Home | Community | Message Board
You are not signed in.
Sign In New Account
Forum Index Search Posts Trusted Vendors Highlights Galleries FAQ User List Chat Store Random Growery


This site includes paid links. Please support our sponsors.

General Interest > Philosophy, Sociology & Psychology
Threaded Mode Threaded  Previous topic Previous  View all topics Index  Next topic Next 

Welcome to the Shroomery Message Board! You are experiencing a small sample of what the site has to offer. Please login or register to post messages and view our exclusive members-only content. You'll gain access to additional forums, file attachments, board customizations, encrypted private messages, and much more!

Shop: Unfolding Nature Unfolding Nature: Being in the Implicate Order   Myyco.com Golden Teacher Liquid Culture For Sale

Jump to first unread post Pages: | 1 | 2 | 3 | 4 |  [ show all ]
Re: Godels Theorem [Re: Diploid]
    #15011601 -

I have little to contribute here but appreciation for the math skills that are apparently here. I can only get the bare jist of what is going on and being discussed but I still love it.  You guys are cool.  I wish I hadn't been so dysfunctional and anxious and stressed as a kid so I could have learned this amazing language.  Carry on. :thumbup:


--------------------
"Don't believe everything you think". -Anom.

" All that lives was born to die"-Anom.

With much wisdom comes much sorrow,
The more knowledge, the more grief.
Ecclesiastes circa 350 BC

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Diploid]
    #15011628 -

xFrockx said:
"It doesnt make sense if you treat 0 as 'nothing' but this system is one which is very close to the notion that nothing is in fact something, just without relevant features. "

So nothing is not nothing then?



well nothing is sometimes nothing. Othertimes its just 'nothing relevant'.


Diploid said:
1/0 =

Suppose I have 6 apples and 3 people to divide them over. How many apples does each person get? 6 / 3 = 2, easy.

Now suppose I have 6 apples and zero people to divide them over. How many apples does each... uh... each... wait, there aren't any entities to finish the question with. There aren't any "things" or people or anything else. Do I rephrase as "How many apples does each non-existing entity get"?

I don't think a non-existing entity can get any apples or anything else for that matter. It's a meaningless question because division by zero is meaningless.

The best you can say is that as the number of people approaches zero, the number of apples each gets approaches infinity. But RIGHT AT ZERO, the question is rendered meaningless.

I would like something other than 'IT JUST ISNT'

The answer you want DOES exist, and it is deep and satisfying, but without the technical background, it won't make sense. That's why in the beginning, the teacher says "just trust me for now, it just isn't".


You havnt really responded to my post. I have accounted for the confusion you find when trying to divide 6 apples between 0 people. because apples are finite and people are finite, the question is 'how many apples will no people recieve?'. The answer is none, no finite people will not recieve any apples, its a nonsense question. It is like asking 'If john has no brother, how many apples will john let his brother eat?'

As for the deeply satisfying answer, you know thats a cop-out, so it is best to say 'I dont know hot to explain it to you, but from what I learned at school/college/internet it makes lots of sense.

Unless you can show me why my system doesnt make sense, it still stands strong. So far it is totally consistent, but Im waiting for a hole to be shown.

But I also am not too hopeful, it is always the case that something new gets rejected by those who have spent a long time or effort learning the previous dogmas.

Also, you are probably right in saying that it would take a long time to explain it to me. But maybe it also wouldnt take too long. I did the highest grade possible maths at school and have maintained an avid interest in number theory ever since. I am rusty with many notions but I can pick them up quickly. So although I will say you are probably right, I will also have my reservations


--------------------

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Noteworthy]
    #15011646 -

"well nothing is sometimes nothing. Othertimes its just 'nothing relevant'."

Nothing is sometimes nothing...

Is your chair sometimes a chair?

Noteworthy, I'm worried about you. Please come back.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15011716 -

Noteworthy said:
Actually 1/infinity does = 0 and 1/0 = infinity


1 divided by an arbitrarily large number does approach 0, so I agree with your first statement even though rigorously speaking we shouldn't treat infinity as a number.  1/0, however, remains undefined.  Observe: if I take 1 divided 0.5, then 1 divided by 0.05, then 1/0.005, and so on, we approach positive infinity.  But if we approach the limit from the negative side like so: 1/-0.5, 1/-0.05, 1/-0.005, and so on, we approach negative infinity.  Thus the limits from both sides do not equal and 1/0 is undefined.


--------------------
We are all in the gutter, but some of us are looking at the stars.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Noteworthy]
    #15011767 -

You havnt really responded to my post.

I know.

1. Although I studied this and used it every day in my career as an engineer, I'm not a math teacher. And I'm not an expert on the subject matter anyway. I'm an engineer. That's like a mathematician wanna-be.

2. If you don't have the technical background learned in two years of university study, anything I say beyond what I already said would be incomprehensible.

how many apples will no people recieve?

No people can't receive anything. They don't exist. The question is what math geeks call "malformed". It's like asking how many riders can a unicorn carry?


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Diploid]
    #15011920 -

Hey so what about my question about how infinity is treated in calc as having finitude?

I'm clueless about it, but since you're not a theorist I would totally understand if you don't know either. :shrug:

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15011937 -

Hey so what about my question about how infinity is treated in calc as having finitude?

That's bizzare, :whoa:  What's the chances of me understanding the answer.  :sad:

Infinitely small. :lol:


--------------------
"Don't believe everything you think". -Anom.

" All that lives was born to die"-Anom.

With much wisdom comes much sorrow,
The more knowledge, the more grief.
Ecclesiastes circa 350 BC

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Icelander]
    #15011965 -

Infinitely (any size here) seems kindof unintuitive to me.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Noteworthy]
    #15012108 -

I think you guys are being way to sloppy here with your notation and conclusions.  Shorthand notation, like multiplying infinity * something, is not useful for elucidating technicalities of mathematics.  Short hand notation is fine between two people who know what is going on behind the scenes, it can be a disaster when trying to understand new, key ideas.

Noteworthy said:
Actually 1/infinity does = 0 and 1/0 = infinity, its a basic notion that I would like you to disprove.



Better to use limit definitions here instead of multiplying by infinity.

Quote:
furthermore, 0, for all practical mathematical purposes, = infinetissimal.



No, no, no.  0 does not equal infinitesimal.  Not ever.  Not for philosophical purposes, not for practical purposes, not in math, engineering or science.

Quote:
infinetissimal+ any number = that number



No. 
Formula: 0 
Formula: 1

Its that simple.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: DieCommie]
    #15012135 -

:thumbup:

Can you answer my question I asked Diploid about infinity in calc being treated as though it can be counted (is finite)? I've had that one a few years now. It seems to me that infinity as it is used in calc isn't being used the same if I were to talk about an infinite space. I see the value in the formalism of "approaching infinity" or "approaching zero" but is that because we're dealing with infinity, or just some kind of formalism?



Extras: Filter Print Post Top
Re: Godels Theorem [Re: deCypher]
    #15012156 -

xFrockx said:
"well nothing is sometimes nothing. Othertimes its just 'nothing relevant'."

Nothing is sometimes nothing...

Is your chair sometimes a chair?

Noteworthy, I'm worried about you. Please come back.


Its not as weird as it sounds.

A rocking chair is a chair. A swivel chair is a chair. They are both chair. But one chair is not another chair. Furthermore if there are a range of chairs in a room, 'chair' could sometimes be one kind of chair and sometimes another kind of chair.

Similarly, one kind of 'nothing' (a more general term) is sometimes another kind of 'nothing' (a more specific term).

But actually id say that nothing is never nothing. Because nothing does not exist.

Once again, not as weird as it sounds when you learn the multiple meanings of the words.

deCypher said:
Noteworthy said:
Actually 1/infinity does = 0 and 1/0 = infinity


1 divided by an arbitrarily large number does approach 0, so I agree with your first statement even though rigorously speaking we shouldn't treat infinity as a number.  1/0, however, remains undefined.  Observe: if I take 1 divided 0.5, then 1 divided by 0.05, then 1/0.005, and so on, we approach positive infinity.  But if we approach the limit from the negative side like so: 1/-0.5, 1/-0.05, 1/-0.005, and so on, we approach negative infinity.  Thus the limits from both sides do not equal and 1/0 is undefined.


Ok heres what I was looking for.

So negative infinetissimal does not seem to work because 1/infinetissimal is positive infinity, and 1/-infinetissimal is negative infinity. Positive and negative infinity are fundamentally different.

However if we add the supposition that there are no true negative infinites or infinetissimals, we actually come to understand that 1/-infinetissimal is irreducibly (1/infinetissimal)*(-1). Thus it becomes (infinity)*(-1)

But yes I have had to remove the very concept of -infinetissimal and -infinity from the system.

On a graph, these values are a point, and nonexistant. In order to plot a value on a cartesian plane, one creates a line from positive parts and a line from negative parts. -1 on the x axis would be one horizontal line '1' long. it would also be a '2' long line and a '3'long line. To see this, we convert -1  into (1)*2 + (-1)*3. The line with the positive portion begins at 0 and goes its value to the righthand. The line with the negative portion begins at the endpoint of the other line, scribing in the left direction.

The reason for no negative infinities seems to be related to the fact that that -1 is subservient to +1. A current stumbling block for the system is understanding why 1*1 = 1, but also -1*-1 = 1


--------------------

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Noteworthy]
    #15012162 -

"-1 is subservient to +1."

Subservient? Does it make it dinner?

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15012207 -

no its metaphoric speak for something that I do not fully understand, it describes the relationship through analogy, because both numbers seem 'drawn towards' the positive value if we imagine that multiplying the values 'changes' them from one value to another.

However I have just been working on this aspect of the system (thanks to decyphers input) to accomodate negative values in a way that is consistent with both addition/subtraction arithmetic and multiplication arithmetic. Its a good thing ive hijacked my own thread here because we are really treading into the deep waters of a long term project of mine to create a logical calculus for arithmetic/algebra that is much simpler than something like what Russel and Whitehead attempted.

At that point it should not be hard to recreate Angular calculus, integrals, and all other mathematical ideas.

Infinity and algebra have not yet been unified in this system but im getting closer thanks to this issue with negative infinities

I dont know if I ever finish it but im in no rush. It comes when it comes.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15012327 -

Subservient? Does it make it dinner?

Who cares about dinner. Does it clean house. That's what I wanna know. :hehehe:

what about my question about how infinity is treated in calc as having finitude?

Calculus treats infinity as infinity and finite values as finite values. I don't think I'm understanding the question. Can you give me an example?


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Diploid]
    #15012362 -

Well some define finite as the opposite of infinite. But I don't see them as opposites in the same way that 1 and -1 are. If something is finite, it can be counted. If something is not finite, it cannot. Like if I say that space is infinite, I'm saying that it has no limits, not that it would "take me forever" to reach those limits. Can't reach limits that aren't there, can you?

So does the infinity in calc reflect the concept of not having finitude (limits), or does it reflect a kind of formalism (what you describe as "getting bigger and bigger") which resembles what would happen if we are counting on and on forever.

Another way to put this, is, is there a difference between infinity and a number that is "going" up or down forever?

Is the concept of infinity that of a number that "moves" up or down forever, or is it the concept of having no limits (not finite)?

I think this may be because when we try to actually grasp infinity the best we can do is count on and on forever, right? But is that dealing with infinity or an never-ending amount of finitude?

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15012420 -

finite numbers each have a unique relationship with each other finite number. In-finite numbers have the same relationship to all finite numbers.
Infinities can take two values, positive and negative.

If you consider positive to be 'up' and negative to be 'down', infinity would occur when you go up forever, or down forever. It also can occur when you go down so far that you drop vertically into a bottomless abyss.
If you are going up and down, you cant really be going up forever or down forever. So you cant really reach infinity that way.


--------------------

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Noteworthy]
    #15012423 -

"If you consider positive to be 'up' and negative to be 'down', infinity would occur when you go up forever, or down forever. "

But what I am wondering if this is the same as the concept of infinity which simply means not being finite. To say that it "goes up" or "goes down" seems to suggest that we're still counting. And if it is infinity, how are we counting?

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15012460 -

infinite means not finite, just like forever does. forever is no finite period of time, it is endless in both directions.

So its both, but the more correct notion is that it is simply not finite. The 'forever' idea is more like an emergent property.

If you have an in-finite amount of coins, you will never stop counting them. This is because you can only count to finite numbers. You count one, and its finite. no matter how many times you add or subtract to your value, it is will end up as a finite number. Youll never stop counting. But you never get there. So when we say its infinite we mean theres no amount of coins that will ever suffice to stop counting. Its all in the imagery


--------------------

Extras: Filter Print Post Top
Re: Godels Theorem [Re: Noteworthy]
    #15012479 -

"infinite means not finite, just like forever does. forever is no finite period of time, it is endless in both directions."

There can be a difference here. We can think of infinity like trying to literally count up or down forever and ever. But this is not the same as being a concept that represents the lack of limits altogether. In this sense, infinity is not countable, it is not finite, it is limitless. It is not a period of time. Not forever. It is a concept that means only that whatever we're talking about is not quantifiable. And that means, not having the property of being able to be quantified.

Extras: Filter Print Post Top
Re: Godels Theorem [Re: xFrockx]
    #15012511 -

But if you count forever, you never stop counting, so you never get a counted value for 'forever'. Thus there is no period of time that limits the counting. Thus there is no finite value that limits the answer to the question 'how many coins did you count?'.

As I said above, The 'infinite'ness is seperate to 'forever' concept but only in the sense that the 'forever' concept involves some sort of story, or practical application of two 'in-finite' values.

I think the problem here is that you are considering 'forever' to be a 'period of time' but a period of time is by definition finite, not infinite.


--------------------

Extras: Filter Print Post Top
Jump to top Pages: | 1 | 2 | 3 | 4 |  [ show all ]

Shop: Unfolding Nature Unfolding Nature: Being in the Implicate Order   Myyco.com Golden Teacher Liquid Culture For Sale

General Interest > Philosophy, Sociology & Psychology
Threaded Mode Threaded  Previous topic Previous  View all topics Index  Next topic Next 

Similar ThreadsPosterViewsRepliesLast post
* a variation on Gödel DividedQuantumM 364 11 06/27/16 09:55 PM
by DividedQuantum
* Kurt Gödel... Ahimsa 501 5 04/27/10 02:03 AM
by morrowasted
* Gödel's Incompleteness Theorems ChiefGreenLeaf 544 2 04/02/08 02:33 PM
by deimya
* Theorem #3 Booby 581 7 11/10/07 07:11 PM
by Icelander
* Shmoopy's Intelligent Design Textbook - $24.95
( 1 2 3 4 all )		 OrgoneConclusion 7,020 75 05/22/09 09:11 AM
by youbreakyoubuy
* New Mathematics Religion?
( 1 2 3 4 all )		 DreamDruids 4,599 64 01/16/16 05:00 PM
by zzripz
* The Mystery of Consciousness
( 1 2 all )		 unsui888 2,506 37 06/01/12 04:23 PM
by redgreenvines

Extra information
You cannot start new topics / You cannot reply to topics
HTML is disabled / BBCode is enabled
Moderator: Middleman, DividedQuantum
2,093 topic views. 0 members, 22 guests and 60 web crawlers are browsing this forum.
[ Show Images Only | Sort by Score | Print Topic ]
Search this thread:

Copyright 1997-2026 Mind Media. Some rights reserved.

Generated in 0.024 seconds spending 0.003 seconds on 16 queries.