Does infinity exist?

[leftrightleftrightleft]

From my understanding of the current Big Bang theory, the universe was necessarily produced from a singularity with an infinite density of matter (as in, all the mass of the universe was placed in a zero volume).

However, like limits in calculus, aren't singularities just mathematical constructs that don't actually have a physical existence?

Limits seem reasonable because they are a mathematical construct that is being used to determine something about something physical (aka using limits to determine the acceleration of a body based on a given function of its velocity).

However, doesn't it seem silly to suggest that a mathematical construct actually exists? How can a singularity exist? Is the Big Bang theory only valid because the math aligns despite the impossibility of the whole idea?

How can an infinity of something actually exist?

 

[acropolis]

One issue with matters like this is that we don't actually know beforehand what is and isn't possible. If the current state of nature is consistent with an infinitely small, infinitely dense region, then it's likely that it existed in such a way. There are many things in nature which are counter-intuitive, though that says much more about the limited nature of human intuition than it does about nature.

There's also not a sharp distinction between mathematical constructs and physical objects. Yes, infinity is a mathematical idea, but it might also be a physical one. Just as something like exponential decay is a mathematical idea that is also a physical reality.

 

[AV1611VET]

(as in, all the mass of the universe was placed in a zero volume)

Was this primeval atom, as it's called, a TARDIS booth?

 

[Wiccan_Child]

From my understanding of the current Big Bang theory, the universe was necessarily produced from a singularity with an infinite density of matter (as in, all the mass of the universe was placed in a zero volume).

The universe was once a tiny speck of space, phenomenally energy-dense, and has been expanding for 13.5 billion years into its current form - this ongoing expansion is called the Big Bang.

We don't know what that speck was really like (there's a limit to how far back we can go, as eventually quantum mechanics and general relativity contradict one another), nor if it was the first thing in existence, but we do know that the Big Bang didn't cause it to come into existence - or rather, if it did, the current theory needs a major overhaul.

However, like limits in calculus, aren't singularities just mathematical constructs that don't actually have a physical existence?

Limits seem reasonable because they are a mathematical construct that is being used to determine something about something physical (aka using limits to determine the acceleration of a body based on a given function of its velocity).

However, doesn't it seem silly to suggest that a mathematical construct actually exists? How can a singularity exist? Is the Big Bang theory only valid because the math aligns despite the impossibility of the whole idea?

How can an infinity of something actually exist?

'Infinity' is a category of numbers, and a conceptually-simple infinity is what happens to 1/x as x tends to zero. What happens at zero? On the one hand, the question makes no sense (you can't divide by zero), and on the other, it 'equals' infinity and minus infinity.

On the one hand, infinity itself doesn't exist, simply because no purely mathematical concept has a pure, Platonic, physical manifestation - there's no 'Cube', no 'One', no 'Infinity'. Nonetheless, there can be one of something, so why can't there be an infinity of something?

Take, for instance, a quantum thermodynamic system - a set of charged particles in a magnetic field, who can be 'up' or 'down', according to whether or not they have energy (heat). Add enough heat, and the temperature rises and rises, hits 'infinite', then goes back round to 'minus infinite' and down the negative axis. Peculiar, but very real.

So, infinity can exist inasmuch as any number can exist. Singularities can either be described as a mathematical approximation - there's no true cube, but there are cube-like structures with cube-like properties - or as "whatever happens when something goes indefinitely to infinity".

Take a black hole. Is that a singularity? On the one hand no, not in the mathematical sense. On the other hand, why not? Density is tending inexorably to infinity, and if quantum mechanics is right, then it hits truly infinite density. It's infinitely dense.

So can singularities exist? Depends . It's largely a matter of semantics, however, and I know Chalnoth disagrees with me on whether or not a singularity can actually exist - I'm inclined to believe they can, inasmuch as a black hole is a singularly, while he does not - but it doesn't disprove the notion of the Big Bang or black holes.

 

[idscience]

From my understanding of the current Big Bang theory, the universe was necessarily produced from a singularity with an infinite density of matter (as in, all the mass of the universe was placed in a zero volume).

However, like limits in calculus, aren't singularities just mathematical constructs that don't actually have a physical existence?

Limits seem reasonable because they are a mathematical construct that is being used to determine something about something physical (aka using limits to determine the acceleration of a body based on a given function of its velocity).

However, doesn't it seem silly to suggest that a mathematical construct actually exists? How can a singularity exist? Is the Big Bang theory only valid because the math aligns despite the impossibility of the whole idea?

How can an infinity of something actually exist?

The bang is a mathematical model. Singularity, Mathematical theory.

 

[idscience]

Was this primeval atom, as it's called, a TARDIS booth?

how can an atom exist in a place where there are no phyical laws? No space for the adam to exist in?\

What is it that space, matter and energy expanded into?

 

[idscience]

The universe was once a tiny speck of space, phenomenally energy-dense, and has been expanding for 13.5 billion years into its current form - this ongoing expansion is called the Big Bang.

We don't know what that speck was really like (there's a limit to how far back we can go, as eventually quantum mechanics and general relativity contradict one another), nor if it was the first thing in existence, but we do know that the Big Bang didn't cause it to come into existence - or rather, if it did, the current theory needs a major overhaul.

You say this like it is a fact. You are right about one thing. The BB is an effect not a cause.

 

[AV1611VET]

What is it that space, matter and energy expanded into?

Genesis 1:1 In the beginning God created the heaven and the earth.

Notice the continuum here?

1. beginning = time
2. heaven = space
3. earth = matter

The BB model has the universe expanding, whereas the Bible says that God stretched it.

There's a big difference: something expands when it is pushed outward; but when it's stretched, it is pulled outward from outside its boundaries.

And for the record, a 'big bang' occurs at the end of time, not at the beginning:

2 Peter 3:10a But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise,

As usual, scientists are mixed up.

 

[Wiccan_Child]

You say this like it is a fact.

Indeed, inasmuch as anything in science is a fact.

how can an atom exist in a place where there are no phyical laws?

Whoever said there were no physical laws? The Big Bang theory relates to the expansion of spacetime; the physical laws were in place. The 'primaeval atom' is a poetic term for what the universe was 13.5 billion years ago, not an atom as understood in modern physics.

No space for the adam to exist in?

The 'atom' is the space.

What is it that space, matter and energy expanded into?

It's not. If you draw dots on a balloon, then blow it up, the dots move away from each other. The 2D surface of the balloon doesn't move into anything, it just expands. The dots aren't moving into some third-party, outside-the-universe, balloon surface, the existing surface is itself expanding, which is what creates the extra space, which is why the universe is getting bigger - space is expanding. It doesn't expand into anything; the question makes no more sense than asking what's North of the North Pole, or before the start of time.

 

[Wiccan_Child]

Genesis 1:1 In the beginning God created the heaven and the earth.

Notice the continuum here?

1. beginning = time
2. heaven = space
3. earth = matter

The BB model has the universe expanding, whereas the Bible says that God stretched it.

There's a big difference: something expands when it is pushed outward; but when it's stretched, it is pulled outward from outside its boundaries.

And for the record, a 'big bang' occurs at the end of time, not at the beginning:

2 Peter 3:10a But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise,

As usual, scientists are mixed up.

Scientists are the ones mixed up because you have a different meaning of the term 'Big Bang' than them? A term with two, equally valid definitions, and they are wrong because they don't use your preferred definition?

Yea, they're mixed up.

 

[dad]

The universe was once a tiny speck of space, phenomenally energy-dense, and has been expanding for 13.5 billion years into its current form - this ongoing expansion is called the Big Bang.

We don't know what that speck was really like

Paleeeese. That silly fairy tale is old and hairy and moldy. Baseless too of course. The fact that you say it as if there was some reality to it speaks to your credibility.

(there's a limit to how far back we can go, as eventually quantum mechanics and general relativity contradict one another),

So you have no idea what you are talking about. No news there.

nor if it was the first thing in existence,

In your fable what was before the magic speck? Inquiring toddlers want to know.

but we do know that the Big Bang didn't cause it to come into existence -

I agree. In fact the big bang did nothing ever to anything.

or rather, if it did, the current theory needs a major overhaul.

Duhh

'Infinity' is a category of numbers,

No. Infinity is more like forever, which leaves time and space time in the dirt.

and a conceptually-simple infinity is what happens to 1/x as x tends to zero. What happens at zero? On the one hand, the question makes no sense (you can't divide by zero), and on the other, it 'equals' infinity and minus infinity.

Eternity is not a numbers game actually.

On the one hand, infinity itself doesn't exist, simply because no purely mathematical concept has a pure, Platonic, physical manifestation -

Relax infinity, despite what Buzz Lightyear might say, is not a mathematical concept.

there's no 'Cube', no 'One', no 'Infinity'.

Says you.
Like you know.

Nonetheless, there can be one of something, so why can't there be an infinity of something?

Because infinity is not a multiple of one.

Take, for instance, a quantum thermodynamic system - a set of charged particles in a magnetic field, who can be 'up' or 'down', according to whether or not they have energy (heat). Add enough heat, and the temperature rises and rises, hits 'infinite', then goes back round to 'minus infinite' and down the negative axis. Peculiar, but very real.

No. Not really. Have you seen one lately???

So, infinity can exist inasmuch as any number can exist. Singularities can either be described as a mathematical approximation - there's no true cube, but there are cube-like structures with cube-like properties - or as "whatever happens when something goes indefinitely to infinity".

Blather.

Take a black hole. Is that a singularity?

No. It is an invention. Something used to explain what is actually not understood.

On the one hand no, not in the mathematical sense. On the other hand, why not? Density is tending inexorably to infinity, and if quantum mechanics is right, then it hits truly infinite density. It's infinitely dense.

Explain? How you think quantum mechanics affects density of anything!?

So can singularities exist? Depends .

They are fantasy.

It's largely a matter of semantics, however, and I know Chalnoth disagrees with me on whether or not a singularity can actually exist - I'm inclined to believe they can, inasmuch as a black hole is a singularly, while he does not - but it doesn't disprove the notion of the Big Bang or black holes.

What people are inclined to believe does not matter much.

 

[Wiccan_Child]

No. Infinity is more like forever, which leaves time and space time in the dirt.

No, infinity is a category of number, and there are different types of infinity. For instance, the number of integers is countably infinity, while the number of real numbers is uncountably infinite. This is a fascinating branch of number theory and has important, real-world applications. You can dismiss it if you want, but unless you can demonstrate that the greatest mathematical thinkers the world has ever seen were, to a one, wrong... well, the ball's in your court.

Relax infinity, despite what Buzz Lightyear might say, is not a mathematical concept.

Of course it is. It is a concept inextricably linked with numbers and basic arithmetic.

Says you.
Like you know.

They are concepts of the mind, idealisations of a pattern. Can you hold 'one' in your hand? Can you hold 'cube' in your hand? Do you even know what a Platonic Form is?

Because infinity is not a multiple of one.
No. Not really. Have you seen one lately???

Yes, I played around with them at university, but that's besides the point: the theory is sound. I can walk you through it, if you like.

Explain? How you think quantum mechanics affects density of anything!?
They are fantasy.

According to quantum mechanics, there is hard limit on density, a point where matter can't be squeezed any tighter. This stands in contrast to general relativity, which posits that there's no hard limit, that matter can be squeezed to a single point of infinite density - that is, "X matter divided by zero volume equals infinite density".

In my original post I should have said 'general relativity', not 'quantum mechanics'.

What people are inclined to believe does not matter much.

It matters when those beliefs are acted upon. Since this is a discussion forum, where we share our ideas and beliefs, it seems a bit odd to lambaste me for participating in the core activity this entire forum is based on.

 

[dad]

No, infinity is a category of number, and there are different types of infinity. For instance, the number of integers is countably infinity, while the number of real numbers is uncountably infinite.

Eternity and infinity consist of more than numbers.

This is a fascinating branch of number theory and has important, real-world applications.

Like?

You can dismiss it if you want, but unless you can demonstrate that the greatest mathematical thinkers the world has ever seen were, to a one, wrong... well, the ball's in your court.

Wrong about...? They reached some conclusion on the concept of infinity that you can talk clearly about here??

Of course it is. It is a concept inextricably linked with numbers and basic arithmetic.

No. It is far bigger. Like eternity.

They are concepts of the mind, idealisations of a pattern.

Nope. What pattern would you offer that you thin reaches into infinity and beyond??

Can you hold 'one' in your hand? Can you hold 'cube' in your hand? Do you even know what a Platonic Form is?

I can hold one girl's hand in my hand. I can even hold a cube. Not like that is real sexy. As for Platonic Form, is that something you think we need to hold in our hand?? Or are you trying to sound smart?

Yes, I played around with them at university, but that's besides the point: the theory is sound. I can walk you through it, if you like.

You have not seen a singularity nor can you walk anyone through one. Be honest.

According to quantum mechanics, there is hard limit on density, a point where matter can't be squeezed any tighter. This stands in contrast to general relativity, which posits that there's no hard limit, that matter can be squeezed to a single point of infinite density - that is, "X matter divided by zero volume equals infinite density".

Mind games. Physical only matter is not what reality is all about. How much we could mentally squeeze it with present state forces is a useless notion.

In my original post I should have said 'general relativity', not 'quantum mechanics'.

OK. You stand corrected.

It matters when those beliefs are acted upon. Since this is a discussion forum, where we share our ideas and beliefs, it seems a bit odd to lambaste me for participating in the core activity this entire forum is based on.

It might matter to your mental well being, but not to universal reality. You may exercise belief here, and that is not what I would 'lambaste' you for. If you relegate and subjugate science and all reality and knowledge to your beliefs alone however, we would need to look at the value of that.

 

[Wiccan_Child]

Eternity and infinity consist of more than numbers.

Indeed: they're categories of numbers.

Like?

The study of infinity and the infinitesimal gives us the calculus, which in turn has created all modern technology. Our world runs on mathematics, our technology is built by an understanding of mathematics, and the mathematical tool with the biggest implications is calculus - which is entirely based upon, and was derived using, an understanding of the infinite.

Wrong about...? They reached some conclusion on the concept of infinity that you can talk clearly about here??

Yes. Among other things, they concluded that infinity was a mathematical concept. You stated that infinity is not a mathematical concept. Ipso facto, you disagree with the world's greatest experts on infinity, on the subject of infinity.

No. It is far bigger. Like eternity.

Eternity is infinity as it relates to time.

Nope. What pattern would you offer that you thin reaches into infinity and beyond??

The pebbles on a beach are roughly ovoid, and it's not a massive leap of the imagination to imagine a perfect sphere - perfect spheres don't exist in reality, of course, but we can still imagine them, we can still manipulate them with mathematics to extract their properties, we can still use them to idealise real-world phenomena, etc.

I can hold one girl's hand in my hand. I can even hold a cube. Not like that is real sexy. As for Platonic Form, is that something you think we need to hold in our hand?? Or are you trying to sound smart?

You doubted me when I said they don't exist. I'm asking you to prove it. If you recall the previous exchange on this point, the term 'Platonic Form' is a well-understood concept in philosophy, dating back to Plato. It refers to the idea that there are real, physical objects of Truth, Beauty, Justice, Cube, etc. It's the idea that justice isn't a set of actions, it's a real and physical concept, humans practice justice, which is a shadow of Justice. Humans build cubes, which are a pale shadow compared to the Cube. That's what a Platonic Form is - it's a semantic abstraction given form.

Why did I use it? Because it's a concise term that clearly and unambiguously encapsulates the concept we're discussing. My apologies if you didn't understand the term.

You have not seen a singularity nor can you walk anyone through one. Be honest.

If you paid attention, you'd realise that that particular comment ("I'll walk you through it, if you like") was relating to quantum thermodynamics and the peculiarities of temperature. This is our previous exchange on this point:

Me: Take, for instance, a quantum thermodynamic system - a set of charged particles in a magnetic field, who can be 'up' or 'down', according to whether or not they have energy (heat). Add enough heat, and the temperature rises and rises, hits 'infinite', then goes back round to 'minus infinite' and down the negative axis. Peculiar, but very real.

You: No. Not really. Have you seen one lately???

Me: Yes, I played around with them at university, but that's besides the point: the theory is sound. I can walk you through it, if you like.

You: You have not seen a singularity nor can you walk anyone through one. Be honest.

Mind games. Physical only matter is not what reality is all about. How much we could mentally squeeze it with present state forces is a useless notion.

Irrelevant. You asked a question, I gave an answer. You asked how quantum mechanics relates to density, and I explained how quantum mechanics relates to density - namely, as it gives a hard limit on just how dense something can be.

It might matter to your mental well being, but not to universal reality.

Since nothing we do matters to universal reality, I fail to see the point in getting worked up about it.

You may exercise belief here, and that is not what I would 'lambaste' you for. If you relegate and subjugate science and all reality and knowledge to your beliefs alone however, we would need to look at the value of that.

Since I don't, your concern is moot.

 

[dad]

Indeed: they're categories of numbers.

No. They are not! God did not use the word eternal as a category of numbers that I recall. If science does that, well, hey, it is a recent player, and not too bright.

The study of infinity and the infinitesimal gives us the calculus, which in turn has created all modern technology.

I suspect that the part of calculus actually used on earth to calculate anything is not infinity, or beyond.

Our world runs on mathematics, our technology is built by an understanding of mathematics, and the mathematical tool with the biggest implications is calculus - which is entirely based upon, and was derived using, an understanding of the infinite.

No, only your hunches of what you call infinite, and even then only in baby steps and degrees applicable to finite temporal state earth. snore...

Yes. Among other things, they concluded that infinity was a mathematical concept.

They are dreaming in the dark.

You stated that infinity is not a mathematical concept. Ipso facto, you disagree with the world's greatest experts on infinity, on the subject of infinity.

They are jokers. Like they would have a clue on eternity and infinity?? No. They are stabbing in the dark, with a blunt toothpick.

Eternity is infinity as it relates to time.

Time is unknown to science. Certainly as it does or does not apply to forever. Time as we know it on earth is only something that is useful on and near earth, and even then, just for the time being!

The pebbles on a beach are roughly ovoid, and it's not a massive leap of the imagination to imagine a perfect sphere - perfect spheres don't exist in reality, of course, but we can still imagine them, we can still manipulate them with mathematics to extract their properties, we can still use them to idealise real-world phenomena, etc.

You could imagine a tooth fairy with pearl teeth too if you like. So?

You doubted me when I said they don't exist. I'm asking you to prove it. If you recall the previous exchange on this point, the term 'Platonic Form' is a well-understood concept in philosophy, dating back to Plato. It refers to the idea that there are real, physical objects of Truth, Beauty, Justice, Cube, etc.

Just one object of beauty? Seems to me there are many. But hey, if you want some beauty angel, who knows?

It's the idea that justice isn't a set of actions, it's a real and physical concept, humans practice justice, which is a shadow of Justice. Humans build cubes, which are a pale shadow compared to the Cube. That's what a Platonic Form is - it's a semantic abstraction given form.

God is real truth and beauty. Plato never included Him, so naturally fell short.

Why did I use it? Because it's a concise term that clearly and unambiguously encapsulates the concept we're discussing. My apologies if you didn't understand the term.

I do now, and still can't hold it in my hand. Neither could Plato.

If you paid attention, you'd realise that that particular comment ("I'll walk you through it, if you like") was relating to quantum thermodynamics and the peculiarities of temperature. This is our previous exchange on this point:

You do not understand things quantum, how would you walk anyone anywhere? Maybe man understands how things related to the quantum work here on earth...or part of it....but that won't help you I suspect.

Me: Take, for instance, a quantum thermodynamic system - a set of charged particles in a magnetic field, who can be 'up' or 'down', according to whether or not they have energy (heat). Add enough heat, and the temperature rises and rises, hits 'infinite', then goes back round to 'minus infinite' and down the negative axis. Peculiar, but very real.

Oh?? Real you say? Can you show us one that did that while you watched?? What things do on earth, or in a different part of the universe, and how long it takes, and why you only guess at.

You: You have not seen a singularity nor can you walk anyone through one. Be honest.


Irrelevant. You asked a question, I gave an answer. You asked how quantum mechanics relates to density, and I explained how quantum mechanics relates to density - namely, as it gives a hard limit on just how dense something can be.

It is relevant that singularities are not something found at Walmart. Have you one in hiding somewhere? How would you walk us through it? The physics and reasoning needed to get one is all we need you to explain. It likely won't fly.

Since nothing we do matters to universal reality, I fail to see the point in getting worked up about it.

I think we matter. So does God.

 

[Wiccan_Child]

No. They are not! God did not use the word eternal as a category of numbers that I recall. If science does that, well, hey, it is a recent player, and not too bright.

I suspect that the part of calculus actually used on earth to calculate anything is not infinity, or beyond.

Then you don't know the first thing about calculus. The only reason we can differentiate and integrate (two extremely important tools used daily in the construction of... well, everything, from architecture to circuitry to stock markets to medicine dosages) is because we know what we do about infinity. Calculus doesn't make sense without infinity, any more than arithmetic does without integers - just as addition is fundamentally rooted in the manipulation of integers, so too is calculus rooted in the manipulation of infinity. It most certainly is a mathematical concept.

No, only your hunches of what you call infinite, and even then only in baby steps and degrees applicable to finite temporal state earth. snore...
They are dreaming in the dark.
They are jokers. Like they would have a clue on eternity and infinity?? No. They are stabbing in the dark, with a blunt toothpick.

Since you have avowedly no idea what infinity is, this line of inquiry is futile. It amazes me that you are using a computer, built on scientific knowledge, to dismiss scientific knowledge.

Time is unknown to science. Certainly as it does or does not apply to forever. Time as we know it on earth is only something that is useful on and near earth, and even then, just for the time being!

Regardless, the concept of the eternal is hardly a difficult one.

You could imagine a tooth fairy with pearl teeth too if you like. So?

You asked for an example as to how an observed pattern can lead to mathematical abstractions, such as infinity. I gave one.

Just one object of beauty? Seems to me there are many. But hey, if you want some beauty angel, who knows?

First, the nature of Platonic Forms is that they are unique objects, the pure essence of a concept. A pretty statue is not the Platonic Form of Beauty.
Second, as I said before, Platonic Forms don't exist. That's my point. Lord only knows why you're harping on about them.

God is real truth and beauty. Plato never included Him, so naturally fell short.

Which shows you don't really know a lot about Plato.

You do not understand things quantum, how would you walk anyone anywhere? Maybe man understands how things related to the quantum work here on earth...or part of it....but that won't help you I suspect.

Nonetheless, if you want to understand how temperature can reach infinity and loop back round to negative temperature, the offer is there.

Oh?? Real you say? Can you show us one that did that while you watched?? What things do on earth, or in a different part of the universe, and how long it takes, and why you only guess at.

You really have a short-term memory, don't you? Not two posts ago I stated that I experimented with such systems at uni - you get a set of charged particles in a magnetic field, give them energy to flip their spins until over half are flipped, then keep adding energy till they're all flipped. That process raises the temperature up to infinity, then further up to minus infinity, then further up still to minus infinity. This isn't some armchair philosophy, these are real experiments.

It is relevant that singularities are not something found at Walmart. Have you one in hiding somewhere? How would you walk us through it? The physics and reasoning needed to get one is all we need you to explain. It likely won't fly.

Since you point-blank refuse to take me up on my offer, you'll never know. But then, even if you did, you'd probably forget what we were talking about halfway through a paragraph.

I think we matter. So does God.

I don't give a hoot what you think, and until God comes down and speaks for himself, I don't give a hoot what you think he thinks, either.

 

[dad]

Then you don't know the first thing about calculus. The only reason we can differentiate and integrate (two extremely important tools used daily in the construction of... well, everything, from architecture to circuitry to stock markets to medicine dosages) is because we know what we do about infinity. Calculus doesn't make sense without infinity, any more than arithmetic does without integers - just as addition is fundamentally rooted in the manipulation of integers, so too is calculus rooted in the manipulation of infinity. It most certainly is a mathematical concept.

If you think calculus deals in real infinity or eternity you don't know the first thing about them, not does calculus. No circuits you can show us involve eternity! Really. Math makes plenty of sense on earth without pretending it goes to infinity and beyond. Call me old fashioned, I like honesty.

Since you have avowedly no idea what infinity is, this line of inquiry is futile. It amazes me that you are using a computer, built on scientific knowledge, to dismiss scientific knowledge.

No one went to infinity to build it...really. Neither did the programming take forever. Hey our Friend lives there!

Isa 57:15 -For thus saith the high and lofty One that inhabiteth eternity, whose name is Holy; I dwell in the high and holy place, with him also that is of a contrite and humble spirit, to revive the spirit of the humble, and to revive the heart of the contrite ones.

Regardless, the concept of the eternal is hardly a difficult one.

No?

You asked for an example as to how an observed pattern can lead to mathematical abstractions, such as infinity. I gave one.

Abstractions are well...abstract. Perfection in beauty and all things is not here on earth in this state. The pearly gates, I assume they are perfect in shape.

First, the nature of Platonic Forms is that they are unique objects, the pure essence of a concept. A pretty statue is not the Platonic Form of Beauty.
Second, as I said before, Platonic Forms don't exist. That's my point. Lord only knows why you're harping on about them.

Did I raise them? No. You toss out other worldly concepts, and ethereal cubes and spheres, and then blame me?

Which shows you don't really know a lot about Plato.

I try to avoid the guy...


"
The image of Greece as the cradle of democracy persists. Along with free political participation and equal rights, sexual tolerance is taken as another token of enlightenment. Stories of Greek homosexual love have titillated public schoolboys over the decades. But ancient homosexuality was different from modern practice. Greek homosexuality almost invariably involved a youth and an older man, a junior and senior partner. According to Sir Kenneth Dover, who wrote a book about the subject, "the distinction between the bodily activity of the one who has fallen in love and the one with whom he has fallen in love is of the highest importance".
The most celebrated account of homosexual love comes in Plato's Symposium, in which homosexual love is discussed as a more ideal, more perfect kind of relationship than the more prosaic heterosexual variety. This is a highly biased account, because Plato himself was homosexual and wrote very beautiful epigrams to boys expressing his devotion. Platonic homosexuality had very little to do with sex; Plato believed ideally that love and reason should be fused together, while concern over the body and the material world of particulars should be annihilated. Even today, "Platonic love" refers to non-sexual love between two adults."


New Statesman - Was Plato the only Greek gay?

Nonetheless, if you want to understand how temperature can reach infinity and loop back round to negative temperature, the offer is there.

Yes please. Enlighten us. Some bits of your education may be useful.

You really have a short-term memory, don't you? Not two posts ago I stated that I experimented with such systems at uni - you get a set of charged particles in a magnetic field, give them energy to flip their spins until over half are flipped, then keep adding energy till they're all flipped. That process raises the temperature up to infinity, then further up to minus infinity, then further up still to minus infinity. This isn't some armchair philosophy, these are real experiments.

Raises temperature to infinity? Explain?

Now just because there is this way to change spins does not mean that this is the way that spins come to be in the far universe, you realize at least that much?

I don't give a hoot what you think, and until God comes down and speaks for himself, I don't give a hoot what you think he thinks, either.

No need, He has a book.

 

[Wiccan_Child]

If you think calculus deals in real infinity or eternity you don't know the first thing about them, not does calculus. No circuits you can show us involve eternity! Really. Math makes plenty of sense on earth without pretending it goes to infinity and beyond. Call me old fashioned, I like honesty.

Mathematics is far older than you, and mathematicians have studied and understood infinity with far greater finesse and humility than you. You insist that calculus doesn't involve infinity? OK then: prove that the differential of x[sup]2[/sup] wrt x is 2x - without using infinity.

No one went to infinity to build it...really. Neither did the programming take forever. Hey our Friend lives there!

Again, I never said it took forever, I said the mathematics behind it involve the infinite - and there are more infinities than 'forever'. Infinite feedback loops, recursive algorithms, even the technology that goes into building such devices ultimately utilizes the mathematical concept of infinity.

No?

No.

Did I raise them? No. You toss out other worldly concepts, and ethereal cubes and spheres, and then blame me?

Yes. You asked how patterns can lead to abstraction, I gave an example. You didn't understand, so I gave another involving Platonic Forms. You didn't understand, so I explained what Platonic Forms were. You still didn't understand. Go figure.

I try to avoid the guy...


"
The image of Greece as the cradle of democracy persists. Along with free political participation and equal rights, sexual tolerance is taken as another token of enlightenment. Stories of Greek homosexual love have titillated public schoolboys over the decades. But ancient homosexuality was different from modern practice. Greek homosexuality almost invariably involved a youth and an older man, a junior and senior partner. According to Sir Kenneth Dover, who wrote a book about the subject, "the distinction between the bodily activity of the one who has fallen in love and the one with whom he has fallen in love is of the highest importance".
The most celebrated account of homosexual love comes in Plato's Symposium, in which homosexual love is discussed as a more ideal, more perfect kind of relationship than the more prosaic heterosexual variety. This is a highly biased account, because Plato himself was homosexual and wrote very beautiful epigrams to boys expressing his devotion. Platonic homosexuality had very little to do with sex; Plato believed ideally that love and reason should be fused together, while concern over the body and the material world of particulars should be annihilated. Even today, "Platonic love" refers to non-sexual love between two adults."


New Statesman - Was Plato the only Greek gay?

As the last statement emphasised, Plato promoted a love of the mind over the body. He was better than St. Peter in squashing the idea of erotic love.

Yes please. Enlighten us. Some bits of your education may be useful.

Raises temperature to infinity? Explain?

Temperature is a measure of how energetic a system's particles are - that is, how often they move or change state due to thermal energy (or 'heat') that exists in the system. Quantum mechanics allows us to look at what happens when you have a set number of point particles, each with a magnetic charge, and put them in a magnetic field. They all orientate to point 'with' the magnetic field. If you give one of them enough energy, it'll 'flip' and point the other way. This energy randomly flits between the particles, so that one particle is always flipped - thus, the system is 'a bit hot'.

As you add more energy, more and more particles get flipped, right? The temperature increases. Once there's enough energy that fully half of the particles are flipped at any one time, the temperature is as hot as it can ever be - the system has a temperature of infinity. Why is this? Surely we can add more energy? Well, yes, we can: and when we do, more than half of all particles get flipped, meaning that a smaller and smaller number are 'unflipped', meaning less and less flips occur per second - i.e., the temperature heads to zero. But clearly it's going up, not down, as we're still adding energy to the system, so what's happening?

Once the temperature goes 'over' infinity, it comes back up the other way: the temperature is in the negative figures. As you add more energy, it heads to zero from the negative axis. Once you've added so much energy that all the particles were flipped, then there's no more flipping. Once that's happened, there's no movement - and the temperature has reached zero once more.

That's how temperature can go from zero, to infinity, to minus infinity, to zero again. This isn't a quirk of the mathematics, this is a real, genuine phenomenon that I've seen during my time at University.

Now just because there is this way to change spins does not mean that this is the way that spins come to be in the far universe, you realize at least that much?

Perhaps, but that's not the point: the particles, here and now, right here on Earth in our lab, do indeed exhibit this behaviour. Whether or not this happens far away or in the distant past, it happens in our lab, today.

 

[dad]

Mathematics is far older than you, and mathematicians have studied and understood infinity with far greater finesse and humility than you. You insist that calculus doesn't involve infinity? OK then: prove that the differential of x[sup]2[/sup] wrt x is 2x - without using infinity.

The marriage [sup] per of the Lamb comes to mind. Writing numbers is not getting to infinity or beyond. One could write this formula for infinity

1i

The 'i' means to the infinite power. You think your letters have more meaning?

Again, I never said it took forever, I said the mathematics behind it involve the infinite - and there are more infinities than 'forever'. Infinite feedback loops, recursive algorithms, even the technology that goes into building such devices ultimately utilizes the mathematical concept of infinity.

That is dreaming. Once you sit there watching an infinite feedback loop for eternity, get back to us. Meanwhile it is pi in the sky.

Yes. You asked how patterns can lead to abstraction, I gave an example. You didn't understand, so I gave another involving Platonic Forms. You didn't understand, so I explained what Platonic Forms were. You still didn't understand. Go figure.

Plato is not someone that interests me.

As the last statement emphasised, Plato promoted a love of the mind over the body. He was better than St. Peter in squashing the idea of erotic love.

It still ain't squashed. Go figure.

Temperature is a measure of how energetic a system's particles are - that is, how often they move or change state due to thermal energy (or 'heat') that exists in the system.

Remember that 'in the system' part.

Quantum mechanics allows us to look at what happens when you have a set number of point particles, each with a magnetic charge, and put them in a magnetic field. They all orientate to point 'with' the magnetic field. If you give one of them enough energy, it'll 'flip' and point the other way. This energy randomly flits between the particles, so that one particle is always flipped - thus, the system is 'a bit hot'.

The randomness I suggest is a feature of this state we live in.

As you add more energy, more and more particles get flipped, right? The temperature increases. Once there's enough energy that fully half of the particles are flipped at any one time, the temperature is as hot as it can ever be - the system has a temperature of infinity.

That is just a name. One neither sees something actually infinitely hot, nor can one say what might ever be. You mean within our laws, it could only be that way....that is not infinity or eternity.

Why is this? Surely we can add more energy? Well, yes, we can: and when we do, more than half of all particles get flipped, meaning that a smaller and smaller number are 'unflipped', meaning less and less flips occur per second - i.e., the temperature heads to zero. But clearly it's going up, not down, as we're still adding energy to the system, so what's happening?

Once the temperature goes 'over' infinity, it comes back up the other way:

Hey it is easy to call something 'infinity'. Reality check...it is inside a lab!

the temperature is in the negative figures. As you add more energy, it heads to zero from the negative axis. Once you've added so much energy that all the particles were flipped, then there's no more flipping. Once that's happened, there's no movement - and the temperature has reached zero once more.

One can play around with present state laws. No surprise there. If we take filing on a thin cardboard, and place a magnet below it, a pattern emerges also. Our present laws work a certain way.

That's how temperature can go from zero, to infinity, to minus infinity, to zero again. This isn't a quirk of the mathematics, this is a real, genuine phenomenon that I've seen during my time at University.

Where infinity is a word unrelated to actual infinity or eternity, yes we can play around and wath how forces and laws work here.

Perhaps, but that's not the point: the particles, here and now, right here on Earth in our lab, do indeed exhibit this behaviour. Whether or not this happens far away or in the distant past, it happens in our lab, today.

Yes, right here in the fishbowl. That is hardly to infinity and beyond in any real sense.

 

[Jazer]

How can an infinity of something actually exist?

The univere is either expanding or shrinking. That can go on forever. They call it the big bang and the big crunch.