Space, Time & Stephen Hawking Jive

[FNHinVA]

I was doing some more searching on the Web and ran across some stuff that gave me a new way to think about this issue.

I believe I would be correct to say that there exist in abstract math, higher physics, etc., contradictory proofs that are – for all appearances - each valid but seem mutually exclusive… sort of a “can’t be… but is” deal. In fact, I believe you alluded to this in an earlier post.

It was inferred in some of the very materials I cited:

“Nevertheless, Zeno's paradoxes are still hotly debated by philosophers in academic circles. Infinite processes have remained theoretically troublesome.”

“It would be incorrect to say that a rigorous formulation of the calculus … has resolved forever all problems involving infinities, including Zeno's.”

I started from (using a convenient reformulation I ran across):

0.9r .NE. 1

(where .NE. can be either “NOT EQUAL” or, (my fave) “NEVER EQUALS.”)

This… to me… is a “self-evident truth.” It requires no proof. I can keep adding 9s until the end of time (and we don’t want to go there) and it will always be true that 0.9r .NE. 1.

But, I now understand that you (and your fellow-travelers – I’d like to shoot some of them too) can use “theoretically troublesome” abstract concepts and “prove” that 0.9r = 1. (And BTW, I don’t blame you; who wants to wait until the end of time to find out what 0.9r comes out to? You guys have stuff to do and need answers NOW.)

This abstract math stuff is your world; you get to make up the rules… even if you can’t always agree on them among yourselves.

I accept that in your world, 0.9r = 1 and that you can prove it. I admit I don’t fully understand some of the concepts used but I’m much closer to “getting it” than I was before I (foolishly) started this thread.

BTW: One “proof” I ran across used set theory to eliminate all numbers smaller than 1 (the limit I acknowledge can’t be exceeded) and leave no possibility other than 1. To the extent I understood it, I liked it better than yours. You are free to feel insulted.

The problem I’ve had is that I was obstinate about rejecting the abstract math proof because it was threatening to my understanding of real stuff. In other words, both can’t be right; I have to reject yours.

Now, as I see it, we have “contradictory proofs” and I can accept it because that kind of stuff happens. It “can’t be… but is.” Both can be right on their own terms and in their own worlds. I just have to accept that you get to do things in your world that I can’t do in my world.

I see the merit in yours; but I’ll keep mine. The calculus works wonderfully in the practical world so that’s cool too. Long live the “limit.”

So it seems futile for me to point out where – in your last post – it still seems to me that you are “jumping the infinity” or “terminating the infinity” or making “simplifying assumptions.” (Although, I have to mention I did get a little chuckle from: “…the upper limit is 1 is sufficient.”) I would just be flogging the “theoretically troublesome” horse and nobody needs that.

In closing…

“Finally, and perhaps most importantly, I will stand against a wall and allow you to personally shoot me for my grievous slights against your character, if and only if you can prove irrefutably, either that space is not continuous or Santa Claus doesn't exist.”

I don’t have to prove anything. If I ever get to Ireland (and I hope to) I’m going to hunt you down like the math dog you are and shoot you anyway. I don’t need no stinkin’ proofs.

And, I KNOW Santa Claus exists; I see him every year at the Mall.

I don’t have to prove space is not continuous; I BELIEVE in the non-continuity. It’s my new religion. I call it Planckism.

Every Full Moon, we will gather around a bonfire of math textbooks and dance nude until the Sun come up. (Although we have no understanding of how that Sun thing works.)

Always fun…

Seeyadowntheroad…

[FNHinVA]

I posted another response to usmhot before I read yours.

If I understand what you are saying, I believe I acknowledge your essential points. To some degree... possibly... maybe... hell, I don't know.

Thanks for your input and thanks esp. for the (rare) kind words.

[FNHinVA]

My last post to usmhot went up before I read this one so - if you are still interested in how my understanding is ever-evolving - check it out. Thx...

[FNHinVA]

Love it... very funny.

About how I feel... I have tried a few times to "... get off stage."

[FNHinVA]

Hey Pair...

I thought you were pissed off at me.

Anyway, your offering is too trivial for me now; I'm on to set theory and other stuff I REALLY can't understand.

Oh, and Planckism... It's the next BIG THING.

Thx...

[PairTheBoard]

[ QUOTE ]
Hey Pair...

I thought you were pissed off at me.

Anyway, your offering is too trivial for me now; I'm on to set theory and other stuff I REALLY can't understand.

Oh, and Planckism... It's the next BIG THING.

Thx...

[/ QUOTE ]

Set Theory eh? Better be careful with that Axiom of Infinity. That's the rabbit hole my friend.

PairTheBoard

[FNHinVA]

I am intellectually fearless. (Translation: too dumb to know when to stop.)

[usmhot]

"Now, as I see it, we have ?contradictory proofs? and I can accept it because that kind of stuff happens. It ?can?t be? but is.? Both can be right on their own terms and in their own worlds. I just have to accept that you get to do things in your world that I can?t do in my world."

Aye, but there's the rub. If you assume that 'infinity' is meaningless and doesn't exist, then you automatically reject the limit proofs - your world.
BUT, you started by assuming _infinity does exist_ so you came into my world - in which the proofs are irrefutable.

"I don?t have to prove anything. If I ever get to Ireland (and I hope to) I?m going to hunt you down like the math dog you are and shoot you anyway. I don?t need no stinkin? proofs."

Unfortunately in Ireland, that will make you just one more gun toting fanatic using a form of religion to justify his cause. I suggest you come in peace [img]/images/graemlins/smile.gif[/img].

"And, I KNOW Santa Claus exists; I see him every year at the Mall."

Hey!!! He's in Shopping Centres (read Malls) here every year too - do you think maybe there are infinite Santa Clauses?

"Every Full Moon, we will gather around a bonfire of math textbooks and dance nude until the Sun come up. (Although we have no understanding of how that Sun thing works.)"

You bring the chicks - I'll bring the math textbooks [img]/images/graemlins/wink.gif[/img]


On a more serious note ...
"I don?t have to prove space is not continuous; I BELIEVE in the non-continuity. It?s my new religion. I call it Planckism."

Leaving all the maths stuff aside, you are subscribing to the Quantum Theory by believing that space is not continuous. (I myself am fully convinced of the results of Quantum Theory, though there remains a lot to be discovered.) However, you realise that the Quantum Universe is even more strange and counter-intuitive than the continuous Universe. If you're going to explore it then you'll have to be prepared to accept things that run contrary to your macro-level experiences and logic - so discounting infinity based maths will have to be the last time you get to do that on an 'intuition'.

[K C]

There's been countless posts after this and you'll have to excuse me as I just jump in here again.

What we're doing here is making infinite divisions of a fixed value. This doesn't speak at all to the fixed value though of course. We really don't need to go any further with this, although it's fun to do sometimes [img]/images/graemlins/smile.gif[/img]

The fallacy of this paradox is of course seeking to objectify it such that we're measuring both distance and time divisively. Naturally by doing this we'll never reach completion, but that's because it's been excluded as a possibility.

KC

[FNHinVA]

“… you came into my world - in which the proofs are irrefutable.”


Understand. Don’t like Math World. Math World strange place.


“… just one more gun toting fanatic …”


I resent that. I am a “gun-stored-in-a-safe-and-secure-readily-accessible-location fanatic.” But I will leave it at home. I no longer have an overwhelming urge to shoot you; you are less annoying when I tolerate you doing strange things in your strange Math World.


Re: Quantum Theory

I think I’ll skip it and go straight to String Theory.

I hear it has 20+ dimensions. That would make the BB&C (baffle befuddle & confuse) factor awesome.

One last question…

What do math mystics do when the limit is 0 (zero) and turns up in some bewildering complex of equations as a divisor? (n/0 = “mathematical absurdity”)

That must be inconvenient. Even in Math World, that must be frowned upon.

I’m guessing you reach into your quiver of “proofs” and draw out one that works in a more convenient manner. Or maybe a “creative adjustment” of the parameters. Hell, even Einstein used that one.

Please answer with minimal BB&C, if possible.

Thanks…

Later…

Afterthought: Google -> Results 1 - 10 of about 103,000 for mathematical absurdity.

I was surprised it was so low. But then even Google doesn’t do infinite searches. It would take too long. We are not safe though... Google is full of PhD Math Mystics so I'm sure searching infinity is a trivial challenge to them. If it can be imagined, a Math Mystic has already done it... in theory.