The Myth of Critical Thinking

Michael 345 said:
I strongly suspect your mathematics and formula to be like a unfortunate child

:)
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Today formulas of physics really look ''like a unfortunate child''
Why?
Because they don't connect in one simple and logical chain of
conclusions that explain Nature, the evolution of Nature.
Henri Poincare wrote:
''Science is built up of facts, as a house is with stones.
But a collection of facts is no more a science than a heap
of stones is a house.''
/ Henri Poincare /

The same is possible to say about a collection of mathematical
formulas which are heap of ideas (some beautiful, some abstract)
===
 
socratus said:
You say: ''Law of Nature are controlled by the mathematics of "values" ''
To control something needs mind / brain.
Does mathematics have mind/brain ?
Are there particles which can carry mathematical (controlled) functions ?

Classic physics obeys deterministic laws.
Quantum physics prefers statistic laws.
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If you are arguing the universe posesses a sentient mind/brain, then you must provide motive.

The beauty of the Mathematical functions is that it needs no motive. Mathematical laws simply allow or disallow and event to occur.

We know that at least this universe has a mathematical function which we, to a considerable extend, have been able to symbolically translate into our mathematics language. The laws of Nature, which are neither good nor bad, but neutral in function.

Moreover, IMO, there is no intent, no goal, that can be associated with a mathematical function.
 
socratus said:
Maybe , one of the aim of mathematical functions is to create
Solar system and conditions for the living planet Earth.
===
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So humans create mathematics so that mathematics can create the solar system and a Earth which can support life

Care to map out how such mechanism works please?

:)
 
socratus said:
Maybe , one of the aim of mathematical functions is to create
Solar system and conditions for the living planet Earth.
===
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Pure Abstract Potentials + Mathematical functions = God, a sentient being who's motive was to create an entire universe, so as to create the probability for the 14 billion year long emergence of probabilistic conditions necessary for life on a single planet, orbiting an average star?
And Mathematical functions were invented to accomplish this probabilistic feat. Sounds rather complicated to me.

What is so special about the earth that sets it apart from all other planets throughout the universe?
There may be more Earth-like planets than grains of sand on all our beaches
New research contends that the Milky Way alone is flush with billions of potentially habitable planets -- and that's just one sliver of the universe. The fascinating question of whether we are alone in the universe basically comes down to some intricate mathematical calculations.
A new study combines exoplanet data from the Kepler Space Telescope with a new version of a 250-year-old method for determining orbital periods and positions of planets. The research calculates that in our galaxy alone, there could be billions of planets hosting liquid water, habitable conditions and perhaps even life.
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https://www.cnet.com/news/the-milky-way-is-flush-with-habitable-planets-study-says/

Thus life emerging somewhere else in the universe is also a mathematically probabilistic event created by the emergenge of local conditions necessary for life to emerge? No "fine tuning" necessary then, hence no motive (critical thinking) necessary to produce a single result.
 
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Write4U said:
Pure Abstract Potentials + Mathematical functions = God, a sentient being who's motive was to create an entire universe, so as to create the probability for the 14 billion year long emergence of probabilistic conditions necessary for life on a single planet, orbiting an average star?
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LOL!

Reading your question whilst sober makes me think to disassociate more from the board and slowly post less and less as I doth find myself conscious of the mishmash twilight zone of "WTF?"
 
socratus said:
Today formulas of physics really look ''like a unfortunate child'' Why? Because they don't connect in one simple and logical chain of conclusions that explain Nature, the evolution of Nature.
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Sounds more like the idealized expectations or concerns of scientism(PDF). Science practice itself doesn't care so much about there being a (no loose ends) network of explanation that's coherent at a broad or general level. Just that one's work at the immediate level of a discipline is internally consistent enough to satisfy any review before publication. (Even the latter is sorely deficient in the social and biomedical sciences and the junk journals of that territory.)

Henri Poincare wrote: ''Science is built up of facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.'' / Henri Poincare /

The same is possible to say about a collection of mathematical formulas which are heap of ideas (some beautiful, some abstract)
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Updated filler for that "heap of stones" metaphor:

Marcus Chown (New Scientist magazine, 10 March 2001, *The Omega Man*): The reason for [Gregory] Chaitin's provocative statements is that he has found that the core of mathematics is riddled with holes. Chaitin has shown that there are an infinite number of mathematical facts but, for the most part, they are unrelated to each other and impossible to tie together with unifying theorems. If mathematicians find any connections between these facts, they do so by luck. "Most of mathematics is true for no particular reason," Chaitin says. "Maths is true by accident."

This is particularly bad news for physicists on a quest for a complete and concise description of the Universe. Maths is the language of physics, so Chaitin's discovery implies there can never be a reliable "theory of everything", neatly summarising all the basic features of reality in one set of equations. It's a bitter pill to swallow, but even Steven Weinberg, a Nobel prizewinning physicist and author of *Dreams of a Final Theory*, has swallowed it. "We will never be sure that our final theory is mathematically consistent," he admits.

Chaitin's mathematical curse is not an abstract theorem or an impenetrable equation: it is simply a number. This number, which Chaitin calls Omega, is real, just as pi is real. But Omega is infinitely long and utterly incalculable. Chaitin has found that Omega infects the whole of mathematics, placing fundamental limits on what we can know. And Omega is just the beginning. There are even more disturbing numbers--Chaitin calls them Super-Omegas--that would defy calculation even if we ever managed to work Omega out. The Omega strain of incalculable numbers reveals that mathematics is not simply moth-eaten, it is mostly made of gaping holes. Anarchy, not order, is at the heart of the Universe.​

Also Stephen Hawking's (and Leonard Mlodinow's) concoction from 2010, which is really just a contemporary recycling of long existing views or prescriptive thought orientations:

What Is Model-Dependent Realism?
http://www.thoughtco.com/what-is-model-dependent-realism-2699404

What isn't emphasized enough in that summary account is that the models would overlap as one becomes more applicable or useful than another for dealing with a specific problem or challenge. Thus there would arguably only be the practical needs of the scientists linking the constructs rather than their actually being integrated underneath by a (scientist-independent) grand abstraction that resolves any incommensurable properties or incompatibilities among them.

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C C said:
"Most of mathematics is true for no particular reason," Chaitin says. "Maths is true by accident."
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That does not appear to mean anything. Obviously proved theorems and statements and so forth are not true by accident - they are true by demonstrated logical agreement with the axioms from which they were proved, a procedure from which all accident has been excluded. That's by definition. And these are the only mathematical entities that have acquired the label "true", afaik.

And just as obviously the agreement of physical reality with some mathematical model is not deserving of the label "true" in any mathematical sense. That is conventional wisdom in the 21st Century. The label "true" in the physical or scientific sense is significantly different, a shorthand for "makes sense and fully agrees with experiment, better than any other we know of".

So what's going on?
 
Write4U said:
What is so special about the earth that sets it apart from all other planets throughout the universe?
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It is special simply because we know of no other and although there should be other similar planets we cant imagine them at all.

Its like having compassion for a family on the otherside of the world ...we can say we have compassion but they are mere words.
Alex
 
iceaura said:
That does not appear to mean anything. Obviously proved theorems and statements and so forth are not true by accident - they are true by demonstrated logical agreement with the axioms from which they were proved, a procedure from which all accident has been excluded. That's by definition. And these are the only mathematical entities that have acquired the label "true", afaik. [...] So what's going on?
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Chaitin's focus is on the "interesting" furniture (especially his own contributions) that acquires membership in mathematics -- which have not been proven or arguably can be proven. This gels to mathematics thereby lacking its own version of a TOE. Some fundamental framework for either integrating the various "rogue islands" and validated theorems together, or a master procedure for generating the entire mathematical population.

"Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous Incompleteness Theorem, which states that in every mathematical theory, no matter how extensive, there will always be statements which can't be proven to be true or false." (Intro from the article below)​

Here's Chaitin's own synoptic account elsewhere, starting with the paragraph just before the subtitle "Why does maths have no TOEs?" and stopping before he ventures into that superfluous "epilog" of philosophical implications.

At one spot he seems to perversely threaten to chip away at "no TOE" with the prospect of: "Rather than attempting to prove results such as the celebrated Riemann hypothesis, mathematicians should accept that they may not be provable and simply accept them as an axiom." Though doubtless he's still relying on the nature of items like "Omega" to elude promotion to that status.

[...] And just as obviously the agreement of physical reality with some mathematical model is not deserving of the label "true" in any mathematical sense. That is conventional wisdom in the 21st Century. The label "true" in the physical or scientific sense is significantly different, a shorthand for "makes sense and fully agrees with experiment, better than any other we know of". [...]
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Yah, it's unclear whether that's a drum which Chaitin himself is even beating directly on. Since in the New Scientist article, Marcus Chown may have tossed that implication with physics in there himself (it occurs only once).

By taking for granted that a writer or speaker has stepped from the authority of mathematics into the authority of a different formal system or domain by just making remarks like "mathematics is the language of physics"... Evaluation of those comments likewise shifts to the expertise and standards of that other enterprise which has borrowed or assimilated such for its own needs and goals. That evaluation including whether or not the stance is held by the discipline at all, or is instead some informal view simply flitting around from practitioner to practitioner. Example being whether or not a "bitter pill to swallow in mathematics" should correspondingly have an effect in physics. Of Steven Weinberg having been justified to lament: "We will never be sure that our final theory is mathematically consistent." Certainty being an orientation supposedly alien to the endeavor beforehand, anyway.

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For the sake of not depending solely on Chown's quoting of Weinberg, here's a similar and more clarified instance of it that Weinberg wrote in "Can Science Explain Everything? Anything?" from "The Best American Science Writing" 2002, edited by Matt Ridley.

There are also limitations on the certainty of our explanations. I don't think we'll ever be certain about any of them. Just as there are deep mathematical theorems that show the impossibility of proving that arithmetic is consistent, it seems likely that we will never be able to prove that the most fundamental laws of nature are mathematically consistent. Well, that doesn't worry me, because even if we knew that the laws of nature are mathematically consistent, we still wouldn't be certain that they are true. You give up worrying about certainty when you make that turn in your career that makes you a physicist rather than a mathematician.

Finally, it seems clear that we will never be able to explain our most fundamental scientific principles. (Maybe this is why some people say that science does not provide explanations, but by this reasoning nothing else does either). I think that in the end we will come to a set of simple universal laws of nature, laws that we cannot explain. The only kind of explanation I can imagine (if we are not just going to find a deeper set of laws, which would then just push the question farther back) would be to show that mathematical consistency requires these laws. But this is clearly impossible, because we can already imagine sets of laws of nature that, as far as we can tell, are completely consistent mathematically but that do not describe nature as we observe it. ​
 
Beer w/Straw said:
LOL!

Reading your question whilst sober makes me think to disassociate more from the board and slowly post less and less as I doth find myself conscious of the mishmash twilight zone of "WTF?"
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Did you read the rest of the post? I suggest to read it more carefully and give it some thought. I believe you might find the gist of irony contained in the posit.

The question mark was to indicate a total denial of the existence of a purposeful, omnipotent god . It was a hyperbole of what a believer would have to argue from the clear and demonstrated mathematical functions by which the universe evolves.

Your reaction was correct, you just read it from the wrong perspective. It was posted in response to "socratus" suggestion that god is a mathematician. (see the quote), which prompted my response of the inherent mishmash suggested in that quote.
socratus said:
Maybe , one of the aim of mathematical functions is to create Solar system and conditions for the living planet Earth.
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I hope, Beer w/Straw, that you do not believe we represent all life in the universe...:biggrin:
 
C C said:
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Finally, it seems clear that we will never be able to explain our most fundamental scientific principles. ​
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Why we don't able to explain ''our most fundamental scientific principles''?
Because Einstein and Infeld wrote in the book “Evolution of Physics” :
“ We have the laws, but we are not aware what the body
of reference system they belong to, and all our physical
construction appears erected on sand ”.
===
What can be reference frame for new ideas?
DISCOVER.
FROM THE AUGUST 2008 ISSUE
Nothingness of Space Could Illuminate the Theory of Everything
Could the vacuum contain dark energy, gravity particles, and frictionless gears?
By Tim Folger. Friday, July 18, 2008
'' When the next revolution rocks physics,chances are it will be
about nothing—the vacuum, that endless infinite void.''
'' Some physicists like to think that M theory will form the basis of what
they call a theory of everything, a set of laws that will completely
describe the universe in all its strangeness, where dark energy, quantum theory,
extra dimensions, and magazine readers will all fit into one tidy package.
But in the end, the key to cosmic truth may well come from another window
on reality, the looming void. A good theory of nothing just might be the
theory of everything physicists have sought for so long.''
http://discovermagazine.com/2008/aug/18-nothingness-of-space-theory-of-everything
#
Paul Dirac wrote:
'‘ The problem of the exact description of vacuum, in my opinion,
is the basic problem now before physics. Really, if you can’t correctly
describe the vacuum, how it is possible to expect a correct description
of something more complex? ‘'
/ Paul Dirac /
================
 
socratus said:
Of course we are not unique civilization.
I think, there are many similar (+/-) Earth planet in the infinite Universe: T=OK.
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Thus you are defending the position that god is a sentience which uses mathematics to purposefully evolve the universe?

Let me shorten my original answer; why would it take a sentient god to use implacacable rules of probability and mathemathematical functions to purposefully accomplish anything? And I might add the question of motive for installing such complicated methods?
 
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