h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Umm... I'm snowed under with work today and don't have the time to get up to speed on the backlog. I'll leave you with two thoughts to be going on with, though (just to keep my end up, as it were ).

If there is such a thing as an objective abstraction, then any two minds should be able to discover it. If it does not 'exist', in some sense, then how do the two minds arrive at it? I'm saying that it must be in some way fundamental to or inherent in the universe the minds are in in order for them to arrive at it. This is 'existence' of a sort. I then go on to say that mathematics is such an abstraction (for this universe, anyway).

The other point is that the universe does have rules, if it did not it would be unable to take on order, always in a random and meaningless state. Chaos, in the mathematical sense, is not the lack of rules but using certain pathological rules that defy analysis. The universe is chaotic, but not unruly. You could argue that rules are only consistent over the temporal and physical locality, but this raises a question mark over long-distance stellar observations.

'Rules' is a slightly dangerous word to use here, it implies someone imposed them on the Universe - I don't think anyone did, but rules are the way in which we see it, because it helps us understand why things happen, and this is all well and good, provided we're willing to accept that we may not necessarily know all the details about why things are acting the way they are, and be prepared to modify our understanding if new things come to light.

Although the very existence of the universe can't be proved, this doesn't help someone trying to live a life in what appears to be a Real World! I happily note your awareness of this, and your well-chosen words. I'm not so happy about being seen as someone who might leap on your back, though.

Pattern-chaser

"Who cares, wins"

I keep saying to myself: "leave this one alone. You (and others) have said all that can be said, and you can't force someone to adopt *your* perspective."

But the much-repeated oxymoron 'objective abstraction' bothers me. At the least, it's disinformation that could derail the thinking of anyone taken in by it. So I'm once again approaching this topic.



If we assume the existence of 'angry concrete', all sorts of absurd consequences follow. The same applies to 'objective abstractions'.

Dictionaries use different terms, but they all seem to agree that something 'abstract' has no existence in the Real World. If abstractions exist - and they surely do! - but not in the Real World, it seems to me that there is only one place in which they can exist: the human mind.

Finally, if we accept (by definition) that something objective is independent of the conceptions and/or perceptions of humans, doesn't it follow that something which exists *only* within the human mind cannot be objective?

Pattern-chaser

"Who cares, wins"

Apologies for derailing the much more important discussion of whether magic exists , but...

"If there is such a thing as an objective abstraction, then any two minds should be able to discover it. If it does not 'exist', in some sense, then how do the two minds arrive at it?"

I suspect your definition of a mind assumes that this mind can understand the rules of logic and believes in them. If so, then your definition is circular. A mind is something that can arrive at mathematics, and mathematics is objective because any mind can arrive at it. If this isn't your definition of a mind, you have to argue that it would indeed arrive at mathematics (or equivalent logical structures). Mathematics might be as little as the accidental product of millions of years of (meaningless) human evolution.

"The other point is that the universe does have rules, if it did not it would be unable to take on order, always in a random and meaningless state."

This doesn't make sense. What do you mean by a rule? Do you mean a physical law, for example in the form of a differential equation? Have you seen "The Matrix"? In that film, it seems as though the world has rules, and almost always the world follows those rules, but certain individuals like Neo (Keanu Reeves) have the ability to bend the rules. How can you assert that this isn't the situation?

To put it another way, suppose I randomly choose fifty numbers between one and a thousand. It might be, it almost certainly will be, that there is no order to these numbers. However, it might be that I randomly choose the numbers in increasing order. There is order here, but it is order that just happens to be there, not essential order that is inherent in the process (which is random). This isn't a totally trite observation though. If we imagine that something like the many worlds interpretation of quantum physics is correct, then even if there is no inherent order in the universe, we shouldn't be surprised at the order we see. If there were not sufficient order to produce us, then we wouldn't be here to appreciate it. (This is the anthropic principle.)

Is there some regularity to events that we've spotted (or think we've spotted? If not, we obviously won't know the rules. If yes, then different reactions are possible. It could be regarded as magic, but someone with a science leaning will immediately suspect the existence of a rule, even if he has no idea of its underlying form.



As above. One person will interpret this as supernatural; someone else will suspect the existence of a meta-rule of which both cases are instances.


Noggin

Is there some regularity to events that we've spotted (or think we've spotted? If not, we obviously won't know the rules. If yes, then different reactions are possible. It could be regarded as magic, but someone with a science leaning will immediately suspect the existence of a rule, even if he has no idea of its underlying form.



As above. One person will interpret this as supernatural; someone else will suspect the existence of a meta-rule of which both cases are instances.


Noggin

*skipping the backlog - which you have to admit can be pretty daunting at times*

"If there is such a thing as an objective abstraction, then any two minds should be able to discover it. If it does not 'exist', in some sense, then how do the two minds arrive at it? I'm saying that it must be in some way fundamental to or inherent in the universe the minds are in in order for them to arrive at it."

Hmm. Not convinced. Our minds are, among other things, pattern-seeking mechanisms. We will look for - and more scarily, we will find - patterns where none exist.

Sure, people will independently arrive at the same scientific or technological conclusion at the same time, (light bulbs, telephones, evolution, calculus).

But they will also independently arrive at the same *incorrect* conclusion about the world. Or come up with similar myths or similar but unconnected interpretations.

...

*Thinks*

...

*Can't think of any decent examples*

...

*Wonders if Queex is right*

...

Actually I can - the four elements of Greek mythology are Earth Air Fire Water - the five elements of Chinese mythology are Earth Air Fire Water Metal.

Which brings us neatly back to Magic...

B

<>

as a matter of fact, they /will/ have a certain order, but that's just a fluke of mathematics. anyway...

Magic. I like magic. I don't care if it's real, it's fun. I'm not going to focus my life on it, because it's less probable than the idea that I need food to live. right? so I enjoy magic in my spare time to ease my mind. To deliberate over its existence seems to me like trying to decide wether or not a drawing is pretty, or perhaps wether or not it's of something (eg Pollock)

I hate quoting DNA but I am strongly reminded of the first few pages of Mostly Harmless - Anything that happens, happens.

It would seem to be bordering on sheer recklessness to assume that we "are" or even that the universe actually "is", let alone that there might be some "rules".

Anything that, in happening, causes itself to happen again, happens again.

DNA - total genius

Another quick response... Work bites.

PC-

"But the much-repeated oxymoron 'objective abstraction' bothers me.

If we assume the existence of 'angry concrete', all sorts of absurd consequences follow. The same applies to 'objective abstractions'."

Hmm. I don't see any contradicion arising from objective abstraction other than the possibilty that existence is not limited to physical presence.

"If abstractions exist - and they surely do! - but not in the Real World, it seems to me that there is only one place in which they can exist: the human mind."

Unless it is somehow inherent in the universe. So, abstractions that are not inherent in the universe are subjective. That makes sense. The dictionary definitions I've seen don't recourse to mentioning a mind, just an 'idea', or concept. The concept might be inherent in the universe.

"Finally, if we accept (by definition) that something objective is independent of the conceptions and/or perceptions of humans, doesn't it follow that something which exists *only* within the human mind cannot be objective?"

But if it doesn't exist *only* in the mind (as above), then it might be.

Dogster-

<<"If there is such a thing as an objective abstraction, then any two minds should be able to discover it. If it does not 'exist', in some sense, then how do the two minds arrive at it?"

I suspect your definition of a mind assumes that this mind can understand the rules of logic and believes in them. If so, then your definition is circular. A mind is something that can arrive at mathematics, and mathematics is objective because any mind can arrive at it.>>

I don't define a mind in terms of mathematics. But a 'thinking thing' might be capable of understanding mathematics, and if mathematics is an objective abstraction then all such maths-capable 'thinking things' should arrive as the same mathematics. As a structure, mathematics does not depend on any mind. It's *true*. Of course, this is at least in part because mathematicians are very clever about their definitions, so things have the properties they want. But, at the basis of maths is the process 'if this thing has these properties, then it also has these properties'. And you can't disprove that. It really is watertight.

<>

It might be, were it not for the fact that the phenemonal universe outside the Earth seems to use the same mathematics. It might be part of the evolution of the universe, but there's no reason to limit it to our planet. Which means it should be an objective abstraction, etc. etc.

<<"The other point is that the universe does have rules, if it did not it would be unable to take on order, always in a random and meaningless state."

This doesn't make sense. What do you mean by a rule? Do you mean a physical law, for example in the form of a differential equation? Have you seen "The Matrix"? In that film, it seems as though the world has rules, and almost always the world follows those rules, but certain individuals like Neo (Keanu Reeves) have the ability to bend the rules. How can you assert that this isn't the situation?>>

Neo just obeys a higher order of rules. Remember that our perception of physical laws is flawed; the 'true' laws are likely to be much more subtle. By rules in this sense perhaps it is better to call it a 'rule of behaviour' which determines what the universe does. If there are no rules, then there is no requirement for any consistency. The sun may come up at 12 noon tomorrow, it may be blue, and we may all turn into water. These rules of behaviour don't have to be tractable or predictable, but they must be there in order for the universe to be coherent. The possiblilities in a non-consistent universe are so great that it's statistically improbable that we'd ever see any consistency. So, it seems that the universe does have these 'rules of behaviour', whatever they may be.

<>

But it would be statistically improbable. And if you continued your observations, the seeming 'pattern' would disappear.

<>

But, again, if this seeming 'order' is only the product of randomness then we would expect it to disappear. There is nothing holding the universe to it so it's going to vanish shortly, even with the anthropic principle. Unless, once these 'random' rules are established they become fixed, in which case they can be considered inherent in this universe, anyway.

The many worlds interpretation allows us to plays with physical constants like Planck's constant or g. But, it does not necessarily allow us to play with mathematical constants. Pi is found not by drawing circles, but by evaluating a power series. You can't change it without seriously messing about with simple things like multiplication.

I don't find it so far-fetched that there may be a set or rules that cannot change under any circumstances, some rules of behaviour that are a consequence of any kind of order. We still have a great deal of leeway in our many universes without recourse to changing mathematics.

PC:

QQ:

Having approached this once more, I'm not going to sacrifice the work done already. So:

We have already agreed that an abstraction is non-physical. We haven't yet agreed that the universe is physical, but I suspect we can? Having reached this point, we have a (non-physical) abstraction that is inherent in the (physical) universe.

Illogical, Captain.

Please explain how an idea - I assume we can agree an abstraction is an 'idea'? - can be inherent in the (physical) universe. Or (better still! ) admit that it simply isn't possible, and let's end this fiasco.

Pattern-chaser

"Who cares, wins"

Abstract - every definition I can find (and I have checked quite a few) says "existing only in the mind".

Objective - every definition I can find for this word says "having actual existence"

"Objective abstraction" = contradiction in terms

However, I think that all of this argument over semantics is obscuring an interesting observation on the nature of mathematics and its relationship (if any) to reality.

Agreed! Let's move on from the semantics, and see what can be gleaned from the observation 'on the nature of mathematics and its relationship (if any) to reality.'

I don't often say stuff as dogmatic as this, but: C'mon, Queex, you're mistaken. Be pleased because you've learned something today. No-one has lost!

Madent: what do you think we have to learn about maths and reality?

Pattern-chaser

"Who cares, wins"

"We have already agreed that an abstraction is non-physical. We haven't yet agreed that the universe is physical, but I suspect we can? Having reached this point, we have a (non-physical) abstraction that is inherent in the (physical) universe.

Illogical, Captain.

Please explain how an idea - I assume we can agree an abstraction is an 'idea'? - can be inherent in the (physical) universe. Or (better still! ) admit that it simply isn't possible, and let's end this fiasco."

The abstraction is a quality of the universe. An attribute. Part of its nature. Of course it's possible. A tennis ball is physical. It has colour, shape and texture. It also has bounce (unless its broken). But you can't point to the bounce. The only difference here is that whereas in a tennis ball the bounce is a product of its other physical attributes, in the universe I'm saying that the physical attributes are a product of the abstraction.

As I've said before, I really don't see what's so difficult to accept about this. All I'm proposing is that the universe is not described in full by its physical properties.

In programming terms, the universe is an object, and the abstraction one of its attributes.

Just for the sake of this illustration, assume a universe with no humans in it at all, and therefore no human minds to hold abstract concepts. If an abstraction is a quality of the universe, I think it's reasonable to expect that this quality will be persistent. So where is it stored? An attribute of the universe must be a part of the universe, mustn't it? Identify for me that part, if you please.

[To those who may not understand why I'm asking stupid questions: Yes, I know that the part of the universe which stores abstractions is non-existent. I'm just waiting for QQ to realise this.]

Pattern-chaser

"Who cares, wins"

P.S. a tennis ball has neither colour, shape, texture or bounce.

-- It has physical dimensions and a location in the universe which lead you to ascribe 'shape' to it.

-- It reflects light in a particular way which you understand as 'colour'.
-- Its surface is contoured in a particular way; you see this as 'texture'.
-- It rebounds from a solid surface according to its physical properties, and those of the surface. You describe this as 'bounce'.

The physical attributes belong to the tennis ball. It can do the stuff it can do without you there to observe or describe it. The abstractions are in your mind; you superimpose your own beliefs onto the physical tennis ball, and end up with something more. This reflects your understanding of tennis balls, and the way they interact with the universe.

Pattern-chaser

"Who cares, wins"

"An attribute of the universe must be a part of the universe, mustn't it?"

No! It is a quality of the universe. Part of its very nature. Not any physical part of it.

"Identify for me that part, if you please."

I don't need to. If it is a quality of the universe, then it is what the universe *is*.

Are you saying, then, that the universe is described in full by only its physical attributes?

Accepting for the moment that we use basically the same language to communicate (although while the PC v QQ debate rages on in the background that maybe a questionable view), when we talk about mathematics at its very simplest then we do indeed agree.

2 plus 2 equals 4, it always equals 4. Not 3 and not 5, just 4.

But that's pure maths.

Applied maths, on the other hand, seems awfully useful at finding new ways for what we "think" of as "us" to interact with what we "think" of as "reality". From making a spear and a fire, to catching and cooking lunch, or blowing up the world with atomic forces and finishing off what's left with chemical weapons, applied maths is a wonderfully useful tool.

The question in my mind is, is it possible for "us" to infer the existence of either "maths" or "reality" from the other, and if so prove their existence?

Or am I following in the well worn footsteps of others and making an enormously simple mistake?