Hey Abra,

Are suggesting we might be 'vaporing', as in clouds, as, 'in the clouds'!!! :)


I'll follow your advice and go for a sail!


So long friend!

Abra,

Great quotes from Feynman! Thanks for that.

>>> So it’s not even constructive to ask “What is a particle? What is a wave?” because sometimes it’s neither. Sometimes it’s just plain weird.

Yes! An electron is an electron, and does as an electron does! It -is- weird, and the whole premise of expecting pre-existing models to give an "understanding" of electrons is flawed (IMO). As you seem to suggest, the whole premise of "understanding" sub-atomic particles by any means may be flawed, also!

I was not suggesting those questions as a way of constructing a (misleadingly) definitive understanding - I was suggesting those questions as a way of -de-constructing- presumed understanding - as in, 'please don't assume physicists are using those words the way we might think they are, or the we will think we understand when we don't'.

On the other hand, there is a world of difference between 'understanding' something and 'identifying known qualities'.
I may not "understand" my neighbor, but I can see that he is about 5'10", overweight, and wears a jogging suit. As you know, physicist believe they have identified a whole slew of 'known qualities' of various subatomic particles (and their behaviors, interactions) - and these specific beliefs are consistent with the evidence regardless of whether anyone 'understands' the particles in question. But you are correct and thank you for furthering the idea of exercising caution regarding what we think we understand.

ya, there are so many 'truths' and absolute truth seems to be the one in question. I'd like to submit an absolute truth in the form of mathematics.

N + 0 = N
N * 1 = N

I think everyone can agree that both of those equations are true. Does that make it an absolute truth? To me, the funny part is that mathematics is an artifical language that represents only concepts but nothing really real.

Don’t even get me started on mathematics.

It’s not as *absolute* as you might think.

Mathematics is a logical construct that is based on axioms. It only holds truth with respect to those axioms. And those axioms have been questioned by many prominent mathematicians. I question them myself. In fact, I actually vehemently hold that the current axioms of mathematics are actually *incorrect*.

How can I say they are incorrect? Incorrect with respect to what? Well, I could write a book on that, in fact I actually started one but never finished it. But I do hold that the following conditional statement is *absolutely* true.

My conditional statement of absolute truth:

“If mathematics is supposed to correctly model the quantitative property of our universe, then our currently mathematical formalism is incorrect.”

In short, I’m saying that current modern mathematical formalism is actually *wrong*.

Now you might think that’s an absurd statement because it obviously works so well and has worked for what appears to be a couple of millennium. But for most of that time the definition of the number one was actually held to be purely intuitive. In other words in most of that time there was no *formal* definition for the meaning of one in mathematics. That idea was assumed to be *obvious*.

Well, in very recent times, less than about 200 years ago, it became clear that we needed a formal definition for the meaning of the number one. (my book is all about why that formal definition was needed, and why it is currently incorrect).

The bottom line is that the formal definition ultimately came from the idea of one man named Georg Cantor. Cantor formally defined the number one using Set Theory and the concept of an “empty set”. I hold that Cantor’s definition is incorrect (see my conditional statement about). In other words, IF you agree that mathematics is supposed to correctly model the quantitative property of the universe THEN a mathematical formalism that is based on the concept of an empty is logically incorrect.

Cantor’s definition is of one is extremely subjective, and not objective at all. I can prove this without ambiguity. Yet, our modern mathematics has accepted this formal definition for our concept of *number*.

I can even offer a *correct* formal definition of the number one. By *correct* I simply mean a definition that is in complete objective agreement with the quantitative nature of the universe. Cantor’s empty set idea is not in agreement with the quantitative nature of the universe and therefore is nothing more than a subjective manmade construct.

I am not the only person who knew this. There where actually mathematicians who were Cantor’s contemporaries who vehemently argued against Cantor’s empty set idea. Unfortunately they did not know how to prove their objections. I now know how their objections can be proven unequivocally.

In any case, the *absolute* truth of modern mathematics is not above reproach. Mathematicians will eventually need to face this dragon. It’s inevitable. This fundamental flaw in mathematics is holding up the whole show in physics and other sciences that are becoming increasingly dependent on abstract mathematics. If mathematics if fundamentally flawed (which it is) then so will be the sciences that use it as their foundation. This flaw will be corrected at some time in the future. There’s no escaping this.

Now you may ask, “Well then why does mathematics work so well?”

Actually it doesn’t. It only seems that way to us because we focus on the finite. Cantors empty set idea poses no threat to problems that are finite. It’s in the realm of the infinite where Cantor’s empty set goes haywire. Science is only just now approaching true investigations into the nature of the infinite, and thus far they have produced nothing but confusion.

Cantor’s formalism (based on an empty set) holds that there are greater and lesser infinities. (you may have hear of this, it’s actually a quite popular and accepted idea). This idea of a multitude of infinites stems directly from Cantor’s empty set. However this idea is “incorrect” relative to the true quantitative nature of the universe. In other words, Cantor’s model of “number” is not the same as the universe’s model of number. Cantor’s idea of number is a purely subjective one, and not objective at all.

Only after Cantor’s empty set has been removed from mathematics can mathematics be freed to properly reflect the true quantitative nature of the universe. However, removing it is not something that the mathematical community is even remotely interested in doing. They are in love with Cantor’s empty set!

So anyway, to make a long story short. Mathematical formalism in its current state may not hold as much *absolute* truth as you might be led to believe. In fact, I actually hold that it is currently false, with respect to the “true” quantitative nature of the universe.

I’ll leave with a quote from a very famous contemporary of Cantor:

"Cantor's set theory will be considered by future generations as "a disease from which one has recovered." - Henri Poincare

Although, thus far we have not yet recovered! I know the answer. I know how to recover mathematics. But I’m not telling. I don’t feel that the human race is ready for that knowledge yet. They are too eager to kill and oppress each other. Let them wait for another few millennia and figure it out on their own. I basically already pointed to the problem in this very post! They just don't know how to fix it, and most aren't even aware that's its a problem. They simply don't see it,... yet. But its resolve is inevitable. It simply must be repaired if we are to move forward.

~ The Dawning of the Truth ~

~~~

I once was happy
when I knew not
Back in the days
when I was a tot

But then I grew
and thought I knew
So thinking thoughts
became my view

Pondering on problems
I so foolishly embraced
Imagining solutions
to the perils that I faced

Then one day an angel said,
“Do you believe in who you are?”
At least I think it was an angel
though it may have been a star

It doesn’t really matter
for both concepts are bizarre
We are them, and they are we
and this is what we are

All that we can really know
from the moment of our birth
Is that moments are what matter
as we live our life on earth

Don’t think about it logically
if you wish to know the truth
Truth is what we’ve always known
since the dawning of our youth

~~~

(Abra 8/5/07)

Ah.... Cantor's "empty set" theory. All those wasted days in Math classes - until I hit Abstract Calculous. That was the end of that. Packed up all the math books and changed my major.
I have to say though Abra - your posts do bring back a few fond memories of axioms and postulates.

I usually suck the thoughts out of people's minds with mind altering methods of mass confusion and red liquorice.

Eljay wrote:
“All those wasted days in Math classes - until I hit Abstract Calculous. That was the end of that. Packed up all the math books and changed my major.”

I don’t blame you! If you actually understood it you’d know that it makes no sense. It seems to me that the only people who can become mathematicians are the one’s who don’t understand it, because if they did understand it they’d know it was wrong! (ha ha)

I’m seriously not joking either.

It is TRUE, that modern mathematicians genuinely don’t care whether mathematics correctly reflects the true quantitative nature of the universe. They freely admit that it’s not a science, (i.e. it doesn’t depend on observational experiment). It’s a purely logical formalism. From that point of view it can’t be argued with. Cantor’s empty set “theory” is a legitimate axiomatic logical system.

The only problem I have with it is that it doesn’t mean anything with respect to the true quantitative nature of the universe. And so from that point of view I need to ask why scientists are using it? Physics has become increasingly mathematical in the past several decades. String theory is entirely based on mathematics. There is no observational evidence for String Theory at all, even the string theorists will openly admit that. The entire theory is based on Cantor’s empty set whether they realize it or not. If Cantor’s set theory is wrong (i.e. if it doesn’t correctly reflect the true quantitative nature of the universe), then string theory has no solid foundation.

I’m not a proponent of string theory anyway. And this is a large part of the reason.

When mathematics goes down (and it must), String Theory will go with it.

It’s not as bad as people might think. The entire cathedral of mathematics won’t topple. Only the last few hundred years of it. All of the mathematics prior to that will stand (which includes calculus) because Leibniz and Newton came before Cantor. In fact, even Weierstrass’ formal definition of the calculus limit will stand. Most mathematicians don’t seriously understand the calculus limit anyway, if they think it solves Zeno’s paradox of motion they clearly don’t’ understand it because I can guarantee you that it does not.

In any case, it’s quite possible that you actually understood calculus too well, and that’s why you realized that it wasn’t making any sense. It’s seriously flawed at the higher abstract levels that you are talking about. This is especially true when speaking of things such as Group Theory, etc.

I believe we were all born into this world with the knowledge of the ages/universe.... what we do with that knowledge is acted out as individual 'choice'.. if we allow our INSTINCTS to rule us.. then I truly believe we are acting on good judgement... we all have the power, the strength and the answers.. some of us just get stupid along the way

Abra;

you said: In any case, it’s quite possible that you actually understood calculus too well, and that’s why you realized that it wasn’t making any sense. It’s seriously flawed at the higher abstract levels that you are talking about. This is especially true when speaking of things such as Group Theory, etc.

Well, I'd certainly had enough classes in it. Can't say that I understood it so well, but I will agree that going from Applied differential equations to the matricies, and permutations of abstract algebra turned my brains into a tossed salad. Thank you for justifying my confusion for me!

Turns out I never needed anything beyond Diff-equations for my chosen career, anyway - so I walked away quite content.

There was or still is a 'Dear Abby' phenomenom, maybe we are seeing the birth of 'dear Abra' !!!

Please take no offence Abra for what I'm about to question here, it is not meant as a verdict nor a judgement. It is a question to help establish whether what you have expressed here, is really what I think you've expressed here.

Here is what you wrote:

"... Although, thus far we have not yet recovered! I know the answer. I know how to recover mathematics. But I’m not telling. I don’t feel that the human race is ready for that knowledge yet. They are too eager to kill and oppress each other. Let them wait for another few millennia and figure it out on their own. I basically already pointed to the problem in this very post! They just don't know how to fix it, and most aren't even aware that's its a problem. They simply don't see it,... yet. But its resolve is inevitable. It simply must be repaired if we are to move forward..."

I could be wrong, but it truly left me with a bad taste of a 'dogma-rhetoric-orthodoxy-ego-based' combo galore!!!
A sort of : "... there is a code to crack, and the winner will be the one whom cracks it! (huge falsehood if there is one) ... And by the way folks I have something to announce: I've cracked the code, and I'm keeping it to myself?!?!?' (Big break with the universe is us, and we are all the universe theory, seems to me?!?!?).

But since it could very well be a poor interpretation on my part, I'll wait for your reply.

And remember Abra, the potential 'break' for me takes place with the 'possible' nature of something you've written, and not you.

Voil wrote:
“But since it could very well be a poor interpretation on my part, I'll wait for your reply.”

If you think I’m claiming to have all the answers to every question you’re definitely mistaken. All I meant by what I said is that I know the solution that Cantor’s contemporaries knew existed but could not find. It’s certainly not the answer to everything.

Moreover, even though it represents a key to further knowledge, it must be understood that it is indeed just a key. I realize the potential of what it can unlock. That doesn’t imply that I have the experience of knowledge to go there on my own.

Have you read “The Trouble with Physics” by Lee Smolin?

Are you aware of the current crisis in physics? Although, there are scientists who reject the notion that there even is a crisis, but there are many who believe there is too. I side with the latter. I’ve studied string theory in some depth and I’m convinced that it’s on the wrong track. This is precisely what Lee Smolin’s book is all about. String theory is totally a pure mathematical construct. It has no sound scientific basis.

In short, I sincerely believe that modern physics has made a wrong turn and is going down a dead-end street. An understanding of why Cantor’s empty set theory does not properly reflect the true quantitative nature of the universe will clearly reveal why string theory is a wrong turn.

I’m confident that all of this is true. That doesn’t mean that I know what the correct turn is for physics. All I know is that they are headed down a dead-end street that misrepresents the true nature of the universe. This is really bad for physics.

Both modern mathematics, and modern physics are going to need to change direction. What that new direction will be I can’ t say. But I can say with confidence that the current direction is incorrect.

I did point to the problem in mathematics, so it’s not like I’m keeping it a “secret”. So did many of Cantor’s contemporaries but no one listened to them. I’m not the only one who sees the problem, but I might be the only one who knows how to fix it. That shouldn’t come as much surprise since no one else is even working on the problem. That vast majority of mathematicians don’t even know or believe that there is a problem.

Even physicists who believe that there is a problem with string theory would never guess that the root of the problem is actually with mathematics. Lee Smolin is thinking purely in terms of how to fix physics, he’s not even suggesting in the slightest that there might be a problem with the mathematics.

So yes, I believe that I know something about where the problem lies and how to repair it. And, in truth, I wouldn’t refuse to divulge that information, but I’m not so sure that I want to just hand it over freely. I started writing a book on it and then asked myself, “Why should I?” Take a look around at the behavior of our governments and their leaders. Why give them any more technological information than they already have? They don’t deserve it. Pure and simple.

Voil wrote:
“(Big break with the universe is us, and we are all the universe theory, seems to me?!?!?).”

No, I didn’t mean to claim that fixing mathematics would yield any prove about the nature of god or our relationship to the universe. I just happened to respond to a post about mathematics in this thread.

Although, I do imagine that fixing mathematics would have profound affects on philosophy as well as science. It’s quite a major change actually, especially concerning concepts such as irrational numbers, the very meaning of number, and most important of all, a better understanding of the nature of infinity.

Will this point to more evidence that we are this universe? Maybe, maybe not. I have no clue to be honest about it. But it will change how we think about the concept of number, especially irrational numbers, quite dramatically.

Humanity will discover this truth eventually, it's inevitable. They just aren’t aware of it today. And they aren’t even studying it because they aren’t even aware that it’s a problem. It’s time for discovery just isn’t ripe right now.

Abra,

THANK YOU!

And forgive me for even thinking that I could have misinterpreted you on this 'cracking the whole thing' thing!!!

With respect to "Have you read “The Trouble with Physics” by Lee Smolin?", Yes, and found it fascinating read, although I was left with the impression that HE WAS pointing to something wrong with the very foundation of "mathematics", upon which the current Physics construct was built?!?!? Although I agree he keeps addressing the symptom and not the source.

As for the rest, I for one am not about to write a book on correcting our current understanding of mathematics. But I do find it fascinating that you might be doing just that. For I am convinced that ours is an eternal mission of 'iterating':
We will keep demystifying what is 'untrue' about what we know to be true at any given time?!?!?

Will we ever get to demystify THE TRUTH?!!? IMO opinion, there is absolutely no point!!! Life without the inexorable mystery it comes in, would hold no more interest to survive and multiply for human beings. NO more need to explore for the sake of exploring!!! That's the end of that stroy IMO.

We are possibly IMO, nothing other than eternal explorers. Need the mystery for the eternal source of stuff to explore. Getting somewhere is pointless!!! We've always been and will always be here/there forever (probably).

And besides...
'... A life unexplored isn't worth living'!!!' (Plato)

Voil,

If you’re interested in this problem of mathematics I can share with you what lead me up to it’s discovery. I stumbled upon it rather accidentally whilst pursuing other things.

I was intrigued be the question, “What is inertia?”

What gives rise to inertia?

I was asking this question before I knew about the Higgs field. So think about this from a pre-Higgs point of view.

I began by studying Einstein’s General Relativity of gravity. Many may not know this, but while General Relativity describes gravity, it doesn’t really say anything about the nature of inertia. It just accepts inertia as a postulate.

I wanted to understand inertia. This has been a quest of mine since I was a pre-teen. Why do things keep moving? Why do they carry kinetic energy? How do they know that they should have inertia? Given a point in time, how does an arrow know that it’s in flight? Freeze time and look at two arrows side-by-side just frozen in the air. Then let time resume. One arrow takes off like a bat out of hell, the other one falls to the ground? Why? Because of their history! One arrow had been shot from a bow, the other was released from my hand at that very point.

But how do the arrows know their history? And any given point in time how does one arrow know that it’s in flight, and the other know that it has been dropped?

This may sound similar to Zeno’s paradoxes of motion, but this is actually a totally different question from what Zeno was asking. (I might add though that Zeno’s paradoxes did inspire me to ask these questions however)

In any case, what is inertia? Physics has no answer. They just define what it is and accept it as a postulate they have no explanation for it. Even today, while they suggest a Higgs field is responsible, even that concept is not fully worked out.

In any case, back to GR (General Relativity). Einstein had thought about inertia too, but could not explain it. Then a fellow by the name of Ernest Mach came along and suggested a possible explanation. However, his explanation required that space be absolute, this flew in the face of relativity, but intrigued Einstein just the same. Einstein actually embraced Mach’s principle of inertia. It started making sense.

But then a pure mathematician came along by the name of Kurt Gödel and proved that Mach’s principle could not be true in a universe which contains rotating galaxies. Well, I was intrigued at how a pure mathematician could prove such a thing so I began to study the works of Kurt Gödel. I discovered that he was very famous for having proven that any mathematical statement that makes reference to the natural numbers is necessarily incomplete and inconsistent. He actually shocked the mathematical community with this proof.

I was also shocked and I needed to know why this way true so I studied the concept deeper. This lead me to inquire about the formal definition of number, that that ultimately lead me to the Cantor’s empty set. Bingo! I found the inconsistency! I found the self-reference that Kurt Gödel had proven must exist in any self-contained axiomatic system. In mathematics that self-reference is the empty set! All of modern mathematics (set theory specifically) rests upon the self-reference of Cantor’s empty set.

This blew me away. Then I asked how could it be fixed? How could the self reference be removed?

This lead me to a contemporary of Cantor name Gusseppi Peano. Peano actually had the correct answer and even presented it to the mathematical community at the time! But they rejected it on the grounds that Peano had no workable definition for it. Plus there was an almost “religious” desire to make the concept of number “pure”. Peano’s idea was “physical” in nature. It was “tainted” with physics. Cantor proposed the idea of starting with nothing! There was no physical attribute associated with the idea of nothing. So Cantor’s idea was seen as being “pure thought”.

This is how CLOSE they were to actually having the “right” concept at that point in time! Peano’s idea was the correct objective idea! But it was rejected in favor of a purely subjective idea of an empty set.

This was a critical turning point for mathematics. All of modern mathematics now rests on Cantor’s subjective empty set.

I then, when back and took Peano’s idea and expanded on it. What if we used Peano’s original idea? Where would it lead? So I built a mathematical system based on Peano’s idea and low and behold it makes absolute perfect sense! It matches the quantitative behavior of the real universe, and it doesn’t produce erroneous multiple infinities. It also explains the true nature of irrational numbers which will be forever hidden in Cantor’s empty set formalism.

So you see. I didn’t actually invent anything. I simply realized that Peano was right all along, and Cantor was wrong. Peano just didn’t know how to sell his idea to the mathematical community. He also never really expanded on it to see where it would lead. Had he done that surely he would have screamed Eureka!

It’s actually much more complicated than presented in this post. But this is the gist of how I made the discovery. Unfortunately none of this has actually answered my original question, “What is Inertia?”

But at least now I understand why modern mathematics is incorrect, and how to fix it. The only problem is that now I'm too burnt out to even care about it anymore.

I just want to compose music and forget about physics and philosophy. I'm tired. I just want to relax.

Have you heard the Flute and Guitar Fantasy I composed?

You can here it here:

http://www.csonline.net/designer/ideas/fantasy.htm

Abra,

Here's my definition of a magician:

'... keep everyone guessing that the reality that they hold to be true, holds within it another possible reality that makes the previous one possibly untrue ?!?!?'

ABRACADABRA... you are just that in your 'posting' name, and in your 'being'; essence.


You wrote:
'... Unfortunately none of this has actually answered my original question, “What is Inertia?”
But at least now I understand why modern mathematics is incorrect, and how to fix it. The only problem is that now I'm too burnt out to even care about it anymore...'



So first you stumble upon something that you couldn't have imagined if you hadn't set out to EXPLORE for something you never found!!! True explorer and open-minded spirit!

But secondly and more importantly,
(I could be way out of line on this one, but what the heck, please forgive me in advance),
... you may not be burnt out at all about the whole subject!

You're probably stumbling, as we speak, upon the architecture to bring your point across, while what is apparent to you, is just '...wanting to learn and compose music', and get away from it all.

In the background, there also is this feverish JSH activity you're keeping up with that is making us all dizzy (intensity). Just polishing up, and prototyping your writng and mass appeal skills!!!

So picture this:

... This incredible singing TROUBADOUR, with great charisma, and pedagogical skills, winnig mass appeal with just his story of stumbling across the thing (not releasing what the thing is), which on its own will confront and shake the scietific community out of its comfortable reality 'hole'.

You will be watching the whole show from your 'fun-loving' troubadour circuit, and the sympathetic agents from the scientific community will do all the ground preparation for the subsequent release of YOUR 'thing'.

"Strategy without tactics is the slowest route to victory. Tactics without strategy is the noise before defeat." Sun Tzu [Wu]

Ain't that the truth!!!

But also, one the most overquoted words straight from our friend Albert:

"The problems that exist in the world today cannot be solved at the same level of thinking that created them."

-Albert Einstein,

The existing problem is 'math', in its essence, given this discussion.
The 'math' problem was creted at specific level of thinking and 'being'. That place is so compromised upon the faulty foundation, it will never accept opposition (probably!).

But much like court jesters; they were the only ones whom could indirectly contest the Monarch's 'edict', and thus carve essential change.

Likewise, Abracadabra, 'THE 'magical mathematical troubadour' will shake the very foundation of today's scientific community, not only coming from a whole other way of thinking, but coming from a whole other way of being, and appealing.

Einstein was smart. But was he the smartest??? NO such thing. HE was jut the most appealing of the smart ones around.
He was playful, didn't take himself seriously, had fun, was passionate, ... and did all that without compromise!!! That's what got his otherwise bright work among bright works.

From my perspective, I don't think you should draw conclusions about the state of your 'project'. If any: I think you're right on track Abra!

Don't just question the universe Abra, trust it a little when it comes to your own mysterious path.

I'm on the troubadour side.


p.s.: Listened to your 'fantasy for flute and guitar',
... just put some words to it and you're ready to tour!!!
Quite impressive!!!

Oh my goodness, I keep putting off posting till I have time to read all these wonderful replies. BUT you all just keep them coming.

So I'm simply going to interject my answer to the topic question. And then later, when I have time to read all, I will be better versed to actually share in the conversation.

Truth, in my opinion, shares the same values as two other words in language. They are love and hate.

We have used these three words to such an extent that we can no longer trust what they mean when they are said or written or implied.

We have, somehow, managed to create these words as a testament to something whose value is so beyond any other expression, that only these words have the ability to encompass the that expression. However, instead of treating these words with a respect that should give them the power they deserve. We have abused them, to suit our own self-indulgent purposes.

I think its sad and I hate the fact that this has happened because, the truth is, I love it when language is used as it was meant to be used.

just had to express my own little example here - from what I've seen, so far, this thread needed a bit of philosophic levity.

<-------- laughing