Tailoring elements demonstrating spacetime transformation?

There are even naturally occurring forms of Al2O3 that are transparent, such as gem quality rubies and sapphires.

 

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Haha, thanks for this.

From these, Chris Nagel certainly looks like a scam artist, deluding gullible investors, rather than merely a delusional inventor. That certainly fits with the vague rubbish in the patent application. Presumably the gullible investors may not know the difference between a patent and a patent application and will be induced to part with money before the examiner chucks it out as worthless.

 

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http://www.hawking.org.uk/godel-and-the-end-of-physics.html

Idiot.

 

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Knowledge is what you know, but intelligence is the comprehension of what you know...

 

Let's see what is the relation according to Hawking:

A popular explanation follows - which was probably the aim of including this.

A triviality. And this triviality gives nothing. Some other, non-obvious connection? Nothing. So that Hawking continues:

and continues with black hole information business. Then returns to Gödel only once:

which is, again, nothing.

So that all what we have learned is, essentially, "this is incompleteness of sort". Wow.

 

That is a substantial triviality you have there.

You might be one of those folks who decided it was nonsense to think that it was impossible to trisect an acute angle with a compass and a straight edge? Gödel's incompleteness theorem explains why that might be, even before you work out the proof that only quadratic operations (and not cubic ones) are possible using those tools. All of plane geometry is self-consistent, and it is also incomplete. It is impossible for it to be otherwise within a finite system of reasoning.

You may have heard that Andrew Wiles (one mentor to my mathematics PhD son) was the one who worked out a proof for Fermat's last theorem by mapping a set of theorems from one mathematical system into another. Gödel's theorem suggests why that strategy would have been necessary. It was because Wiles understood the theorem that he was able to accomplish something that had eluded mathematicians attempting to prove it since the 17th century. Fermat might have found such a mapping himself, and we may never know what it was. But it is doubtful even Fermat would have grasped what Gödel proved.

Or if you are a real dullard, you probably believe that you can capture all of the relationships that exist in the physical universe simply by counting things, or that truth is something that is as absolute in the real word as it is in your finite mind? Symbols are the tools of finite minds. If you can read it, it is because a finite mind wrote it. Symbols do not capture the flavor or texture or the essence of anything because they are as limited a form of communication as your finite mind is capable of dealing with.

Gödel's incompleteness theorem is a formal statement of the limitations of those symbols and systems of logic mathematicians prefer to use. It is not simply about the Liar's paradox, which actually is a trivial example. What is not to "get" about that? Trivial? Sure. As trivial as your current mindset seems to be. And as such, unworthy of any further analysis. I tried to summarize that in a single word. Did you not understand?

Hawking evidently believes it has application to the mathematics associated with physics or else he would not have written what you just seem to have read. It appears not everyone agrees with your assessment of its value.

 

One of the great things about the mammalian neocortex is that it is possible for minds so equipped to become obsessive about anything. Religion or science, creative writing or manipulating mathematical symbols are all more or less equally eligible as objects of our obsessions. One of the downsides of that same mind architecture is its propensity for obsessing over things that make no sense at all. Thanks for illustrating this better than I ever could.

Such a mind works out problems in exactly the same way that evolution does, for the same reasons, and with the same good results if the process continues long enough, albeit quite slowly. Try EVERYTHING. No holds barred. Even utter stupidity makes perfect sense. Believe it.

Let's all "manipulate the geometry of spacetime" to produce new materials with metal fatigue. I'm obsessed already. Aren't you?

 

I agree. I read the Hawking piece and I too would not interpret the reference to Godel's theorem as anything more than a possible analogy, for what may - or may not - be a similar state of affairs in our attempts to model the physical world. As I read it, he is not saying Godel's theorem says anything about physics: he is merely speculating that physics may be intrinsically incomplete in a similar way.

 

That was the only point I was trying to make. My apologies if it did not work. Have to try everything, you know.

 

I tend to ignore such 1 word summaries without arguments. The link was an argument, I have answered. You have misunderstood the answer - what I have named trivial was not Gödel's theorem, but the idea that, because physical theories use mathematics, they cannot go beyond the limitations which have been proven for mathematics.

Gödel's theorem applies to every mathematical theory which contains elementary integer arithmetics. So, it in a very trivial way applies to the usual mathematics applied in every physical theory.

 

The examples I provided were for integer arithmetic, but the theorem is not limited in the manner you suggest, and is easily extended beyond that domain.

Do you know any mathematical structure of any variety that does not have a finite number of provable theorems? If you think you do, does your candidate math have any limitations on the kinds of relationships it can express by means of existing notation?

Most maths that have a finite number of provable theorems typically have a few that are difficult to impossible to prove, even by mapping them to other maths with analogous representations. Some of those holes big enough for logical structures to get lost in; like a swiss cheese.

These are not trivial omissions. They are what keep mathematicians of all varieties employed trying to solve. Physics differs only in the additional constraint that bindings to physical reality must be represented in any mathematical modeling. There are many who simply ignore this constraint, which is fine; just don't expect much new physics to pop out of their heads that makes any more sense than they do.

 

Probably because it's a sock puppet of the scam artist.

 

How can you know something without comprehending it?

 

You're just making up bullshit. You should quit acting like you know what you're talking about.

 

Come on. The way we tell the distance between stuff is we measure it. Appears isn't a scientific term. You should learn some physics so you can actually formulate a coherent thought on the subject.

 

If there is no time or space to measure (distance) then how can you become capable of making a measurement?

 

I can know that we have ten digits in our number system, but to use it properly I must comprehend the logical extentions.

In other words the whole is greater than the sum of its parts, you can count all the parts in a puzzle and know all them, but to put the puzzle together you must have a vision which is built throught comprehending the appropriate logical extension of each individual part.

 

Some notes about Gödel's incompleteness theorem from other forums for those interested in further reading about it:

http://math.stackexchange.com/quest...ödels-incompleteness-theorems-in-layman-terms

If there exists a set of axioms which comprise a complete system of mathematical reasoning, it will contain at least one theorem which although true, will not be provable. If such a theorem does not exist, then the system is incomplete.

So the choices are: Either the system will be consistent but incomplete or if complete, it will be inconsistent.

Wolfram puts it this way (paraphrased): "Any system complete enough to formulate its own consistency can prove itself if and only if it is inconsistent."

Hilbert: "We must know, we will know." Gödel: "We won't know, we can't know."

There is no attempt at a formal proof of Hilbert's statement, nor of Donald Rumsfeld's equivalent statement about "unknown unknowns".

No wonder confusion is so easily exploited by folks like Chris Nagel. What he says is so inconsistent, we must assume that his understanding is more complete than ours.

Funny how well that idea works most of the time.

 

Science is very specific stuff. Making up your own version without any scholarship results in non specific bullshit. If you can't figure that out then pick a different subject. So you get to make a choice. Am I more interested in my bullshit interpretation or am I more interested in the actual science. You're trying to give a lecture on how stuff works when you don't even know what the stuff is. And no I'm not going to address your ignorance when you're trying to tell me how it works. If you ask a question you'll get a real response.