Was Einstein too optimistic?

oldman

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

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.

Cosmologists know a lot about expansion, but...

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

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.

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 possess deep understandings of abstract notions that couldn't've even been dreamed 200 years ago!

oldman

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?

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 :)

/Fredrik

oldman

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?

(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

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

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

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

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

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

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

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 particualr 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