Math and Reality. What is the deep connection?

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apeiron

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So even if it were true that the constants of nature were fine tuned into values compatible with life by a Universal Mind. It still can be modelled by math? It's like this. Big Bang might occur to seed life and mind. Now this can explain how our mind can tap the Mind of the universe and even make us possess the power to create/uncreate reality (nothing that Miracles occured down the centuries where Saints can bilocate (be in 2 places at once) and even levitate as well as numerous phenomena documented by many sources). So you mean all these can be modelled by math? If so, then it is part of physcis and not metaphysics (which can't be modelled by math). In other words, any measurable effects can be modelled by math, is this what you are saying?

"There are more things in Heaven and Earth, Horatio than are dreamt off in your philosophy".
OK, so now you want to make me regret taking your questions seriously :smile:.

Miracles would have to count as observables to fall within the realms of scientific discussion. So you say these things happened, but if there is no good evidence so far as the rest of us are concerned, then there is no real interest in debating the implications for theory.

And the universal mind seems to me a vacuous concept unless it can be pinned down as a formalism that is at least potentially measurable. If you can provide a source that does that for you, please do.

Peircean semiotics is for example a kind of "universal mind" approach - but nothing like what you probably mean here.

So time to source your model of the universal mind, citing some mainstream philosophical approach. But it is unlikely I would have much to say about it.
 
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OK, so now you want to make me regret taking your questions seriously :smile:.

Miracles would have to count as observables to fall within the realms of scientific discussion. So you say these things happened, but if there is no good evidence so far as the rest of us are concerned, then there is no real interest in debating the implications for theory.

And the universal mind seems to me a vacuous concept unless it can be pinned down as a formalism that is at least potentially measurable. If you can provide a source that does that for you, please do.

Peircean semiotics is for example a kind of "universal mind" approach - but nothing like what you probably mean here.

So time to source your model of the universal mind, citing some mainstream philosophical approach. But it is unlikely I would have much to say about it.
Ok. Miracles can be observable too and can be modelled by math. Now let's not discuss further on this lest this thread be locked. Let's go back to GR, SR QM and be within just its small circle. Anyway. I just found out about Brian Greene new book "The Hidden Universe
... I'm listening to MP3 now about chapter 10 called "Computers, Universes and Mathematical Reality". It sounds interesting.
 
Ok. Miracles can be observable too and can be modelled by math. Now let's not discuss further on this lest this thread be locked. Let's go back to GR, SR QM and be within just its small circle. Anyway. I just found out about Brian Greene new book "The Hidden Universe
... I'm listening to MP3 now about chapter 10 called "Computers, Universes and Mathematical Reality". It sounds interesting.
No rogerl, you don't throw out "mathematically modeled miracles" and walk away. You should be worried about your fate, not the thread's.

Please, do explain in accordance with PF guidelines or retract your claim. And roger... I'm in a mood to hurt someone, so lets not make this emotionally painful.
 
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No rogerl, you don't throw out "mathematically modeled miracles" and walk away. You should be worried about your fate, not the thread's.

Please, do explain in accordance with PF guidelines or retract your claim. And roger... I'm in a mood to hurt someone, so lets not make this emotionally painful.

Ok. I'll retract it. Mind has nothing to do with the Big Bang or the Constants of Nature. General Relativity, Special Relativity and Quantum Mechanics are the final words and we are bound to them. Our brain is just emergence of biochemistry. And the world is just pure physical, with no possibility of anything higher. If I need to delete the threads.. just let me know as one can only delete them within 2 hours.
 
Ok. I'll retract it. Mind has nothing to do with the Big Bang or the Constants of Nature. General Relativity, Special Relativity and Quantum Mechanics are the final words and we are bound to them. Our brain is just emergence of biochemistry. And the world is just pure physical, with no possibility of anything higher. If I need to delete the threads.. just let me know as one can only delete them within 2 hours.
No, this works for me. :smile:
 
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Brian Green new book is very interesting... so relevant to many of the topics we discuss like Mathematical Reality. I wonder what would happen if superstrings and branes are just figment of the imagination. Lee Smolin believes in "Trouble with Physics" that they may not be real.. instead of 20 constants of nature.. we now have over 250 constants of nature if Superstrings are real.. so maybe some other Ultimate Symmetry can bind all that can explains the constants? He who discovers it can win 2 Nobel at the same time.. lol
 

apeiron

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Brian Green new book is very interesting... so relevant to many of the topics we discuss like Mathematical Reality. I wonder what would happen if superstrings and branes are just figment of the imagination. Lee Smolin believes in "Trouble with Physics" that they may not be real.. instead of 20 constants of nature.. we now have over 250 constants of nature if Superstrings are real.. so maybe some other Ultimate Symmetry can bind all that can explains the constants? He who discovers it can win 2 Nobel at the same time.. lol
So long as you realise these guys are beating each other up over the 2% they don't agree on rather than the 98% that they do.

The 2% is of course where they make a career for themselves.
 

Ken G

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The key question may be whether we are imagining the symmetries as something we are breaking away from, or headed towards. Are they in the universe's past, or in its future?
Another duality. Perhaps it could never be one without the other-- the symmetries from our past that are breaking gives meaning to the concept of past, and the symmetries we are breaking toward give meaning to the concept of future. The duality gives meaning to the concept of time.
I think we can say the universe is a highly broken symmetry from the point of view that it is a long way from the infinite dimensional space it could be. Being 3D is a highly reduced state of affairs - very asymmetric when you compare 3 to infinity. But then a complete breaking of that infinite symmetry would be to arrive at a 0D point.

However, a point or singularity is again a highly symmetric state itself - infinity of another kind as you point out.
Yes, probably the near-symmetry is that the potentially infinite dimensional universe is "modded out" by the four dimensions of spacetime, much like the integers mod 4. The other dimensions are probably not completely gone-- there would be a hierarchy of these nearly unbroken symmetries, the nearly unbroken symmetry between time and space, and the nearly unbroken symmetry of the 11 dimensions of M-theory (if it is a valid theory). So we cannot completely mod out the dimensions above 4, but we nearly can, and most likely we could not completely mod out the dimensions above 11, but we nearly can, etc. ad infinitum. We live in the world of the most broken symmetry, the symmetry between space and time and the mod 4 symmetry of spacetime, with only ghostly hints of the higher-order much more nearly unbroken symmetries. Since we see what we understand, our minds automatically collapse those nearly unbroken symmetries into obscurity, until very careful and high energy observations resurrect them.
There are in fact two extremes of order in an ideal gas. One pole of order is where all the particles are trapped in the same small corner (and so will want to spread out randomly). The other is where all the particles are trapped in an exact lattice configuration, completely regular in their placing (the situation covered by the third law of thermodynamics).
Yes-- delta functions in the two complementary variables of "x" and "k" space. Another duality-- one gives us constructive interference with location, the other constructive interference with motion. Neither by themselves has any meaning-- location means nothing without motion to connect locations, and motion means nothing without locations to connect. Since neither can trigger recognition in us without the other, what we see as reality must involve a blend of both, a blend that is not a pure state of either. Equilibrium between the poles.

So there could be a good reason why reality ends up poised between infinite dimensionality and zero dimensionality here. There could be a logical reason for the nearly broken state (as it is in fact a fully broken or entropic state once you recognise that the extremes of symmetry or order are dichotomous and being maximally broken falls somewhere between the two states as an equilibrium balance).
Yes, and I think that reason must have to do with what we count as important, worth noting. Our intelligence has evolved to notice an incredibly tiny fraction of "what is really going on", and label it as "important", because that's how we get power over our environment, and that's how we survive. It's as much about us, about how we think about reality, as it is about reality itself (another duality-- neither would mean anything without the other).
Another quick point is that your translational symmetry argument holds true I believe only for flat space (of any number of dimensions).
Yes, symmetries in GR are local, they have differential generators rather than global ones. Not that I'm any GR expert.
 
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So long as you realise these guys are beating each other up over the 2% they don't agree on rather than the 98% that they do.

The 2% is of course where they make a career for themselves.
Have you read Smolin's "Trouble with Physics"? He wants us to go back to fundamentals and try to understand for example what made QM ticks. He even thinks the entire Superstring theory is false.. so I wonder what 98% are you talking about. I know he digs for Loop Quantum Gravity.. but he is saying quantum mechanics needs to be reinvestigated because the unification may not be along the superstring programme. Anyway. After rereading the book. I realized that there are two kinds of physicists, the realist and the other one. Einstein, Schroedinger's are realists.. like Smolin, in that they want to look for a physical side to the theory. But the other parties like Feynman, Julian, 't Hoofe... mathematical beauty is enough without regards to any physical basis or mechanism. This is why I wonder what math has to do with reality because it can give us insight if Smolin has basis of the need to look for the physical side of it or just pure mathematical investigations in the case of the others without regards for what form of structure or nature reality have take.
 
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Lee Smolin wrote about the following in Trouble with Physics (just brief quotes):

"In the approach of particle physics developed and taught by Richard Feynman, Freeman Dyson, and others, reflections on foundational problems had no place in research"

"However, as I will argue in detail in the pages to come, the lesson of the last thirty years is that the problems we're up against today cannot be solved by this pragmatic way of doing science. To continue the progress of science, we have to again confront deep questions about space and time, quantum theory, and cosmology"


Do you guys believe in Smolin approach? If Smolin is right and we don't do re-investigation of foundational problems, we will never have any TOE. So it's NOT like we have to find the TOE first and then contemplate on the insight later. I still can't decide if Smolin is right or wrong.. and this is why I asked the initial questions in the thread.
 
Lee Smolin wrote about the following in Trouble with Physics (just brief quotes):

"In the approach of particle physics developed and taught by Richard Feynman, Freeman Dyson, and others, reflections on foundational problems had no place in research"

"However, as I will argue in detail in the pages to come, the lesson of the last thirty years is that the problems we're up against today cannot be solved by this pragmatic way of doing science. To continue the progress of science, we have to again confront deep questions about space and time, quantum theory, and cosmology"


Do you guys believe in Smolin approach? If Smolin is right and we don't do re-investigation of foundational problems, we will never have any TOE. So it's NOT like we have to find the TOE first and then contemplate on the insight later. I still can't decide if Smolin is right or wrong.. and this is why I asked the initial questions in the thread.
I think you should look at what QM has correctly predicted, despite detractors and want of a single Interpretation. Then, you draw your own conclusions, I'm not sure there is a right one.
 

apeiron

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Do you guys believe in Smolin approach? If Smolin is right and we don't do re-investigation of foundational problems, we will never have any TOE. So it's NOT like we have to find the TOE first and then contemplate on the insight later. I still can't decide if Smolin is right or wrong.. and this is why I asked the initial questions in the thread.
I think Smolin is right (along with Laughlin, Prigogine and other good critics of the reductionist status quo). Something is lacking, and it is a systems perspective. :wink:

But equally, that does not obselete all that has been achieved with reductionist approaches - all the varieties of mechanics like quantum mechanics, classical mechanics, relativistic mechanics, statistical mechanics.

These models are good, simple and effective. So whatever comes along as a TOE has to be able to incorporate these various models - and indeed incoporate reductionism as a metaphysics.

My only beef with Smolin is that he has not really understood the systems view (he just seems busy trying to reinvent it eventually).

So it is about re-investigating the foundations of science's metaphysics. And it is something high energy physicists ought to be doing (as biologists, for instance, have already done it).

Replacing particles with strings or loops is still thinking like atomists. But replacing particles with resonances or solitons is thinking like a systems thinker.

Yet what you can guarantee is that a re-investigation is not going to replace atomism with any kind of supernatural ontology, like the mind of god or whatever. Well, given what some physicists will say to sell their books, perhaps this cannot be promised :smile:.
 
As if, were there a god, we'd want to know its mind. Sounds to me like a rather frightening proposition, I'd prefer nature red in tooth and claw.
 

Ivan Seeking

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Lee Smolin wrote about the following in Trouble with Physics (just brief quotes):

"In the approach of particle physics developed and taught by Richard Feynman, Freeman Dyson, and others, reflections on foundational problems had no place in research"

"However, as I will argue in detail in the pages to come, the lesson of the last thirty years is that the problems we're up against today cannot be solved by this pragmatic way of doing science. To continue the progress of science, we have to again confront deep questions about space and time, quantum theory, and cosmology"


Do you guys believe in Smolin approach? If Smolin is right and we don't do re-investigation of foundational problems, we will never have any TOE. So it's NOT like we have to find the TOE first and then contemplate on the insight later. I still can't decide if Smolin is right or wrong.. and this is why I asked the initial questions in the thread.
So, according to Smolin, in order to fine a TOE, you have to put the shoe on the other foot?
 
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I think Smolin is right (along with Laughlin, Prigogine and other good critics of the reductionist status quo). Something is lacking, and it is a systems perspective. :wink:

But equally, that does not obselete all that has been achieved with reductionist approaches - all the varieties of mechanics like quantum mechanics, classical mechanics, relativistic mechanics, statistical mechanics.

These models are good, simple and effective. So whatever comes along as a TOE has to be able to incorporate these various models - and indeed incoporate reductionism as a metaphysics.

My only beef with Smolin is that he has not really understood the systems view (he just seems busy trying to reinvent it eventually).

So it is about re-investigating the foundations of science's metaphysics. And it is something high energy physicists ought to be doing (as biologists, for instance, have already done it).

Replacing particles with strings or loops is still thinking like atomists. But replacing particles with resonances or solitons is thinking like a systems thinker.

Yet what you can guarantee is that a re-investigation is not going to replace atomism with any kind of supernatural ontology, like the mind of god or whatever. Well, given what some physicists will say to sell their books, perhaps this cannot be promised :smile:.
Where did you hear about replacing particles with resonances or solitons? Any references? Superstrings is the only game in town. If it was false, everything flows down the drain and millions of dollars lost (in institution fundings). Our last great breakthrough in physics occured in 1973. After that. It's just about properties of materials, physics of biology, dynamics of vast clusters of stars. We didn't have new fundemental discovery like the Dirac Equation or unification of electric and magnetic field. The Large Hadron Collider can spell the difference but they decrease it from 14Tev to mere 7Tev from the SCC plan of 40Tev in the 1980s. What if new phenomenon occurs at 8Tev, Then we miss it.
 
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Where did you hear about replacing particles with resonances or solitons? Any references? Superstrings is the only game in town. If it was false, everything flows down the drain and billions of dollars lost. Our last great breakthrough in physics occured in 1973. After that. It's just about properties of materials, physics of biology, dynamics of vast clusters of stars. We didn't have new fundemental discovery like the Dirac Equation or unification of electric and magnetic field. The Large Hadron Collider can spell the difference but they decrease it from 14Tev to mere 7Tev from the SCC plan of 40Tev in the 1980s. What if new phenomenon occurs at 8Tev, Then we miss it.
You're so wrong in so many ways it makes my head spin. The LHC is mostly probing for another particle to fit the standard model... only indirectly in ANY way MIGHT it support string theory... and that's unlikely. Keep reading.
 

apeiron

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Where did you hear about replacing particles with resonances or solitons? Any references?
I thought you were reading Smolin's Trouble?

Even he mentions Laughlin, Volovik, Xiao-Gang Wen, and Olaf Dreyer - see p247.

Superstrings is the only game in town. If it was false, everything flows down the drain and billions of dollars lost. Our last great breakthrough in physics occured in 1973. After that. It's just about properties of materials, physics of biology, dynamics of vast clusters of stars. We didn't have new fundemental discovery like the Dirac Equation or unification of electric and magnetic field. The Large Hadron Collider can spell the difference but they decrease it from 14Tev to mere 7Tev from the SCC plan of 40Tev in the 1980s. What if new phenomenon occurs at 8Tev, Then we miss it.
This is sounding hysterical now. I mean superstrings might believe it is the only game in town but...:frown:

I agree that money could have been much better spent supporting systems science of course. Yet the LHC is still going to probe the EW breaking scale and find something important. That seems like 90 percent certain. If it is not the Higgs, not Susy, it still has to be something going on at that energy scale.

You have to admit that you don't actually know much about the physics you want to criticise. That is plain in that you are quoting from popularisations and have made some very basic mistatements.

That is not a problem if you are just interested in learning. But you have to earn the right to be as critical as you are now being.

Smolin may sound critical, but he of course has earned the right - and his criticisms are not exactly what you seem to think.
 

Ken G

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Certainly it is hoped that the LHC might find new phenomena not currently predicted, which would reinvigorate the need to discover fundamentally new theories. The fact that it would probably not interface with string theory is what many view to be the primary problem with string theory-- it's just too far from what we can observationally constrain.
 
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I thought you were reading Smolin's Trouble?

Even he mentions Laughlin, Volovik, Xiao-Gang Wen, and Olaf Dreyer - see p247.



This is sounding hysterical now. I mean superstrings might believe it is the only game in town but...:frown:

I agree that money could have been much better spent supporting systems science of course. Yet the LHC is still going to probe the EW breaking scale and find something important. That seems like 90 percent certain. If it is not the Higgs, not Susy, it still has to be something going on at that energy scale.

You have to admit that you don't actually know much about the physics you want to criticise. That is plain in that you are quoting from popularisations and have made some very basic mistatements.

That is not a problem if you are just interested in learning. But you have to earn the right to be as critical as you are now being.

Smolin may sound critical, but he of course has earned the right - and his criticisms are not exactly what you seem to think.
Oh. When I mentioned billions of dollars down the drain. Of course I didn't mean the Large Hadron Collider. I mean all the Ph.Ds and research programs and research funding all over the world is on superstring theory. Lee Smolin mentions that. This is the context of what I meant billions are down the drain (or more like million of dollars).


Anyway. I read Smolin book a few years back and now just rereading it and at the same time listening to Brian Greene new book in mp3. Also I mostly forgot what I read after a few months.

I just want to know how math is related to reality. In the initial message of this thread. I wonder how our reality can work with the dirac equation enough to predict the existence of the positron. This is not answered and my title was supposed to be "why does dirac equation work?" but changed it last minute. I mean. In newtonian mechanics, trajectory can be modeled by math, but dirac equation, it's very abstract and yet reality can conform to it. Why. This is what I simply want to know.

I own about 50 pop-sci books like Lisa Randall Warped Passage so I know stuff like the Hierarchy Problem but I still don't know how math correponds to reality, which is not discussed in most of the books.

About the LHC. I know Higgs, Supersymmetry is its main target. But it also can detect missing energy enough to discover hidden dimensions.. which could say a thing or two about whether Superstrings are on the right track or not.
 
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You're so wrong in so many ways it makes my head spin. The LHC is mostly probing for another particle to fit the standard model... only indirectly in ANY way MIGHT it support string theory... and that's unlikely. Keep reading.

Oh. When I mentioned billions of dollars down the drain. Of course I didn't mean the Large Hadron Collider. I mean all the Ph.Ds and research programs and research funding all over the world is on superstring theory. Lee Smolin mentions that. This is the context of what I meant billions are down the drain (or more like million of dollars).
 
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Admit that millions of dollars given in institution funding can go down the drain if string theory is wrong. Smolin said that "The aggressive promotion of string theory has led to its becoming the primary avenue for exploring the big questions in physics. Nearly every particle theorist with a permanent position at the Prestigious Institute for Advanced Study, including the director, is a string theorist... "" The same is true of the Kavli Institute of Theoretical Physics. Eight of the nine MacArthur Fellowships awarded to particle physicists since the beginning of the program in 1981 have also gone to string theories. And in the country's stop physics departments (Berkeley, Caltech, Harvard, MIT, Princeton, and Stanford), twenty out of the twenty-two tenured prefessors in particle physics who received PhDs after 1981 made their reputation in string theory or related approaches".

Sorry for quoting it (would quote no more). I pay big taxes and don't want it down the drain. Had they contribute the money instead on the SCC funding in the 1980s. We could already have answers. What they do instead is kill thousands of civilians in Iraq with the money! So what do you say we rally in front of the Senate.. lol.. just kidding...

If the LHC misses on the higgs and supersymmetry and the new phenomenon occurs at the 15Tev. Then we may miss it in our lifetime. And for some of us.. it is unacceptable. TOE can benefit our lives greatly. I want it to happen in my lifetime. Don't you?
 
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My only beef with Smolin is that he has not really understood the systems view (he just seems busy trying to reinvent it eventually).

Perhaps he has understood what others have failed in his field - that probing the limits of reality is actually asking "What is existence?"

Having read the book, i'd say that Smolin does understand that the primitive view of an ever-expanding, existential solid piece of matter(we happen to call Universe) existing into the uncreated and non-existent void(we naively call "non-existence") is deeply wrong.

The problems with QM are problems of existence(what it is and how it takes place - it turns out existence is much weirder), not ones of reality.

We don't have to separate reality from existence and I don't think that we can continue the pursuit to understand reality and leave existence to philosophy. Because they are actually one and the same. There is no difference between reality and existence, is there?
 
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[...]but I still don't know how math correponds to reality[...]
Welcome to the club! Nobody KNOWS for sure, but it certainly is not something simple. You set out to learn science because you think you will get all of "The Answers", as though the world were a collection of answers, but this is never what happens. I don't know why this is a popular way to think, is it slightly fed by the way education is presented? As a static body of facts? I don't know. Point of the random rant is, you must seek to view things from a new perspective and thing about things in new ways and understand the complex relationships between things rather than look for The Answers.

No, the money will not be "wasted". Wrong doesn't mean "wasted" science needs wrong, it provides perspective on how nature works. Just because it isn't "The Answer" doesn't mean it doesn't help us think about reality in a new way. Doesn't mean it hasn't spawned useful research and developed new mathematics.

I pay big taxes and don't want it down the drain
Oh please! Now your being nitpicky. Of all the things you could worry about for where your tax money goes your worrying about the tiny percentage that goes to string theory? I have no stats, but considering Science funding as a whole is tiny compared to where your money goes, string theory is nothing. Complain about something else, don't use your precious money as a justification for why it is "wasted".


TOE can benefit our lives greatly. I want it to happen in my lifetime. Don't you?
TOE? Popular books seem to peddle the TOE, what makes you think the TOE is even possible? What is a TOE? Some magical machine that if we put numbers in we get some laplacean universe where we know everything? Why do you seek to know everything?

It seems you think science is in some one-to-one correspondance with how nature "actually is" and once we find the right equations we have "figured out" lawful reality. Maybe maths relation to reality seems so confusing to you because you believe they are at opposite ends of a dichotomy. Physics is "concrete" and Math is "abstract". Look closer and you may find that the boundaries between black and white are not quite so defined.

Perhaps Maths is a psychological tool we use to conceptualize the world, and we use experimentation to act in the world and subject phenomena to a greater number of combinations and theorize about them.

Gasp! but then everything I think about what science is telling me could be false?
Maybe, depending on what false is, what your conceptions of truth are and if science is even actually telling you that as opposed to you reading that into science?


Sorry for quick rant, I don't mean to sound harsh if I do that isn't my intent. Please be willing to fundamnetally alter the way in which you view reality. If you are not willing to do that, you don't want "The Answers" all that much.
 

Ken G

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And another way to make that point is, science is not supposed to be about replacing evidence-free belief systems with evidence-based belief systems, it is supposed to be about a completely different attitude toward the meaning of what "truth" is. It starts with a healthy skepticism that there is any such thing as truth, other than a "current state of understanding." I've never liked "TOE" language because it's really a false lesson in science.
 

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