MWresearch

Prove it.

 

I was simply pointing out that "obviously, there are finite amounts of real objects" is neither obvious nor necessarily true. If you want to move the goalposts, that's fine with me.

Anyway, according to our models, there are a finite amount of objects in any finite space. Since we cannot measure outside of the hubble volume, our measurements of the universe are confined to finite space.

I don't think we've ever encountered anything that we've "measured" as infinite. By it's very nature, it is impossible to count to infinity.

Thank you for your continuing contributions, Acme.

 

 

So...

What is this thread for?

Is it just a trolling exercise?

I provided an answer multiple times, you simply have to read the recent posts that contain it.

 

You said "there are finite amounts of real objects" not "there are finite amounts of real objects that [have] measured".

 

If the universe is infinite, there are an infinite number of real objects. Whether we can measure them or not.

Regardless of semantics, it is a fact that people have measured finite amounts of objects. Whether or not you want the parameters of measurement to encompass the whole universe is arbitrary.

If you want you can say all measurements are an illusion, but then you would have no basis to say all measurements are an illusion.

 

Arbitrary

Generic

Subjective

Stupid

Pointless

Random

Meaningless

 

The problem is not that items on the list are "vague", it is that the defintion of the list is vague, undefined, arbitrary and entirely subjective. You suggest that the items should be "unique" in some way, but there is a massive amount of overlap and duplication so none of them are unique in any meaningful way.

 

For example you have the following items, all of which could be covered by the first item (or several of the others): Mineral, Mountain, Lava (or magma), Mud, Ophiolite Crust, Radioactive Material, Sand, Shale. And these could be described by one or more of the following "unique" adjectives from your list (and others): Amorphous, Ancient, Atomic, Changing, Eroded, Heavy, Igneous, Molten, Plentiful, Primordial, Undulating.

 

You also have some made-up words in the list.

 

This list is as useful as writing a program that picks random words from a dictionary. Your attempts to justify it by referring to non-existent or poorly-defined "parameters" makes it clear that the entire enterprise is arbitrary and meaningless.

As I already pointed, I took too much liberty in assuming too many people would understand the concept of the list by means of sociability. As I also said, the list will be modified to reflect a more strict categorical organization in the future.

One thing that has not been entirely clear to me is whether you are making any distinction between collective nouns or individual nouns and if so on what basis?

Well, with the same parameters that apply to the materials and phenomena, the standard is any adjective that can physically describe those materials or phenomena.

What is 'real' and what is an 'object'? To the second question: the boundary of what constitutes an object, and how many there are, is arbitrary. Is a wall a plural of objects (bricks) or a single object?

Objects that are real occupy nonzero quantities of dimensional space. If an object does not exist, it will not have any dimensional coordinates or capacity for empirical measurement. Take this apple I'm holding. It has 0 length, 0 width and 0 height, and no one can observe it, not even me. As a scientist, would you tell me that apple exists?

I think it's more accurate to say that certain physical systems can be modeled using the mathematics of complex numbers. Whether complex numbers (or indeed, real numbers) exist in their own right is a matter of philosophy.

 

Edit: One representative discussion can be found here: http://philosophy.stackexchange.com/questions/451/do-numbers-exist-independently-from-observers.

It is not a matter if philosophy if you consider our label of numbers to be different than the inherent values themselves. Obviously, there are finite amounts of real objects.

Well, if real numbers or values exist, mustn't imaginary values as well? Like I said, they appear everywhere in nature, yet they are no where to be found with our eyes.

I know you didn't. I did.

 

You still haven't answered my questions.

 

A reminder of my questions:

 

These questions have already been answered. If you have further misunderstanding, I suggest looking up the words "breanstorm," "save," "organize" and "time."

What is it about the number e? Why does e come up in so many core aspects of nature?

Alright, I see what you're saying. The situation then is that you're standing at a height of three meters, dropping a bowling ball, and then trying to determine at what time the bowling ball will be at a height of four meters. But a height of four meters doesn't lie on this parabola, so there's no solution. Of course, in practice, you could drop the bowling ball onto a machine that will catch the ball and launch it with enough force to send the ball four meters or higher into the air, but then, mathematically, you're dealing with a different parabola.

 

Edit: Just randomly decided to search for "imaginary time" and this came up: http://en.wikipedia.org/wiki/Imaginary_time. But it's something you'd probably want to discuss in the Physics forum.

No imaginary time makes sense in terms of treating imaginary numbers as this extra dimension and it is used in line-integrals to define probabilistic paths of particles, like if there's extra actions that happen in each particular moment in time to allow particles to move as they do. But still, treating this one special square root of negative one as its own entire dimension just be multiplying it by different real numbers, like 1i, 2i, 3i, 4i just seems like too much for one number to account for, and we can't even see it.

But with that physical situation, I'm confused as to when you say there is no solution. Is there not an imaginary solution? On which coordinate in time is that imaginary dimension perpendicular too? Can I say at y=0, there's some imaginary time where the ball was at 4 meters? How would I go about making sense of the solution i? It seems imaginary numbers encompass all of nature, they must be around somewhere...

It kind of seems like wolfram is saying that at an imaginary perpendicular axis in time where t is t=+/- i when real time = 0. A lot functions also make sense when you overlap their complex and real components, like the symmetry of the logarithm function that you'd expect from being the integral of 1/x, except with an addition +pi or the symmetry of the square root function

My point is that calling it that is vague and not in any way an answer to my very direct and simple questions.

Except I did not call the list vague, I said there are some items on the list which may be vague. There is a difference between "all" and "some."

As I said, there are items which may be vague or blatantly obvious but still fit the parameters, so I put them on.

I'm sorry, but that really isn't an answer. Calling it a pre-made brainstorm is just another way of saying that it's a pointless list of arbitrary things. What is it a brainstorm for? What kind of problems would a person need to have answered for them to need this list? How is this list useful?

When I look up brainstorm in the dictionary I do not find "pointless list of arbitrary things." Sorry, you are incorrect.

This is what I mean with the physical problem

http://www.wolframalpha.com/input/?i=solve+-x%5E2%2B3%3D4+for+x

Please see my above post. You have not answered my question.

Which I already answered, in the simplest and foremost response, it is a pre-made brainstorm. As far as I know, there is no need for further specification. Perhaps in your clearly superior being as an empress of everything, there is some extra dimension of the information in the question which I cannot see.

Also, I would think that things such as fire are useful in one of those incredibly obvious ways that rather negates the need to consult a list.

Like I said, with rules that I hold even myself to, I must put items on the list that fit the parameters, even if they are vague or blatantly obvious. But, since something like fire is so exceedingly well-known, it shouldn't be difficult to overlook.

As far as I could see, based on your responses to John Cuthber, you are not interested in substances scientists or people from more specialised areas find intriguing. This isn't a matter of how progressive I am or am not, it is a matter of you not being able to clearly articulate how this list is to be used. You claimed earlier it would be useful to chemists. I am one and it isn't. You claimed that people get paid to calculate coefficients of friction and that they could find it useful, but clearly most of the items on that list would not be useful to them at all.

Based on my response to John, I am in fact interested in substances that specialized scientists come up with, but only as much as any other person's response, they must follow the parameters the same as everyone else. It is simply the case that they may be less likely to contribute as much as other members because their dedication to a specific area of science must come at the cost of learning other things, like modern culture, which, seems to have been established as a problem for some. I also cannot logically agree that most items would not be useful to a variety of scientists. Obviously, fire has its uses, glass has its uses, rocks have their uses, plasma has its uses, electricity has its uses, energy has its uses, superfluid, different oils, water, wood and many other items have their uses.

You also only work on a specific type of chemistry currently, likely for only a specific company for an extended period of time. It is in no way logical for you to assume you represent all chemists.

Simply put, this list is meant to act as a pre-made brainstorm, saving people time and organizing items in one place if they want a list of more commonly known substances and phenomena and possibly exposing people to new substances and phenomena they somehow never heard of, allowing them to learn if they choose to research further.

 

I'll try. Just let me know which part(s) need clarification beyond what Wikipedia can provide.

 

 

Yes. We can induce a total order on the complex numbers by moving up along the imaginary axis and then right along the real axis, i.e. [math]a + bi < c + di \iff [(a < c) \textnormal{ or } (a = c \textnormal{ and } b < d)][/math]. So for example, i < 100i < 1 < (2 - 100i). It's an odd sort of ordering if we're looking at the numbers in terms of their conceptual magnitude, but as far as I can tell it does satisfy the axioms.

 

We can also induce a partial order on the complex numbers using the concentric circles of magnitude mentioned earlier, counting clockwise around each circle before moving to the "next." It's probably easier to think about this in terms of polar coordinates, in which we can say that [math](|z_1|, \theta_1) < (|z_2|, \theta_2) \iff \left(|z_1| < |z_2|\right) \textnormal{ or } \left(|z_1| = |z_2| \textnormal{ and } \theta_1 < \theta_2\right)[/math]. However, this is a bit unsatisfying since it means, among other things, that 1 < -1.

Hmm, I think I see where the ambiguity lies. If the imaginary component is bigger than that of another, but the real component is smaller than that of the same other, you cannot determine which is fundamentally greater? That seems to imply imaginary numbers have no precedence over real numbers, its as if they were never related to real numbers at all, completely independent like its own dimension which I guess explains the orthogonality.

For practical purposes, lets say I'm dropping a bowling ball from a height of 3 meters, but I solve for 4 meters of a downward parabola with a maximum. Where is that imaginary solution in physical reality? Where is that extra imaginary dimension I'm not seeing?

Thank you for those. It appears the crust is more or less always stable except for specific events where it must adjust due to the loss of angular momentum.

Also, no. We are not making strict guidelines or rules for your own list, that's your job. And we sure aren't making this a sticky.

Well that's the shame, some other site will eventually, possibly not geared towards science and they will seep traffic from what would have otherwise helped this site and expose more people to in-depth science. But, I can see that diversifying and collaborating on something that clearly both layman and scientists can contribute to and discuss would be too progressive of you, too much in the interest of others and would deflect attention away from your superiority over all other beings as the empress of everything, clearly refraining is the better move for the site.

the

 

 

The direction of an axis showing the square roots of a negative number is ORTHOGONAL to the positive number line not in the opposite direction

The negative number is what's going the opposite direction, not the output of the square root function over the negative portion of the domain.

Then let's start with 0. What is i compared to 0i? i seems to possess some nonzero distance from the origin, doesn't it have to be greater than or less than 0i? Perhaps it is just that i isn't comparable to real numbers, and thus complex numbers containing both a real and imaginary component are inherently incomparable, but that doesn't answer why imaginary numbers aren't comparable in the first place. So you have the square root of a negative number that's going in the opposite direction of the positive direction on a number line, big deal, why should that create all this anti-symmetry and contradictions of logic? It's like i is its own universe somehow.

If you graph sqrt(x) the imaginary range in the negative domain still makes some physical sense, it still functions as some base unit you need to multiply by itself to achieve that specific length, which, is symmetrical to the principal roots when you overlap the plots of the function in both the real and complex plane. For some reason, these lengths transfer to a different kind of number line.

We need to be careful with our terminology here. The standard order we use with the real numbers is not a well-order, since a well-order requires that any non-empty subset has a least element, which is not true of the reals (consider, for example, the interval (0, 1)). It is, however, a total order.

 

If we assume the axiom of choice, then we have the (logically equivalent) well-ordering theorem, which states that any set can be well-ordered. So while the standard order on the reals is not a well-order, if we assume the axiom of choice, then there does exist a well-order for the reals, as well as a well-order for the complex numbers. Whether the order is meaningful, much less useful, is another story.

 

However, what we can't achieve with the complex numbers is an ordered field structure, since the square of any non-zero element of an ordered field must be positive, but we have i² = -1.

 

Edit: If we try to order the complex numbers simply according to their magnitude, then we find that infinitely many complex numbers share any given magnitude. Looking at the complex plane, what we see is each magnitude |z| represented by a circle of radius |z|. This is what studiot was saying. So for instance, looking strictly at magnitude, -1 = i = 1 = -i. What we can do in that case is define the equivalence relation ~ such that z₁ ~ z₂ if |z₁| = |z₂|. But all we accomplish with that is mapping each equivalence class to a real number, thus it's not exactly a mathematical breakthrough and doesn't really accomplish what we want.

I see more clearly where the infinite numbers are coming from, since imaginary numbers in a way act like their own dimension that also acts to treat fundamental operations differently, whereas just real numbers on a number line would not create a circle of possibilities. Is there any manner of expressing that one complex number is greater than or less than another at all?

My point here is very simple: What if relativity and all of its implications, were just the product of context?

 

What if we shifted the very notions and axioms that physics rests upon. Why is time important? How is then and now different? What if we did consider distance in a different context? With a different deffinition? Making such claims as: there is no difference between point A and point B, even though A=/B, the difference might be just... how we think of it.

 

Why is distance importat? Why is distance relevant? On what do we base any given proposition for its relevance? What is distance? (in a spatial sense)

 

My point is not about trying to rebute relaitvity in any way, but more, to try to expand on it, to see under what kind of train of thought it was concieved, what it relied upon, on what ideas, and to see if it missed something or theres something more. If the ground itself on which it is standing is also dependent on even lower ground (not the newtonian ground).

 

Ill leave it at that.

When you say relativity, do you secretly mean special relativity and general relativity, where time dilation and length contraction are important factors? Or are you referring to the very act of taking on a different point of view?