In 'The Black Hole War,'
Stanford University physicist Leonard Susskind
recounts his long history of scientific conflict with famed cosmologist Stephen Hawking
(whose concession letter he prints).

By John Johnson Jr., Los Angeles Times Staff Writer
July 26, 2008

For two decades, Stanford University physicist Leonard Susskind battled cosmologist Stephen Hawking over the behavior of black holes. Hawking said that when black holes eat their fill, they disappear, taking with them everything they consumed over their billions of years of existence. Susskind found this idea so disturbing that he publicly declared war -- a conflict he describes in his new book, "The Black Hole War." In a conversation before a recent appearance at the Los Angeles Public Library, Susskind recounted his long struggle to "make the world safe for quantum mechanics."

How did this war with Stephen Hawking come about?

I was a particle physicist when I was invited to an event at Werner Erhard's house in 1981. Erhard [founder of the est self-awareness movement] admired scientists and liked to listen to them debate. At one of his events, I met Stephen Hawking. Stephen discovered an amazing fact, which is that black holes evaporate. It's like a puddle of water out in the sun.

OK.

So the question is, What happens to the information trapped in the black hole? Stephen said it was lost forever. Stephen didn't just say it, he proved it. At least he convinced himself and everybody else mathematically that it was true.

And you felt that was wrong.

It violates one of the fundamental principles of physics, which says nothing is ever lost completely. You may say, "How can you say information isn't lost? I can erase information on my computer." But every time a bit of information is erased, we know it doesn't disappear. It goes out into the environment. It may be horribly scrambled and confused, but it never really gets lost. It's just converted into a different form.

In your book, you compare Stephen Hawking to the White Whale and yourself to Ahab.

I obsessed over this. This was never a matter of personal animosity. But he couldn't see how damaging this would be to the rest of physics. And he didn't see what a great resolution might come out of it if thought about in the right way. I love the man, but I wanted to grab him by the neck and shake him a little bit. Stephen would just smile and say, "I'm right and you're wrong."

That's a pretty heady debate for someone who started out as a plumber.

I was from a poor Jewish family in the South Bronx. My father was a plumber, but when I was 16 he got sick and I had to take over. Being a plumber in the South Bronx wasn't fun.

When did physics come along?

I was going to engineering school but fell in love with physics. When I told my father I wanted to be a physicist, he said, "Hell, no, you ain't going to work in a drugstore." I said, No, not a pharmacist. I said, "Like Einstein." He poked me in the chest with a piece of plumbing pipe. "You ain't going to be no engineer," he said. "You're going to be Einstein."

What is the great resolution you referred to?

One result is something called Black Hole Complementarity. Let's say Alice falls into a black hole while Bob stays on the outside and watches. Nothing drastic happens to her when she crosses the event horizon [the point of no return around a black hole]. Of course she's eventually going to get it. On the other hand, there is another picture of the black hole, where every bit of information that you throw onto the horizon of a black hole gets sort of stuck on the horizon and builds up a soup of information bits. And this soup is hot, about a 100 billion billion billion degrees.

So Alice would get burned up?

We have a dilemma. One theory, based on general relativity, simply says Alice just floats past the horizon. That would be Alice's view of things. But Bob's view of things, if he believes in quantum mechanics, is that Alice falls into this soup of hot bits and her molecules are ripped apart. So, which one is correct? Alice can't both be killed at the horizon and not killed at the horizon. The answer is they are both correct.

How can that be?

These two ideas are not in conflict because to be in conflict, there has to be a contradiction. Well, nobody can see a contradiction for the simple reason that nobody can send a message from the inside of a black hole. Alice can't send a message saying, "Bob, I'm OK, don't worry about me," because the message can't get out of the black hole. Yet everything Bob sees is consistent with saying that Alice was thermalized.

It's difficult to see how both can be true.

We've had these things before in Einstein's thought experiments. Einstein, in the special theory of relativity, proved that different observers, in different states of motion, see different realities.

There's another strange theory that's come out of this battle, isn't there?

Yes, the Holographic Principle. A hologram is a two-dimensional sheet, such as film, which codes three-dimensional information. A simple way to say it is that the black hole horizon is like a hologram. The horizon of the black hole is like the film, and the image is the stuff that falls into the black hole. It's extremely unintuitive. According to this theory, the exact description of a region of space -- no matter how big -- is like a film on the boundary, where complicated and extremely scrambled versions of that space are going on. So in that sense, the universe is like a hologram.

Stephen now agrees that the information is not lost when a black hole evaporates.

Yes, he's seen the light. When he sees the light, he's very magnanimous.
[Susskind pointed to a page in his book, where a concession letter from Hawking is printed.]

Are there are any evaporating black holes in our region of the universe?

No. They are all accreting [still eating]. Black holes are much, much colder than their surroundings in space. That means heat flows from the surrounding space into the black hole. If we wait for a long, long time, the universe will expand, it'll cool, and eventually empty space will become colder than the black holes. When that happens, they will start to evaporate. But don't hold your breath.

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Could believers and non-believers in an afterlife both be correct?

Yes, imo I have mantained for some time now that one of the fundamental aspects that God (or whatever) built into the fabric of the universe (and therefore our existence) is situational irony. Everything has two meanings. The first element of creation is light (according to Genesis anyway), an element that behaves both as a particle and as a wave, which is contradictory and ostensibly impossible. Light is irony in pure form, which is why Heidenberg's Uncertainty Principle is the chief governing law of the universe. The act of observation in itself alters the outcome. I believe this factor of irony is inherent to the process of growth and change. The Unified Field Theory is a pipe dream, imo.

God, this brings back memories. I studied this kind of stuff relentlessly when I was in my twenties. It drove me to madness, which is why I gave it up for the most part. I still study these kinds of things intermittently when a particular topic or theory strikes a chord. I'm currently re-reading a book called God's Secret Formula by Peter Plichta. In it, he basically shatters centuries of preconceived notions about physics, mathematics and chemistry, although to a large degree you kind of have to take his word for it, as he doesn't always go too far in depth regarding the equations and such. Its written for the layman to understand, except the last chapter which kind of gets complicated. Anyway, its basic premise is that the fabric of the universe is built on the pattern of the prime numbers, specifically on the first three numbers 1, 2 and 3. Combinations of these three numbers present higher equational patterns in nature (6 + or - 1 in probabilty events, 19 + 1 in chemistry, or the "threefold nature of the universe" in things like organic chemistry - single bonds, double bond, triple bonds). His main grip against past scientists in the field of physics, math and chemistry is that the fundamental laws or equations inherent in these fields are simply taken at face value without examining or asking WHY they exist in this or that particular form. The table of elements is his main example, why in this order and why with these specific numbers of electrons, nuetrons, etc. He says its explained by the prime numbers and makes a pretty concinving argument.

And anyway...
it all breaks down to space and time being a four-dimensional mathematical construct, whereby one dimension exists inside a two dimensional form, two dimensions exist inside a three dimensioal form and three dimensions exist within a four dimensional form. Each form anticipates the next level, meaning that random chance exists inside of order, even though it isn't really random after all, except that it is.

Life is a conundrum...with the infinite and unique prime numbers representing everything that is infinite and unique in the universe, including all of us. However, because of the nature of numbers, this infinite and unique universe exists within a finite mathematical construct and must conform to that construct at all times. Does that make sense?

Everything has two meanings. Everything. But its specifically built that way.

Yes, one of Plichta's theories in the book is that there are two kinds of space, a three dimensional space which encompasses matter and a fourth dimensional space which is the mathematical construct that must exist IN ORDER for three dimensional matter to exist. In essence, any order of form must anticipate, or connect to, a higher order merely to exist, otherwise space an time are meaningless and would cease to exist in and of themselves (and this includes orders of operation, orders of events, etc). Time = movement and movemnt = time. However, the real conundrum is that the higher order must exist for the lower order to exist, and yet the lower order must imagine or anticipate the higher order in order for the higher order to exist. Each one's existence appears on the surface to be the initiator of the other's existence.Which came first, the chicken or the egg?

The fundamental underlying point of Plichta's book, though its not explicitly stated this way, is that the laws governing the universe are built on a principle of +1. There is an ordered system, and attached to each system is the principle of +1. +1 is the uncertainty/chaos part of the equation. +1 is Heidenberg's Uncertainty, or the probability of chance in a Plinko game, or any thought or action you might create. But...since +1 is automatically built into any system, the system is inherently mathematically ordered. THe short explanation is that lif cannot and would not exist without this simple equation. Without it there is only stasis and no need for space or time.

If anyone has read or is familiar with Arthur Koestler's book The Ghost in The Machine he goes in depth into this principle of orders anticipating a higher level, concentrating on the ways individual cells in the body bond to create higher orders or how a single cell from your kneecap can be transplanted to your eye and then become an eye cell.

Plichta's book is really fascinating and I would recommend it as required reading for anyone remotely into physics, chemistry or mathematics. The real basic underlying premise is that God created an ordered identifiable system that is not, however, static. The number line is effectively proof of a higher order, being, intelligence, whatever you want to call it. It is God's abacus. The pattern of prime numbers are the building blocks for anticipation and ascension from lower orders into higher orders.

Look at the number line. The number line exists without us ever existing, we just attached characters to it to describe it in mutually practical terms. We then created the seemingly irrational number "0" because it inessence was needed for higher logic equations (and the Phoenecians or whoever realized this intuitively). To the right of the number 0 are the rational numbers and to the left are negative integers. The number line is infinite in both directions. Out of this infinite line we derive finite equations to detail and desribe everything, but those equations also already existed with or without us. This also leaves open the possibility of humans evolving into Godhead.

Everything having two meanings (or interpretations), anticpating the higher level, the probabilities of random chance, all these things are infact connected to each other. Your feet are going to be on the ground, but your head is there to move you around.

I don't explain it all too well, I'm leaving out a lot of stuff.
My point was that its is firmly built into the fabric of everything that conflicting or seemingly mutually exclusive elements do exist together at the same time. This...is the fundamental paradox of existence, and its the one that is difficult for people to really accept because it defies our standard notions of logic. So Jeff, all that was meant to answer your question about believers and non-believers, I just get carried away with it, which is why I stopped caring so much about it in the first place. Its endlessly fascinating, and that's exactly the problem.

Here's a simpler explanation about order and chaos:
Imagine the number line as space/time/infinity and that it represents four dimensional possibility (chaos, infinite possibilites).
The equations that are created out of this number line represent the three dimensional world (order and structure).
The equations exist within the number line sysytem.
The equations need the infinite number line in order to be brought into existence.
The infinite number line, in order to exist, needs the equations to justify or "prove" its own existence.

It is theoritcally possible to cryogenically freeze a human body at just the right speed and temperature so that all the molecules in that body will cease all movement before those molecules can begin the process of degradation or disintigration. If this freezing of all movement occurs successfully, time will cease to exist for that body, and that body can be later (years later) thawed out at just the right speed and temperature (the harder part of the two) and brought back without any damage. Meanwhile, time will have continued unabated for all organisms outside of that body. This is the domestic parallel to the case of an astronaut flying to Alpha Centauri and back who will have aged at a much slower rate than the rest of humanity.
The number line is absolute, but within that number line all equations are relative and can be altered or tweaked.

Matter = Movement = Space = Time. All are dependent on each other.

Matter, in fact, CAN be created by Man. The highest numbers on the table of elements (above 100) ARE elements of matter that have been created by Man, but are so unstable they only exist for fractions of a nanosecond.

In fact, we are evolving into Godhood by figuring out and learning from the lessons of our creator. The same way a child does from a parent. Imo.

Thus the Universe regards itself, and realises it is self-aware.

I realise I'm getting away from the original topic but I find this interesting.

When you look at the number line and pick out the primes, at first it doesn't appear to yeild a pattern, or any kind of substantial form.
But Plichta saw it in a different way. He chose to represent it as threaded around enlarging circles, like a clock. When one looks at it like this, it begins to take on a new dimension.



The circled numbers are the primes. When we add the larger circles that continue the number line we get this image:



The original pattern of the coupled prime numbers doesn't continue as on the first circle, except intermittently. But...every 6th number along the number line will have a prime on one side or the other or on both sides, thus the 6 + or - 1 equation. This equation figures prominently in probability matrices, like the example of the Plinko game.

Now, and this is where it really gets interesting...anyone here who has studied any nuclear physics (raise your hands) will notice something striking about these two images. They are reminiscent of the electron shells that surround the nucleus of an atom. And like an atom, the first circle (shell) has an ordered pair, or pairs, and all the successive circles (shells) appear to be randomly ordered.

Scientists have debated and conjectured for a long time now about how these electrons in an atom are structured on the shells, because they seem to "jump" from one shell to another...or...they seem to be in two places at the same time. There are all kinds of theories about it. Many just take it as a matter of course that the exchange of electrons is just random and the purpose for these actions is unknown. However...the 6 + or - 1 principle that shows up in the pattern of prime numbers is, in Plichta's opinion, the precise principle that guides the exchange of electrons within an atom.

And then there's the table of elements. Element number 1 has 1 electron, element number 2 has 2, and so on, and that's how we achieve each element's atomic number. This goes on through the number 106. The first 85 are listed as the stable elements (though two are missing, numbers 43 and 61, because they only exist as by-products of nuclear fission). The pattern of prime numbers seem to explain how each shell of electrons is added, and ordered, for each successive element along the table. So, according to Plichta, the elements are built on the math of the prime numbers. It appears to be a pretty convincing argument.

The book also details many other natural patterns, or constants, that occur in nature, and goes even further into detail about several other patterns that emerge intact among the table of elements. Its really some wild stuff, baby!

Two more interesting points about the primes:

- the number 144 doesn't have a prime on either side and so does not conform to the 6 + or - 1 principle. But this anomoly may be part of yet a higher or longer pattern. One of the really difficult things about calculating the prime numbers, or patterns among primes, is that when you get up to really high numbers its almost impossible to draw out a full length number line to find them. And just as impossible to draw out say, 100,000 large expanding circles to easily see the patterns. Some savants can claculate them into the 100,000 range and it takes super computers to do it beyond that. In fact, since the number line is infinite we don't really know the full extent of the pattern.

- If you look at figure 2 from above, you'll immediately notice that all the primes fall along 8 spires proceeding out from the center. Plichta calls this The Prime Number Cross. That's certainly a clear pattern.

Btw, in figure 2, if you look closely, you'll notice that there are two numbers (-1,1) just inside of the first circle, with the number 1 then repeating as the first number on the first circle as 1 squared. I can't remember exactly why Plichta did it this way, I think it has something to do with the number 1 not usually being associated as a prime number because -1 squared is 1.

Please, Forum, forgive me if this is incoherent. I've never really thought about it before reading chrestus's posts earlier today (thanks, chresty!).

I don't see why the "God or no God" question is even important. After all, if there IS a God, he's certainly just as heartless as cold physical mechanics; if there isn't, then it's a wonder pure physics managed to produce beings that--no, WHO--feel the need to believe in God. I mean, what's the difference between an omnipotent God who does basically nothing (or as good as nothing) and a universe full of energy that tends to behave in a certain way, forming superstrings and such?

As for the number line as proof of God's existence, I think the argument stretches pretty thin. After all, a circle is a fairly arbitrary shape (and shapes are relatively arbitrary concepts, anyway), and any arrangement of numbers can easily be manipulated into a "meaningful" shape. If I wanted to prove to you that prime integers formed stars, I would simply make a circle of such a size (capacity) that, when you expanded it into a few thousand concentric circles, a star would appear, sketched out in prime numbers.

Numbers, too, are arbitrary. It's important to remember that actual NUMBERS don't even appear very often in nature. I mean, it's easy to say "I have three apples," but the truth of that statement actually depends on what your definition of an apple is. If, suddenly, you decided that one of your apples wasn't even an apple, could you really be certain ever again that you actually had a given number of apples? Well, yes you could. But a part of you would know that you are being irrationally certain. Numbers are the invention of humanity, and they're more a quick-fix than a reliable system. So to claim that there are indeed two electrons in a shell...tough call. Let's just cross our fingers and hope that they ARE both electrons, and don't just behave similarly. If you don't take that leap of faith, even observable quantities get pared down to this: One. You can look at an apple and say, "THIS is an apple." Then, when you see a similar fruit, you can say, "This is ALSO an apple." But you can't be sure you're right. So you can only ever be sure that you have one apple.

It's all relative, after all. That's why you're so likely to find a RATIO in nature, as opposed to an integer. I mean, what numbers actually DO appear in nature? Pi, for one. e, for another. The square root of two, sometimes, and that ever-popular 1.618. But the only reason 3.141592...whatever is so common is that it appears as a ratio (of the circumference to the diameter of a circle, as some factor in the equation for the circumference of an ellipse, etc. The units of pi are arbitrary, ALWAYS. It's never possible to claim that the diameter of a circle is always 4, and its circumference is always 4pi. Four of what? Miles? Inches?

Speaking of distance: Distance itself is only a ratio. A kilometer is--what?--some arbitrary fraction of the distance from equator to pole (on Earth, of course), or something. This means that every single distance you can ever measure is really a ratio of one segment to the length of the segment that connects the equator and the pole. As in, "The distance from Liverpool to Timbuktu is such-and-such a portion of the distance from the equator to the pole."

And that's how everything is. It's all ratio, all relative, and doubly so because it's dependent upon what we can observe. This, as Einstein showed us, is not by any means a stable or trustworthy standard. So: To someone ON Earth, the distance from equator to pole would be such-and-such; for someone WATCHING Earth fly past, however, it would be quite different. So if you were to watch Earth fly past, and then apply a certain fraction of the distance between equator and pole as a unit of measurement, then YOUR measurement of the distance between, say, Alpha Centauri and Betelgeuse would be much different from the measurement of somebody on Earth, even if they used the same fraction of the distance from equator to pole as their unit of measurement.

So, if you were to say, "It's so-and-so kilometers from Earth to Mars," well, that depends on what your definition of a kilometer is. Again, integers = man-made tools (I of course acknowledge the huge part women played in the creation of these tools).

Ratios, however, are entirely observable as long as the relative motion between observer and observed remains constant. So I can actually tell you with relative certainty that the diameter of a circle = circumference / pi (pi, of course, being nothing more than "circumference / diameter"--it's all a bit...circular). I CAN'T tell you that the diameter of a circle is 3. Unless, of course, I first assign it a completely arbitrary unit. This is what we humans do. So as long as two people are looking at it from the same vantage point, the distance from Earth to Mars is DEFINITELY a certain ratio of the distance from equator to pole. It's all a matter of general agreement.

However:

Jeff Truzzi wrote:

Could believers and non-believers in an afterlife both be correct?

I don't think so. Even if "reality" is really just "the shared OR individual human perception of reality," I don't think these can both be true. Think about it this way: If an atheist is correct, then human perception itself evaporates after death. If a Christian is correct, then human perception is perpetuated in some sort of spiritual state called Heaven (or Hell). But if the perception of reality can be traced back to the human brain (thus allowing for divergent but true perceptions), and (according to the atheist) the human brain ends at death, then ALL perceptions of reality (including the perception that reality has ended) become impossible, post-mortem. So, according to an atheist, the very IDEA that you're in Heaven is impossible once you're dead. While alive, it's quite possible to perceive that you're alive and well inside a black hole, just as it's possible to perceive that the person you just watched enter a black hole was cosmically ripped apart. After death, according to the atheist or "tooth-fairy agnostic" (me), it's impossible to perceive anything. But according to the God-believer (Truzzi), it isn't. Once we're dead, we can't both be right.

But here's the thing: As long as we're alive, both perceptions can be perfectly true. To my mother, right now, there is an afterlife. To me, there isn't. So, to me, all the people who have gone before have evaporated. To her, they're just waiting. She's convinced. I'm convinced. It's all relative. For now. But as soon as we die, it goes one of two ways: I'm right, and we're all consigned to oblivion...or SHE'S right, and our consciousness is perpetuated. Now, here's where it gets weird. IF she IS right, then it IS possible for us to both be right. After all, I could just perceive that I am (and everyone else is) no more, while she perceives that she (and everybody) still exists. However, if I am right, then she can't perceive anything, and neither can I, and neither can anyone, and nobody exists. It all depends on whether consciousness after death is a reality, and there's this strange branching duality there, with HER branch branching again into another split reality, and so forth.

Oh my God, this makes so little sense. Fortunately, though, there's a very simple experiment we can--and will--perform that'll settle the issue once and for all.

Good discussion. Clovers.

"God or no God" is just a name implying whether the universe is self aware or not. That's all my God is: a self-aware universe. And the math is its building blocks. I don't go for the Christian ideas of judgement, magic tricks, heaven & hell. But I don't believe us humans are the most highly evolved and advanced beings in the universe, either.

Reality is subjective, and (according to Einstein) can be different for different observers in different frames.
Some believe this could open a door.
Others believe it doesn't.
And our beliefs are our realities.

You're welcome, Clovers my good man! And I'm always interested myself when the conversation turns to these things. That's a heady post you've made there, I've been thinking today about the issues you raise, and since there's a lot of info there to be kicked around I'm going to quote from you and offer my opinions on each paragraph, in order to keep track. I don't intend this as a rebuttal but I do disagree with the use of the word arbitrary as I think you're applying it here, so I just want to offer up my take on it and then, you know, we can:
1. Agree to disagree
2. Find a common ground, if one exists
3. Start a blood fued with outrageously inflammatory invectives, blow up the forum and then make it our life's obsessions to hunt down and destroy each other, leaving our friends and loved ones behind to pick up the pieces.

Golly, let's hope it doesn't come to that. We'll just file that under "last resort."

Clovers wrote:

I don't see why the "God or no God" question is even important. After all, if there IS a God, he's certainly just as heartless as cold physical mechanics; if there isn't, then it's a wonder pure physics managed to produce beings that--no, WHO--feel the need to believe in God. I mean, what's the difference between an omnipotent God who does basically nothing (or as good as nothing) and a universe full of energy that tends to behave in a certain way, forming superstrings and such?

The problem, as I see it, with the "God is a heartless monster" point is that it doesn't leave any room in between this and the "God is all loving" point for any other, possibly unknown or unknowable, information. Its just the other side of the same coin, imo. For myself, I leave the room open for all kinds of possibilites, that God is not perfect and can't simply affect everything that is set in motion, that 90% of these bad things that happen are really due to human error and bad judgement, human free will. I also leave open the possibility that human suffering, as extreme and ugly as it is, is a part of the process of learning and understanding and growing by which the human race might evolve into a higher form. And I do see this evolution as a very real thing, a very real and tangible possibility. Out of the most horrible painful events can come great human kindness and understanding (and forgiveness), things which may never have been imagined otherwise. That is, imo, a certain kind of knowledge which enlarges the mind and the soul, and enlarges the possibilities. I don't say that this absolutely is the way, only that I leave open the possibility. But I would say there is as much evidence to support these claims, though it requires a deeper philosophical view to see it, as there is to suggest that God is heartless or imcompetent.

Its not an easy lesson, to be sure. As always, I tend to liken it to the relationship between a parent and a child. Growing up yeilds many difficult and painful lessons, and some of these lessons are intentional. To the child, the parent is a big meany, and a lot of the lessons are confusing and appear to be arbitrary. But a parent cannot simply tell the child "the trugh" because they can't reasonably process the information in a practical or meaningful way. I'll grant that most parents do not intentionally attempt to harm or kill their children..but sometimes they still die inspite of all our protections and guidance. Loved ones dying is the final lesson of what I was on about in the first place, that uncertainty and unpredictability, are built into the system of existence, into the fabric of reality, and therefore they are a part of life that is to be dealt with and/or learned from, and possibly overcome. The hardest lesson of all is to try and see these things not as a child might see them, but to make that intellectual/emotional leap to the next level and see them as parts of a larger picture, and to anticipate intuitively the logic of it without completely understanding all the reasons or all the information.

Clovers wrote:

As for the number line as proof of God's existence, I think the argument stretches pretty thin. After all, a circle is a fairly arbitrary shape (and shapes are relatively arbitrary concepts, anyway), and any arrangement of numbers can easily be manipulated into a "meaningful" shape. If I wanted to prove to you that prime integers formed stars, I would simply make a circle of such a size (capacity) that, when you expanded it into a few thousand concentric circles, a star would appear, sketched out in prime numbers. Numbers, too, are arbitrary. It's important to remember that actual NUMBERS don't even appear very often in nature. I mean, it's easy to say "I have three apples," but the truth of that statement actually depends on what your definition of an apple is. If, suddenly, you decided that one of your apples wasn't even an apple, could you really be certain ever again that you actually had a given number of apples? Well, yes you could. But a part of you would know that you are being irrationally certain. Numbers are the invention of humanity, and they're more a quick-fix than a reliable system. So to claim that there are indeed two electrons in a shell...tough call. Let's just cross our fingers and hope that they ARE both electrons, and don't just behave similarly. If you don't take that leap of faith, even observable quantities get pared down to this: One. You can look at an apple and say, "THIS is an apple." Then, when you see a similar fruit, you can say, "This is ALSO an apple." But you can't be sure you're right. So you can only ever be sure that you have one apple.

I don't think numbers are arbitrary, myself. There are an exact number of atoms in the universe. I can assign a character to represent that number, but my existence and my observation doesn't change the number, even if my observation is incorrect. I have no say in the amount, only in the way that amount is described. I guess one can argue over whether atoms actually exist at all but where does that lead? Some things have to be assumed based on the evidence for us to get anywhere. I make a distinction between believing that atoms exist in some kind of form and having to know every exact nature and dynamic of an atom and how it precisely behaves to believe in it. I don't know the latter but I believe in the former. Also, if I call every object into question, not only does this discussion become moot but every moment of my existence, every action I may undertake is moot and therefore I should just give up and die. That doesn't seem like a rational way to be, imo. Philosophically, its fine, but I have kids and whatnot. I have to assume a certain fixed point of understanding, of common reference.

Numbers are not a human invention, imo, but how we describe them is. If all the world had developed exactly like it is except that there were no humans, and one apple fell from an apple tree and then an hour later a second apple fell right beside it, how is that not a number of apples? They don't even have to fall from the tree. You can all it five apples but it doesn't change the number of apples. To me, it doesn't make any difference if I'm confused about what an apple is, there is still an exact number of hairs on the body of the warthog that comes to eat the apples that fall from the tree. There is an exact number of all the objects that exist, regardless of what they are called, or what they look like or what shape they have. This is true whether or not I am here to observe it or attempt to describe it. It seems to me that to say otherwise is tantamount to saying nothing exists at all. And that just leads us right down the path to nowheres-ville, man.

Your apple analogy seems to be dependent on defining what an apple is in order to number it/them. As in, you can't count to the number three unless you have three apples, and since you can't decide what an apple is, therefore there is no such thing as the number three. But if I lose my right hand to a mountain lion, I now have half as many hands. I am decreased by an exact number of hands, of which there is no question. If I lose the other hand to a bear, I have zero hands. I cannot lose any more hands. I had this amount of hands, then I had ONE hand, and then I had none. It doesn't matter what I call it or how I observed it, the reality is still there for me. Two hands are better than one, and one is better than none.

Clovers wrote:

It's all relative, after all. That's why you're so likely to find a RATIO in nature, as opposed to an integer. I mean, what numbers actually DO appear in nature? Pi, for one. e, for another. The square root of two, sometimes, and that ever-popular 1.618. But the only reason 3.141592...whatever is so common is that it appears as a ratio (of the circumference to the diameter of a circle, as some factor in the equation for the circumference of an ellipse, etc. The units of pi are arbitrary, ALWAYS. It's never possible to claim that the diameter of a circle is always 4, and its circumference is always 4pi. Four of what? Miles? Inches? Speaking of distance: Distance itself is only a ratio. A kilometer is--what?--some arbitrary fraction of the distance from equator to pole (on Earth, of course), or something. This means that every single distance you can ever measure is really a ratio of one segment to the length of the segment that connects the equator and the pole. As in, "The distance from Liverpool to Timbuktu is such-and-such a portion of the distance from the equator to the pole." And that's how everything is. It's all ratio, all relative, and doubly so because it's dependent upon what we can observe. This, as Einstein showed us, is not by any means a stable or trustworthy standard. So: To someone ON Earth, the distance from equator to pole would be such-and-such; for someone WATCHING Earth fly past, however, it would be quite different. So if you were to watch Earth fly past, and then apply a certain fraction of the distance between equator and pole as a unit of measurement, then YOUR measurement of the distance between, say, Alpha Centauri and Betelgeuse would be much different from the measurement of somebody on Earth, even if they used the same fraction of the distance from equator to pole as their unit of measurement. So, if you were to say, "It's so-and-so kilometers from Earth to Mars," well, that depends on what your definition of a kilometer is. Again, integers = man-made tools (I of course acknowledge the huge part women played in the creation of these tools). Ratios, however, are entirely observable as long as the relative motion between observer and observed remains constant. So I can actually tell you with relative certainty that the diameter of a circle = circumference / pi (pi, of course, being nothing more than "circumference / diameter"--it's all a bit...circular). I CAN'T tell you that the diameter of a circle is 3. Unless, of course, I first assign it a completely arbitrary unit. This is what we humans do. So as long as two people are looking at it from the same vantage point, the distance from Earth to Mars is DEFINITELY a certain ratio of the distance from equator to pole. It's all a matter of general agreement.

Again, I say that you are confusing what something is called as it is observed with what it is, regardless of the observation. Calling the distance from the pole to the equator a mile or a kilometer or a foot doesn't alter the distance between the pole and the equator. Its only relative to the observation; the distance betwee the pole and the equator itself is not relative. Its specific and exact. Einstein's theory doesn't change the objects (or the speed, since it was dealing with the speed of light) it only changes the observation. The distances, the speed, etc, remain exactly what they are with or without us. Ok, so fair enough.
In practical terms, these differences in observation are neglible. We were able to gauge how much fuel was needed to get to the moon and back, even if we didn't know the exact empirical distance.

The point in all this, as I see it, is that our observations alter the outcome, the definition, etc, and I'll grant you that. I will say though that they don't alter them enough to mean anything or make a difference. Its the difference between having 10% of the information and 84% of the information. The fundamental difference between our two sides of these discussions (including the God one) is that you won't commit to anything unless its 100%, and I'm saying I will at 84%.

We all take things on faith every single day. When you get into a car you have faith that you won't be killed. When you drop your kids off at school you have faith that they won't die there. If you didn't, you wouldn't be able to function in society. But you can tell the difference between 10% and 90%. If there's a 10% chance you'll die in the car, you might still get in. If there's a 90% chance, you won't.

Regarding ratios:
Well, I think my arguments already mentioned cover this, for me. Pi and Eulor's constant are just that, they are constant. If the entire universe and everything in it truely were random and chaotic, without any order or design built in, then there's no reason to assume that any type of order would evolve out of it. Assuming that an order would develop is just as illogical as assuming that there is, or isn't, a god. Its also illogical to assume that the chaos that comes out of order is really actually chaos. However, we do these things based on practical concerns, we fill in the gaps either out of our (mis)understanding about how things work, or to mitigate the results of our perception of "chaos." Scientists, and non-believers, or athiests, whatever, rely on their faith in chaos just as much as believers rely on their faith in a design. The idea of design, however, appears to me to be more logical and rational, and I find this especially true if we are using "the observation and evidence of the world around us" as our guide. Even given the inepitude and unrelability of human observation, the evidence points more toward design than random chaotic evolution, in my most humble opinion. The idea of chaos as a whole system, for me, just strikes me as exactly what it says. No order. If you recognise order, then the system isn't chaos, its order with the perception of chaos. And that is where our arbitrary methods of inadequate observation truly come into play and reveal themselves, imo.

What planet do you superior beings hail from? Do you come in peace?