Is Our Chemical Knowledge Truly Infinite?

[Kherubin]

I'm interested in philosophers' opinions on a question that I posed in another forum (https://www.physicsforums.com/showthread.php?t=496119).

As I say in my latest post, the entire thread was sparked by the comments of the Philosopher of Chemistry, Joachim Schummer:

We have no reason at all to assume that the realm of possible substances is limited. If we take that seriously, we must assess the finite growth of chemical knowledge against the background of an infinity of possible knowledge. An infinite realm of possible substances corresponds to an infinite amount of possible knowledge that we not yet have. To be sure, the fast increase of our chemical knowledge decreases our lack of knowledge in a certain sense. But that does not matter. Mathematics forces us to accept that a finite decrease of an infinite amount does not affect the infinity at all. As a consequence, whatever the rates of growth of chemical knowledge will be, that does not change the fact that our knowledge gap is infinite and will remain infinite in the future. -- Coping with the Growth of Chemical Knowledge

Do you agree with his appraisal of the chemical enterprise or not?

Thanks for your time,
Kherubin

 

[apeiron]

I'm interested in philosophers' opinions on a question that I posed in another forum (https://www.physicsforums.com/showthread.php?t=496119).

As I say in my latest post, the entire thread was sparked by the comments of the Philosopher of Chemistry, Joachim Schummer:

We have no reason at all to assume that the realm of possible substances is limited. If we take that seriously, we must assess the finite growth of chemical knowledge against the background of an infinity of possible knowledge. An infinite realm of possible substances corresponds to an infinite amount of possible knowledge that we not yet have. To be sure, the fast increase of our chemical knowledge decreases our lack of knowledge in a certain sense. But that does not matter. Mathematics forces us to accept that a finite decrease of an infinite amount does not affect the infinity at all. As a consequence, whatever the rates of growth of chemical knowledge will be, that does not change the fact that our knowledge gap is infinite and will remain infinite in the future. -- Coping with the Growth of Chemical Knowledge

Do you agree with his appraisal of the chemical enterprise or not?

Thanks for your time,
Kherubin

Hi Kherubin - you've asked a similar question in two threads. What seems key to answering the question is that you have both potentially an infinite number of discoveries, but also differing weights or values that apply to each of those discoveries. Clearly, some discoveries will be far more important than others.

The kind of statistical distribution we would normally expect in such a situation of free growth (and unpredictable significance of any individual event in that growth) is a power-law one.

So we could reason from this that science is indeed unlimited and big surprises may occur "forever". But equally, most of the big ones will be clustered early on, becoming more infrequent with time. The classic low hanging fruit story.

As to the second question, do paths taken close forever the paths not taken?, I don't really think so. This would be because the net is cast quite widely, and there is also a reasonable record of all the directions ever taken because we have libraries. Ideas not developed several centuries ago could still be picked up and bear fruit in the future.

 

[Pythagorean]

there are many questions in science that, upon being answered, create thousands more questions, each of which could potentially create thousands more.

the only real limitation is funding; commerciability, public/military/government interest

 

[Kherubin]

Thanks for your replies.

Hi Kherubin - you've asked a similar question in two threads.

Interesting, I had not considered it that way. In what particular respect do you consider them to be similar questions?

Thanks,
Kherubin

 

[apeiron]

Interesting, I had not considered it that way. In what particular respect do you consider them to be similar questions?

Both view our possible knowledge of reality as an infinite phase space to be filled by random search. The domain of the knowable seems unlimited in principle, and our scientific endeavours are evolutionary - unguided and constrained by their own history. So how can we be sure our search is maximally efficient?

Your chemistry question asked, if the space is infinite, surely it must swallow up any attempts to fill it? My reply was that the space could be both infinite and unfillable, but also most of what matters is nearest at hand. As would be modeled by a powerlaw.

Your unique histories question asked, if the search is historically constrained, then can it access all corners of this phase space - even our coverage of the "near at hand" might be gappy.

Again, the answer would be that the model of processes that are both historically-constrained, but also maximally space-filling, would be a powerlaw one, such as the dissipative branching of a river tributary systems or blood flow in the lungs.

So an "ideal" version of scientific search would have this character - a random branching that would fill all the available space no matter how the tree of knowledge happened to form.

Both your questions thus seemed to boil down to a concern over the size of the domain and the unguided, historically-constrained, nature of the search.

I would add that there is more to the search for knowledge than this.

Science emphasises what can be measured - the hunt for particular impressions of nature. Knowledge is an accumulation of (possibly infinite, and randomly located) information that adds up to some sum.

But there is also the philosophical search for ideas about nature - the generalisation of the particular to extract global truths.

The two ways of achieving knowledge - by measuring particulars and inducing universal principles - are obviously complementary, each stimulating the other on. This is basic modelling theory, basic semiotics.

But it also means that our search for knowledge is not actually so random and blind, so bound to an exhaustive space-filling search algorithm as my first quick answer would imply. We can induce general principles and then deduce expectations from them. An example in physics would be a belief in symmetry that then leads a scientist like Einstein to focus his search on an explanation that increases symmetry.

 

[Kherubin]

Thank you very much for your answer. Truly informative.

As you say, however, isn't the maximally-space-filling algorithm idealistic?

Is it not contingent upon the intuition and inspiration of individual scientists?

Do you think that, as a species, our cumulative insight, perspective and wisdom is sufficient to fill every corner that this 'powerlaw' algorithm has the potential to?

Are there scientific truths beyond our grasp simply for lack of the individual minds necessary to reveal them?

Or is the scientific search sufficiently general as to mean that this is no real concern?

Thanks for your time and thoughts,
Kherubin

 

[epenguin]

There could be a lot more chemistry - but I wonder if it wouldn't be a lot more of the same thing? I actually got to feel that is all there is before the end of my chemistry education!

Or taking the opposite view I could say it is natural science that is finite, while engineering, making new combinations of natural materials, including chemical synthesis and processes (chemical engineering etc,) is potentially infinite.

 

[apeiron]

As you say, however, isn't the maximally-space-filling algorithm idealistic?
Is it not contingent upon the intuition and inspiration of individual scientists?
Do you think that, as a species, our cumulative insight, perspective and wisdom is sufficient to fill every corner that this 'powerlaw' algorithm has the potential to?
Are there scientific truths beyond our grasp simply for lack of the individual minds necessary to reveal them?
Or is the scientific search sufficiently general as to mean that this is no real concern?

One usual way of thinking about this is to ask if an alien intelligence would come up with the same science (and philosophy, presumably). That was a big debate when they attached messages to those satellites.

http://en.wikipedia.org/wiki/Pioneer_plaque
http://en.wikipedia.org/wiki/Voyager_Golden_Record

You also have to consider what knowledge is for. So knowledge is actually normally about pragmatics - achieving control over our worlds. This may be a serious bias that does indeed limit the kind of searches we make (or fund!).

And I think it is clear to see that bias at work. Particle physics gets a big boost because some people with big money want to make weapons. Computers come to seem really central as an explanation of reality because again IT makes big money and encourages a lot of people to view reality through a computational lens.

Personally, I think that any alien intelligence would have to follow a fairly convergent path. Intelligence or consciousness by definition (by our own best models of the process) would have to have that purpose of wanting control over its world. And control has to come via a knowing that is an interaction between general ideas and particular impressions (broad theories, precise measurements). So similar intellectual process, similar world, similar results.

This is of course a more Darwinian view of knowledge. You started out with a view of knowledge perhaps as a passive, abstract, objective, exercise - a dispassionate gods-eye view. But is any knowledge actually like that?

No, it is about constructing a model that relates to reality in a way that achieves some purpose (ie: control) and thus has a fitness criteria that allows evolutionary advance. Then you need the other ingredients of variety (individuals and groups making their haphazard best guesses) and a reason for differential survival (certain ideas getting funded and feted, the others being encouraged to wither and die ).

So when it comes to the "phase space of chemistry", we are striking out in a particular way, in search of the knowledge that maximises our control over chemical processes. The search is Darwinian in character - which is efficient. It does not rely on individual genius but collective blundering to advance. And I would expect the results to naturally fall into a powerlaw story of diminishing returns because we would begin with control over the "near at hand", the easiest pickings, and seek to achieve control over the increasingly complex or fine-grained.

 

[Kherubin]

Interesting.

From this perspective, apeiron, you see chemistry (and other sciences) as a Darwinian extension of biological evolution, stemming from a need to control.

That brings to mind two questions. The first is whether or not science can 'evolve' along non-Darwinian lines or with different selection pressures.

The second, which, admittedly, you have a good go at answering in your previous post, is whether biological (or cultural) evolution naturally produces intelligent creatures with a thirst for control. If we had evolved a more potent moral compass, or a broader, less selective perspective on what knowledge was valuable (i.e. minus the bias toward the profitable or powerful) would we have the same chemistry (or science) we have today? Indeed, if this had been the case, would we have risen to our current position 'in charge' of the planet?



Thanks epenguin.

but I wonder if it wouldn't be a lot more of the same thing?

In what regard would you consider it to be the same?

while engineering, including chemical synthesis and processes (chemical engineering etc,) is potentially infinite.

How does this infinite nature arise?



Thanks for your ideas,
Kherubin

 

[epenguin]

Thanks epenguin.


In what regard would you consider it to be the same?


How does this infinite nature arise?

I didn't say I am right or objective. I found organic chemistry at first fascinating - just the fact you could make these things imitating nature or producing something that was never in nature as far as we know. Found the main lines of types of compounds and syntheses interesting. At the end instead it seemed to pile up more of the same thing, maybe it was infinite but the interest of it did not seem to be. And chemistry in the last half-century hasn't been exactly the same cutting edge of science that biology or fundamental physics have. Maybe it is different if you are specialist discovering new ways.

So my second, contrary, point is the creative combinations of stuff, are sort of infinite. Like the relation of the limited number of kinds of brick and strut and the infinite possibilities of architecture and civil engineering. Anyway if it is finite we shall not see the end in our lifetimes. I should not say a word against chemistry which is already too neglected and mistreated, for any student starting career interested today, they should look into 'Green Chemistry' - surely a big and beneficent future.

 

[Kherubin]

Like the relation of the limited number of kinds of brick and strut and the infinite possibilities of architecture and civil engineering.

I have to confess, I am truly ignorant of these things but if the number of kinds of bricks is finite, isn't the number of possible buildings (certainly of any given size), while quite probably fantastically large from our perspective, also finite?


Thanks for your time,
Kherubin

 

[apeiron]

From this perspective, apeiron, you see chemistry (and other sciences) as a Darwinian extension of biological evolution, stemming from a need to control.

Not sure exactly what you mean here. But yes, the biological mind is in a modelling relationship with reality - it exists for the purpose of prediction and control. And then science and other forms of knowing are natural expansions on this.

That brings to mind two questions. The first is whether or not science can 'evolve' along non-Darwinian lines or with different selection pressures.

Again this is a little opaque. What is non-Darwinian? But if you are asking about whether there could be other biologies with radically different purposes and so different kinds of selection criteria, I think the argument is that all biology is entrained to the second law - entropification is its universal purpose.

But anyway, it seems clear enough that science is set up as a Darwinian competition of reality models. (And also that the result of all our scientific knowledge is an unparalleled success as an entropy producing species. )

The second, which, admittedly, you have a good go at answering in your previous post, is whether biological (or cultural) evolution naturally produces intelligent creatures with a thirst for control. If we had evolved a more potent moral compass, or a broader, less selective perspective on what knowledge was valuable (i.e. minus the bias toward the profitable or powerful) would we have the same chemistry (or science) we have today? Indeed, if this had been the case, would we have risen to our current position 'in charge' of the planet?

There you go. A biologist now just accepts that entropy production is what life and mind are all about. That is its higher purpose (even though it strikes people as a lowly ambition). Any other purpose would be unnatural.

OK, things are more complicated because humans have become also self-aware. They can appreciate they are mortal and also that their natural inclinations could lead to "bad outcomes" for the species, or the planet. So other selection criteria may be entering the picture.

Maybe Kurzweil, de Chardin and others are right. We are about to make some transition from entropy-based existence to some kind of information-based one. This could be a very "alien" thing compared to what we have been familiar with and could lead to some other selection criteria or purpose when it comes to modelling (perhaps more about creating worlds than just living in them).

It makes for pleasant science fiction if nothing else. And now I've half convinced myself there is something in the idea.

But if knowledge remains about control over the means of entropy production, then the best that can be said for humans and their science modelling is that they will get better at modelling (and believing) the long-term consequences of their actions rather than just acting short-term and evaporating the planet one way or the other.

Humans can still serve the second law by lasting a long time and in the end disposing of a greater overall quantity of entropy than we are likely to do going flat out in the crude way that we are presently.

OK. This is getting off-topic. But I think it is crucial to epistemology that there is a "natural" story on knowledge. There is a reason why we have ended up modelling reality in the style we have. And to do something else would be difficult. Against the grain. (Except unless we are moving towards an information-based existence where we do just end up sitting back, looking around, understanding in a contemplative non-consuming way.)

 

[Kherubin]

I apologize if I am being in anyway confusing.

To clarify some of my points:

Again this is a little opaque. What is non-Darwinian?

Your appraisal of science operating by Darwinian mechanisms seems very valid indeed. However, others forms of evolution have been conceived. In the context of our biology they appear incorrect, but possibly as a means of cultural (& scientific) evolution on some far-flung planet, they could be in operation.

For example, Lamarckism holds (and I am paraphrasing here, so please forgive me any evolutionary biologists out there) that any oft-used trait becomes stronger, while that which is not used withers and dies. Furthermore, these acquired traits can be passed down to further generations. It seems to me that this too could be a reasonable basis on which to build a science as opposed to the throw everything at it and see what sticks mentality of Darwinism.
These are the kinds of things I was referring to when talking about non-Darwinian.

different kinds of selection criteria

In this regard, I was actually considering cultural, not biological evolution. As an example, should an alien culture not generate the economic system that we have developed, it seems to me counter-intuitive to say that they would use 'funding' as a basis for which scientific avenues to pursue. Perhaps easing the suffering of their population or the oppression of other species would instead guide their science.

There is a reason why we have ended up modeling reality in the style we have. And to do something else would be difficult.

Sorry, but could you please clarify this point? What is the reason? To minimize the build-up of entropy in the short-term (& is this what you mean by control)?

Thanks,
Kherubin

 

[apeiron]

For example, Lamarckism holds (and I am paraphrasing here, so please forgive me any evolutionary biologists out there) that any oft-used trait becomes stronger, while that which is not used withers and dies. Furthermore, these acquired traits can be passed down to further generations. It seems to me that this too could be a reasonable basis on which to build a science as opposed to the throw everything at it and see what sticks mentality of Darwinism.

I get you. Habits that develop. That would seem more like a scholastic tradition where the elderly pass down their wisdom to pliable apprentices. And nothing much changes.

There are certainly cultures on Earth that have been both brilliant and yet not aggressively progressive. We could just contrast east vs west.

But then where two cultural styles exist, there is the potential for a competition which becomes Darwinian.

In this regard, I was actually considering cultural, not biological evolution. As an example, should an alien culture not generate the economic system that we have developed, it seems to me counter-intuitive to say that they would use 'funding' as a basis for which scientific avenues to pursue. Perhaps easing the suffering of their population or the oppression of other species would instead guide their science.

Societies are based on a balancing of competition and co-operation, so evolution would be a tuning of that balance. Go too much in either direction and societies would not be able to sustain themselves.

So on that basis, I would expect any alien society to share the same essential dynamic, but it could be set to a different balance (just like east and west?).

Sorry, but could you please clarify this point? What is the reason? To minimize the build-up of entropy in the short-term (& is this what you mean by control)?

Not to minimise but maximise entropy production.

See for example - http://www.lawofmaximumentropyproduction.com/

 

[Kherubin]

I would expect any alien society to share the same essential dynamic

Wouldn't it be interesting to have a society that gathered knowledge for knowledge's sake? I think then that you would have a culture that maximized the power-law trend that you originally spoke of and truly gathered all knowledge available to it at a given time.

See for example - http://www.lawofmaximumentropyproduction.com/

Thank you for the link apeiron. I apologize if I do not fully grasp it.

Didn't Erwin Schrodinger himself say, however, that life itself is built on negative entropy?

Furthermore, isn't this control you speak of as a goal of science an attempt to locally minimize entropy?


Trying to bring the thread slightly more back to topic, I am just interested to know how possible it is to produce an infinity of products from a finite number of constituent parts in a finite space.

 

[apeiron]

Didn't Erwin Schrodinger himself say, however, that life itself is built on negative entropy?

Furthermore, isn't this control you speak of as a goal of science an attempt to locally minimize entropy?

Schrodinger certainly did - and What is Life is a great book. But structure or negentropy arises because of its ability to produce heat or entropy. The balancing act for life is to generate entropy at a rate that does not blow its own structure apart. And then if a lot of living systems are in competition, then the one that gets closest to the edge is the winner.

Though, as in the battle between weeds and trees, today's winners can be tomorrow's losers.

Really here, we are talking about politics and economies. Science is just the means to their ends. So science is set up as a pure open-ended search for knowledge. But in practice it is locked into a technological quest for control over nature, the amplification of human actions in the world.

Trying to bring the thread slightly more back to topic, I am just interested to know how possible it is to produce an infinity of products from a finite number of constituent parts in a finite space.

This seems different to the OP to me.

But the question appears to be the same as that faced by biology itself. The genetic code uses only four bases and so only 64 three-base codons. Which in turn code for about 20 amino acids (with some redundancy) and a stop signal. Out of that you can spin an infinity of protein combinations if the size of the resulting proteins is unconstrained, or at least some very vast number of proteins if size is ultimately constrained (as it must be if the proteins have to be inside the cells they serve).

So the secret of life is that it can generate a huge space of possible proteins. Pretty much anything is out there waiting to be selected. And then is can explore this space by Darwinian search to make its selection.

Note the irony. By restricting greatly the choice of bases and codons - a rigid local constraint of just the same four bases and only three-base combination codons - you get a matching explosion in combinatorial possibility.

So atomising - creating a minimal collection of finite parts - is how you get a near infinite variety in the first place. Less becomes more. Local constraints generate global freedoms.

You seemed to think the two things might be contradictory when they are instead mutually necessary, or complementary and synergistic.

 

[Kherubin]

Thank you for the explanations apeiron. I think I better understand.

And then if a lot of living systems are in competition, then the one that gets closest to the edge is the winner.

Why is this the case? What does going 'close to the edge' allow you to do that being more restrained does not?

technological quest for control over nature

Isn't this an attempt to locally lower entropy? Or does it naturally fail through heat production?

This seems different to the OP to me.

I'm interested in what you thought the OP to be querying. What did you think I was asking about?

So atomising - creating a minimal collection of finite parts - is how you get a near infinite variety in the first place. Less becomes more. Local constraints generate global freedoms.

Surely, however, a larger, finite collection of parts expands massively the global freedom you have? A 4-base codon system with a concomitant expansion of the amino acid repertoire would massively expand the reach of biology.



Thank you for your patience,
Kherubin

 

[apeiron]

Why is this the case? What does going 'close to the edge' allow you to do that being more restrained does not?

Isn't this an attempt to locally lower entropy? Or does it naturally fail through heat production?

Clumsy fingers just erased a longer answer. So just a short reply now.

Dissipative structure theory is a little too complex and "under construction" to give you quick answers. Yes, there is a tension between efficiency and consumption. Early in lifecycles, growth is fast and low in constraints, later it slows down to become leaner, but also more brittle.

But as I say, there are a lot of views. If you are interested, these show the degree of the variety.

http://en.wikipedia.org/wiki/Extremal_principles_in_non-equilibrium_thermodynamics
http://ncatlab.org/johnbaez/show/Maximum+Principles
http://en.wikipedia.org/wiki/Non-equilibrium_thermodynamics#Entropy_in_evolving_systems

Surely, however, a larger, finite collection of parts expands massively the global freedom you have? A 4-base codon system with a concomitant expansion of the amino acid repertoire would massively expand the reach of biology.

Yes a possibility. And oh look, someone did it
http://bytesizebio.net/index.php/2010/02/17/codon-is-now-a-four-lettered-word/

As to why a triplet code, there has been plenty of speculation. I believe some have said a doublet code would be physically too cramped to hold the amino acids as they are being assembled into a chain. And so perhaps a quartet would leave them too far apart. Thermostability is a big issue too. Not sure if a quartet would flex too much to get the job done.

Anyway, the reasons are sure to be physical constraints that make three optimal as four would seem easy to evolve if it had some clear advantage.

 

[Kherubin]

Thanks again for the links.

This seems different to the OP to me.

Now I'm just really interested in what you thought the OP to be querying. What did you think I was asking about?


Kherubin

 

[apeiron]

Now I'm just really interested in what you thought the OP to be querying. What did you think I was asking about?

Is it true that "An infinite realm of possible substances corresponds to an infinite amount of possible knowledge that we not yet have."

And I replied that scale considerations mean that is also possible under this argument that the biggest discoveries might be the closest at hand.

 

[Kherubin]

Is it true that "An infinite realm of possible substances corresponds to an infinite amount of possible knowledge that we not yet have."

Is there a way in which this would not be the case? A case in which an infinite realm of possible substances leads to a finite amount of knowledge?


There may, however, be other limits. I think it quite probable that a 'selective' limit to our knowledge may exist in the form outlined by John D. Barrow in his book on the limits to science. The analogy he uses involves an infinite chain of 'boxes' containing information and is outlined below:

Another possibility is that we might have access to only one box in every ten of our never-ending line. Our exploration of Nature would then never be more than 10 per cent efficient, even though there would be no end to the number of things that we could discover. In this case, there are 'selective' limits to what we can know but not absolute ones. One can refine this picture even further. It would be possible for us to have an unending growth of knowledge which unveiled only an infinitesimal part of what could be known at that stage. If the unknowable things were densely packed like the collection of all decimal numbers (including unending ones) and what could be known was the collection of things labelled by the infinite list of whole numbers 1,2,3,4,5 . . . and so on, then we would always have missed finding an infinite number of things, even if we never missed any of the whole numbers in the list. This distinction between selective limitations on our ability to find out everything within some domain, like every variety of chemical molecule or every possible game of chess, and boundaries which we cannot cross, appears first in the writings of Immanuel Kant. -- The Limits of Science and the Science of Limits

What do you think?
Kherubin

 

[apeiron]

There may, however, be other limits. I think it quite probable that a 'selective' limit to our knowledge may exist in the form outlined by John D. Barrow in his book on the limits to science. The analogy he uses involves an infinite chain of 'boxes' containing information and is outlined below:

I think the analogy betrays a misunderstanding about the nature of modelling. Knowledge is not really a collection of discrete objects, data items, such as one could find in a series of closed boxes.

Instead what we are actually trying to do is extract general principles, general laws as the result of having made careful observations.

It would seem that the space of possible events to observe may be very large, but not infinite. Our visible universe contains only a finite amount of information, so that would be a physical limit on knowledge (but not a selective one).

And then how many laws or generalisations do we need to "model everything"? Maybe not even that many.

And certainly, our mental image of the search for these global principles should not be of objects hidden away in boxes over an unlimited array of locations. Instead, these principles have a size that spreads itself over varying extents of the domain of our ignorance. So the very large ones (like a Theory of Everything) would cover pretty much everything by definition.

So I don't think Barrow's approach decides anything here. It is the wrong kind of analogy right from the start.

 

[Kherubin]

Instead what we are actually trying to do is extract general principles, general laws as the result of having made careful observations.

I think that this is a very valid appraisal of the goals of physics, but it is far from a complete goal of science. Both chemistry and biology DO attempt to extract general principles (stoichiometic laws, laws of genetic inheritance) amidst a great deal of other things.

As Rutherford said:

"All science is either physics or stamp collecting"

But we should be careful lest we forget the importance of stamp collecting. A great deal of time is spent by chemists in discovering new compounds and by biologists in discovering new species. Isn't it fair to say that this type of knowledge too has a place alongside the generalization of observational and experimental discoveries?

It would seem that the space of possible events to observe may be very large, but not infinite. Our visible universe contains only a finite amount of information, so that would be a physical limit on knowledge (but not a selective one).

Certainly at any given time this is true. However, should our universe, in actuality, be infinite in extent and our light sphere continue to grow, the amount of knowledge available in this way would be infinite over an infinite stretch of time.

And then how many laws or generalisations do we need to "model everything"? Maybe not even that many.

Again, this only holds to a certain extent. I think that we would both agree that we are far from in a position to qualify just what 'everything' is. If any of the multiple multiverse hypotheses put forward ultimately prove to be true, then I think the notion of 'everything' becomes severely diminished if not meaningless, since our 'everything' simply becomes on of many.

And certainly, our mental image of the search for these global principles should not be of objects hidden away in boxes over an unlimited array of locations. Instead, these principles have a size that spreads itself over varying extents of the domain of our ignorance. So the very large ones (like a Theory of Everything) would cover pretty much everything by definition.

I certainly think that the analogy can stretch to cover differently-sized boxes without falling flat. In this regard, and I apologize if I am abusing the analogy somewhat, then a 'theory of everything' would simply be a larger box, which, through its sheer power, contains within it the explanation of a great many smaller boxes. That, however, is not to say that there could not be an unlimited number of boxes beyond it.

Is this fair or am I crazy (or both?),
Kherubin

 

[apeiron]

I think that this is a very valid appraisal of the goals of physics, but it is far from a complete goal of science. Both chemistry and biology DO attempt to extract general principles (stoichiometic laws, laws of genetic inheritance) amidst a great deal of other things.

All science seeks general principles the same as physics - it is how modelling works.

But we should be careful lest we forget the importance of stamp collecting. A great deal of time is spent by chemists in discovering new compounds and by biologists in discovering new species. Isn't it fair to say that this type of knowledge too has a place alongside the generalization of observational and experimental discoveries?

But does the discovery of another beetle species feel like an increase in meaning or just in information? Beyond a certain point, new instances are telling you nothing new. But I guess I could never get the point of stamp collecting

Certainly at any given time this is true. However, should our universe, in actuality, be infinite in extent and our light sphere continue to grow, the amount of knowledge available in this way would be infinite over an infinite stretch of time.

Good luck making use of knowledge at the heat death. And also dark energy suggests now that even at t=infinity, we don't get to everything sharing our light cone.

Again, this only holds to a certain extent. I think that we would both agree that we are far from in a position to qualify just what 'everything' is. If any of the multiple multiverse hypotheses put forward ultimately prove to be true, then I think the notion of 'everything' becomes severely diminished if not meaningless, since our 'everything' simply becomes on of many.

I haven't been arguing that we can know reality in any complete way. But on the other hand, I also find it amazing how well we are doing. So glass half full or half empty - depends what kind of guy you are.

I certainly think that the analogy can stretch to cover differently-sized boxes without falling flat. In this regard, and I apologize if I am abusing the analogy somewhat, then a 'theory of everything' would simply be a larger box, which, through its sheer power, contains within it the explanation of a great many smaller boxes. That, however, is not to say that there could not be an unlimited number of boxes beyond it.

Or rather, it would be the box that we are within? Indeed the biggest of the boxes we are within.

 

[Kherubin]

But does the discovery of another beetle species feel like an increase in meaning or just in information? Beyond a certain point, new instances are telling you nothing new. But I guess I could never get the point of stamp collecting

True enough, but any increase in information IS an increase in knowledge. Whether it has meaning or not is a subjective conclusion.

Good luck making use of knowledge at the heat death.

Call me an optimist, but I think that with trillions of years of supra-exponential technological evolution the heat death of the universe will be a positive 'walk in the park'.

And also dark energy suggests now that even at t=infinity, we don't get to everything sharing our light cone.

How so? I would be greatly obliged if you could explain. Due to accelerated expansion, at t=infinity, the expansion rate becomes so great as to be beyond our capacity to contain (or comprehend)?

I also find it amazing how well we are doing.

I concur. For a ragtag shambles of adolescent hairless apes on a planetary backwater, I don't think we're doing too badly at all.

Or rather, it would be the box that we are within? Indeed the biggest of the boxes we are within.

I think that together we have milked this analogy so much that I am starting to become claustrophobic .

 

[Kherubin]

I would like to know precisely what other people think it means for the SO(4,2)xSU(2) periodic table outline in the following link (http://www.springerlink.com/content/j303171428652143/fulltext.pdf) to have an a priori infinite number of elements.

The author decrees that the 'observable elements and/or particles correspond to only a few of the allowed quantum mechanical states'. What, therefore, do the other quantum mechanical states correspond to, elements or isotopes that we have not yet discovered, or states which are unachievable, in principle?

Thank you for your help,
Kherubin