Einsteins last years with Godel were ignored for 50 years, UNTIL NOW! We still stand at the frontier

As a warning this post is going to be long, maybe multiple threads. But the information in is worth it. *snorts last 'sugar' pill*

The solid mathematical foundations that a lot of these modern day Nobels are awarded for, have a slightly darker and mirkier past in a historical context. And in fact, the whole materialist myopic view of linear maths as revealing deeper and deeper truths to us about the universe is fatally flawed from the get go. It's a story of how some of our most intellectually stimulated minds untied the previously cosy relationship the universe seemed to have with the certainties of mathematics, and how these facts have been acknowledged but largely ignored. It's a story of how such deep questions being asked back then of such high importance resulted in the fact that when some of the greatest minds of the time engaged their mind with such questions their brain dare not look away from the evidence that perplexed them so much, and how pursuit of meaningful answers to these issues pushed them first to the brink of insanity, then over to madness and suicide.


But for all the humain tragedy of great minds lost due to seeking meaning from life from maths and logic, what they saw is still true - the intellectuals at the time that took over the consensus opinion, assigning Einsteins work greater credibility than the original creator himself did, whilst in the case of Godels work largely ignoring it; so to this date we have yet to inherit at large the conclusions they themselves made.


Now, the world that they saw, we still stand at the frontier of as much as they did over fifty years ago.


George Cantor (1845-1918) was a religious professor of maths who started a paradigm shift in the world of established maths and science, that maybe he did not appreciate at the time. The profundity of a brand new question, not based on previous knowledge or even a similar school of thought in maths at the time; he asked himself "how big is infinity"?


It’s just an incredible feat of imagination. It’s, to me, the equivalent of taking mind enhancing drugs for that era (1800-1900) Others before him, going back to the ancient Greeks at least, had asked the question but it was Cantor who made the journey no one else ever had, and found the answer. But he paid a price for his discovery. He died utterly alone in an insane asylum.


The question is what could the greatest mathematician of his century have seen that could drive him insane?


Cantor had auitary hullicinations from a little boy that he attributed to god as calling him to maths. So for Cantor, his mathematics of the nature of infinity had to be true, because God had revealed it to him.


Cantor soon discovered he could add and subtract infinities conceptually, and in fact discovered there was a vast new mathematics opening up infront of him - maths of the infinite. This out of the boxing thinking had revealed something special, and he could feel it as a sort of profound insight into the nature of maths he was previously blind to.


By 1884 Cantor has been working solidly on the Continuum Hypothesis for over 2 years. At the same time the personal and professional attacks on him for his heretical "maths of the infinites" had become more and more extreme. Due to this, the following may of that year he had a mental breakdown. His daughter describes how his whole personality is transformed. He would rant and rave and then fall completely and uncommunicatively silent. Eventually he is brought here to the NervenKlinik in Halle, which is an asylum.


Even after concerted further effort he could still not solve the Continuum Hypothesis, he came to describe the infinite as an abyss. A chasm perhaps between what he had seen and what he knew must be there but could never reach. He realised that there’s a way in which in order to understand something you have to look very hard at it but you also have to be able to sort of move away from it and kind of see it in a kind of wholistic context, and the person who stares too hard can often can lose that sense of context.


After the death of a close relative, Cantor went on to say that he "could no longer" even remember why he himself had left music in order to go into maths. That secret 'voice' which had once called him on to mathematics and given meaning to his life and work. The voice he identified with God. That voice too had left him.


Here I divert from Cantor, because if we treat Cantor’s story in isolation it does little to bridge the gap in the idea that Cantor had dislodged something was part of a much broader feeling of that time. That things once felt to be solid were slipping. A feeling seen more clearly in the story of his great contemporary- a man called Ludwig Boltzmann.


The physics of Boltzmann’s time was still the physics of certainty, of an ordered universe, determined from above by predictable and timeless God-given laws. Boltzmann suggested that the order of the world was not imposed from above by God, but emerged from below, from the random bumping of atoms. A radical idea, at odds with its times, but the foundation of ours. Ernest Marc one of the most influential er philosopher of science at that time stated: 'I cannot see, I don’t need it, they do not exist so why we should bring them in the game.'


Worse than insisting on the reality of something people could not see, to base physics on atoms meant to base it on things whose behaviour was too complex to predict. Which meant an entirely new kind of physics – one based on probabilities not certainties. Boltzman worked tirelessly at his idea irrespective, and as Boltzmann got older and more exhausted from the struggle, he'd get mood swings, mood swings that became more and more severe. More and more of Boltzmann’s energy was absorbed in trying to convince his opponents that his theory was correct. He wrote, “No sacrifice is too high for this goal, which represents the whole meaning of my life.”


The last year of Boltzmann he didn’t do any research at all, I’m talking about the last 10 years. He was fully immersed in a dispute, philosophical dispute, tried to make his point – writing books which were most of the time the same repeating the same concept and so on. So you can see he was in a loop that didn’t go ahead. By the beginning of the 1900’s the struggle was getting too hard him.


Boltzmann had discovered one of the fundamental equations, which makes the universe work and he had dedicated his life to it. The philosopher Bertrand Russell said that for any great thinker, “This discovery that everything flows from these fundamental laws… comes”, as he described it, “with the overwhelming force of a revelation: like a palace emerging from the autumn mist, as the traveller ascends an Italian hillside,”

And so it was for Boltzmann. But for him, that palace was at Duino in Italy, where he hung himself.


A new generation of mathematicians and philosophers, were convinced if only they could solve the problem of the nature of infinity Maths could be made perfect again.

Godel was born the year Boltzmann died 1906. He was an insatiably questioning boy, growing up in unstable times. His family called him Mr Why.


What Godel later showed in his Incompleteness Theorem is that no matter how large you make your basis of reasoning your axioms, your set of axioms in arithmatic there would always be statements that are true but cannot be proved. [.....]

What Godel later showed in his Incompleteness Theorem is that no matter how large you make your basis of reasoning your axioms, your set of axioms in arithmatic there would always be statements that are true but cannot be proved. No matter how much data you have to build on, you will never prove all true statements.


There are no holes in Godels argument. It is, in a way, a perfect argument. Thus the present tense of this paragraph, it stands impeach-ably strong to this day. The argument is so crystal clear, and obvious.


To this day, very few want to face the consequences of Godel. People want to go ahead with formal systems, and Godel explodes that formalist view of mathematics that you can just mechanically grind away on a fixed set of concepts. There’s a very ambivalent attitude to Godel even now a century after his birth. On the one hand he’s the greatest logician of all time so logicians will claim him but on the other hand they don’t want people who are not logicians to talk about the consequences of Godel’s work because the obvious conclusion from Godel’s work is that logic is a failure - let’s move onto something else, as this will destroy the field.


Godel too felt the effects of his conclusion. As he worked out the true extent of what he had done, Incompleteness began to eat away at his own beliefs about the nature of Mathematics. His health began to deteriorate and he began to worry about the state of his mind. In 1934 he had his first breakdown. But it was after he recovered however, that his real troubles began, when he made a fateful decision.


Almost as soon as Godel has finished the Incompleteness Theorem, he decides to work on the great unsolved problem of modern mathematics, Cantor’s Continuum Hypothesis. Godel, like Cantor before him, could neither solve the problem nor put it down - even as it made him unwell. Again, the mind so engaged the brain dare not look away from the evidence that perplexed the mind so much. He calls this the worst year of his life. He has a massive nervous breakdown and ends up in a sanatoria, just like Cantor himself.


Alan Turing is the next person to enter this brief history. Turing was most well known for breaking the Enigma code; but he is also the man who made Gödel’s already devastating Incompleteness Theorem even more devastating.


Computers being logic machines was Turings predominant world view, and he showed that since they are logic machines incompleteness meant there would always be some problems they would never solve. A machine fed one of those problems, would never stop. And worse, Turing proved there was no way of telling beforehand which these problems were.


With Gödels work there was the hope that you could distinguish between the provable and the unprovable and simply leave the unprovable to one side. What Turing does, is prove that, in fact, there is no way of telling which will be the unprovable problems. So how do you know when to stop? You will never know whether the problem you’re working on is simply fundamentally unprovable or extraordinarily difficult. And that is Turing’s Halting Problem.


Startling as the Halting problem was, the really profound part of Incompleteness, for Turing, was not what it said about logic or computers, but what it said about us and our minds. Were we or weren’t we computers? It was the question that went to the heart of who Turing was.


This tension between the human and the computational was central to Turing’s life – and he lived with it until, the events which led to his death. After the war Turing increasingly found himself drawing the attention of the security services. In the cold war, homosexuality was seen as not only illegal and immoral, but also a security risk. So when in March 1952 he was arrested, charged and found guilty of engaging in a homosexual act, the authorities decided he was a problem that needed to be fixed.


They would chemically castrate him by injecting him with the female hormone, Oestrogen.
Turing was being treated as no more than a machine. Chemically re-programmed to eliminate the uncertainty of his sexuality and the risk they felt it posed to security and order.
To his horror he found the treatment affected his mind and his body .He grew breasts, his moods altered and he worried about his mind. For a man who had always been authentic and at one with himself, it was as if he had been injected with hypocrisy.


On the 7th June 1954, Turing was found dead. At his bedside an apple from which he had taken several bites. Turing had poisoned the apple with cyanide.


Turing had passed, but his question remained. Whether the mind was a computer and so limited by logic, or somehow able to transcend logic, was now the question that came to trouble the mind of Kurt Godel.

[.....]

[Godel] Having recovered from his time in the mentally unstable sanctum. But by the time he got here to the Insititute for Advanced Study in America he was a very peculiar man. One of the stories they tell about him is if he was caught in the commons with a crowd of other people he so hated physical contact, that he would stand very still, so as to plot the perfect course out so as not to have to actually touch anyone. He also felt he was being poisoned by what he called bad air, from heating systems and air conditioners. And most of all he thought his food was being poisoned.


Peculiar as Gödel was his genius was undimmed. Unlike Turing, Godel could not believe we were like computers. He wanted to show how the mind had a way of reaching truth outside logic. And what it would mean if it couldn’t.


So, why so convinced was Godel that humans had this spark of creativity? The key to his belief comes from a deep conviction he shared with one of the few close friends he ever had, that other Austrian genius who had settled at the Institute, Albert Einstein.


Einstein used to say that he came here to the Institute for Advanced Studies simply for the privilege of walking home with Kurt Godel. And what was it that held this most unlikely of couples together. On the one hand you’ve got the warm and avuncular Einstein and on the other the rather cold, wizened and withdrawn Kurt Godel. The answer for this strange companionship comes I think from something else that Einstein said.. He said that "God may be subtle but he’s not malicious." And what does that mean? Well, it means for Einstein is that however complicated the universe might be there will always be beautiful rules by which it works. Godel believed the same idea from his point of view to mean, that God would never have put us into a creation that we could not then understand.


The question is, how is it that Kurt Gödel can believe that God is not malicious? That it’s all understandable? Because Gödel is the man who has proved that some things cannot be proven logically and rationally. So surely God must be malicious? The way he gets out of it is that Gödel, like Einstein, believes deeply in Intuition - That we can know things outside of logic, maths and computation; because we just intuit them. And they both believed this, because they both felt it. They have both had their moments of intuition, moments of sudden conceptual realisation that were by far more than just chance.


Einstein talked about new principles that the mathematician should adopt closing their eyes, tuning out the real world you can try to perceive directly by your mathematical intuition, the platonic world of ideas and come up with new principles which you can then use to extend the current set of principles in mathematics. And he viewed this as a way of getting around the limitations of his own theorem. He no longer thought that there was a limit to the mathematics that human beings were capable of. But how could he prove such subjectives?


The interpretation that Gödel himself drew was that computers are limited. He certainly tried again and again to work out that the human mind transcends the computer. In the sense that he can’t understand things to be true that cannot be proved by a computer programme. Gödel also was wrestling with some finding means of knowledge which are not based on experience and on mathematical reasoning but on some sort of intuition. The frustration for Gödel was getting anyone to understand him.


Gödel was trying to show what one might call mathematical intuition of the kind we see in the brains of Synesthesia Savants such as Daniel Tammet in current times, and he was demonstrating that this is outside just following formal rules. What he had shown was that for any system that you adopt, which in a sense the mind has been removed from it because it's you that's used to lay down the system, but from there on mind takes over and you ask what’s it’s scope? And what Gödel showed is that it’s scope is always limited and that the mind can always go beyond it.


Here’s the man who has said, certain things cannot be proved within any rational and logical system. But he says that doesn’t matter, because the human mind isn’t limited that way. We have Intuition. But then of course, the one thing he really must prove to other people, is the existence of intuition. The one thing you'll never be able to prove. It would be synonymous in many regards to trying to prove the strong version of the gaia hypothesis.


Because he couldn’t prove a theorem about creativity or intuition it was just a gut feeling that he had and he wasn’t satisfied with that. And so Gödel had finally found a problem he desperately wanted to solve but could not. He was now caught in a loop, a logical paradox from which his mind could not escape. And at the same time he slowly starved himself to death.

[....]

Even though he’d shown that logic has certain limitations he was still so drawn to the significance of the rational and the logical. That he desperately wants to prove whatever is most important logically even if it’s an alternative to logic. How strange and what a testimony to his inability to separate himself - to detach himself from the need for logical proof; Gödel all of all people.


Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.


Logic had revealed the limitations of logic. The search for certainty had revealed uncertainty.


The notion of absolute certainty, is, there is no absolute certainty, in human life, in maths, in logic neither in science. The only certainty that has withstood the test of time to date is; that what we think is certain and true has a limited axiomatic scope, and the conscious mind is the only force in the universe that can transcend proclamations of truth by virtue of conceptualising and defining its limited scope, thus transcending certainties to higher values of truth it itself previously set the scope of. In this regard, focussed right by powerful minds, it's self transcendental, and could maybe eventually (if the trend continues) reveal a realm approaching the maths and dimensions of the infinite, where the amount of axioms nears the infinite and where logic and turing machine computation as we recognise it simply fails and we end up with a conscious internal universe of immense complexity, the complexity of which our current maths, computer models and materialistic sciences could not even begin to comprehend.

Maybe such an immensely universally complex system already exists. And maybe its the field of consciousness everything in the existing universe shares. We just have to reach a higher state of consciousness and awareness to become aware of the conscious attributes of things we don't typically ascribe consciousness to. Everything is alive, just at different levels all relevant to each others level of conscious transcendance.

Bzzzzzt. Reality check. Thats the dream (italisized). The optimist in me hopes, my realist side scorns.

But if consciousness in its normal form is indeed non computational, non algorithmic and not based on logic (incompleteness theorem) associated with turing machines then how are we ever going to try to understand it in terms of them without just tying ourselves up in knots made of the same paradoxes that drove the aforementioned geniuses mad?

And how can we solve the mystery of consciousness if neuroscientists do indeed have the cause and effect the wrong way round? It seems explaining consciousness with reductionist examining of brain function is a fruitless, but yet noble, quest many have embarked on. Consciousness is universal.

To finish, applying Godels theorem more vigorously to current dominant paradigms could have such a catalysing effect in developing new, mathematically sound theories, based on more creative functions of human inspiration.

I revel in scientific unknowns and theories being falsified and replaced by a better theory, personally. I have no pet theory I'm emotionally attached to.

But some would likely end up having breakdowns comparable to the ones mentioned above, if say the Big Bang theory was proved wrong or statistically impossible based on the sort of scientific reasoning we would subject to other areas of science, or evolution insignificant in the large scheme of things, what would the reaction be? I get a lot of religious zeal when I dare argue with cosmologists, always on the attack implying an emotional attatchment to their theory. I don't know how their egos could handle it ... and if we should be sensitive or blunt.

The problem is that today, some knowledge still feels too dangerous.
Because our times are not so different to Cantor or Boltzmann or Gödel’s time.
We too feel things we thought were solid, being challenged, feel our certainties slipping away.
And so, as then, we still desperately want to cling to belief in certainty.
It makes us feel safe.
At the end of this journey the question, I think we are left with, is actually the same as it was in Cantor and Boltzmann’s time.
Are we grown up enough to live with uncertainties?
Or will we repeat the mistakes of the twentieth century and pledge blind allegiance to yet another certainty?

Thanks for reading

"The last proceeding of reason is to recognize that there is an infinity of things which are beyond it. There is nothing so conformable to reason as this disavowal of reason."

Blaise Pascal (1623-1662)

Quite a long read that was, but I enjoyed it. Those are the kind of posts that make you want to learn more.

Hmm...interesting. Since i know little about this, i would have to cross check a little.

reply to post by ZeuZZ



Amazingly thought provoking. Thank you for sharing, wish I could give you ten stars. This coming from a man who has replyed to maybe 5 threads in 3 years.

I tip my hat to you Sir ......................or Madam, whatever the case may be.

Jeez, I wish I could communicate my thoughts as well as you...

Though, I still don't understand what you mean by "Until Now."

I believe science should always be agnostic--accept a theory or established fact and build upon
it, but stop short of the announcement of declarative truth. The only thing we know, is that we don't know
very much, and what we think we know could be wrong. That notion applies to all the accepted laws
of the universe we have so far established...and probably what drives these geniuses to the brink
of insanity.

I'll make a declarative statement...infinity is a truth. And qualify it with the simple notion that
you can always add one to the sum, or that you can always divide a sum by one half. That is
proof of a mathematical infinity....but I could be wrong

Great post........

reply to post by ZeuZZ

I enjoyed the read...

I purchased and read Gödel, Escher, Bach: An Eternal Golden Braid when it first came out in 1979...
...but I am richer now with your background information.

unicate my thoughts as well as you...

Though, I still don't understand what you mean by "Until Now."

Sorry guess that is a bit dated now.

I mean until NOW.

actually wrong, NOW seems more likely. No, Now.

PPS: I posted this first on a private blog where out of the box scientists share their findings a few months back, and revised it recently here which took a few hours. I got my sources from the autobiographies, and biographies of the people closest to the people mentioned, and a vague memory of something I watched years ago about einstein, which I watched years back thats faded completely from my memory. What mainstream science tends to do in cases such as this is they dont hide the information, they scatter it between literary jargon and scientific words that have no meaning to most of the population so they fail to see the bigger picture. But of course a few non scientists are brilliant literalists, which are great to employ when you think a underlying issue is being covered up with unnecessarily confusing jargon. And expert in that field might be just as good, but if its justice of a language then they will do.

reply to post by ZeuZZ


Thanks so much. Your information forces the reader to feel such empathy for these great minds, and the paradox that stretched them to the brink. I particularly liked your description of Godel's and Einstein's acknowledgement of the limitations of math as a representational language. Someone in another thread earlier today said as much in that we may be faced with trying to understand something through a representational language that is inherently flawed in its ability to accurately represent, and therefore, it cannot express through equational analysis purely what cannot be entirely contained or represented by numbers and equations.
Whatever the truth of that, the history of these men's endeavors never fails to be fascinating from whatever perspective you hearken from.

Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.

Had Cantor stuck with music...

Music is higher revelation than wisdom and philosophy... Music is the mediator between spiritual and sensual life.

There is no loftier mission than to approach the Godhead more nearly than other mortals and by means of that contact to spread the rays of the Godhead through the human race.

-Ludwig van Beethoven

"She gave me numbers... I gave her rhythm." -Americanist


en.wikipedia.org/wiki/Menger_sponge


The Universe resides on certainties. A System... We are merely the antenna - throughput.


System of Truth

I'll make a declarative statement...infinity is a truth. And qualify it with the simple notion that
you can always add one to the sum, or that you can always divide a sum by one half. That is
proof of a mathematical infinity....but I could be wrong

Just to bite at this, infinity is not a truth, more a concept used in mathematical theory, and maths can never give you truth as stated above by Godels incompleteness theorem. In the real world of science it bears absolutely no relation to anything the scientific method has ever discovered, or likely ever will. We have never found a ruler of infinite length, a star of infinite mass, a singularity of infinite density, or for that matter, science has never even discovered a singularity. Science inferes that such things may exist as if they do this theory will work out very easily; but thats more showing a failing in our current understating of the phenomenon and theory, than revealing some sort of deeper truth about what we have merely inferred has to exist in the first place.

The reason being is that we invented a singularity. Its a point on a piece of paper. It has no size, no properties, it just has locality. In relation to infinity and maths we will never find an infinite number but there are certain advanced ways that the concept of an infinite number can be used to produce logical conclusions (thought some dispute this )

This might scramble your brain Sorry.

Infinity plus one is infinity.
Half of infinity is infi in terms of letters. But half of an infinite number is still infinite.

Want to see you brain explode? :p

Watch this, its supoosed to be a simpler explnation on the nature of infinity for people that find it easier to learn maths by pictures and real world object exmaples. Starts at 13:30.

Be be honest, it confused the # out of me half the time too for a long while.

If you watch the whole documentary linked above, you will find that even in the mainstream scientific community the notion of infinity is still contentious to some. Its a scientific view that never has anyone measured something with an infinite vaue vs mathematicians view that use infinities all the time to explain problems. Both do this to an extent, but mathematicians are the worst. Especially when they stop looking for proof of this infinite value 'thing' and assume their maths works so it must be right.

System of Truth


Science? Truth? Those two words dont even do together. Science does not give you truth, it merely gives you internal self consistency that you can extensively cross reference and interdisciplinary test, but it will never, and should never claim to, give you truth.

Science evolves.

It doesn't declare truth, then stop.

It never mentions absolutes like that, if its real science.

Ok, the craziness here has gone far enough. Allow me to shoot down your childish misunderstandings.

Originally posted by ZeuZZ
Just to bite at this, infinity is not a truth, more a concept used in mathematical theory [...] In the real world of science it bears absolutely no relation to anything the scientific method has ever discovered, or likely ever will. We have never found a ruler of infinite length, a star of infinite mass, a singularity of infinite density, or for that matter, science has never even discovered a singularity.

Hate to tell you (heck, who am I kidding, love to tell you) this is nonsense. Infinity is a perfectly concrete, reasonable concept that is totally understood and accepted by all competent scientists and mathematicians.

Saying infinity is something weird is the same as saying the interval
0 < x < 1
means something's "wrong" with the number one, because no point in this interval can ever get to 1, because they're all less than 1. Indeed, the intervals
0 < x < 1
and
0 < x < infinity
are identical in all of their properties! They are homeomorphic.

And infinities show up in plenty of every-day calculations. For example, in phase transitions (such as between liquid and solid water) certain functions that describe them, or their derivatives, become infinite. Not "big" or "approximately" infinite, honest-to-god infinite. This is what a phase transition means. It's why the different phases are so distinct.

Another example, in a superconductor, the electrical resistance is exactly zero and the conductivity is literally, actually, equal to infinity.

Shockwaves, such as a sonic boom caused by when an aircraft breaks the sound barrier, are formed when certain terms in the equations describing them become equal to infinity.

Certain every-day effects are described by adding together an infinite number of terms. For example, an engineer may calculate how strong a material is by summing an infinite number of terms together and getting an exact answer.

There are tons and tons of other examples in physics where infinities show up every day, and are real, concrete, and even measurable things!

And none of this at all is poorly understood or controversial. It's been well understood for centuries, in fact!

As for Godel's theorem, you (and tons of other people) have it all wrong, too. It's an interesting theorem, but it doesn't mean what you say it means. All it says is that certain kinds of mathematical frameworks aren't strong enough to prove statements larger than they are, and that some statements about all possible combinations of statements in the framework are stronger than the framework, and thus can't be proven within it. Neither of these results are surprising. (What's interesting is the details; exactly what kinds of frameworks can and can't do this (e.g., the Peano axioms do not satisfy this, and can be proven, where ZFC cannot), and what impact this has on current results (very little), etc.)

At any rate, Godel's theorem has no impact on science whatsoever, because of the kinds of questions they're interested in answering v.s. the kind mathematicians like to answer.

reply to post by ZeuZZ


Yes, well...you did scramble my brain--no scientist and certainly no mathematician here.
What I am is a ultracrepidarian from this post....who didn't quite finish ninth grade

Haven't had time to look at the vid yet but I will...

As for infinity, I can't really even begin to understand the concept, though I think about it quite a bit.
I was just showing how proving something in the abstract doesn't equate to truth in the real world.
Like when Einstein said the SOL was the maximum speed limit of the universe...I don't buy it, and
think he should have left a little room for equivocation....the earth after all (even though it appears
to us that way from our perspective....isn't/wasn't really flat...

Originally posted by ZeuZZ
System of Truth


Science? Truth? Those two words dont even do together. Science does not give you truth, it merely gives you internal self consistency that you can extensively cross reference and interdisciplinary test, but it will never, and should never claim to, give you truth.

Science evolves.

It doesn't declare truth, then stop.

It never mentions absolutes like that, if its real science.

That's why I referred to it as a system... Uncross your eyes for a second.

Originally posted by Moduli
Ok, the craziness here has gone far enough. Allow me to shoot down your childish misunderstandings.

Originally posted by ZeuZZ
Just to bite at this, infinity is not a truth, more a concept used in mathematical theory [...] In the real world of science it bears absolutely no relation to anything the scientific method has ever discovered, or likely ever will. We have never found a ruler of infinite length, a star of infinite mass, a singularity of infinite density, or for that matter, science has never even discovered a singularity.

Hate to tell you (heck, who am I kidding, love to tell you) this is nonsense. Infinity is a perfectly concrete, reasonable concept that is totally understood and accepted by all competent scientists and mathematicians.

Saying infinity is something weird is the same as saying the interval
0 < x < 1
means something's "wrong" with the number one, because no point in this interval can ever get to 1, because they're all less than 1. Indeed, the intervals
0 < x < 1
and
0 < x < infinity
are identical in all of their properties! They are homeomorphic.

And infinities show up in plenty of every-day calculations.

100% agreed, so far. Props to your comprehension of ∞, so far,

For example, in phase transitions (such as between liquid and solid water) certain functions that describe them, or their derivatives, become infinite. Not "big" or "approximately" infinite, honest-to-god infinite. This is what a phase transition means. It's why the different phases are so distinct.

I think you are confusing the extremely sparse field of phase transitions which can be applied to all sorts of fields of science? from acoustics to the EM spectra. Maybe you are referring to graphical paradoxes of representing infinities that were not measured but were of limit to the scale and algorithm in a specific case?

Maybe the latent-heat contributions implying an infinite slope in the heat capacity of a phase transition Its not an infinite measurement. Generally anything has infinite height on a graph, but we make the scale that implies this infinity in the first place, also, somewhat ironically, we made the height scale algorithm ourselves.

Its a flaw is science give misinterpretation of data significant meaning, You might say, indeed, it has a infinite height, but 0 width. So it doesn't even exist at all. ?

So no real world significance at all, mostly mathematical and graphical confusion between functions and distributions.

Many analogous functions like the Dierac-delta-function, despite its label as a function, is a distribution, not function. It is a distribution, so it really should be called the The Dierac Distribution which has a certain differentially curve bounded area that 'technically' has infinite length.

Thats not measuing something in nature with an infinite value. Its a human misunderstanding on distributions and functions, confusing different graphical, algorithmic ways and spacial ways to represent data.

So save the time, instead of graphs, or maths, or hypostatizations, can you show me where we have ever in situ measured something with an infinite value?

As much as infinity is an essential part of maths, I totally agree, and a part of science that many dont like (they can not experimentally prove it, which is kind of the whole point of the scientific method). Such scientific infinities dont show a deeper understanding but our ignorance in thingking we understand them by maths.

Maths lives in a different reality to science, self complimentary as they seem.

Nature is awesome, and science is how we explain it. Maths is the code of nature, but not a constituent of it.
A fool thinks he is wise, a wise man knows himself to be a fool.
As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.
I don't believe in mathematics. (Albert Einstein)

So,

can you show me where we have ever in situ measured something with an infinite value?

edit on 7-7-2012 by ZeuZZ because: (no reason given)

Originally posted by ZeuZZ

can you show me where we have ever in situ measured something with an infinite value?

Yes, all of the things I said. E.g., the conductivity of a superconductor is measured to be equal to infinity.

You not understanding them doesn't mean something's wrong with infinity. The fact that it's used everywhere in science and math, and no scientist or mathematician has a problem with it should indicate to you that it is not science that has the problem with infinity.

Reality doesn't care about your hangups or misunderstandings.