other observations of super novae that have occurred recently?

- Does the detection of a neutrino burst give you enough information to connect it with a super nova event (such as the direction the neutrinos came from, etc)? If not then it's possible that neutrinos from SN1987a could have been detected over a long period in 1982/83 without any way of determining whether they came from SN1987a or some other source.

- Were there any neutrino bursts detected in 1982/83?

As swansont mentioned, possibly no one was looking for neutrino bursts in 1983/84. I would hope that if there are any known detections of bursts from back then, that someone has checked to see if they might correlate! Otherwise, with no news about it either way I'd assume that it's because there have been no measurements (either of a burst or of a lack of bursts) that could support or oppose the idea of neutrinos arriving years before a supernova is visible.

I think that's what the answer to your first suggestion is. I got a bit stuck thereafter, trying to tie this probability with the probability of those N members being chosen from the first subset, the one that contains X members.

I haven't worked through the math or logic of the first part, but I'll go on to this part.

The first part deals with the probability P of an arbitrary selection of N elements matching in sets A and B (and importantly if you haven't done it*, it must also include the probability that the remain elements don't match).

http://en.wikipedia.org/wiki/Combination

_X C _N ("X choose N") tells you the number of different ways of choosing N elements from a set of X members.

Each of these possible subsets are similar and each has a probability of P of matching exclusively to sets A and B.

Each of these possible subsets is equally likely to be chosen as an "arbitrary selection of N elements".

Each of these possible subsets are unique, so the possibility of choosing one vs another is mutually exclusive. That means that you can just add up the probabilities of any one of them matching (which is P), for each of the possibilities of actually choosing that group.

So the final answer should be: P * (_X C _N)

If it's confusing, consider it to be rephrasing the question to be: "What is the probability that this group of N elements from A matches exclusively with B, or that this other group of N elements does, or that this other group does (and so on for each possible group of N)?"

* Glancing at your solution to the first part, I'm guessing that it doesn't take this into account? If you calculate the probability that all N elements match, but leave open the possibility that additional elements will match, then the probabilities of one combination matching vs another are not mutually exclusive or whatever, and the second part won't work.

1. E_loss = 0 (Assuming closed system)

2. f = random()

6. v = [0, 1, 0, 0] (With a coordinate system aligned in standard configuration???)

8. f = sin(x)

Is this a cryptologic word puzzle? Are my guesses at all close?

I have a problem which I will first state formally and then give some real-life context. Any help appreciated!

Suppose I have a set with T members. I randomly choose a subset with X members. Independently of that, someone else randomly chooses a subset with Y members. Without loss of generality, assume X <= Y. Given a number N (N <= X), what is the probability that the two subsets have exactly N members in common?

I would try this:

Suppose you have your set A, and the other has their set B.

For an arbitrary subset of A, with N members, what is the chance that each of the subset's members is in B?

Also what is the chance, assuming that each of the subset's members is in B, that each of the remaining members in A is not in B?

Then use combination to find the number of ways to choose a subset of A with N members.

Without filling in the details, I don't know if this work properly and simply enough. Is it enough to inspire a solution???

And if the above is correct, one could make a statement following which the ruler is a clock for all FOR different from the ruler's FOR. IOW the ruler is not a clock only for its own FOR.

I think you're hiding flawed logic in a fog of vagueness. Relativity is not so flimsy, and it's easier understood when you state everything clearly.

First of all, I don't think "a ruler is a clock" is meaningful. How is it a clock? The answer to that question is what makes it a clock (or not a clock, depending on how you answer). Eg. it's not just a ruler that makes a clock, but a ruler and a light source and a light detector, or some other combination. In this case, the ruler moving against an incline makes your clock. Even if you're not moving relative to the ruler, it is still moving relative to the incline, so it can still be used as a clock in the ruler's frame.

Second, clocks measure proper time. (I suppose you could build an apparatus that doesn't, and still behaves like a clock... then maybe you could call it something like "a clock with a limited domain" or something like that???) The universe is consistent, so if one observer observes that a device accurately measures proper time (and is thus a clock), then all observers will observe observations that are consistent with that (everyone will agree that the device measures proper time).

For example, following Galileo's experiment: putting a ruler inclined and making a small sphere rolling upon it.

When the sphere passes by over a line of the ruler, one unit of time has passed.

Of course the problem arises that if my lines on the ruler are equidistant, I will measure time as accelerating.

No, you would measure the sphere to be accelerating.

The reason you can measure time this way is that the ball is moving in a precise, consistent, known way. It is known that it is accelerating, and the rate of acceleration is known (as a function of g and the angle of the ramp; they would need to be precisely fixed and/or known in order to use this to tell time precisely). So you can create a formula to describe the movement of the sphere, and find t from that, and if everything's accurate you'll find t to behave just as expected. Changing the spacing of your tick marks doesn't affect time, nor does the angle of the ramp, though they'll affect the formula and measurements.

Perhaps you can create some useful time-like property measured by equal spacing of lines on the ruler, but that isn't time (as measured in consistent intervals by other clocks).

What is their purpose according to the world of psychology?

Do they even need to have a purpose? Could it be just part of the brain continuing to function when it is not really needed? In that case it might be like asking "What is the purpose of a sink with a leaky faucet when no one is using it?"

Then the question might become "What (if any) are the advantages offered by dreams?" If there are evolutionarily significant advantages, I suppose you could say they have a purpose or developed a purpose. I don't have any clue whether dreams came "for free" along with brains, or if they evolved later as separate brain functions.

It's not hard to guess at some possible advantages offered by dreams. They offer practice for cognitive skills. They offer time to contemplate situations when there aren't more immediate things for the brain to deal with; one can simulate decisions or emotional responses to different situations, so when faced with real situations the brain already has experience dealing with similar things.

To be correct, without friction the ball will not roll, it will slide. I could have put a square in place of the ball.

Sorry, I was wrong. You are correct. http://www.newton.de...05/phy05139.htm

My reasoning is bad because the ramp doesn't just provide an upward force that counteracts gravity (preventing the ball from accelerating at free-fall speeds), it also provides a horizontal force that causes the ball to accelerate horizontally too. It seems that the composition of these two force components will act normal to the ramp?, which for a ball will make a line between the point of contact and the ball's center of mass. This removes any "off-balance" force that could cause the ball to tip.

However I don't think the same reasoning applies to a square block in general, if the block could be positioned with a corner (single point of contact) against the ramp, which could be done so that the normal force doesn't intersect the center of the block, then the normal force could provide some rolling torque to the block. In the typical starting case (probably also a stable state if the block was allowed to slide indefinitely), with the edge of the block flat against the ramp, any amount roll would cause one of the corners to become a "pivot point" which would tip the block back toward "flat against the ramp", so I guess even if it started off-balance on a corner then a rolling angular velocity couldn't accumulate for long or something, and would instead oscillate while approaching 0? Just like a block that is off-balance on a horizontal surface will roll, but only so much that it will rock back and forth and settle into a state with 0 roll. A block that is flat against the ramp will not be off-balance, no matter what the angle of the ramp is, because the force acting on the block and ramp is normal to the ramp.

I don't wish to suffer my wife's anger.

You cut a piece out of the brownie and didn't even align to the edges and you're hoping to not suffer her anger?

Here's the only idea I could think of:

To be correct, without friction the ball will not roll, it will slide. I could have put a square in place of the ball.

On an incline steeper than 45 degrees, a square shape (as in a side view like the diagram's) will always be off-balance, and I believe should always tip over even while it's sliding, so it should develop a rolling angular momentum even though it is sliding frictionlessly. For steeper inclines: The rate of acceleration of tipping or roll would approach 0 as the acceleration approached g, which would (only?) happen if the angle of the ramp approached 90 degrees. Anyway the rolling momentum would be very little on a short ramp as in the example, especially with a square shape starting flat against the ramp.

On any incline a ball should be always off-balance. If there's no friction then the ball's roll should have no effect on its linear movement (the movement could be entirely described as sliding even if it is also rolling).

If we replace the ball with a square, and then replace the ramp with stairs, we should be able to describe setups where a block still slides down the stairs, or where it only tips and rolls down the stairs (and slides too?, maybe necessarily), or where it doesn't move at all.

Sorry, this is getting further off topic... I think it's interesting but it doesn't make a difference to the puzzle.

Under standard concept, and on all known spacetime diagrams, the Moon in the past is a point on a line that extends along time. The Moon through time is not a point, but a line.

The line is a world line. It's a line through two dimensions (on a 2d diagram at least). One represents time, the other represents... space! It is not a line through time, it is a line through spacetime.

Which means that contrary to space, where an object change coordinates, in time an object does not change coordinates but "develop" in the form of a line. The object is presumed to be remaining at all its past coordinates. (or i have a bad understanding)

No, the object doesn't remain at its past coordinates, it moves through both space and time.

What remains at past spacetime coordinates is "events", including if you will the event of "being" at a certain location at a certain time. The moon of some moment in 1969 was at some location and that event is fixed there and then.

We are certain of this to the degree that we are certain of our understanding of applicable aspects of spacetime and reality etc.

To say that the world line "develops" along one dimension and "changes" along another dimension, makes me think that you may have some additional assumptions that are getting in the way of understanding this. I don't think I understand it enough myself, or can explain it any better than has already been explained in this thread, but perhaps someone else can. I think the confusion comes from assuming something more than what was said, so there may be some important bit of information that is missing in these explanations which you are filling in with incorrect assumptions??

The moon, an object, usually refers to a ball of mass as it exists in one specific place and time. The moon described by its world line, something that "is" in all the places its ever been, is not an "object" that has an existence in reality as we know it. The world line is fixed in the 4d spacetime manifold. It only "develops" from the perspective of one who sweeps a plane along the time dimension... which essentially corresponds to our perception of the 4d spacetime manifold. When you view a spacetime diagram, you can look at the whole thing at once. But the way you would experience it in reality is not as a 2d diagram (experiencing it all at once) but as a line that sweeps along the time dimension. If this is confusing it's probably because I don't know the right words or even the right understanding!

And for time,

paraphrasing: "the time coordinate can become "empty" as the object that used to be there moves away".

I would paraphrase it thusly: Given that the moon "occupies" some given 4d spacetime coordinates...

For space: At another time, the moon might not occupy that same space.

For time: At another location, the moon does not occupy that other location at the same time.

When you're talking about the moon moving away, you're talking about another time.

If you're talking about one specific value for time, then the moon has a fixed spatial location for that fixed time.

Sorry, I don't seem to be understanding what you're saying.

We simply can make the statement that the Moon is not in 1969 any more, so I guess the coordinate is empty. But it is simply a guess. To be sure, I'd like to have a look there to see if the Moon is in 1969, but I cannot. A fellow scientist in present time 42 Light Years away from us can have a look there. The problem is that I cannot have any communication with that fellow scientist (even if he existed). If I go and travel 42 LY away, I will still be upon the surface of Earth's light cone, so I will never be able to see again the Moon in 1969. I am a prisoner of SOL. How can I get away and be sure that nothing else occupies Moon's ancient coordinates?

No, it doesn't make sense to say "the coordinate is empty". An event happens at a particular place and time (a 4d point on the spacetime manifold) and that point is fixed in 4d. It doesn't change. See http://www.scienceforums.net/topic/59951-inflation-and-causality/page__view__findpost__p__627339

The spatial coordinate can become "empty" as the object that used to be there moves away (so XYZ="where the moon was in 1969", T="2011" could be "empty"), but the spacetime coordinates of an event such as those involving the moon landing, will always be associated with those events.

As I've already mentioned (#39), we know things about the past and the future, to varying degrees of certainty, due to physical laws, and we also know things about the past to varying degrees of certainty, due to memory (which also involves physical laws, allowing information to propagate through confined locations or something). Our conviction comes from our level of certainty of available information and of the physical laws.

I'm not sure if the question is "Since we can't directly see the spatially near, temporally distant past, ...

... how do we know it hasn't changed?" -- The answer is that the spacetime manifold is fixed. Or,

... how are we certain that it happened as we say it did?" -- We are very very certain of the laws that connect those past events to current events, and of the directly visible information that is causally connected to those events (photographs, millions of human memories, etc).

We're not that certain of everything. We know the solar system formed, and it contains clues about how it formed (ie "memories"), and we can observe other systems forming (visible accretion discs) and consider it likely that ours formed the same way that others did (due to "physical laws"). So we think specific events happened in the past, many of which we're not that certain of.

My take on this:

F:

To say that the height the ball will reach after reaching its minimum is 3m assumes that the ball is perfectly elastic and there is no loss of energy anywhere, which I don't think falls under the umbrella of "excluding any friction".

However the elasticity etc is not specified, and the "maximum" height is asked for, so I think it's fair to assume best-case conditions of no loss for "maximum possible height".

Technically, the question doesn't even specify that the "max height" is only after reaching its minimum, and the ball is already at 3m at the start so its max height cannot be any less than that.

C:

Typically a ball will roll down the incline and acquire angular momentum, which might allow it to roll up the incline after hitting the "wall". To see this effect, roll a rubber ball along the floor against a flat wall, and the ball can bounce with some vertical component to its velocity. Without knowing the properties of the ball etc it would be impossible to calculate C.

However, this doesn't apply to the puzzle because it relies on friction in order to convert the ball's angular momentum into linear momentum.

Excluding all friction, the ball would slide down the incline, but it would also roll (I think) because the downward gravitational force is the same throughout the volume of the ball but the upward force of the plane is off-center, allowing the ball to constantly keep tipping faster off balance as it slides down. This is beside the point of the puzzle though.

I think that the " final theory" will be much simpler in almost every way, as well as more logical than any of today's theories. Most everything in theory's models that have excessive complication will be eliminated. All of the major theories of today such as Special Relativity, General Relativity, Quantum Mechanics, the Standard Model Particle Theory, The Big Bang Theory, -- all will be almost entirely replaced by simpler conceptual models that will have kinship with each other enabling them to all be tied together theoretically. Mathematics will then become more of a servant of these models rather than the foundation essential.//

I think it will be "less logical", or at least have less correspondence to a "common sense" understanding of reality.

My idea of what a ToE will look like is "Emergence", where the other theories you mention are emergent aspects of some more-fundamental description of the universe, of which we only see and experience emergent aspects. Gravity, particles, geometry etc would all be emergent. What I don't have a guess about is whether we would be able to figure out "the absolute fundamental nature" of the universe, or if it might be possible that any more-fundamental model of the universe that we could describe could itself be emergent from some other model.

I think that any such fundamental models could be described mathematically, so I doubt that all of math could be emergent.

Perhaps I'll start a new thread before I ramble off topic...

Note: If my equation is correct, there will never be a more powerful equation, nor will there ever be a more complex structure, therefore, this equation if accurately descripted. would be the "master equation" with all other equations and geometries being a subset.

 

Is an equation like this thought possible? Has there been talk about an equation like this? What would the ramifications of this equation be?

Don't Gödel's incompleteness theorems imply that this is impossible? Wouldn't such an equation have to transcend the set of all mathematical equations?

http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

I can't imagine anything like what you're talking about, where it must be simple enough that "cursory glances" show meaningful things, yet complex enough to describe everything. So I'm curious about your motivation for writing it. Is it just an idea you're imagining, or is it based on a real equation (or even the hint of one)? If the latter then I'm interested in what your perception of gravity is, and why it would make you think that everything mathematical can be deduced from it. My opinion is one of doubt, but also puzzlement.

http://gizmodo.com/5...ource=pulsenews

 

So wait, is it actually a spinning column of water-ice? How does it kill everything it touches? How does the difference in pressure trigger it exactly?

No. It's not really a tornado.

It freezes them and encases them in ice (it kills everything that gets stuck in the ice, not everything that touches the outside, as can be seen in the video where starfish are crawling over it).

I don't think it has anything to do with difference in pressure.

This is curious and I want to guess at what's happening here. I don't know for sure though. Guesses:

- As saltwater contacts the cold air, it is cooled enough to be able to freeze. The ice that forms from saltwater is purer water (less salty) than the water it froze out of. This means that this very cold saltwater is essentially separated into less-salty ice, and more-salty water, both of which are at temperatures low enough to freeze ice out of the (normal-salty) water. The cold, saltier brine is able to remain as liquid because it is extra salty!

- The saltier brine is heavier and sinks into the surrounding seawater. Because it is so cold, it is able to freeze ice out of the surrounding (less-salty) water. This creates a tube through which it can flow.

- The tube grows and eventually reaches the bottom. At that point, the extra-salty cold brine flows along the sea floor. It is essentially a freezing cold liquid being poured through a less-cold liquid. Anything that has the cold liquid being poured over it can become frozen, and anything that has ice form around it can become trapped in the ice.

I don't see how you're proposing anything new here, other than "don't use this particular word, use another with the same exact meaning."

 

We can call the phenomenon "Time Hooplah", but it still shows the SAME effect. So why is it different, and why does it matter.

The difference is that if you say the words "time dilation" you are reifying time, by making "something" of "it". What is "it" that dilates?, one might reasonably ask.

When you use the words "event duration of physical processes dilation", you are simply describing that durations become longer in certain circumstances. It's easy to see that durations can "become stretched out" without having to "be something" that can be stretched out. But with the word "time"... uh...

Well see, they're just different, because they're different words. I know it doesn't make any sense when I say it, but owl will explain this all much better than I can.