Is Einstein's statement about the comprehensibility of the world justified?

[oldman]

Was Einstein too optimistic?

The most incomprehensible thing about the world is that it is
comprehensible

I’m beginning to suspect that this philosophical view is nonsense. There seem to be
many aspects of the physical world that are really difficult to understand and fully
accept. But then lots of people grasp stuff better than I do.

I’ve been trying to devise a way of finding out if people, especially those with a
philosophical approach, agree that Einstein’s statement was justified or not. I’ve here
listed in an attempted neutral sort of way some things I’ve have battled with and failed to fully grasp at one time or another. The list I’ve compiled is incomplete (I’m puzzled about many more things than I list) but because this is a physics forum, the list biased that way.

Here is a list of eight puzzling aspects of the physical world that some folk seem to
comprehend and accept. But some people don’t. How do they strike you?

1. When ‘elementary particles’ like electrons pass one at a time through two slits and
impact a screen as localised particles. Yet their separate impacts are distributed like
diffracted waves.

2. Quantum systems are supposed to exist as a probabilistic superposition of states
until somebody measures one of their observable properties. The system may then
'collapse' into a single state, so preserving the separate integrity of system and
observer. But perhaps there are multiple physical realities that combine a superposed
state of system and observer.

3. Every observer experiences a (possibly unique) physical world in which distance and
time (and therefore speed) are operational concepts personal to that observer. There is
no such thing as a unique and universal ‘physical reality’ out there.

4. If you travel to Alpha Centauri and back and your watch tells you one second has
elapsed, you will find that your twin, who stayed at home, has aged more than
you have.

5. It’s not possible to accelerate matter until it can be measured to be traveling faster
than light. Therefore kinetic energy must be thought of as stored mass that increases
with measured 'speed'. Mass and energy are taken to be equivalent, as a working
hypothesis.

6. Once upon a time -- very long ago -- the universe was a perfectly isotropic and
homogeneous, perhaps spatially infinite and ultra high-energy thing.

7. The biological phenomenon of Batesian_mimicry in say, butterflies, that makes
some of them look as if they have been exquisitely designed to look dangerous,
evolved by pure happenstance.

8. The odd social behaviour of Australian Bowerbirds and their fascination with the
colour blue, is hardwired stuff. Their behaviour evolved in a Darwinian way, just as sociobiologists suppose many of our own behaviours did.

A scoring scheme along the lines I’ve set out below might be a way of seeing how
positive or negative your opinion of Einstein’s statement is. I’ve arbitrarily assigned
these scores for possible views.

4 : I understand and accept this aspect of nature, fully and fundamentally
3 : I accept it as the reasonable justified view of experts:
2 : I believe it because in textbooks or by teachers I’m told it’s so:
1 : It’s probably correct but details need amplifying or modifying:
0 : No comment; I don’t know, or the proposition is badly put:
-1: It’s probably wrong -- at least it’s not the whole truth or all the truth.
-2: It’s just the way things are, as created by Someone.
-3: I have my own theory about this.
-4: This is simply incredible. It’s nonsense.

Any comments? Or things to add to the list? Or a different way of scoring such a list?

 

[LightbulbSun]

I’m beginning to suspect that this philosophical view is nonsense.

How so?

 

[Hurkyl]

Well, one problem with your list is that it doesn't reflect the current state of scientific knowledge!

2. Quantum systems are supposed to exist as a probabilistic superposition of states...

If it was just that, then there would be no 'problems'. The thing that distinguishes quantum mechanics from classical mechanics is that probabilistic superpositions are not enough to describe what we see.

3. Every observer experiences a (possibly unique) physical world in which distance and
time (and therefore speed) are operational concepts personal to that observer. There is
no such thing as a unique and universal ‘physical reality’ out there.

I'm not sure where you got this idea. I don't know of any scientific theories that say we live in different 'physical realities' just because we are using different metersticks.

6. Once upon a time -- very long ago -- the universe was a perfectly isotropic and
homogeneous, perhaps spatially infinite and ultra high-energy thing.

Surely you don't mean perfectly? I'm pretty sure no scientific theories assert that.

7. The biological phenomenon of Batesian_mimicry in say, butterflies, that makes
some of them look as if they have been exquisitely designed to look dangerous,
evolved by pure happenstance.

It sounds like you're referring to the theory of evolution -- but that says it was natural selection, not pure happenstance.

 

[oldman]

Well, one problem with your list is that it doesn't reflect the current state of scientific knowledge!

My list may well present my own distorted reflection of the current consensus, and your comments are helpful. Thanks. I tried to focus on aspects of this consensus which have puzzled me. I think they've also puzzled more knowledgeable folk!

... The thing that distinguishes quantum mechanics from classical mechanics is that probabilistic superpositions are not enough to describe what we see..

And this is why nobody can claim to fully understand quantum mechanics, I guess. Nicely put.

...I don't know of any scientific theories that say we live in different 'physical realities' just because we are using different metersticks.

Well, SR and GR tell us that spacetime is the malleable and dynamic arena shaped by observer observation and gravity in which we live and perceive 'physical reality'. Until 100 years ago we were unaware of how very different perceptions of time and distance could be. But now that we splurge on apparatus like the LHC and theorise about places where the Schwarzschild geometry rules we are well aware that perceived reality is not invariant. And what is perceived with meter sticks, radar and clocks, is!

Surely you don't mean perfectly? I'm pretty sure no scientific theories assert that.

You' re right. I was ignoring primeval quantum fluctuations in the time of quantum chaos that might have preceded the BB.

It sounds like you're referring to the theory of evolution -- but that says it was natural selection, not pure happenstance.

But pure happenstance mutations of DNA is what underlies natural selection!

I guess I was trying too hard to be neutral and oversimplified my list.

How so?

I don't quite know how you want me to respond. Could you amplify, please?

 

[Hurkyl]

And this is why nobody can claim to fully understand quantum mechanics, I guess.

That doesn't follow... While my comment does bring up something that is difficult to understand from classical intuition (and thus giving problems to scientists 100 years ago, as well as today's laypeople, or even technical people who have only been trained in classical mechanics), it doesn't intimate that those trained in quantum mechanics are uncapable of developing an understanding and intuition for the quantum mechanical.

 

[Fra]

"The most incomprehensible thing about the world is that it is at all comprehensible."

Does anyone know in what original context Einstein fired this comment? I admit that I don't have a clue. but to play the game of random associsions...

Spontaneously, my first association reading this goes to learning and evolution. Given a totally ignorant observer, how is it that it can learn? How does it "know" howto learn? How do you know that your bets will give a return?

I think it doesn't. However, there will be a selection in favour of those who make the right bets. Thus part of the intelligence, implicit in the makeup of matter and life, is I think evolved.

This may be farfetched, but I could imagine one possible meaning of the quote in the context of a kind of induction like to rephrase...

The most incomprehensible thing about induction is that it works.

In this interpretation of Einsteins quote (I know what he said, but not what he meant; I can only guess) I think it's plausbile, but then perhaps there is a posible way of understanding it and that's to cnosider the alterantive.

In the context of evolution, I seems almost self-evident that something that "doesn't work", will not be preserved. So the fact that we seem, against the odds, to acquire and understanding of the world, might be "understood" as the only reasonable outcome of an evolutionary abstraction?

/Fredrik

 

[Fra]

3. Every observer experiences a (possibly unique) physical world in which distance and time (and therefore speed) are operational concepts personal to that observer. There is no such thing as a unique and universal ‘physical reality’ out there.

Hey Oldman, if I am pulling this discussion in an unwanted direction let me know, but maybe we can even associate this question as analogous to the meaning of that quote of of Einstein!

The question that a subjectivist/solipsist inclined system (like me) would ask is then:

If it is really true that there are not universal truths out there and more or less everything is fundamentally a matter of point of view, then the largest question of all is, how can this be, and still the word sticks together!?

Ie. the most incomprehensible thing is that we do comprehend, can also be modulated into that "given the mess", it is incomprehendable that this game we all life has any degree of coherence at all?

Like above, my personal "philosophical answer" to this, is that the key is evolution. The *selection* of observers, is what makes the world stick together, because everything that is in some sense "possible", does not actually happen.

/Fredrik

 

[Fra]

My thoughts still have momentum from the above post, interfering with my recent reading up on Popper.

The most incomprehensible thing about induction is that it works.

I think Popper, turned his failure to understand the utility of induction, to question that it works. Ie. his failure to "comprehend the comprehension itself" self-inhibits the very comprehension.

Now I'll stop.

/Fredrik

 

[oldman]

That doesn't follow... While my comment does bring up something that is difficult to understand from classical intuition (and thus giving problems to scientists 100 years ago, as well as today's laypeople, or even technical people who have only been trained in classical mechanics), it doesn't intimate that those trained in quantum mechanics are uncapable of developing an understanding and intuition for the quantum mechanical.

Not for a moment would I deny that those trained in Quantum Mechanics (QM) develop an understanding and intuition for the subject. But 'understanding' is a tricky concept. Let me illustrate this by considering a phenomenon that involves circular motion -- which to many people can be somewhat unfamiliar.

Imagine yourself facing north, holding a spinning bicycle wheel at arms length by its axle, which you grip on either side of the wheel. Imagine the the axle to be horizontal. If you were to turn suddenly to face east (or west), keeping the axle horizontal you would find, perhaps to your surprise, that the wheel would try to twist your outstretched arms and dip its axle towards the vertical. At first you might not 'understand' this behaviour. But later, if you encounter some strange behaviors of spinning tops or gyroscopes you could liken them to the now-familiar behaviour of the bicycle wheel, and claim that to some extent you understood tops and gyroscopes. In this case understanding means 'placing an experience in the context of familiar happenings'.

Alternatively you might immediately realize that the wheel axle tries to dip because the northerly and southerly momenta of the top and bottom parts of the wheel have to be deflected in opposite directions, say toward the east and west. These changes of momenta are effected by the forces you exert to keep the axle horizontal, which constitute a twisting couple. In this case your understanding is one level down, as it were, and perhaps more satisfying. But it is still not complete, because it relies on concepts of momentum and force. Although these, are ultimately mysterious, they are still pretty familiar to most people. Again understanding means 'placing an experience in the context of the familiar happenings, or in this case concepts'.

It seems to me that with QM the ultimate and mysterious level where one cannot rely on having a context of familiar experience is reached more quickly as you dig deeper. I'm thinking of things like the wave-particle duality, Schroedingers Cat and the decoherence or collapse of the wave function. Then training that develops "an understanding and intuition for the quantum mechanical" may not yet result in full understanding, in the sense I've mentioned.

On a lighter note --- if you doubt that circular motion is a bit mysterious, try this: hold a tennis racket out by its handle, with its face horizontal. Perfect tossing it up so that it flips exactly one turn, carefully about as horizontal an axis perpendicular to its handle as you can, catching it by its handle. You may drop it a few times before getting this right. Then before a toss note which face (rough or smooth) is uppermost. Check after tossing it and you'll find that mysteriously it always manages to land with the other side in your hand. You may not understand why a 180 degree turn about its long axis creeps in, but tennis players are quite familiar with such strange behaviour! The reason is too mathematical to write down here, and I think can't be 'understood' in the sense I have used. Just like parts of QM!

 

[LightbulbSun]

I don't quite know how you want me to respond. Could you amplify, please?

Please explain to us why you think the Einstein quote you've cited in your OP is nonsense?

 

[LightbulbSun]

"The most incomprehensible thing about the world is that it is at all comprehensible."

Does anyone know in what original context Einstein fired this comment? I admit that I don't have a clue. but to play the game of random associsions...

I think he was referring to the foundations of physics.

 

[Fra]

I think he was referring to the foundations of physics.

I'm not aware of that, or are you referring to "the foundation of physics" in the general sense rather than a book/article then I figured that much :)

/Fredrik

 

[russ_watters]

I didn't read the whole thread, but it seems to me the problem is an over-reading of the quote. It is trivially true that we don't know everything there is to know and won't for a long time, if ever. That doesn't have anything to do with whether it is possible for us to know all the laws that govern science. But it is a philosophical requirement for scientists to believe it is possible to know a lot more (but not necessarily all) of what there is to know - otherwise, there would be no point in pursuing science.

In short, though, I think the statement is simplistic and thus it can't be assumed he meant that it should be taken for granted that we will eventually know everything there is to know in science.

Also - everyone knows/accepts/agrees there are things that science doesn't yet have explanations for. So there is no need to use specific examples when examining the philosophical statement. They aren't relevant.

 

[Hurkyl]

Then training that develops "an understanding and intuition for the quantum mechanical" may not yet result in full understanding, in the sense I've mentioned.

I'm not sure how you conclude that. Going by the definition

In this case understanding means 'placing an experience in the context of familiar happenings'.​

it's sort of trivial to gain an understanding of anything -- if you study it long enough, it becomes something familiar.

 

[oldman]

Please explain to us why you think the Einstein quote you've cited in your OP is nonsense?

Yes, this clarifies your question. Thanks.

It's nonsense because comprehending or understanding something is not the same as describing it or knowing about it. Very obvious if that something is your opposite sex! I guess Einstein just couldn't resist making such a superficially clever remark. He comprehended so much more than others.

Science describes phenomena and generates knowledge about them. Sometimes (see the OP) this is insufficient for comprehension. For example, we know a lot about the expansion of the universe, which is easily described by a metric, but it sorely puzzles many who post here. It generates a plethora of attempted clarifications here and elsewhere. See the Cosmology forum.

 

[Hurkyl]

For example, we know a lot about the expansion of the universe, which is easily described by a metric, but it sorely puzzles many who post here.

Why do you think the "we who know a lot about the expansion of the universe" and the "many who are puzzled by it" are the same group?

 

[oldman]

...the problem is an over-reading of the quote...

Or perhaps we are just reading it differently. I do agree with what you say about scientific knowledge and scientific laws, but this wasn't quite what I was taking issue with.

- everyone knows/accepts/agrees there are things that science doesn't yet have explanations for. So there is no need to use specific examples when examining the philosophical statement..

Nevertheless I hope the examples I've given in the OP can't hurt ---- at least they point to cases where I think knowledge alone has proved insufficient for comprehension.

 

[oldman]

Why do you think the "we who know a lot about the expansion of the universe" and the "many who are puzzled by it" are the same group?

It's the difference between knowing and understanding again. We do know a lot about expansion -- like the Hubble plot, how at the top end it deviates from linearity, what expansion extrapolated backwards points to, etc etc.

But the fact that Scientfic American saw fit to pay Lineweaver to publish an article explaining what expansion is, and numerous threads and posts in the Cosmolgy forum are evidence that a lot of folk don't understand expansion. I think Marcus there has the best take on it, but I'm still not sure that I grasp its meaning properly. Perhaps because GR and curved space touch on matters beyond our regular experience? We're so mesoscopic!

 

[Hurkyl]

It's the difference between knowing and understanding again.

I'm not convinced. It still looks like the difference between "person uneducated in a scientific topic" versus "person educated in a scientific object.

e.g.

We do know a lot about expansion -- like the Hubble plot, how at the top end it deviates from linearity, what expansion extrapolated backwards points to, etc etc.

Cosmologists know a lot about expansion, but...

But the fact that Scientfic American ... publish an article ... a lot of folk don't understand expansion.

People learning from Scientific American do not know a lot about expansion.

There was never a question (was there?) that laypeople do not have a good understanding of scientific topics. But that fact doesn't tell us whether or not the scientists who devote their time and energy to study and research are capable of developing a good understanding.

 

[oldman]

There was never a question (was there?) that laypeople do not have a good understanding of scientific topics. But that fact doesn't tell us whether or not the scientists who devote their time and energy to study and research are capable of developing a good understanding.

Of course you are correct. It seems to me that you may be thinking that I'm implying that researchers don't understand what they're doing --- perhaps you yourself are actively engaged in research, in which case you would find such a suggestion quite unacceptable.

But in fact I'm suggesting no such thing. After spending my life in physics, publishing and luckily not perishing, I know very well how different is the understanding and knowledge of researchers from laymen. I understand the inticacies and mathematical structure of my own field very well indeed. But there are in physics many things we don't understand, especially when we are trying to describe domains we don't have direct access to --- the very small and the very large, beyond our experimental or observational grasp, say beyond the standard model or in cosmology.

What I'm talking about is the possibility that we may be incapable of understanding, at a fundamental level, some of the puzzles in QM and phenomena like gravity, because of our mesoscopic experience and nature --- where and what we are. For instance, gravity is very adequately described by GR, less so by Newton's law. But the mechanism (for lack of a better word) by which mass distorts spacetime is a mystery and may remain so, just as in classical times nobody understood exactly why there was such a thing as Newton's law, or how mass attracted mass.

So please don't think I'm trying to denigrate science. But I'd like to persuade folk that it may just have limits!

 

[Hurkyl]

If I may digress slightly...

In the early 1800s, a brilliant mathematician named Niels Henrik Abel made the following observation:

There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes.​

I find this quote markedly similar to the one by Einstein you gave in the opening post. This was an era of mathematics when the real analysis was being developed, and mathematics was still a 'by the seat of your pants' endeavor -- and Abel was perplexed that the methods of the time were proving effective at understanding the frontiers of analysis.

One of Abel's main messages (and one of his greatest contributions) was the insistence on greater rigor in mathematics. To provide my interpretation of it: one needs to stop relying on their 'a priori' intuition, and start forming a new and more reliable understanding of the subject through study and experiment. (Rigor being used as a reliable way to reason about things we do not yet fully understand, and for validating our work)

I think my interpretation of the spirit of Abel's contribution is relevant to physics, and quite similar to some of the lessons Einstein taught us (and QM also): one cannot impose our intuition on the universe. Instead, we must be willing to formulate a new understanding based upon the results of our study of the universe.

What I'm talking about is the possibility that we may be incapable of understanding, at a fundamental level, some of the puzzles in QM and phenomena like gravity, because of our mesoscopic experience and nature --- where and what we are.

I'm interpreting statements like this as being pessimism that what I just said cannot be done -- that one cannot let go of their a priori intuition and formulate a new understanding based upon the results of observation. I really think such pessimism is unfounded; yes, QM and gravity seemed really puzzling 100 years ago... but have become more and more understood by researchers in those fields as time has gone on.

And if that limited evidence isn't enough to inspire optimism... take a look at the field of mathematics which already underwent this paradigm shift, and now produces experts who possesses deep understandings of abstract notions that couldn't've even been dreamed 200 years ago!

 

[oldman]

One of Abel's main messages (and one of his greatest contributions) was the insistence on greater rigor in mathematics. To provide my interpretation of it: one needs to stop relying on their 'a priori' intuition, and start forming a new and more reliable understanding of the subject through study and experiment. (Rigor being used as a reliable way to reason about things we do not yet fully understand, and for validating our work)

...one cannot impose our intuition on the universe. Instead, we must be willing to formulate a new understanding based upon the results of our study of the universe.

I agree that one cannot rely on intuition --- the universe is much too strange for this, as Einstein and the quantum physicists of the 1920's revealed. You suggest that 'we should instead "formulate a new understanding based upon the results of our study of the universe". But this seems a rather vague prescription for going beyond the standard model!

I've also been suggesting also that intuition fails us, in the sense that fundamental elements of physics may be beyond our understanding. You seem to place a mathematicians emphasis on "rigor being a reliable way to reason about things we don't understand". Indeed I've known many mathematicians who tear their hair out about lack of rigour in physics. But physics works differently (with exceptions) in basing itself on experiment, observation and rough working hypothesis, which may later acquire rigor or be discarded if predictions are not confirmed.

Nowadays our study of the universe has become difficult and expensive as regards observation. The situation is not likely to be improved by the twin disasters of quenching at the LHC and financial meltdown in NY. So what are we to do? In my opinion an emphasis on rigor in devising theoretical schemes leads to adventures in mathematical ratiocination like string theory. How do you think we should proceed?

...QM and gravity seemed really puzzling 100 years ago... but have become more and more understood by researchers in those fields as time has gone on.

Yes, as far as details go. But there hasn't been a great deal of progress in fundamental understanding, as far as I know.

I suppose you're right in opposing pessimism. But I do wish I understood the old puzzles a bit better. Or that some clever folk would finally resolve them for me.

 

[Fra]

I don't mean to repeat my personal opinions, but I'd like to inject...

I think there is an important point (commonly ignored indeed) between the process whereby scientific theories becomes established(corroborated), and the established theories/knowledge. This process does include not only the concept of falsification or formal proofs, it also includes the idea of hypothesis generation and selection, prior to the state where and deductive reasoning is not easily applied.

This distinction is I think an abstraction that also applies to pure mathematics. I think this has been argue not only by amateurs like myself, but also by some mathematicans like George Polya.

I think this is more than just curiosity, but some feels very uncomfortable with these fuzzy things, and seem to deny it's relevance.

I agree that what's commonly called intuition is both doubtful and paradoxally fruitful is more clearly seen if one considers the logic of induction. So either you may think that this is crap and not worthy of a physicists, mathematicians or scientists, or you may take on the task to scientifically try to analyse the logic of induction. Some people like E.T Jaynes has taken this seriously, and as to how this can be prove it's power, it's that understanding the "inductive processes" migh help us to exploit it even harder.

/Fredrik

 

[Fra]

There are many funny both wise and funny quotes from this man :)

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment.

Observe also (what modern writers almost forgot, but some older writers, such as Euler and Laplace, clearly perceived) that the role of inductive evidence in mathematical investigation is similar to its role in physical research.

/Fredrik

 

[oldman]

There are many funny both wise and funny quotes from this man

Is this the same Polya who wrote "How to solve it" ? I have this tucked away somewhere and will re-read it if it is. By the way, nobody has yet answered your question (post#6) of where the quote from Einstein in my OP came from. I have to confess that I don't know either -- everybody seems to be familiar with it, though. My Google skills are inadequate to find its origin.

About inductive reasoning. Is this it?

The expansion of the universe means that the proper physical distance between a pair of well-separated galaxies increases with time, that is, the galaxies are receding from us.

(my emphasis).

Here Peebles is using the word 'receding' in the ordinary sense of 'moving away'.
But a distinction can be made between motion, as we ordinarily know it and use it in physics, say in the dynamics of projectiles and in Special Relativity, where speeds cannot exceed c, and in General Relativistic expansion, which can carry objects further apart at superluminal rates. Whether we should refer to such expansion with unqualified ordinary words like 'receding' or superluminal 'speeds' is a moot point, don't you think?

This is a prime example of confusion developing because the phenomenon being considered is beyound our complehension in the context of our mesoscopic experience. We can't use ordinary words to describe it.

 

[Fra]

Is this the same Polya who wrote "How to solve it" ? I have this tucked away somewhere and will re-read it if it is. By the way, nobody has yet answered your question (post#6) of where the quote from Einstein in my OP came from. I have to confess that I don't know either -- everybody seems to be familiar with it, though. My Google skills are inadequate to find its origin.

About inductive reasoning. Is this it?

Yes, it's the same Polya, and he has written some about inductive reasoning. Et Jaynes has expressed that Polya was one of those who inspired him to continue, and develop further this "tradition". Et Jaynes is unfortuantely dead but he has written the book "Probability theory: The logic of science", but the later parts of the books are missing. He tries to formalise inductive reasoning as an extension of logic and show it's viability in physics. Others strongly influence by the same spirit is Ariel Caticha, who has the vision that General relativity may be a consequence of the rules of inductive reasoning. He is as far as I know working on a book on "information physics", that will take this traditions longer than did Polya and Jaynes, but somewhat in a similar spirit. But it is quite clear that not many see the potential power of this approach.

I think the point is that even mathematicians use inductive reasoning in the reasearch, but that is not what you see in the final papers. The final result is always cleaned up, presenting typically a deductive reasoning. But it's a mistake (IMHO at least) to trivialise reasearch and learning processes to the falsification or formal proofs of hypothesis and conjecturs. The problem of generating good hypothesis and conjectures, rather than "random conjectures" does matter. Once a conjecture or hypothesis is on the table, that hardest task is already made. Also the process of "finding a proof" to a mathematical conjecture, to give it the status of say a theorem or something, is a creative process. And first the mathematicians may come up with a "conjectured proof", ie a deductive sequence that could be a proof, then the conjectured proof needs to the "tested" - checked for consistency, before it actually constitutes an accepted proof.

/Fredrik

 

[lonton]

That is too detailed to be trusted.

 

[Fra]

Here is another Polya quote

To be a good mathematician, or a good gambler, or good at anything,
you must be a good guesser.

and I think this is not to be interpreted so that mathematicans do random guesswork, on the contrary, does it suggest the importance of the step of "hypothesis generation" in the scientific process. And the internal workings of hypothesis generation is what is the focus in inductive reasoning.

It is not about mistaking inductive reasoning for deductions, as some silly critics seem to think. Example such as the chicken and the farmer, who learns by induction that the farmer is nice because he brings food every day, until the day when he gets his head chopped. The question is, that the problem posed is intrinsic to the chicken. Not intrinsic to the logician telling this story and lauging about it.

The inductive reasoning clearly works in conjunction with abstractions such as falsification and corroborataion, or formal proofs in the case of mathematics or logic. A strategy that doesn't acknowledge the important of both will I think be crippled. Someone who refuses to make guesses, will find everything incredibly difficult. The human mind do guesswork all the time, and its' called learning.

Critics to inductivism, argue that learning should be by incremental deductions (this was poppers vision) but then I think what the variable seem to ignore is that effienecy of hypothesis generation. I read Poppers book and he does in my opinion avoid this issue, or rather dismisses it to psycological scienecs, this is in direct contrast to for example Ariel Catichas thinking, that, like me, thinks that there is strong correlation between the fundamental laws of nature, and the logic of inductive reasoning.

/Fredrik

 

[Borek]

So please don't think I'm trying to denigrate science. But I'd like to persuade folk that it may just have limits!

It may have. However, so far each time we have thought there is a limit to our understanding it turned out we were wrong. So experience tells us that there are no limits.

Sure, absence of evidence is not an evidence of absence, so we can be wrong.

 

[Fra]

Is this the same Polya who wrote "How to solve it" ? I have this tucked away somewhere and will re-read it if it is.

I should add that while I'm aware of that book, I did not read it. And I do not know to what extent that book alone elaborates on the deeper ponderings I've suggested here, and that some other people who in a certain sense tried to take some of Polyas spirit to the next level are working on. I *suspect* that book is more practical though. Ariel and others are IMO aiming to take this to yet a higher level. This is something I find very intersting and promising. When it comes to physics this enter the topic from the angle of probabability theory, combinatorics and maxent principles.

So if you pursue this stuff, you might want to look further than Polyas "how to solve it", but as said I don't have that book myself.

/Fredrik

 

[oldman]

... However, so far each time we have thought there is a limit to our understanding it turned out we were wrong. So experience tells us that there are no limits...

I should have written "we have limits" or "our understanding has limits" rather than "science has limits", but my excuse is that science can be regarded as synonymous with human understanding --- it's just organised, understood human knowledge, after all.

Yes, I agree, we keep on making the mistake of thinking that the end of science is nigh, but just as we proclaim this fallacy new discoveries are made. John Horgan's has written an entire book about this, called "The End of Science''.

But I have little doubt that we have already encountered our limits, several times. I listed some instances in my OP. Just think: how much of nature do our fellow creatures on this planet understand? -- animals from aardvarks to living zygotes, say. Not as much as we do, I think you'd agree. So why expect our understanding to be unlimited? Theirs isn't.

And if you think we are the absolute pinnacle of creation, compare such limited animals not with sophisticated folk like Einstein and the partners in Goldman Sachs, but to our ancestors who roamed the African veld 50 kiloyears ago, and you may get my point. We haven't evolved much since those days and our remote ancestors were no doubt just as
smart (or dumb) as us.

 

[Borek]

And if you think we are the absolute pinnacle of creation

I don't think that way, looking around I am rather surprised we get that far. And I don't reject the possibility that we will face the wall one day. But so far - so good.

 

[oldman]

I think the point is that even mathematicians use inductive reasoning in the research, but that is not what you see in the final papers. The final result is always cleaned up, presenting typically a deductive reasoning... Once a conjecture or hypothesis is on the table, that hardest task is already made.

Yes, I agree with much of what you say in this post. There's always plenty of window dressing in the final published product of research. But then the purpose of publishing it is to have others understand and accept your work. They don't need to know about the troubles and false starts that most research involves, as it's very name implies.

To misquote Henry Ford: scientific history is bunk. But to many it's interesting bunk, of course. The important thing in research is to focus hard on the problem at hand and not worry too much about the methods you use to solve it. Just do it, with whatever comes to hand!

 

[Fra]

Beeing aware of some of the various attitudes towards this out there, I think it's worth noting that these things - the ideas of induction - can be considered at different levels or abstractions.

First we have the meaning of induction applied to human reasoning, as an attempt to understand and analyse human reasoning. The fuzziest form of this is to dismiss this into psychology, and here the induction is more of a qualitative nature. Ie. it does not described by mathematics.

The next level is to quantify this, and considers "degrees of plausability" as real numbers, which ultimately are argued to follow the axioms of probability and where these things is equipped with mathemtics, and this may help explain a few real world pehenomena such as game theory applications, economics etc, but the idea that all players acts somewhat rationally on given information. This alone will predict various types of group behavour, and various game-type equilibria.

So far it's no news.

But, the next level, is to consider that even physics, physical systems, atoms particles are like players in a game, that does act upon information at hand only (note that this has similarities to the principle of locality!). But this then, comes with a range of new complications. For example, particles don't have brains (unlike players in a game), so it means that one needs to explain the process of selection between possible actions in a different way. Maybe something like random disturbances, that then due to the initial constratins do diffuse as per a particular distribution. This would suggest that the actions of physical interactions should "look like" systems interacting, but where the action of each part is determined by the "information it has" about it's environment. This will naturally give rise to things like inertia, as in resistance against change, depending on the complexity of the parts.

This is what I tried to convey in the other thread. This is very controversial and very non standard, but it's IMHO the natural extension to the spirit advocated by the mentioned scientists. But there are different variations of this. ET Jaynes argued in favour of real numbers from start, I think differently. Ariels suggestions - to suggest that GR is a physical consequence of thinking that physical interactions are like responses based on incomplete information, is a deep insight IMO and not as stupid as it first sounds. And if he is right, some of the current approaches to quantum gravity may be due to a akward way of presenting the problem. I adhere to that view. But I'm in minority and it's hard to convey what isn't a thery, but rather a special way of analysing the problem.

/Fredrik

 

[Chrisc]

I've always considered Einstein's quote to simply mean there is a questionable extent to which the observed (universe) can objectively be the observer.
Humans are made of the stuff of the universe and governed by the laws we seek to discover.
It has been said many times in many different ways, but my favourite analogy is: What does my tongue taste like?
I think Einstein was simply expressing the incomprehensible nature of comprehending what is inseparable from the comprehender.