Infinity, Sets, and Causality

[Gurnsey]

Musings on this as it relates to the beginning of the universe and causation! Jump in to correct, argue or discuss.

Representation vs. Concept: Infinity

First, let's differentiate a concept, and the way we represent that concept. "Unit" is a concept based on something being. I'm not sure that "Unit" is based on anything. "Unit" can be represented in many ways; for now, let's represent "Unit" as *. Many times this is represented as 1, but this makes it hard to seperate "Unit" from the next concept.

Now suppose we have sets of "Unit" ("Unit"s grouped together) - how "big" are the sets? "Magnitude" is the concept of how big the sets are. {*} is defined as a set of a certain magnitude, 1 in a lot of representation. {*, *} has a magnitude of 2 in Decimal, 10 in Binary, 11 in Unary, and Two in English. Decimal 10, Binary 1010, Unary 1111111111, and English Ten all represent the same set are equivalent - I can ask for Decimal 3 frogs or Binary 11 frogs and I will end up with the same set of frogs, if frog is our "Unit", {frog, frog, frog}. These are all examples of positive integers, a certain type of finite magnitudes, as I have no easy way to represent part of a "Unit".

You can also have direction, such as positive or negative numbers. We call negative direction taking things away, and positive direction adding things to, but if I say -3, it's still the set {***}.

Sets of finite magnitude are most easily understood since we have direct experience with them - the number of stones in a pail, the average number of socks lost per person in the wash last year (which is something abstract and not physical); the number of grains of sand on a beach at a certain moment in time is a very large set, but finite. There are a lot of rules that you can use with the magnitudes of finite sets - addition, subtraction, multiplication, division, less than, greater that and so on. We are very familiar with the magnitudes of finite sets - The positive integers are all magnitudes of finite sets.

Sets of infinite magnitude are harder to understand since we don't have any direct experience with them - they are impractical. It's hard to define precisely a set of infinite "Unit" and be able to do anything with it; {..., *, *, *, ...} doesn't tell us much. So, we use sets of sets - usually, sets of the magnitude of finite sets. For instance, the positive integers: if we put all the positive integers in a set, how "big" is it? Let's represent that set as {1, 2, 3, ...}. If those "numbers" are the magnitudes of finite sets, it's {{*}, {*,*}, {*,*,*},...}, but the first representation is easier to handle. However, the only reason this is the set of positive integers is that I said so - you assume that the ... means that the next one will be 4, and then 5, but what if it is 0 or -100? Well, because 4 comes next! We impose order on the set only because it makes it easier to represent.

Inifite sets can be bounded or unbounded too, which again we don't have direct experience with - if we put 'infinite' stones in a bucket, we'd think that no matter how small the stones were, you'd never get an infinite number of them in a mop bucket. Howver, the magnitude of the set of all real numbers between 0 and 1 is inifinite, but each member of that set is less than 1 and more than 0.

What differentiates infinite from finite then? Any easy way to tell is to try to apply the rules we are familiar with for finite magnitudes and see what happens.

An infinite set "never ends". What if we define infinite (represented by B for this) as so many, that you add itself to it and still have B, or

B is infinite.
0 is not infinite.

B = B + B

Then, by algebra

B - B = B

0 = B

B or infinite is not in the same class of representation as, say, 12, and the same rules don't apply to it (I know this is faulty logic and missing some steps). It's hard to define what infinite is, but it is not too hard to define what is not infinite - all the things that work with the rules we expect such as addition and subtraction.

The question, "What is infinity plus one?" has no meaning - you can't add one and infinity and come up with an answer any more meaningful than to "What is a pile plus one?".

Back to the quote at hand

Taking the ponts above that a) sets are ordered to make them more easily represented and B) the same rules don't apply to infinite magnitudes as to finite ones, lets look back at the quote.

The “directions” I was referring to in the example {. . ., -2, -1, 0, 1, 2, 3, . . .} was from smaller to larger – I presume that you’ll grant that this set does indeed possess some elements that are smaller than others, and that it is ordered from left to right to display that.

Further, isn’t it an essential property of infinity that it be infinite in regards to either increase or decrease of the property it describes? and thus that infinity must possess direction? For even if something is infinitely the same, how can it be so except in  regard to an increase of time? 
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Let's take {. . ., -2, -1, 0, 1, 2, 3, . . .} as the set of all integers. The question is, where does it start, and where does it end? Well, represented like this, and with the elypsis (sp?) taken to mean "and so on forever", it doesn't start or end! YOu might say, well, it starts at negative infinity and ends at positive infinity, but we've already decided that the same rules don't apply to 0, 1, 2, and 3 magnitudes as to inifinite magnitudes. The same set can be represented as {0, 1, -1, 2, -2, ...}, which has a start, but no end. The same set as {0, -1, 2, -2,...,1} is not a good representation, but does indeed have a start and an end - but it could start and end anywhere really, depending on how you ordered it.

Inifinite as I have defined it (the magnitude of a set of units) is non-directional - it only goes one way ("up" in the counting sense).

As far as time goes, this is where causality comes in.

Causality and Time as a 4th Dimension

I bet we can all imagine the universe as a 4-dimesional thing: you need 4 measurements (distances) to find a certain thing, three spatial coordinates (call them x, y, z) and a time coordinate (t). Missing one, you won't find the thing - it does no good to look for Duncan Donuts at x, y, z if you don't know when it is there. Also, it would do no good to go there and expect to find it a x, y, and t if you show up 30m underground (if z is a measure of height relative to some reference).

If we looked at a set of coordinates (x,y,z,t) in 4-dimensional space, how would we order them? We could order them first by x, so that the set is {...,(-1,y,z,t), (0,y,z,t), (1,y,z,t),...} - the direction of this ordering is abitrary, and is based on the distance from some arbitrary reference coordinate.

We could order it by t, which would also be based on the distance to an arbitrary reference point, but what does distance in t mean? What makes something more or less "t long"?

Causality gives a direction and meaning to our order in t. For us to be able to interpret the universe, if the stuff in the universe can be described by coordinates in the set we mentioned, causes must happen before effects, and this gives us an order: effects have a value of t that is more than their cause. So, the coordinates describing my butt sitting on my chair goes before the series of coordinates of the chair breaking because I sat on it.

An awfully Anthropic view, but very scientific: we observe that causes come before in time from effects. As soon as we observe an effect happening before a cause, this is out the window, but how would we know that something is a cause when it happens after the effect? How would we prove it scientifically? Who knows.

Where does the Universe start in time? Where does it end?

If we say the Universe is again a set of coordinates ordered by cause-before-effect in t, where does it start or end? Does it need to?

If time 'starts' somewhere, then that coordinate has no cause in the Universe (or else another coordinate would go before it, and would be the start). I guess it could have a cause in some other set, but it all breaks down there as far as our rules go. If it 'ends', then all coordinates, if followed in cause-effect order, eventually causes no effect in the Universe, though it could cause one in something that isn't the Universe.

It could have a start but no end, an end but no start (depressing, eh?), or no start and no end.

There are two ways it could have no start and no end in time: it could either go on infinitly in both directions (there's always a cause before this, and a cause after this), or it could wrap around (for instance, a->b, b->c, c->d, d->a).

What the beginning, end, or wrap of time really represents and means, is beyond me.

Long and rambling, but not infinite!

[Raelynn]

I'm a math guy and not so much a physics guy, so I'll mostly talk about the math side.

Representation vs. Concept: Infinity

First, let's differentiate a concept, and the way we represent that concept.  "Unit" is a concept based on something being.  I'm not sure that "Unit" is based on anything.  "Unit" can be represented in many ways; for now, let's represent "Unit" as *.  Many times this is represented as 1, but this makes it hard to seperate "Unit" from the next concept.

Now suppose we have sets of "Unit" ("Unit"s grouped together) - how "big" are the sets?  "Magnitude" is the concept of how big the sets are.  {*} is defined as a set of a certain magnitude, 1 in a lot of representation.  {*, *} has a magnitude of 2 in Decimal, 10 in Binary, 11 in Unary, and Two in English.  Decimal 10, Binary 1010, Unary 1111111111, and English Ten all represent the same set are equivalent - I can ask for Decimal 3 frogs or Binary 11 frogs and I will end up with the same set of frogs, if frog is our "Unit", {frog, frog, frog}.  These are all examples of positive integers, a certain type of finite magnitudes, as I have no easy way to represent part of a "Unit".

You can also have direction, such as positive or negative numbers.  We call negative direction taking things away, and positive direction adding things to, but if I say -3, it's still the set {***}.

Sets of finite magnitude are most easily understood since we have direct experience with them - the number of stones in a pail, the average number of socks lost per person in the wash last year (which is something abstract and not physical); the number of grains of sand on a beach at a certain moment in time is a very large set, but finite.  There are a lot of rules that you can use with the magnitudes of finite sets - addition, subtraction, multiplication, division, less than, greater that and so on.  We are very familiar with the magnitudes of finite sets -  The positive integers are all magnitudes of finite sets.

This was a fairly good description of sets using easy to understand analogies. :)

Sets of infinite magnitude are harder to understand since we don't have any direct experience with them - they are impractical.  It's hard to define precisely a set of infinite "Unit" and be able to do anything with it; {..., *, *, *, ...} doesn't tell us much.  So, we use sets of sets - usually, sets of the magnitude of finite sets.  For instance, the positive integers: if we put all the positive integers in a set, how "big" is it?  Let's represent that set as {1, 2, 3, ...}.  If those "numbers" are the magnitudes of finite sets, it's {{*}, {*,*}, {*,*,*},...}, but the first representation is easier to handle.  However, the only reason this is the set of positive integers is that I said so - you assume that the ... means that the next one will be 4, and then 5, but what if it is 0 or -100?  Well, because 4 comes next!  We impose order on the set only because it makes it easier to represent.

All of math is based on Peano's Principles, which basically say 1+1=2 so the natural numbers exist. Just about everything in math is based on this principle. If you don't assume that it's true, then everything in math, not just sets, becomes defunct.

Inifite sets can be bounded or unbounded too, which again we don't have direct experience with - if we put 'infinite' stones in a bucket, we'd think that no matter how small the stones were, you'd never get an infinite number of them in a mop bucket.  Howver, the magnitude of the set of all real numbers between 0 and 1 is inifinite, but each member of that set is less than 1 and more than 0.

What differentiates infinite from finite then?  Any easy way to tell is to try to apply the rules we are familiar with for finite magnitudes and see what happens.

To make things even more confusing, there are as many real numbers between 0 and 1 as there are all the real numbers :blink:

An infinite set "never ends".  What if we define infinite (represented by B for this) as so many, that you add itself to it and still have B, or

B is infinite.
0 is not infinite.

B = B + B

Then, by algebra

B - B = B

0 = B

Here's the big complaint that I have. Infinity is a concept, not a number. This means that you can't actually do arithmetic operation on it. Because of this, the math, though it seems true, doesn't hold.

B or infinite is not in the same class of representation as, say, 12, and the same rules don't apply to it (I know this is faulty logic and missing some steps).  It's hard to define what infinite is, but it is not too hard to define what is not infinite - all the things that work with the rules we expect such as addition and subtraction.

The question, "What is infinity plus one?" has no meaning - you can't add one and infinity and come up with an answer any more meaningful than to "What is a pile plus one?".

This basically says what I had said above. Since it's a concept instead of a number, methods that we attach to numbers don't work with infinity.

Back to the quote at hand

Taking the ponts above that a) sets are ordered to make them more easily represented and B) the same rules don't apply to infinite magnitudes as to finite ones, lets look back at the quote.
Let's take {. . ., -2, -1, 0, 1, 2, 3, . . .} as the set of all integers.  The question is, where does it start, and where does it end?  Well, represented like this, and with the elypsis (sp?) taken to mean "and so on forever", it doesn't start or end!  YOu might say, well, it starts at negative infinity and ends at positive infinity, but we've already decided that the same rules don't apply to 0, 1, 2, and 3 magnitudes as to inifinite magnitudes.  The same set can be represented as {0, 1, -1, 2, -2, ...}, which has a start, but no end.  The same set as {0, -1, 2, -2,...,1} is not a good representation, but does indeed have a start and an end - but it could start and end anywhere really, depending on how you ordered it.

Inifinite as I have defined it (the magnitude of a set of units) is non-directional - it only goes one way ("up" in the counting sense).

I don't believe that your third definition is a legal definition, but I don't know a ton about sets. In terms of numbers, it is commonly accepted that there is a "positive infinity" and a "negative infinity", which arise from going in each direction. Since you talk only of the number of elements, you are actually using a function to turn turn the elements of the set into the elements of a set of positive numbers. This means that there can only be a positive infinity in your definition, because you start at 0 and count upwards. This doesn't mean there can't be a negative one though.

Personally, I believe that the positive and negative infinity are connected an possibly the same. If you allow for that, geometrically all polynomials with power of any number, positive or negative, would be continuous, as opposed to the current definition which only allows for polynomials with positive powers to be continuous. This of course is a discussion all on its own.

As far as time goes, this is where causality comes in.

Causality and Time as a 4th Dimension

I bet we can all imagine the universe as a 4-dimesional thing: you need 4 measurements (distances) to find a certain thing, three spatial coordinates (call them x, y, z) and a time coordinate (t).  Missing one, you won't find the thing - it does no good to look for Duncan Donuts at x, y, z if you don't know when it is there.  Also, it would do no good to go there and expect to find it a x, y, and t if you show up 30m underground (if z is a measure of height relative to some reference).

If we looked at a set of coordinates (x,y,z,t) in 4-dimensional space, how would we order them?  We could order them first by x, so that the set is {...,(-1,y,z,t), (0,y,z,t), (1,y,z,t),...} - the direction of this ordering is abitrary, and is based on the distance from some arbitrary reference coordinate.

We could order it by t, which would also be based on the distance to an arbitrary reference point, but what does distance in t mean?  What makes something more or less "t long"?

Causality gives a direction and meaning to our order in t.  For us to be able to interpret the universe, if the stuff in the universe can be described by coordinates in the set we mentioned, causes must happen before effects, and this gives us an order: effects have a value of t that is more than their cause.  So, the coordinates describing my butt sitting on my chair goes before the series of coordinates of the chair breaking because I sat on it.

An awfully Anthropic view, but very scientific: we observe that causes come before in time from effects.  As soon as we observe an effect happening before a cause, this is out the window, but how would we know that something is a cause when it happens after the effect?  How would we prove it scientifically?  Who knows.

I like this definition of time, but it is based on a one-dimensional time, which may or may not be the case. I personally think time is greater than 1 dimensional, though it may possibly be 0-dimensional (time is an instant, we just interpret it as something else). The two dimensional time also leads to some other theories I have concerning ghosts, gods, and some supernatural phenomenon, but again that's another discussion.

Where does the Universe start in time?  Where does it end?

If we say the Universe is again a set of coordinates ordered by cause-before-effect in t, where does it start or end?  Does it need to?

If time 'starts' somewhere, then that coordinate has no cause in the Universe (or else another coordinate would go before it, and would be the start).  I guess it could have a cause in some other set, but it all breaks down there as far as our rules go.  If it 'ends', then all coordinates, if followed in cause-effect order, eventually causes no effect in the Universe, though it could cause one in something that isn't the Universe.

It could have a start but no end, an end but no start (depressing, eh?), or no start and no end.

There is another mathematical theory call the Incompleteness Theorem which states that there always exists some problems which cannot be solved using only the rules of a certain set. This goes along with what you state here, that there may be an explanation if we expand our set outward to include another set as the cause.

There are two ways it could have no start and no end in time: it could either go on infinitly in both directions (there's always a cause before this, and a cause after this), or it could wrap around (for instance, a->b, b->c, c->d, d->a).

What the beginning, end, or wrap of time really represents and means, is beyond me.

Long and rambling, but not infinite!

Cyclical time would be interesting. It's one of the common theories of time. The other possibility is that there exists something that breaks causality, something that is only a cause, and not an effect. Just because no one has found it, doesn't mean it doesn't exist. :)

These are actually some of the topics I thoroughly enjoy talking about. It's been fun writing out this response.

[LemmingofGlory]

First, let's differentiate a concept, and the way we represent that concept.  "Unit" is a concept based on something being.  I'm not sure that "Unit" is based on anything.  "Unit" can be represented in many ways; for now, let's represent "Unit" as *.  Many times this is represented as 1, but this makes it hard to seperate "Unit" from the next concept.

The things in a set are called "elements." And using * to represent an arbitrary element makes me wince.

I can ask for Decimal 3 frogs or Binary 11 frogs and I will end up with the same set of frogs, if frog is our "Unit", {frog, frog, frog}.  These are all examples of positive integers, a certain type of finite magnitudes, as I have no easy way to represent part of a "Unit".

Repetition in a set does not change the set, so { frog, frog, frog } = { frog }. Since you say you have 3 frogs, we assume the frogs are distinct so let's indicate that: { frog1, frog2, frog3 }.

You can also have direction, such as positive or negative numbers.  We call negative direction taking things away, and positive direction adding things to, but if I say -3, it's still the set {***}.

In a set, you don't have direction. You need something more sophisticated than a set if you want to talk about direction. Look up posets.

Sets of finite magnitude are most easily understood since we have direct experience with them - the number of stones in a pail, the average number of socks lost per person in the wash last year (which is something abstract and not physical); the number of grains of sand on a beach at a certain moment in time is a very large set, but finite.

Your descriptions are not what you think you're describing.

The stones in the pail are a set, where each stone is an element. The cardinality of the set is the number of stones, say #. "The number of stones in a pail", as a set, is { # }. Similarly, "The average number of socks lost per person in the wash last year", as a set, is the one-element set containing that number. And "the number of grains of sand on a beach", as a set, is a one-element set containing that number.

Sets of infinite magnitude are harder to understand since we don't have any direct experience with them - they are impractical.  It's hard to define precisely a set of infinite "Unit" and be able to do anything with it; {..., *, *, *, ...} doesn't tell us much.

You're over thinking this; don't make something sound difficult when it isn't. Everyone has that moment when they're learning to count where they say "Oh, I could go on and never run out of numbers, couldn't I?" That's direct experience with an infinite set.

  Let's represent that set as {1, 2, 3, ...}.  ...  However, the only reason this is the set of positive integers is that I said so - you assume that the ... means that the next one will be 4, and then 5, but what if it is 0 or -100?  Well, because 4 comes next!  We impose order on the set only because it makes it easier to represent.

Firstly, one who talks about a set having a "next" element does not understand what a set is. A sequence, on the other hand, does have a "next" element.

Secondly, I disagree with your point. You claim that we assume a reader would infer 4 and 5 would also be elements of {1, 2, 3, ...} because of an ordering. The reader would infer 4 and 5 are also elements not because of ordering, but because of association. They identify the set based on representative elements. For example:

{ The Hobbit, The Lord of the Rings, ... }

There are many possible ways for a reader to label this set (which is one reason why listing elements is not a terribly good way to represent a set), but if a reader said "Books by Tolkien" they would do so based on the representative elements of the set.

What differentiates infinite from finite then?  Any easy way to tell is to try to apply the rules we are familiar with for finite magnitudes and see what happens.

Bad criteria.

B is infinite. 0 is not infinite.

Then, by algebra
B + B = B
B - B = B
0 = B

I know you're trying for a proof by contradiction, but your second step is still bull#$%&. oo - oo is undefined. Who told you the additive inverse of oo is -oo? Nobody, because it's not.

Better Criteria:
(1) Is it possible to count the elements? If not, the set has an infinite number of elements. (e.g. the real numbers)
(2) If it is possible to count the elements, will counting ever cease? If not, the set has an infinite number of elements. (e.g. the natural numbers)

To be sure, these are two different notions of infinity.

Let's take {. . ., -2, -1, 0, 1, 2, 3, . . .} as the set of all integers.  The question is, where does it start, and where does it end?  Well, represented like this, and with the elypsis (sp?) taken to mean "and so on forever", it doesn't start or end!  YOu might say, well, it starts at negative infinity and ends at positive infinity, but we've already decided that the same rules don't apply to 0, 1, 2, and 3 magnitudes as to inifinite magnitudes.  The same set can be represented as {0, 1, -1, 2, -2, ...}, which has a start, but no end.  The same set as {0, -1, 2, -2,...,1} is not a good representation, but does indeed have a start and an end - but it could start and end anywhere really, depending on how you ordered it.

Whoever told you the ideal way to represent a set was to list elements needs to have their crack taken away. And that aside, seeing the integers thrown around like a $4 whore is making me nauseous.

If you really want to bake your brain, play with this set for a little while: { z | z is Complex and | z | <= 1 }. Frankly, I think it's a better example for the sort of set you're looking for ("no beginning and no end") because you don't have to eliminate fifty different ways someone might list the elements.

-Lemmy

[--Pete]

Hi,

Musings on this as it relates to the beginning of the universe and causation!  Jump in to correct, argue or discuss.[right][snapback]98731[/snapback][/right]

Well, Lem has already pretty well killed this thread. And he is right -- discussing these topics without a firm basis in analysis is pretty well a waste of time.

For myself, I'm staying out of it beyond this post. If one really wants to get a hint about set theory, this is a pretty decent introduction, and this is my usual source for brushing up on subjects long ago learned and mostly forgotten. Since I've done damned all in analysis and the foundations of math since spring of '73, I can contribute little (except, probably, misinformation) to what Lem has said.

In a sense, math is a game. It has its rules and is, like most games, defined by those rules. And the only real way to understand it is to play it -- i.e., work lots of problems, do a lot of derivations, prove a lot of theorems. What a thread like this usually ends up doing is little more than showing why it takes ten years and a Ph.D. in math to understand a lot of these concepts -- there is no easy 'Camino Real' to math proficiency.

--Pete

[Occhidiangela]

What a thread like this usually ends up doing is little more than showing why it takes ten years and a Ph.D. in math to understand a lot of these concepts -- there is no easy 'Camino Real' to math proficiency.

--Pete
[right][snapback]98812[/snapback][/right]

As Ben Hogan remarked once about the golf swing: "the secret is in the dirt." ;) Thanks for those links, will help me work with daughter in Calculus this year.

Occhi

[Gurnsey]

Hi,
Well, Lem has already pretty well killed this thread.&nbsp; And he is right -- discussing these topics without a firm basis in analysis is pretty well a waste of time.
...[right][snapback]98812[/snapback][/right]

Er, discussing politics or religion without a firm basis in either is also a waste of time - but people do it, and can still get something out of it.

Writing a post like mine was an exercise to me of explaining something that I liked when I learned about it, that came up in another discussion. What it, of course, proves (and I realized this while writing it) was that I didn't understand it (or remember it) as well as I thought - there is nothing like trying to 'teach' something to someone else to get your brain moving on a subject.

While I understand that it may take years and years and a degree and whatnot to fully understand something, I bet something could be done to improve my analysis skills and make my post less a waste of time.

The original thought that sparked this and then I took waaaay to far was, is time infinite? bounded? if so, how, and how can we make a good example to show what this is like?

Sorry, but two of these posts have seemed too much like "sit down and shut up, little boy".

I wish I did something well enough to be considered an expert in it...I program computers, do some mechanical design, carpentry, can sail, write fiction occasionally (badly) and non-fiction (instruction manuals and research) a lot, can't really sketch but do some clay sculpting, I sew occaisionally, know how to fence well enough to teach beginners, am pretty good at creating and revising Standard Operating Procedures (relates pretty closely to programming, in the end), know enough math and physics to get in trouble (obviously), have a pretty solid grounding in electric and electronics theory and application, and about a billion other things...I'm hungry for knowledge and experience, if not for the classroom environment.

The list of things I do badly is pretty easy: I am the only person I know who can kill a fake plant :P

[Occhidiangela]

I am the only person I know who can kill a fake plant :P
[right][snapback]98830[/snapback][/right]

*Sean Bean/Borommir voice*
"It's a gift." :lol:

Occhi

[Gurnsey]

As Ben Hogan remarked once about the golf swing: "the secret is in the dirt."&nbsp; ;)&nbsp; Thanks for those links, will help me work with daughter in Calculus this year.

Occhi
[right][snapback]98820[/snapback][/right]

Calculus us the first thing that I found some people just could not take - I tutored linear algebra and calculus in college.

Man, was that a hard one. Good luck if your daughter needs your help!

[Gurnsey]

Cyclical time would be interesting.&nbsp; It's one of the common theories of time.&nbsp; The other possibility is that there exists something that breaks causality, something that is only a cause, and not an effect.&nbsp; Just because no one has found it, doesn't mean it doesn't exist.&nbsp; :)

These are actually some of the topics I thoroughly enjoy talking about.&nbsp; It's been fun writing out this response.
[right][snapback]98743[/snapback][/right]

One problem with cyclical time might be the idea of entropy.

Another way to define the direction of time is that time is in the direction of the increase of entropy. Entropy is the measure of how low of an energy state something is in - everything seeks out the lowest energy state it can be in. Object under the pull of gravity have potential energy; they seek to 'get rid' of this energy by falling towards the source of the gravity (which leads to all sorts of orbital fun if more than one source is in the system). Electrons seek the lowest 'orbit' or energy state they can be in - the fun here is that only certain energy levels are 'allowed' by the conditions. Entropy increases as things find lower energy states; while locally, things might gain energy (you lift a weight up from the floor), overall, entropy still increases (you radiate heat based on your effort into the surrounding room, go thermodynamics). In any case, overall, entropy always increases as time increases. Entropy (t) < Entropy (t+1)

The problem with cyclical time is that you get to a certain time again! Is it that same t the second time around? if t1 is a certain time, and t2 is the same point the second time around, does Entropy (t1) = Entropy (t2)?

[Occhidiangela]

One problem with cyclical time might be the idea of entropy.

Eeverything seeks out the lowest energy state it can be in.&nbsp; ==

The problem with cyclical time is that you get to a certain time again!&nbsp; Is it that same t the second time around?&nbsp; if t1 is a certain time, and t2 is the same point the second time around, does Entropy (t1) = Entropy (t2)?
[right][snapback]98838[/snapback][/right]

NIce play on words on the second bit, but the first bit I am not so sure of.

"Everything seeks out the lowest energy state" would tell me that the Big Bang is not a viable event. How then do we account for anything at a high energy state?

This supposition would seem to place energy and gravity into discretely separate domains. I am not sure that squares with common cosmological theory. My brain hurts.

Occhi

[--Pete]

Hi,

Er, discussing politics or religion without a firm basis in either is also a waste of time - but people do it, and can still get something out of it.[right][snapback]98830[/snapback][/right]

Not at all. Neither politics nor religion are axiom based logical systems. Thus everybody can have and does have a basis in them, whether that basis is formed from sound opinion or superficial prejudice. Indeed, discussion about topics such as religion and politics end up being discussions about the postulates (the axioms), which is where most discussions in mathematics start. Questioning the axioms themselves is meta-mathematics, a branch of philosophy often practiced by mathematicians.

Writing a post like mine was an exercise to me of explaining something that I liked when I learned about it, that came up in another discussion.&nbsp; What it, of course, proves (and I realized this while writing it) was that I didn't understand it (or remember it) as well as I thought - there is nothing like trying to 'teach' something to someone else to get your brain moving on a subject.

A good reason to post. Since a lot of reference material is available on the web, perhaps it would have been a good idea to have refreshed your memory prior to posting. After all, if your intent was to teach, then you probably did not want to spread disinformation.

While I understand that it may take years and years and a degree and whatnot to fully understand something, I bet something could be done to improve my analysis skills and make my post less a waste of time.

Yes, and it is amazingly simple. If you find analysis interesting, then pick up a textbook on the subject; there are a couple available, used, from amazon.com for less than $50. The price is comparable to a game, and the time you'll get to enjoy it is probably longer than Black & White ;)

Oh, and BTW -- it does no good (or not much) to just read the book. You also need to work out the problems. But not all of them, just those you can't figure out.

Of course, if you are really interested, you might be able to find a course, but that depends on where you live.

Sorry, but two of these posts have seemed too much like "sit down and shut up, little boy".

Sorry about that. But look at it from the opposite viewpoint. Asking a mathematician (or any other professional who has spent years learning his specialty) to explain his specialty to you, in detail, and well enough that you can argue with him, is insulting. By doing so, you are either implying that he is mentally defective or that you are so far superior in intellect, that you can learn in a few hours what took him years. And being offended when that is pointed out to you is pretty immature.

I wish I did something well enough to be considered an expert in it...I program computers, do some mechanical design, carpentry, can sail, write fiction occasionally (badly) and non-fiction (instruction manuals and research) a lot, can't really sketch but do some clay sculpting, I sew occaisionally, know how to fence well enough to teach beginners, am pretty good at creating and revising Standard Operating Procedures (relates pretty closely to programming, in the end), know enough math and physics to get in trouble (obviously), have a pretty solid grounding in electric and electronics theory and application, and about a billion other things...I'm hungry for knowledge and experience, if not for the classroom environment.

Being a generalist is good, and generally more useful than being an expert in some extremely narrow field. But if you are hungry for knowledge and experience, perhaps it would be better to make a post with questions than one with (possibly incorrect) answers.

The list of things I do badly is pretty easy: I am the only person I know who can kill a fake plant :P

That is impressive :)

--Pete

[BruceGod]

You seem to have forgotten the other dimensions! You only state four, when in fact there are more. For example, space-time is wrinkled. This is caused by the gravitational fields of really heavy things, i.e. planets, stars, black holes, etc. (Black holes are actually singularities, but we're using familiar terms here.)

Time in an intense gravitational field is slower than outside it. This has been scientificaly proven. Example A: If you were to sit at the bottom of Death Valley (a really low point), for a time X, and a second person were to sit at the top of Mount Everest (a really high point), then they would observe you sitting there for longer than the amount of time than you observed.

Therefore, space-time is wrinkled, with time passing differently based upon subtle gravitational effects. Now, if you could make a straight hole through space-time (which appears to be curved), that would be a wormhole. We're already up to six dimensions!

Furthermore, if you believe that there are alternate timelines (and there is no evidence as yet to disprove their existence), then that would be a 7th dimension, as you would have to know which timeline you are in to find a specific object. For example, there would be an infinite number of timelines where we didn't win the Civil War, an infinite number where we did, and infinite number where Hitler stuck to being an artist, etc.

Also, there may be "parallel universes". This is a bad term because some of those "universes" would likely intersect at some point, and since the universe is everything, they wouldn't technically be one. But, in these theoretical places, the laws of physics might be different. Cause could very well precede effect.

And what of other planes of existence? Are all those people who claim to have visited a so-called "astral" or "ethereal" plane hallucinating? Are they all liars? When phenomenon is wide-spread, there is usually a real-world explanation for it all. Occam's Razor (although not always the best method) would assume that the simplest explanation is that alternate planes of existence do, in fact, exist.

So now we're up to 9 dimensions. And since the universe appears to have no beginning or end, and to account for being able to get to any point in it, the shape of that universe would appear to be a Mobius Strip. So, if you imagine the 9-d universe as a plane, and twist it to form a Mobius Strip, you get a ten dimensional universe.

Sorry for the rambling there, but I thought that at the very least, this would spark some lively discussion on the "true" nature of the universe.

[Guest]

No.

Real/physical dimensions beyond 4 are not "proven". And Im not talking about the sematics of theory here. I mean they are not accepted as true by the majority of the scientific community.

Neither theory of Relativity requires more than 4 dimesnsions.
You definetly didnt prove it here.

On the other hand they do exist and work as mathmatical constructs.

[--Pete]

Hi,

Actually, none of the examples that you give are 'dimensions' in the mathematical sense. It would help if anybody interested in these topics bookmark Wikipedia and MathWorld and spend a few minutes looking up what they want to say before posting nonsense. For instance, had you taken a little while to read about dimensions, you would have seen both why your examples are poor and have seen some good examples.

You seem to have forgotten the other dimensions! You only state four, when in fact there are more.
[right][snapback]98911[/snapback][/right]

Depending on the universe of the subject under discussion, there may be anything from zero (admittedly a dull case) to infinite (any number of functional spaces such as Hilbert, Fourier, etc.) dimensions. In general relativity (GR) there are, indeed, only four dimensions. Theories which embed GR in higher dimensions are *not* GR but, theories *about* GR.

For example, space-time is wrinkled.

Yes, but that is a property of four dimensional space-time relative to Euclidean space time (i.e., observed space time has a non-Euclidean metric). It is not, and does not require, an additional dimension.

Now, if you could make a straight hole through space-time (which appears to be curved), that would be a wormhole. We're already up to six dimensions!

This is just a topology question in four dimensional space-time and requires no additional dimensions to describe.

As to the rest of your statements, besides the fact that they border more on meta-physics (or even fantasy), none of the things you mention are geometric dimensions. So, while they may add complexity to the discussion, they do not add dimensions in the mathematical or physical sense.

--Pete

[BruceGod]

Hi,

Actually, none of the examples that you give are 'dimensions' in the mathematical sense.&nbsp; It would help if anybody interested in these topics bookmark Wikipedia and MathWorld and spend a few minutes looking up what they want to say before posting nonsense.&nbsp; For instance, had you taken a little while to read about dimensions, you would have seen both why your examples are poor and have seen some good examples.
Depending on the universe of the subject under discussion, there may be anything from zero (admittedly a dull case) to infinite (any number of functional spaces such as Hilbert, Fourier, etc.) dimensions.&nbsp; In general relativity (GR) there are, indeed, only four dimensions.&nbsp; Theories which embed GR in higher dimensions are *not* GR but, theories *about* GR.
Yes, but that is a property of four dimensional space-time relative to Euclidean space time (i.e., observed space time has a non-Euclidean metric).&nbsp; It is not, and does not require, an additional dimension.
This is just a topology question in four dimensional space-time and requires no additional dimensions to describe.

As to the rest of your statements, besides the fact that they border more on meta-physics (or even fantasy), none of the things you mention are geometric dimensions.&nbsp; So, while they may add complexity to the discussion, they do not add dimensions in the mathematical or physical sense.

--Pete
[right][snapback]98913[/snapback][/right]

Yes, but as space-time is depicted as planar, it must have a direction to wrinkle in. Also, wormholes are like tesseracts, in that they pierce through space-time. Hence, another direction at right angles to space-time. Yes, the rest are highly theoretical, and/or fantastical, but there is at least a great number of reports for them, are there not? And, there has yet to be any serious inspection into whether or not they do in fact exist. Also, it wasn't meant to be as serious as you're making it out to be. Just to start those brain cells rubbing and sparking together.

[Guest]

You are taking metaphors like "wrinkle" as literal.

Thats silly in a thread about math.

[--Pete]

Hi,

Yes, but as space-time is depicted as planar
[right][snapback]98917[/snapback][/right]

Not by any informed person since 1916.

it must have a direction to wrinkle in.

If you are familiar with the concept of a metric, then you should be able to rebut your own argument. If you are not, then you don't know what you are saying.

Also, wormholes are like tesseracts, in that they pierce through space-time.

Tesseracts don't 'pierce' through anything. They are simply the extension to four dimensions of the square (2D) and the cube (3D). And a better analogy to wormholes is the handle in a coffee cup (or, equivalently, the hole in a donut), which pierces a three dimensional object and does it *in* 3 dimensions.

Hence, another direction at right angles to space-time.

Bull.

Yes, the rest are highly theoretical, and/or fantastical, but there is at least a great number of reports for them, are there not?

There are a few speculations for some of them, most largely discredited.

And, there has yet to be any serious inspection into whether or not they do in fact exist.

Since there is no way that those speculations can be studied or tested in the first place, it is little wonder that no one has studied them.

Also, it wasn't meant to be as serious as you're making it out to be. Just to start those brain cells rubbing and sparking together.

Nonsense does not spark useful thinking. You might as well have quoted Jabberwocky. Indeed, it would have been better in that Carroll's nonsense is at least amusing.

--Pete

[Raelynn]

No.

Real/physical dimensions beyond 4 are not "proven". And Im not talking about the sematics of theory here. I mean they are not accepted as true by the majority of the scientific community.

Neither theory of Relativity requires more than 4 dimesnsions.
You definetly didnt prove it here.

On the other hand they do exist and work as mathmatical constructs.
[right][snapback]98912[/snapback][/right]

I think the current top number of dimensions I've heard is 12 in addition to time. Of course these are theoretical as you had said.

As an interesting side note, several years back (4-5 years) I saw an article in my physics class that suggested that gravity worked primarily in the 4th physical dimension (not time but something else). If this was true, it could show why there is such a discrepancy between the strength of gravity compared to electical, strong, and weak nuclear energy. They were trying to measure the gravitational force of objects which moved extremely small distances. The idea was something like if they measured a greater tahn normal force, then they were right.

It's kind of hard to describe, especially since I read it so long ago.