studiot

I think that 'cause' and 'scale' are extraneus parameters that do not bear upon 'emergence' or have at best only the loosest of connection to it.

I am not sure if I proposed an atom bomb explosion as an emergent phenomenon back along but the echange at 'critical mass' is such a change. (Just fancied a change from my arch as a conversation subject)

Testing in the UK is far more complicated that this and has been subject to different rules at different times throughout. Further the government has just announced that the lateral flow chromatography will now be accepted instead of PCR, for the political expediancy that it failed to provide suficient proper tests which are now being rationed. I say proper tests rather than PCR because up to 1/2 million health workers and 1.5 million social care workers are regularly using an alternative to PCR - a saliva test - as a matter of course several times a week. This is still a laboratory test but results are returned much more quickly. Also the UK has remained very open to travellers in and out during the whole pandemic. This has been 'controlled ?' by a PCR testing regime, more stringent than for the general population at large. Finally some employers have been funding their own worker testing regimes. However the tests are conducted, the results are all supposed to be reported to the government, though not everyone does so.

Thank you for the replies. There is another more worrying possibility that is the reason I posted. I note no one has replied to my comment. We had a long period of level or slowly declining cases, hospitalisations and deaths until 3 - 4 weeks ago. Too many thought that meant it was the beginning of the end and began to relax. Then the case rates skyrocketed, but the hospitilisations did not go up. 3 weeks ago I watched the hospitalsations go through the 6000 barrier. Deaths still steady at about 50 per day. Then hospitilisations started rising fast but deaths kept steady. Last week deaths started rising into the low hundreds. 3 days ago we had 1000 deaths and are now in the higher hundreds. Furthermore we now have several treatment drugs in use that were unavailable in the first two waves. Looking at the small amount of current data I wonder and fear that omicron simply takes longer to work it harm.

The question of cheating is as old as education itself. I do know that at least some universities have adopted methods of countering the latest wave via the internet either buying essays etc or just blatantly copying of the net. However I won't detail any to avoid this becoming a cheat recipe book for casual readers. Don't forget that the staff are also intellingent folks too. I will relate a different form of cheating from 50 something years ago. In my first year we did a lot of wet chemical analysis, using standard reagents prepared by the lab techs. One such session I couldn't get my titrations to work out. I chose to report my results as observed anyway. The following week, after marking (that took longer back then), almost everyone except myself was marked down for haveing fiddled their readings to get the correct (expected) results. I actually had appropriate results for the reagents actually supplied. The staff had deliberately mislabled them becuae they suspected dreading s were being doctored on a large scale

Thank you. I also realise another characteristic of emergence I haven't mentioned. If you some bricks, you can build some sort of structure, even if just a pile. But unless you have enough bricks you cannot build an arch. In other words, the emergent phenomenon only emerges when all the necessary precursors are in place. The change from no emergence to emergent is sudden. This is consistent with the link to Catastrophe theory I referred to earlier in the thread.

Here are today's UK figures from the BBC Note how the hospitilisation and then deaths lag behind the cases, but they are now catching up.

I haven't used it for a while but Redo-Backup is free (open source project) and works really well. https://sourceforge.net/projects/redobackup/ You make a byte by byte copy of the entire or part of the hard drive or chosen partition onto other media such as DVD/USBstick/Hard drive (spare) etc. Then the backup software copies the other way when needed and handles wiping and repartitioning you hard drive automatically. Unfortunately it won't do servers.

Wow ? Is this an example civility left over from your defunct forum ? You referenced the Stanford Encyclopedia of Philosophy, to which I pay a subscription.

Wow I'm completely blown away by this completely incorrect statement from a recognised authority. Wet, Wetting and Wetness and molecules are precisely defined terms in the physical sciences which arise from surface tension effects. Since ST arises from differential interactions between at least five molecules and wetting between at least two of these, ascribing any wetness to a single molecule is nonsense. Incidentally I prefer to use two words rather than strong and weak plus one word (which actually inefficiently makes three words to learn) for different concepts. So I use emergent and arising.

I didn't think of that. +1 There is a more detailed discussion here. I am not an expert on number theory, I find the minutiae rather boring after a while. https://math.stackexchange.com/questions/823970/is-i-irrational

Can't see why. e and pi are irrational (and also trancendental but that is irrelevant here). i and 1 and 0 are all rational. So proceed as follows [math]{e^{\pi i}} + 1 = 0[/math] Euler Rearrange [math]{e^{\pi i}} = - 1[/math] Raise each side to the power -i [math]{\left( {{e^{\pi i}}} \right)^{ - i}} = {\left( { - 1} \right)^{ - i}}[/math] Which is [math]\left( {{e^{ - i\pi i}}} \right) = {\left( { - 1} \right)^{ - i}}[/math] Which is [math]{e^\pi } = {\left( { - 1} \right)^{ - i}}[/math] Which is an irrational number raised to an irrational power expressed as a rational fraction of two rational numbers.

The Navier Stokes equations are readily derivable equations connecting perfectly well defined mathematical entities. However they are non linear and as such have only few known particular solutions in simple cases. We do not have a general solution, although the existence and uniqueness theorem suggests there must be one. That is why there is a prize offered for a general solution. Well I can't go with this definition, since it rules out my arch. But it is an interesting proposal and admittedly narrow. @joigus and I seem to be dancing around one characteristic that you have named 'novel'. Thank you for your explanation of that use of novel. I agree but suggest that by itself novel is too brief as others have read it differently. Your Nature article also acknowledges the problem of including a time factor in any definition. The one characteristic is the idea of a large number of parts/components/elements combining in some way to produce the emergent effect as a result. The Nature articles implies this can only happen with an infinite count. I hold that the number need not even be large, let alone infinite, although it could be. Going back to my arch consider the following thought experiment (which is actually possible in practice). Take a bunch of wooden bricks (I say wooden because ceramic ones could break during the experiment). Toss them up into the air to land in a jumbled heap. Sooner or later a few of these will land in the configuration of an imperfect arch. Further trials will bring better and better arches. So the 'emergence' of an arch configuration has a statistical dependance. The probability of a perfect arch is very small, one in a very large (perhaps infinite) number. Chemical reaction dynamics has a similar statistical dependence. The rate of a reaction product being formed depends upon the probabilities of the right configuration of the right molecules occurring. Unlike the arch, we do not know the right configuration or the right molecules for the formation of Life, so we cannot substantiate the hypothesis that Life is an emergent phenomenon that occurred this way. It is worth noting that in the case of the arch we know both the right elements and the right configuration so we can deliberately construct an arch, ie change the probabilities to approach certainty. So I would like to propose a modification to @Eise proposal that instead of saying it does not matter what the elements the phenomenon emerges from, to certain formative elements must be present and correctly configured, but it does not matter how they themselves arise or arrive.

Are you referring to euler's identity ? [math]{e^{\pi i}} + 1 \equiv 0[/math]

Developing the concept of necessary and sufficient sounds good to me. +1 A work in progress sounds good to me. +1 Good question worth exploring +1 irreducible ? out goes Joigus' reference to elements. Nor does my arch example fit. Unpredictable ? people have built weak arches but theya re predictable. Novel ? Arches have been around thousands of years. But perhaps arch action is not emergent. As I said it is difficult and I am not offerering a definition, just trying to help.

So by this definition a pile of broken egg or humpty dumpty shells or perhaps the ashes of a burnt letter are emergent phenomena. I think that tying down the concept is really difficult and that there are as many definitions as there are definers. Nevertheles it can be a useful concept. Thank you again for introducing the subject +1

I agree but my point is that I don't think your definition is enough to make a phenomenon special enogh to be called emergent. I agree that you may or may not know where the phenomenon arose or came from. My example with the light is just such. I see light. It could have come all the way from the furtherst star in the universe or the candle by my bedside, it doesn't matter. I don't atually need to know its source. But I don't call it an emergent phenomenon, just light. Yet it conforms to your definition quoted above. That is why I say your definition is too broad. Please also note it is a horse and cart or a horse and carriage ( both precursors of the abbreviation car) Sorry to hear about the covid problems in the Netherlands. We didn't make it to Leiden this season as we didn't last season either. My nephew and niece made it back there, don't know when or how they will be able to get back (to work) in the England. They did get a luxury BA flight for £20 though as no one wanted to go to Schipol before Christmas. On another tack entirely, I can udnerstand why people think perhaps Schrodinger leads to an emergent phenomenon. When we solve the equation we use (introduce) suitable boundary conditions and then find quantum numbers 'emerging' from the solutions in the form of values where the solution can be set to zero in a periodic fashion. I prefer to observe that this is common with many equations and nothing special at all. Consider the following much simpler equation x2 -4 = 0 therefore x is 2 (yes or minus 2) Now change this to x2 - 4 = 5 Now x is 3. Nothing special at all. Wouldanyone say the numbers 2 or 3 emerge from this ?

There is no paradox. As an engineer have you considered the work done moving the magnet ?

Whilst I agree with you about the QM and programming, there are many sorts of computer whose working do not depend upon QM. Some of these are purely mechanical from astrolabes and orrerys to slide rules, some are electrical, some elctromechanical, some fluidic. De Morgan can also be demonstrated with a variety of devices. I shan't tell him if you don't But no, I mean that I can tell when there is day and when there is night around me. I don't need to see or know the source of any light but I don't consider any light I do see to be 'emergent'. Pretty well everything in this universe had a beginning, a middle and an end but I don't consider that because everything came from something that went before it, it is therefore emergent.

The quality (not qualification) or characterisitc of being emergent applies to a phenomenon, not to an equation. However I think that since emergence only occurs in special circumstances, these special circumstances need be incorporated in any description or specification of an emergent phenomenon. As a for instance, my earlier example of arching action. Despite the antiquity of the arch, we do not have an 'equation' to this day that properly describes arch action, although we understand it. Furthermore arch action only occurs in particular circumstances.

Well I think it is neither unreasonable, nor unexplained. 'Unsuprising' would be theonly un-word I would choose. The whole issue reminds me of (I think it was Strange who first said it here) of the story of the puddle. The puddle who woke up sentient one morning and said to himself. "Wow look at that, this hole fits me so well, it must have been made for me!"

The existence and uniqueness theorems.

In my view no wave equation qualifies as emergent, as you have to know the wave variable to have the equation in the first place. I think you condition is too broad by itself, though it is an interesting approach. +1 I don't agree that the Gas Laws show any emergent features. I do strongly agree with your second example of 'clusters'. I expect you have done a lot of simulation theory. I am not sure about 'free will' and like you I don't know about time as emergent phenomenon. Back to your condition. I look around and sometimes see light and sometimes see darkness. I fail to class either of these as emergent, but by tour condition they would be. I walk along the street and see a fish lying there. I can't know how it got there so that would make it an emergent phenomenon. (This example is inspired by today's local news about a seal pup that walked into a bar in Bristol)

Yes probability and probability density are different. I have already defined probability. Probability is a non negative number less than or equal to 1. 'Probability density' is introduced to overcome the problem of division by zero, as with all densities. Probability density is a function.

What an excellent post. +1 And isn't 'regularity' a superb word since not only does it apply to so many different branches of Mathematics in some wya, but it is a general word that has not been hijacked by any discipline. Regularity appears algebra in Group theory, in geometry in polygons and other figures, in the solution of differential equations many of which are important in Physics such as Schroedinger, the Wave eqaution. May I suggest that electrons would be a better example than water molecules since H2O and D2O have some different physical properties ?