Is the geometry of the world the source of what we call math ?

[granpa]

you seem to want to take abstract ideas like space and numbers and turn them into something concrete. either that or do away with them entirely. I'm not sure which.

there's something called 'mistaking the map for the territory'. I wonder if that's what is going on here?

 

[2foolish]

Yes, science makes use of logic. That does not imply that logic is synonymous with science.

Actually it is, an act of observation is an act of detection, is an act of interaction - contact. So it is logic, you can't detect something is there without logic. You can't escape the functional nature of detection and recursive feedback of the logic of detection.

There are different logics for different systems, you're confusing the misuse of logic with the proper use of logic.

Consider the question: Does the truth contain logic? Is existence truth? If the answers to those aren't yes. Then the whole of science collapses. The whole of science begins with things that exist, that you can sense. It begins with sensory experience, an act of sensation is an act of detection, the act of feedback, in that - this is not that. That's all I need to demonstrate you're not grasping what I said.

 

[2foolish]

I can't figure out what figurative meaning you could possibly intend by this comment. But I will point out that, taken literally, it is obviously false.

No it isn't, you just don't have the research background. You're thinking about one interpretation of boolean logic (the one you were taught), incorrect concepts (the interpretation of logic you were taught) must necessarily lead to incorrect judgments if what was taught was only half the story (partial understanding of boolean algebra). There are other expressions and understandings which are being worked on right at this very moment. Consider: http://www.lawsofform.org/aum/prolog.html

 

[2foolish]

This is patently false. pi can be represented, for example, as a symbolic constant, and thus requiring only a few bits of storage.

You're missing the point, if you were to calculate it out it would continue on forever, i.e. expanded the expression. for instance I can store 0.333 repeated in a computer as
1/3, but that does not make it's decimal expansion any less real.

As CRGreathouse advised in the first reply to your opening post:

I would be careful to distinguish numerals from numbers.​

Numerals are a form of object (one-ness) in and of themselves, you could simply use the representations to count i.e. the recursive nature of images (pictures within pictures), if what you were doing was stated.

 

[2foolish]

space is not geometry anymore than sheep are numbers even though they may often be counted.

"Time and space and gravitation have no separate existence from matter. ...
Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning."--Einstein

Relativity -- gravitational lensing, yes space is geometry, that is a surface of a kind, it's just a surface of a different nature (i.e. counter intuitive)

 

[granpa]

you are thinking in terms of real bumps while I am thinking in terms of bumps in a distribution. plot each of the random bubbles by its characteristics (shape, size) and most would fall into a Gaussian distribution but the other 2 (I should have made it many more than that) clearly fall outside that. that's a distinction. that's what I was talking about when I mentioned the random stains.

I know what 'three' means. I am suggesting that it is an 'empty' word, as the chinese say, derived in some bizarre and meaningless way from the root idea of being 'third'.

I tend to believe that only nouns, verbs, and possibly conjunctions are 'real' words. all others are derived from those or they are 'empty' words.

The problem is you have it backwards, the bumps are what is real. Your distribution is a reflection (an image, a photograph) of what is i.e. think of the order of operations, photon bounces/is ejected from object (carrying information) hits your eye, eye translates the signal. The signal reaches your mind, mind derives a thought from the information your eye has received, therefore when you 'self generate' ideas, you got those ideas from the outside world first. Therefore in our minds we're really just manipulating 'holographic' reflections of what is on the outside. If you actually had to make your bumps in a distribution out of real stuff in the real world, you would find out things. This is why I always transport mathematical reasoning back into the 'real world' I think terms of "What would it be made of?".. if this is 'infinite' in terms of our thoughts (i.e. if we had infinite strings of data), but if we actually had to make say pi out of stuff in the real world. We would run out of stuff to make distinct numbers from, therefore. Pi is "infinite" only in imaginary space, in the real world, pi ends (i.e. when you make pi with stuff).

In a computer pi would have to be stored somewhere, pi would fill up any amount of memory, hard disk space, and processing power you could throw at it, therefore, pi in the real world is truncated, it eventually ends somewhere when you consider the real world is made of stuff.

what does pi have to do with anything. I'm baffled.

 

[granpa]

"Time and space and gravitation have no separate existence from matter. ...
Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning."--Einstein

Relativity -- gravitational lensing, yes space is geometry, that is a surface of a kind, it's just a surface of a different nature (i.e. counter intuitive)

as far as I'm concerned, space is just an aether which itself does not exist 'in space' and therefore the abstract idea of space has no physical reality outside of that (and that is how I interpret his statement). but I'm not supposed to talk about that so let's not get into it.

 

[2foolish]

what does pi have to do with anything. I'm baffled.

My first point was things are made of stuff in the real world, they don't go 'on forever' if you transport infinite numbers to the outside world and unpack them (calculate them fully, instead of just expressing them as stored function). That was my point with pi and making it with real stuff, i.e. doing the calculations with physical objects. One could express pi as a stored function (i.e. like how 1/3, when calculated becomes 0.33333 repeated indefinitely), but if you unpacked it you could never have enough stuff to store all the digits. My second point was that acts of Detection/observation necessitates calculation with real stuff.

http://en.wikipedia.org/wiki/Super_PI

 

[granpa]

My first point was things are made of stuff in the real world, they don't go 'on forever' if you transport infinite numbers to the outside world and unpack them (calculate them fully, instead of just expressing them as stored function). That was my point with pi and making it with real stuff, i.e. doing the calculations with physical objects. One could express pi as a stored function (i.e. like how 1/3, when calculated becomes 0.33333 repeated indefinitely), but if you unpacked it you could never have enough stuff to store all the digits. My second point was that acts of Detection/observation necessitates calculation with real stuff.

http://en.wikipedia.org/wiki/Super_PI

so? what does that have to do with anything. what are you arguing against? if that's the answer then what's the question?

 

[2foolish]

so? what does that have to do with anything. what are you arguing against? if that's the answer then what's the question?

You said:

but geometry is an outgrowth of math. its 2 dimensional mathemetics (or rather, multidimensional mathematics). geometry therefore can't be as fundamental as your are thinking.

I'm claiming the opposite, math is an outgrowth of world geometry, when you consider that for you to even have a thought, or a perception, you use binary logic (is a surface there yes or no? did it make contact, yes or no?, etc ,etc) else you could not see, think and move in the real world.

http://en.wikipedia.org/wiki/Empirical

A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses.

Therefore, an act of observation is an act of detection, i.e. back to boolean logic (feedback loop), yes it is there, no it is not.

 

[granpa]

math is an outgrowth of world geometry, when you consider that for you to even have a thought, or a perception, you use binary logic (is a surface there yes or no? did it make contact, yes or no?, etc ,etc) else you could not see, think and move in the real world.

well we are talking about 2 different things here. when I say 'outgrowth' I mean that the axioms that form the basis of that particular field are based upon the underlying (and simpler) field.

when you say 'outgrowth' you are referring to the process in which it is discovered by the mind. yes we are born with certain instinctual skills like vision and the ability to process spatial data. that primes the pump so to speak and curiosity drives us to discover more and more things. but that is very different from what I meant.

 

[granpa]

what have I stated that wasnt empirical (except for aether theory. let's not get into that)?

 

[ronjanec]

I am trying to figure out what in the world you guys are talking about! I personally believe math and most geometric figures were invented by man (no triangles exist outside of Earth etc.) Infinity is only conceptual... ??

 

[granpa]

I am trying to figure out what in the world you guys are talking about!

so am I.

 

[granpa]

perhaps it would help if I explained why I say geometry is an outgrowth of math. think first of a number line. from that we get numbers that add subtract multiply and divide.

distances in euclidean geometry add and subtract just like regular numbers and multiply when finding areas. the only difference is that there is an extra axiom defining the length of the hypotenuse. (different ways of defining the length of the hypotenuse give rise to different geometries). without that axiom 2 dimensional math would be impossible.

so you can see that multidimensional math is based on regular math but has an extra axiom.

 

[ronjanec]

Thanks granpa I thought I was starting to lose it! And I think I might even agree with some of what 2foolish was trying to say if I could better understand the point he was trying to make here.

 

[ronjanec]

Let me put it this way and I spent a lot of time on this before: I believe circles only exist on earth. I personally believe prehistoric man took one of the first wheels and learned to divide this into the geometric figures we use today. The point being the subdivided geometric symbols can then only exist on Earth because of the original source.

 

[granpa]

Let me put it this way and I spent a lot of time on this before: I believe circles only exist on earth. I personally believe prehistoric man took one of the first wheels and learned to divide this into the geometric figures we use today. The point being the subdivided geometric symbols can then only exist on Earth because of the original source.

something can't exist unless it has a source? what is your point? like I asked earlier, if that's the answer then what's the question?

 

[ronjanec]

I am saying a triangle can't exist anywhere else in the physical universe because it was originally derived from something that only exists on earth. Many spheres yes but no squares rectangles etc.

 

[ronjanec]

The point also being that math may have started from geometry or prehistoric man dividing up one of the wheels and may have also been derived from prehistoric man dividing up the "journey" of the sun "across" the eastern southern and western horizons for timekeeping purposes with noon being the first fraction or half...

 

[granpa]

I'm not sure how serious you are (if you are serious at all) but if I understand you right then basically you would classify 'things' by how they are discovered rather than by their characteristics.

a triangle isn't a three sided polygon its a figure invented by some prehistoric man and passed down through the ages.

 

[2foolish]

I am trying to figure out what in the world you guys are talking about! I personally believe math and most geometric figures were invented by man (no triangles exist outside of Earth etc.) Infinity is only conceptual... ??

You're missing the point "geometry" is a concept that is made of actual stuff and it was derived from somewhere. i.e. geometric figures exist outside of your mind. The information about the subject of geometry/math as we are taught it was conceived by someone else. In other words you didn't come up with it yourself and for someone to have come up with it, there was a process by which the person or people came up with it recorded. The whole point was to understand the process by which knowledge (bits of information) comes into being in the first place, where it comes from, what it's made of, etc, and the process that enables it (transmission/reception/detection).

This is about the information the senses receive from the world through light and energy. i.e. you can only detect something is in front of you because you've received information that it exists. The missing concept is - collision detection, or refraction/reflection, and transmission of information via photons to receptors in the eye, etc.

 

[2foolish]

well we are talking about 2 different things here. when I say 'outgrowth' I mean that the axioms that form the basis of that particular field are based upon the underlying (and simpler) field.

Yes but all mathematical fields rely on concepts of this is not that, i.e. distinctions on a surface or in an image, they rely on our pre-computed, pre-converted sensory data, which we received from the outside world via the senses. This is my point, what we call math is a re-arrangement of pre-existing stuff into distinct patterns. Next is the problem that axiom's themselves are made of logic, i.e. pre-axiomatic logic. The structure of an axiom has to be formed made of something somehow.

when you say 'outgrowth' you are referring to the process in which it is discovered by the mind.

When I say outgrowth, I mean derived, received, communicated. Our math is a reflective/instanced expression of world geometry, i.e. the concept of distinctions re-arranged into different patterns.

yes we are born with certain instinctual skills like vision and the ability to process spatial data. that primes the pump so to speak

But that's the whole point, there is pre-computed math, i.e. subsurface data that the whole of what our conceptions of math sits upon, i.e. pre-logic-data that forms thoughts and structures within our minds.

The fact that you can shape, detect and modify your own thoughts proves they are made of actually existing stuff. To deny it leads to contradiction.

 

[granpa]

but the brain can reprogram itself through introspection. a sort of internal error correcting system.

 

[ronjanec]

I did not mean that I classify things by how they are discovered: A thing is a independent physical existence existing somewhere that is made of some form of physical material and has its' own individual phyical characteristics.

I was trying to say there are no pyramid type structures existing anywhere else in the physical universe besides earth. The point was also invented by man and does not exist anywhere else in the physical universe and this means the physical universe could not begin in a the structure of a point like many have said.

Yes geometric figures are made of actual stuff and exist outside the mind if man produces them like the pyramids and the point. (The geometric figure of the sphere exists independent of man)

I apologize for not making myself clearer.

 

[granpa]

once again. if that's the answer then what's the question?

 

[ronjanec]

An interesting question would be how could the physical universe have begun in the geometric form of a point when man invented the point like most other geometric forms and the point could not exist in the physical universe before this in any form...

 

[granpa]

I did not mean that I classify things by how they are discovered: A thing is a independent physical existence existing somewhere that is made of some form of physical material and has its' own individual phyical characteristics.

and 'things' that don't exist? unicorn?

 

[Hurkyl]

Actually it is, an act of observation is an act of detection, is an act of interaction - contact. ...

Blah, blah, blah. You've said a lot and none of it relevant to the charge levied against you -- your approach is not that of formulating theories and testing them empirically, and thus it fails to be scientific.

There is nothing wrong with using unscientific means to study a subject for which the scientific method is inappropriate or otherwise impractical -- but pretending it's science just makes you look foolish. That said, I'm not convinced the scientific method is neither inappropriate nor impractical...

No it isn't, you just don't have the research background. You're thinking about one interpretation of boolean logic (the one you were taught), incorrect concepts (the interpretation of logic you were taught) ...

Or maybe... just maybe... it could be that I have some expertise in this area and really do have some clue what I'm talking about? But white honestly, no expertise is needed to see that my statement was correct: the successor function is a one-to-one binary relation on natural numbers, whereas boolean logic is not. Thus, your claim that "The successor function is in fact what boolean logic is," when taken literally, is obviously false.

One of the primary indicators of a crackpot is when they respond to criticism by accusing everyone else of incompetence.

You're missing the point, if you were to calculate it out it would continue on forever, i.e. expanded the expression. for instance I can store 0.333 repeated in a computer as
1/3, but that does not make it's decimal expansion any less real.

I'm confused -- you appear to be acknowledging the fact that it is possible to store, in finite space, a number whose decimal representation is nonterminating... but you also appear to be sticking to your claim that one needs infinite space to store pi...

My first point was things are made of stuff in the real world, they don't go 'on forever' if you transport infinite numbers to the outside world and unpack them (calculate them fully, instead of just expressing them as stored function). That was my point with pi and making it with real stuff, i.e. doing the calculations with physical objects.

Except you've at least two problems:
1. You've confused the number pi with an abstraction -- that numbers can be represented by infinite strings of decimal digits.
2. You are insisting upon a particular means of representing infinite strings of decimal digits, despite the fact better representations are available.




Shifting gears a bit...

when you consider that for you to even have a thought, or a perception, you use binary logic (is a surface there yes or no? did it make contact, yes or no?, etc ,etc)

At the psychological level, there is plenty of reason to believe humans do not use binary logic exclusively, or even predominantly. To invoke a saying: "The world is not black and white, but instead made of shades of gray". At the biological level, the brain appears to be operating mainly through electromagnetic fields.

You repeatedly make assertions like this: I'm going to insist that you attempt to argue your case.

 

[ronjanec]

A Unicorn does in fact exist at least in this conversation and I would classify this as a imaginary thing.