The Nature of Number

[Bernard]

Alack Jonathan, philosophical havens are only ever as real as numbers. Math is a descriptive way of understanding phenomena. It is never the phenomena it gets involved with and only exists within the visualizations of self-generating awarenesses, such as ourselves. Descriptions are the by-products of our awareness rather than the structures of it. So mathematics is, at most, part of the wake of our direct experience of reality. We can certainly make use of the wake to propel further mathematical descriptions, wherein math appears almost as a separate entity to ourselves able to generate reality, when in fact we are only further generating realities of ourselves.

[Satyr]

Yes...or to put it another way:
The mind when it generalizes/simplifies it places boundaries around phenomena, essentially detaching them form their temporal/spatial reality and making them static and immutable.

Take a tree, for example.
Man calls it "a tree" ...the "a" signifying one..."tree" signifying a pattern of recognized predictability.

But what is a tree when at all instances it changes? Do we ever refer to the same tree, and if we expand our event horizon, our perceptual boundaries, does the tree not cease to exist beyond a certain point?
So, when we speak of a tree we are designating a certain perspective, bounded by a time and spatial scale - that is by reducing the dimensions - of what Dawkins called "middle world" and this dynamic, process which is never totally the same and which is retained as a unity within our memory by using, like I said, patterns of repetitive consistencies (in other words similarities), we call by the static symbolic title "tree".

[Bernard]

And when 'tree' is summoned for us we get something visual rather than say what a bat would get or a butterfly, or a tree for that matter (not going into tree consciousness again here). Math may sort of form a tree image by way of fractal, but if it comes to say, scent, it could not create anything we would recognise, nor could it compound multiple sensory data to replicate it in any functional manner whatever. I think if something is to be an ultimate constructor of reality it needs the highest degree of practical functionality in producing animate forms from the get-go and from within any moment spontaneously, and math just doesn't have that sort of energy.

[Jonathan.s]

Math is a descriptive way of understanding phenomena. It is never the phenomena it gets involved with and only exists within the visualizations of self-generating awarenesses, such as ourselves. Descriptions are the by-products of our awareness rather than the structures of it. So mathematics is, at most, part of the wake of our direct experience of reality. We can certainly make use of the wake to propel further mathematical descriptions, wherein math appears almost as a separate entity to ourselves able to generate reality, when in fact we are only further generating realities of ourselves.

I am not referring to 'generative abilities', but predictive abilities. If all math did was describe things, then it would not be able to predict things which have never previously been described. But mathematical reasoning enables us to predict with certainty things which would remain unknown to us by means of sensory experience alone. (Einstein's theories in particular are a brilliant example, but the whole progression of mathematical physics serves to illustrate the general idea.)

We might conjecture that rationality is the 'by-product of awareness'. But that doesn't really come to terms with the question of what rationality (numeracy, logic) is, and why it can be used to discover novel facts about the world. I am not claiming to understand what number is, or how it is that we have come to understand it. I do notice however that the responses here assume that this is something that we must be able to 'explain' in terms of evolutionary development. But I think this is simply an assumption. This is the view called 'the naturalization of reason' - it assumes that reason itself is something that can be understood solely in terms of adaptive necessity.

[Bernard]

The mother of invention, necessity, is not such an easy lady to dismiss like that. WE say that math predicts, but actually it follows our predictions. Its a shortcut tool, which is another way of defining a description. Math's great facility is to describe our predictions efficiently so that they can be pulled off the shelf quickly for use in predicting further predictions. Its still the user ability here, not any inherent ability in math.

Just because rationally has come about through adaptive necessity doesn't lessen the awesome process by which it comes about. Human awareness reflects upon itself, shutting out impulses from the immediate environment in order to do so. Other creatures will just use impulses from their environment and leave it at that, but in the case of humans, awareness acknowledges itself and becomes aware of being aware. It would appear a rather useless mechanism until noticed that self awareness can be stored at varying intensities and qualities and so become a series of reference points, which can be connected into paths that we call logic - all without any aid from external impulses.

[Satyr]

And when 'tree' is summoned for us we get something visual rather than say what a bat would get or a butterfly, or a tree for that matter (not going into tree consciousness again here). Math may sort of form a tree image by way of fractal, but if it comes to say, scent, it could not create anything we would recognise, nor could it compound multiple sensory data to replicate it in any functional manner whatever. I think if something is to be an ultimate constructor of reality it needs the highest degree of practical functionality in producing animate forms from the get-go and from within any moment spontaneously, and math just doesn't have that sort of energy.

Yes...and the first practice is survival. It is on the excesses that man creates.
A species procreates when it can spare energies and has enough of them left-over from his self-maintenance needs.

Same goes for human creativity and pro-creativity.
It is leisure driven by need which makes man think beyond the immediate and the self-comforting and self-sustaining.
It is only when the belly is full that man can contemplate food and feeding. Before that the need is to pressing to allow him the luxury of introspection.

Some weaklings prefer the mysterious for then any inanity can remain plausible...even that of a universal consciousness, pre-existing all life.
It takes courage to peer into the void and to accept what one sees.

Intelligence is not enough.
When you are weak and needy, when need dominates you, then all you can think of is fulfilling that need.

[Jonathan.s]

Well, thanks for the responses, but I don't think that anything has been said which disproves that number is real and that it is non-physical. And I don't think the ability to reason can be meaningfully understood in purely biological terms - it is an example what Raymond Tallis has called 'biologism' in this book, which is reviewed in Philosophy Now.

[Notvacka]

It takes courage to peer into the void and to accept what one sees.

And here is where your logic breaks down, where what you mean to say is contradicted by what you say, by the very words you use:

It takes courage to peer into the void...

But curiosity conquers fear every time...

...and to accept what one sees.

Accept what one sees? You don't see anything when you look into the void, do you? So, what is there to accept, but the limits of your vision? Do you jump to the conclusion that the void is empty? Do you turn your back on it, satisfied with what you don't see? Do you flee from it, afraid to venture forth blindly? Do you wait for something to emerge from nothingness? Or do you try to fill the void with your own imagination? And what courage is required?

[Bernard]

Well, thanks for the responses, but I don't think that anything has been said which disproves that number is real and that it is non-physical. And I don't think the ability to reason can be meaningfully understood in purely biological terms - it is an example what Raymond Tallis has called 'biologism' in this book, which is reviewed in Philosophy Now.

I see reason as an outcome of being aware, how is awareness equivalent to biology? Numbers are as real as our reflections and ideas are. Are ideas solid? Many say not, though we do talk of 'concrete ideas' and the like.

[Jonathan.s]

Numbers are as real as our reflections and ideas are.

They are considerably more real than many of our ideas or reflections, though. As I said before, if you're mixing explosives, and you get a number wrong, then look out.

The fact is, we can get maths wrong. So the question is, when we do that - it is wrong, compared to what?

As Nagel comments, reason imposes itself upon us.

[Satyr]

Well, thanks for the responses, but I don't think that anything has been said which disproves that number is real and that it is non-physical. And I don't think the ability to reason can be meaningfully understood in purely biological terms - it is an example what Raymond Tallis has called 'biologism' in this book, which is reviewed in Philosophy Now.

What an excellent display of your inherit loyalty to Cartesian logic, my good sit.

Fabulous reasoning.
It's not physical it is mental...the mind/body duality comes to save us, yet once again from the corners our retardation has placed us in.

[Satyr]

It takes courage to peer into the void and to accept what one sees.

And here is where your logic breaks down, where what you mean to say is contradicted by what you say, by the very words you use:

It takes courage to peer into the void...

But curiosity conquers fear every time...

You are struggling, dear; trying too hard.
Sit down, take a deep breathe, disengage your pussy by pulling your hand off of it and continue....

Curiosity simply means interest in the unknown. I am curious not because I know but because I do not.
Curiosity is the hunger for the absolute.
We can compare it to the physical kind of hunger we feel which is also a need for fulfillment which is always partial and ephemeral.
We hunger because we are imperfect entities. this hunger, this need, is the sensation of this absence...you might call it void, the Buddhist will call it emptiness.
The mind experiences this absence as curiosity; the body, which is the same Becoming in another context, experiences it as hunger, or sexual urge.
I am curious because I am ignorant; I am hungry because I am imperfect. I experience my own imperfection in my hunger for the other...but since the other is also imperfect this hunger is never fully satiated.

The unknown is always a source of anxiety.
The otherness is what confronts us because it is unknown.

You meant to say "understanding conquers fear".
But you were quick on the draw, weren't you woman?
You just shot yourself in the groin...leaving a new void where your testicles and penis might have been.
Now, you are female.

Accept what one sees? You don't see anything when you look into the void, do you?

Poetic license, dear woman.
Seeing a void is frightening. Have you peered into the void in your mind?
I'm looking at it right now...scaaaary.

So, what is there to accept, but the limits of your vision?

The absence of an absolute and all that this absence entails.

Preempting your next "curiosity" allow me to offer some terms denoting the absolute, as it is created in the human mind but does not exist anywhere outside of it:
God...Here....Now.....One....Thing...Self...Static...Inert....Immutable....Omniscient....Omnipotent....Perfect....

The absolute can be anything precisely because it is absent. In fact, that we are even referring to it is presupposing it...like we presuppose the 1 so s to get the 0.

The mind has evolved some clever tricks to create these abstractions and one method is generalization an other is simplification.
Again no two minds are equal and so no two generalizations are of the same quality and no two simplifications are of the same quality.

---A generalization is the extrapolation of a rule, a norm, a pattern of behavioral consistence from a small pool of evidence, either experienced or acquired through second-hand experiences (knowledge).
Here we must go into the two kinds of methods for acquiring and understanding patterns. They spell the difference between being a herd manimal and a more freer-spirited one, a pack animal.
The mind generalizes constantly. It does not postpone judgment so as to gather more evidence, it does so quickly and efficiently. The purpose the mind evolved was to play this role.
This is why it is hilarious when liberals and douche-bags accuse others of generalizations. Take the concept of "human" - if anything it is a far more general concept than any given about race or sex, yet it is more readily accepted because it fits into a cultural norm and it offers soothing relief to the domesticated cattle who have to be kept happy, inebriated and productive.

All of science, in fact, is based on generalizations.
Science takes a few specimens, for example, and deduces general behavioral traits for an entire species across time.
It then tests these conclusions simply increasing the experiential data and so increasing the probabilities that its conclusions are more correct than not.
It also tries to explain why exceptions to the rule occur, because exceptions always occur since existence is dynamic and mental models are static representations of it.

---A simplification is the other method - it consists of cutting away extraneous sensual data so as to place a noetic boundary around a phenomenon.
Like when we take a snapshot of something we freeze it, by eliminating all dimensions except three, and simplifying the event which was multidimensional.
The mind does this effectively.
We invent machines that copy our evolved methods of perceiving, trying to represent reality as close to the original as possible.
This makes it possible to create a more extraordinary version of reality...a Hpyerreality as Baudrillard called it...but this too is another matter.

Now, by placing ambiguous boundaries around a phenomenon we can turn it from dynamic to static, so as to incorporate it within our mental abstractions.
We automatically, intuitively or consciously, cut away arbitrarily the phenomenon from its background and its past, essentially turning it into a metaphor or a representation of what was experienced.
This is what gives us the illusion that there is such a thing as a static, immutable, state...when in fact it is we who have constructed it, by simplifying our experience, so as to make it useful.
When retards take these abstractions literally they fall into the error of confusing their own conceptions for the real world.

This, of course, is also why we get paradoxes.
A paradox is produced when the mental constructs, and the logic they imply, do not correspond to what is experienced; it is the divergence experienced when we juxtapose an ideal with the real. The most common forms are linguistic, since language is a code representing mental abstractions.
A language, including math, is an artistic form. It is a way of representing, in a static, codified, form, a dynamic environment of (inter)activity.

Do you jump to the conclusion that the void is empty?

Do you?
I do not believe in absolutes, therefore an absolute void, or an absolute nil, is not a fantasy I ascribe to.

Do you turn your back on it, satisfied with what you don't see?

I look closer...particularly when I do not like it.

Do you flee from it, afraid to venture forth blindly?

Anxiety, dear woman, is an aspect of becoming aware.
How one deals with it is what makes one courageous or cowardly.

Why would I blind myself when I have eyes to see?

Do you wait for something to emerge from nothingness?

Displacing your own desires upon me is how you expose yourself.
The only thing I expect is in me.

Or do you try to fill the void with your own imagination? And what courage is required?

Why would I fill anything when it is streaming with activity?

The imagination was meant to project a construct into the void, the unknown, of the future.
But her, as well as with everything living, no two imaginations are created equal...and so some project shallowly and wrongly, others only shallowly, while others project further ahead and a few of those accurately.
Those last ones we call "genius".

[Bernard]

Numbers are as real as our reflections and ideas are.

They are considerably more real than many of our ideas or reflections, though. As I said before, if you're mixing explosives, and you get a number wrong, then look out.

The fact is, we can get maths wrong. So the question is, when we do that - it is wrong, compared to what?

As Nagel comments, reason imposes itself upon us.

But that is merely a case of deifying or anthropomorphising math, as this particular primate does for anything that presents a very high survival content in his toolbag. We turn choice ideas into greater realities than what they deserve to be: the primary example is monotheistic God. This had a huge value as an idea for the Jews during an epoch when kings and leaders fell like nine pins under the constant onslaught of the Assyrian armies. What is more reliable than math/logic in our age, why not then animate it and make penalties in regards transgression against it. Any idea given inflated value will inevitably produce its own counter negative value. The question is really a matter of revaluation.

[Jonathan.s]

But that is merely a case of deifying or anthropomorphising math

Not at all. It is simply providing support for the original argument, that number is real but not physical.

There is a well-known essay called The Unreasonable Efficiency of Mathemateics in the Natural Sciences - http://www.dartmouth.edu/~matc/MathDram ... igner.html .It is related to this idea.

Behind this idea is the observation of the role that mind plays in generating reality. But I'll leave that for now.

[Satyr]

What does "real but not physical" mean?

Read Jaynes.

The mental processes producing the imagery are real. The image is a symbol referring to nothing but the sensual data that were incorporated in producing it.