Balancing theories and empirical data, especially concerning string theory

[jaketodd]

The following discussion is from reading this short paper:

The dangers of non-empirical confirmation
https://arxiv.org/abs/1609.01966

The following are quotes from the paper, and my observations and questions.

"excessive reliance on non-empirical evidence compromises the reliability of science"
However, many theories turn into fact, and so we can't dismiss them as useless before they are matured.

What is it about string theory that seems so unconvincing? Maybe the fact that it's been in existence for decades, with still no empirical data?

"Scientists have always relied on non-empirical arguments to trust theories"
Not truly ethical scientists.

"powerful theoretical, non-empirical, motivations for creating, choosing and developing theories"
Yes, when established fact points in the direction of something new, that's a lot better than just convoluted complexity.

"In Bayesian theory, “confirmation” indicates any evidence in favour of a thesis, however weak"
The however weak support might just be how many people a "scientist" can convince, mystify, and create followers.

"Bayesian confirmation theory allows us to talk about the spectrum of intermediate degrees of credence between
theories that are “confirmed”, in the common sense of the word, or “established”, and theories which are still
“speculative”, or “tentative”. But doing so it obfuscates precisely the divide that does exist in science between a
confirmed theory and a tentative one. We trust the existence of the Higgs particle, which is today the weakest of
the confirmed theories, with a 5-sigma reliability, namely a Bayesian degree of confidence of 99.9999%. In their domains of validity, classical electrodynamics or Newtonian mechanics are even far more reliable: we routinely entrust our life to them. No sensible person would entrust her life to a prediction of string theory."
It seems like these scientists are way over-eager to accept and proliferate theories, which are interesting, but don't have enough, if any, empirical data, even after plenty of time for those theories to produce experiments, which can test them.

"Why is this relevant for non-empirical confirmation? Because non-empirical evidence is emphatically insufficient to increase the confidence of a theory to the point where we can consider it established; that is, to move it from “maybe” to “reliable”"
Although, if a theory, even if not supported by empirical data, is strongly implied by existing confirmed fact, then that does half the work of calling a new theory good.

"we all tend to be blinded by our beliefs"
Confirmation bias, and the power of suggestion.

I think a lot of scientists, and especially string theorists, escape into complexity - betting that no one has the incredibly advanced math to disagree with them. But the lack of empirical data speaks volumes, even if you don't understand all their advanced math.

"string theorists commonly claim that string theory has no alternatives (“the only game in town”)"
Sounds like turf protection. Publish, and convince, or perish.

"Scientists that devoted their life to a theory have difficulty to let it go, hanging on non-empirical arguments to save their beliefs, in the face of empirical results that Bayes confirmation theory counts as negative."
Devotion without skepticism is a beast, especially when you have a wild card theory that is so nebulous, that it can never be proven wrong. And, by this same token, can never be proven right; because it can just morph into a form that isn't proven right.

I did a check, and there still isn't any empirical, experimental evidence for string theory.

So, what do you guys think about all this, and string theory? If you want to talk about other areas of physics theory that are related to these ideas, start a new thread, and let me know, so I can read it.

Thanks!

Jake

 

[Demystifier]

String theory is really a formal science, even though it is usually not classified so. A formal science does not need to be empirical. https://en.wikipedia.org/wiki/Branches_of_science

 

[mitchell porter]

Except for neutrino masses, the empirical framework of particle physics has been the same for fifty years - the "standard model".

This is not due to theoretical stagnation - it just turned out that all reproducible particle phenomena for the next fifty years, fit into the framework that came together in the 1970s.

One way to put it, is to say that all phenomena up to experimentally accessible energy levels, involve standard model fields and particles, and nothing else.

What empirical clues do we have to guide us? There's gravity. There are the ambiguous clues from astrophysics and cosmology. There is the technical structure of the standard model - the symmetry groups and fermion representations. And then there are the two-dozen unexplained parameters, whose values are assumed, in order to predict everything else - the coupling constants and particle masses.

That's the empirical guidance that we have. Meanwhile, what theoretical ideas do we have?

For gravity, we have general relativity. For everything else, we have gauge theory, a kind of quantum field theory. And then we have an enormous amount of work on generalizations of these theoretical concepts, that includes "grand unification" and "supersymmetry", and whose apex is string theory.

There are also a variety of other theoretical frameworks, but with a few notable exceptions (that can actually be subsumed into string theory), they don't actually work that well.

It is actually a natural thing, to try to explain all the features and parameters of the standard model, as arising from a string theory vacuum. String theory has all the right ingredients, and in principle, once you choose a "vacuum" (e.g. a shape for the extra dimensions), that will determine what all the couplings and masses are.

However, there are a few problems for this agenda. Foremost is that there is some enormous number of string vacua, and in practice, it is incredibly hard to calculate the couplings and masses for any given vacuum. They depend e.g. on the values of extra-dimensional radii, and other geometric quantities, that minimize the energy of a given extra-dimensional shape, and those problems are very hard. For them to become tractable will probably require a combination of mathematical conceptual advances and artificial intelligence estimation techniques.

There are also some other problems, which could in the end turn out to be hints for how to progress, without just doing a brute-force march through a googolplex string vacua, looking for the real world.

The fact that nothing but standard model particles have turned up, is not just frustrating for physicists seeking fresh empirical guidance, it is actually somewhat perplexing. Before the Higgs boson was actually found, theorists thought they had figured out that heavy virtual particles would render the Higgs itself untenably heavy, unless there was some symmetry among the new particles that made these virtual influences cancel out. It was therefore expected that along with the Higgs, other new particles with similar masses would turn up, such as supersymmetric partners of known particles.

For string theory, this meant that the "phenomenologists", the string theorists who try to identify string vacua that are empirically promising, also worked under the assumption that they needed to find supersymmetric models in which supersymmetry was broken at energies close to the "Fermi scale", where the Higgs and the other known particles live.

But instead, the Higgs turned up alone, without any partners, and at an oddly meaningful value of the mass, all of which suggests that some quite unfamiliar finetuning mechanism is at work. This is a problem not just for string theorists, but also for the field theorists who are the actual majority of particle theorists. New ideas are needed, new ideas are being produced (though of course opinions vary on which, if any, are good ones), and the implication for string phenomenology is, that string theorists need to be looking at vacua somewhat different to the ones they have been looking at until now.

I could go on to talk about other clues that are being neglected, but these become increasingly arcane or controversial, whereas there is a fairly broad consensus that the absence of other new particles at the Fermi scale is a big clue that something unexpected is at work.

I'll mention one other thing, which is that the physics of quarks and gluons is already very string-like, and in fact string theory originally emerged from attempts to model the hundreds of different types of short-lived particles that were discovered in nuclear physics from the 1950s forwards. Those early string models were eventually replaced by the theory of quarks and gluons, but decades later, people began using string theory (in its modern form) to approximate the complexities of subnuclear physics once again. This is a kind of backdoor approach to obtaining the standard model from string theory, whose potential is greatly underappreciated in my opinion.

There's a lot more I could talk about, but to sum up, string theory is deservedly alive and well, but the 1980s triumphalism that was popularized by string theorists like Brian Greene and Michio Kaku was dealt a blow - along with all other ideas regarding physics beyond the standard model - in the years after 2012, when the Higgs turned up alone, against the expectations of almost all theorists, inside and outside string theory. Instead of being guided to the next level of physical understanding by a plethora of new supersymmetric particles, we face the more austere challenge of extracting deeper insight from what we already knew - the couplings, the particle masses, the anomalies in astrophysics and cosmology. There is plenty of opportunity for hard work and genius insights to produce a breakthrough here, there are plenty of people still trying to make progress, and only time will tell which, if any, will successfully take us "beyond the standard models".

 

[Structure seeker]

String theory is a framework in which theories can be thought up and is very useful as such. The problem is only that nobody seems to know (or even to care) how to make a string theory that gives the Standard Model.

 

[malawi_glenn]

and is very useful as such

Examples?

 

[Structure seeker]

Examples?

I can explain it by a parallel: thanks to Newton we can simulate galactic and cosmological history. This makes it possible to check general things like whether enough spiral galaxies appear in a certain theory of cosmological history like Lambda-CDM. If we want to use a different dynamical model (not based on Newton) there must be good reasons for it, such as relativistic speeds or too high temperatures.

The same way, string theory is a framework that only allows certain sets of elementary particles. If we want to use a particle set that is not allowed in string theory, we must devise another framework that validates the possible existence of elementary particles or extend string theory to allow for it. Or you should give a reason why such a framework does not exist. If these conditions are not met, there remains space for deeper fundamental understanding.

Of course, string theory is not proven yet. However that does not demotivate the enthusiasm that came from the unexpected theoretical discoveries of unification, M-theory dualities and such. There is more reason to examine string theory besides the (not yet apparent) practical applications. Even if it only gives new math without current applications. It's a real deep dig for truth, and it can therefore be expected that it lasts a long time before practical applications arise. Just look at Maldacena's result that could describe dynamics near a black hole due to the AdS-CFT correspondence.

 

[malawi_glenn]

AdS-CFT correspondence you say, that is one example. I do not think that makes string theory qualify as "very useful".

String theory for me, is like math - a formal science - as @Demystifier put it.

 

[mitchell porter]

nobody seems to know

There are enormous numbers of string models that produce standard model fields at low energies. However, the counterparts of standard model parameters, in those string models, are hard to calculate. Most of them are going to be standard models in which the basic fields are right but the couplings and masses are all wrong.

As I mention in #3, one way to deal with this is to just grimly march through all the known possibilities, with the assistance of mathematicians and machine learning, trying to calculate enough to test or falsify each in turn. In a preliminary form, this kind of effort has already been underway for years, as computers are used to search the enormous number of possible modeels.

However, most work on the empirical side is still done by human beings looking for string models that have some qualitatively appealing feature, like small dark energy or a heavy top quark.

or even to care

The annual conference on this topic starts next week in Korea.

 

[Fra]

It is actually a natural thing, to try to explain all the features and parameters of the standard model, as arising from a string theory vacuum. String theory has all the right ingredients, and in principle, once you choose a "vacuum" (e.g. a shape for the extra dimensions), that will determine what all the couplings and masses are.

However, there are a few problems for this agenda. Foremost is that there is some enormous number of string vacua, and in practice, it is incredibly hard to calculate the couplings and masses for any given vacuum.

For them to become tractable will probably require a combination of mathematical conceptual advances and artificial intelligence estimation techniques.

It has always been my opinion that the above "problem" is created because string theory avoids addressing some fundamental problems already in QM foundations, such as the role of the observer. In string theory the background "is" implicitly the observer, and this is exactly where there seems to be so many choices that we are a bit lost. And the reason the background is given, is in order to be conservative, as anything else risks deforming alot of the QM foundations.

I think this is not just a mahtematical problem but a deeper, conceptual one. Within string theory I guess this would relate to possible interpretations of "physics" of selection of backgrounds, in a nonperturbative model, but what progress is there here? Do most string theorists consider this landscape problem as a mathematical problem??

The angle I would enjoy seeing from actual string theorists here, I have never seen, so I think it takes a different paradigm of thinking about this?

/Fredrik

 

[jaketodd]

String theory is really a formal science, even though it is usually not classified so. A formal science does not need to be empirical. https://en.wikipedia.org/wiki/Branches_of_science

I looked that up. So, you mean string theory is purely mathematical? Math is beautiful, but without experimental confirmation... right?

 

[jaketodd]

However, there are a few problems for this agenda. Foremost is that there is some enormous number of string vacua, and in practice, it is incredibly hard to calculate the couplings and masses for any given vacuum. They depend e.g. on the values of extra-dimensional radii, and other geometric quantities, that minimize the energy of a given extra-dimensional shape, and those problems are very hard. For them to become tractable will probably require a combination of mathematical conceptual advances and artificial intelligence estimation techniques.

A lot of this is over my head. But, using artificial intelligence to work on physics is extremely compelling to me.

Thank you!

 

[jaketodd]

Is string theory continuous or discrete?

Thanks

 

[malawi_glenn]

Is string theory continuous or discrete?

In what sense?
Now you are off on a tangent, again, like all in all your other threads.

Before even making this thread, what was your current understanding of string theory?

 

[Vanadium 50]

Is string theory continuous or discrete?

The papers come one at a time, so it is discrete.

 

[jaketodd]

In what sense?
Now you are off on a tangent, again, like all in all your other threads.

Before even making this thread, what was your current understanding of string theory?

I'm sorry. I really am. I didn't mean to go off on a tangent. I was just wondering if there are smallest units to strings. So please forget my question, and let's stay on topic, like you recommend.

Again, I apologize!

 

[Demystifier]

I looked that up. So, you mean string theory is purely mathematical? Math is beautiful, but without experimental confirmation... right?

Not exactly. First, math is not the only formal science. Second, math is not without a confirmation; just the opposite, a proof of a theorem is the strongest form of confirmation that humans ever developed.

 

[Fra]

I'm sorry. I really am. I didn't mean to go off on a tangent. I was just wondering if there are smallest units to strings. So please forget my question, and let's stay on topic, like you recommend.

Again, I apologize!

In the normal construction of string theory, the strings are by assumption elemetary continous strings.

Wether this makes sense to postulate is a different question. I'm not a string advocate, but when I try to "meet" string theory from my own preferred stance, it is alot easier to make sense of for me at least, of one assumes that the continous string really is an "approximate" in a high complexity limit of something simpler that can be related to distinguishable discrete events. The problem is that a whole continous string embedded in a higher dimensional space, obvious encode ALOT of information! And just way too much to be palatable as a starting point IMO. It if wasn't for the higher dimensional space, it would be just about as unpalatable as using the real number as a starting point for conditional probability theory. It is a valid embedding yes, but the embedding is too large, so it we get lost in the structure of the embedding strucutre.

Not sure how many inside the string community that entertain these ideas though.
But related papers...

Reformulating String Theory with the 1/N Expansion
"We argue that string theory should have a formulation for which stability and causality are evident. Rather than regard strings as fundamental objects, we suggest they should be regarded as composite systems of more fundamental point-like objects. A tentative scheme for such a reinterpretation is described along the lines of 't Hooft's 1/N expansion and the light-cone parametrization of the string."
-- https://arxiv.org/abs/hep-th/9405069

Stable String Bit Models​

"In string bit models, the superstring emerges as a very long chain of "bits",in which s fermionic degrees of freedom contribute positively to the groundstate energy in a way to exactly cancel the destabilizing negativecontributions of d=s bosonic degrees of freedom....
"
--https://arxiv.org/abs/1402.7362

/Fredrik

 

[jaketodd]

Not exactly. First, math is not the only formal science. Second, math is not without a confirmation; just the opposite, a proof of a theorem is the strongest form of confirmation that humans ever developed.

But a proven beautiful math theorem is only even better if it can be directly linked to reality.

 

[jaketodd]

For example, Cantor's work. Different sized infinities are very compelling, especially the absolute infinite. But are those proofs ever linked to observable phenomena? Or is it purely mathematical philosophy?

 

[Fra]

The way I see it - conceptually - good mathematical representations and theories is dualy related to reality in terms of their economy of information capacity resources, such as memory and computational capacity.

If you alot of memory but very little processing power, certain dual formulations my be more "economical" than if you have small memory but high processing power. But given time, they can come to to the same answer. I think of this as a more specific implementation of the normally fuzzy occams razor. Ie. what is the simplest solution, may well depend on the observer. Which in turn translates into understanding what observers are likely abundant in nature as they are the ones that naturallly select the optimal representations.

In this abstract sense, there is a connection with abstract frameworks such as string theory or similar ones and reality, but this connection is I think mainly a tool for theorists that should prove itself by finding the answers faster than those lacking the tool.

So the abstract mathematics beeing useful in physics hopefully tells us something about nature, otherwise it would not be useful. But it is easy to mix up the complexions of nature, and the complexions of the embedding theory. This is I think what happens and why we have problems with renormalizations that lead to finetuning when cured.

/Fredrik

 

[ohwilleke]

A few thoughts.

1. There are lots of string theory vacua, but it has recently become clear that the vast majority of them are in the Swampland, i.e. inconsistent with quantum gravity.

2. There are strong hints that supersymmetry (which folk theorems say is always present in realistic version of string theory) does not exist and there are either no BSM particles or very few BSM particles (gravitons and maybe also a gravitino, or something related to neutrinos, or cosmological inflation .or one or two related to dark matter/dark energy).

3. There are strong hints that dark matter and dark energy are gravitational/modified gravity phenomena without needing any new particles.

4. The SM is mathematically consistent up to the GUT scale.

5. Gauge unification is increasingly disfavored empirically.

6. Majorana mass neutrinos which are favored strongly by string theorists, may not be a thing. There is thus far no positive evidence for them.

7. The hunt for GUTs is coming up empty after several decades of concerted efforts. But, any string theory should have a GUT-like portion once you disregard the gravitational side.

In short, the SM is looking more and more complete or very nearly so. For a long time sting theorists were looking for new particles to be dark matter or dark matter sector candidates and put the SM on the path towards gauge unification, and that isn't panning out. So, full fledged M-theory seems more and more unlikely given what we know.

But, making a theory that parsimoniously includes the SM and a GR-like quantum gravity and almost nothing else is much harder than making a theory that includes them and also a lot of other junk that we have no evidence for the existence of.

It would be really nice to be able to take the SM plus string theory approaches to quantum gravity together and ditch the rest, but string theory seems to be a package deal.

 

[Fra]

A few thoughts.

1. There are lots of string theory vacua, but it has recently become clear that the vast majority of them are in the Swampland, i.e. inconsistent with quantum gravity.

So far the landscape, once you disregard the swampland is still too large. This isn't my area but I think the idea of the swampland program is to make the constraints stronger and stronger, so that at high energies the landscape is grossly narrowed down, to the point where it's managable.

This in itself, makes sense to me, as even from the perspective of interacting agents, "high energy" has a natural dual view that can be understood without string theory. If an observer/agent studies increasinly higher energies, it means that observer-side of the cut, must be able to encode all this energy, and generate the high energy probes etc. But at the same time when looking at the hamiltonian, which supposedly describes "interacting agents" (which here is synonmous to the elementary particles) they are bound to get smaller and smaller, the higher the energy from the perspective of hte first agent. So; the "inside view" is expected to become simpler and correspond to "low complexity" of the inside agents. This is the trick that might "constrain" or be used to select among the possible high-energy pictures from the first observer. So the lower possible mass limit of the inside view, should match the highest possible energy limit from the external perspective. Ideally this should prevent us from a landscape problem?

But the way this is attempted in string theory seems quite ad hoc, and I have so far never seen a string paper that brings clarity to this. I rather view it as a messy pathwork of mathematical conjectures, that one tries to make fit together without any conceptual understanding. This is my main objection to the string program and which is why I have no motivation for it.

This is actually why I find some ideas behind emergent strings from discrete sets, more appealing.

/Fredrik

 

[jaketodd]

https://link.springer.com/article/10.1007/s10701-022-00601-w

"The transcendental expectation of string theory is that the nature of the fundamental forces, particle spectra and masses, together with coupling constants, is uniquely determined by mathematical and logical consistency, non-empirically..."

Some years ago, Gerard 't Hooft posted "How to Become a Good Theoretical Physicist", which is more inclusive than just string theory but which you'll probably still find a valuable list. Here's what he recommends for mathematics:

https://physics.stackexchange.com/a/195051

The math foundations needed to understand string theory:
"Primary Mathematics":

Natural numbers: 1, 2, 3, …
Integers: …, -3, -2, -1, 0, 1, 2, …
Rational numbers (fractions): 1/2, 1/4, 3/4, 2379/1773, …
Real numbers: Sqrt(2) = 1.4142135… , π = 3.14159265… , e = 2.7182818…, …
Complex numbers: 2+3i
, eia=cos(a)+isin(a)
, … they are very important!
Set theory: open sets, compact spaces. Topology. You may be surprised to learn that they do play a role indeed in physics!
Algebraic equations. Approximation techniques. Series expansions: the Taylor series.
Solving equations with complex numbers. Trigonometry: sin(2x)=2sin x cos x, etc.
Infinitesimals. Differentiation. Differentiate basic functions (sin, cos, exp).
Integration. Integrate basic functions, when possible. Differential equations. Linear equations.
The Fourier transformation. The use of complex numbers. Convergence of series.
The complex plane. Cauchy theorems and contour integration (now this is fun).
The Gamma function (enjoy studying its properties).
Gaussian integrals. Probability theory.
Partial differential equations. Dirichlet and Neumann boundary conditions.

"Advanced Mathematics":

Group theory, and the linear representations of groups
Lie group theory
Vectors and tensors
More techniques to solve (partial) differential and integral equations
Extremum principle and approximation techniques based on that
Difference equations
Generating functions
Hilbert spaces
Introduction to the functional integral
There is almost nothing on these lists that's jumps out at me as unnecessary for string theory, with the possible exception of probability theory (and even then, it's so baked in to quantum mechanics that it'd be hard to leave it out.)

--

From all of this, it seems conclusive that a) string theory has no empirical evidence, and b) the string theorists retreat into the complexity of their math when threatened. There's an old saying that "nothing gets them more than the things they don't understand."

 

[Fra]

https://link.springer.com/article/10.1007/s10701-022-00601-w

"The transcendental expectation of string theory is that the nature of the fundamental forces, particle spectra and masses, together with coupling constants, is uniquely determined by mathematical and logical consistency, non-empirically..."

My biggest problem is not that vision, but that the starting point of string theory already has a bit too much baggage so that that it brings us into a fine tuning trap where the there is no method of determination of the constant. Probably because it's supposedly a "conservative" extension of QFT, where one just replaces the point with a compactified string. And there is to my knowledge no conceptual guidance or motivation for these "strings", like what is the conceptual meaning of this "string"? In intro string theory texts, the introduction of the litteral string is extremely naive. It's basicallay litteraly a classical string. One empirically originated idea to "strings" was some early attempts to describe the strong interactions in the 60s, but now we have QCD.

If you ignore the conceptual and foundational weaknesses just build from it, things get of course extremly complicated and one can loose the perspective. One thing that IS interesting that has occured to be several times, but that I never seen in a string paper, is that the step from point to string, may the step from the discrete to the continuum in disguise - can we understand this in a different way? For example in terms of constructing probability theory from discrete events? IF anyone can point to a string paper that explores this, I would be interested in that.

/Fredrik

 

[jaketodd]

Ya, "strings" seem pretty arbitrary to me too. I saw a documentary that covered it a bit. It basically said that some guy, randomly reading a document, found some mathematical version of a "string," and that's how it all started with string theory. Pretty much unsubstantiated and meaningless, but they hide behind all their advanced math. Publish or perish.

I think calling a point discrete and a string continuous, is letting them blind you. Points have no size. So, if anything, points are continuous, and strings (I'm assuming having size), are discrete, if they really are fundamental. Having a minimum size means discrete.

 

[Fra]

I think calling a point discrete and a string continuous, is letting them blind you. Points have no size. So, if anything, points are continuous, and strings (I'm assuming having size), are discrete, if they really are fundamental. Having a minimum size means discrete.

I will not attempt to elaborated it but a vague hint to stimulate own thinking is in an interesting old blog from John Baez.

https://math.ucr.edu/home/baez/nth_quantization.html

It puts the question in an perspective, where one can consider how uncertainty or quantizations steps can be iterated, to increase dimensionality, so one can assiate orders of quantization p-branes.
0-brane ~ a point
1-brane ~ string
2-brane ~ membrane

What i find interesting is the probabilistic part of the quantization, and that it can be interated. Then one can ponder around this, and maybe find some interesting ideas, that relates a distinguishable state, between a continuum of distinguishable states.

/Fredrik

 

[jaketodd]

0-brane ~ a point
1-brane ~ string
2-brane ~ membrane

So, the string theorists are trying to claim both continuous (0-brane) and discrete perspectives (>=1-brane)?

 

[jaketodd]

Are 0-branes considered basic and continuous, and the higher dimensional branes built on the 0 ones?

 

[Structure seeker]

As far as I can understand 0-branes are the usual non string theory particle models and n-branes are considered as model for any n that might be interesting. I think most models assume all particles to be the same n in the model as n-brane, but not sure. It just seems logical because most models want to retrieve 10D string theory and n is then the number of dimensions minus 9.

The number of dimensions when a string is a hollow tube 2-brane or somehow an n-brane is fixed for n fixed, because anomaly cancellation happens perfectly only in that dimension.

 

[jaketodd]

How does a person construct a discrete object from purely points? It would require infinite points. That gets into counting infinities, with some infinities larger than others... set theory.

 

[Fra]

How does a person construct a discrete object from purely points? It would require infinite points. That gets into counting infinities, with some infinities larger than others... set theory.

Not sure I follow you here. But without diverging too much, the kind of question I intented to to ask is was rather more like

How does a finite physical observer, construct and encode at least apprioximately or as a limiting case, a continous map from it's discrete observations (detector clicks if you want), ie or how to go from a boolean [true,false] to a a real number [0,1]. Indeed here, one runs into the question of how far the observer can count? And what happens then?

And then the association from there to strings, n'th quantisation orf p-branes, vs (n+1)'th quantized (p-1)-branes is fun and interesting association.

I admit it's a long wild train of thought but can someone come up with an "interpretation" of a string, from this puzzle? Ie something that is more satisfying than simple thinking it's litteraly a mechanical string, given that we seem to agree that it's very ad hoc. This is why kind of thought that ran to my head when i read that baez post years ago.

/Fredrik

 

[jaketodd]

I think the fact that humans etc. can comprehend infinity, and with set theory, different-sized infinities, shows that we are not "finite" observers.

 

[jaketodd]

So, is there ever a time when a theory should be disregarded, long term? If it's had many years to produce results, and it hasn't, is there a time when resources should stop being used for it? Sometimes the resources used are in the millions or even billions of dollars. And brain power can be refocused, so effort is producing actual verifiable progress with other theories. But what's the threshold? When is it time to call it quits on a theory?

 

[Vanadium 50]

Sometimes the resources used are in the millions or even billions of dollars.

Please give an example of spending billions of dollars on a theory that should be abandoned. Multiple examples would be even better.

 

[Demystifier]

I think the fact that humans etc. can comprehend infinity, and with set theory, different-sized infinities, shows that we are not "finite" observers.

Humans comprehend infinity by reducing it to something finite. All explanations of infinity take a finite number of symbols.

Or to paraphrase Janis Joplin, infinity's just another word for something left to gain.