studiot

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 ?

Since several people liked my comment, (Thank you all) , I will expand a little. The issue here reaches many parts of theoretical Mathematics, but one part goes to the heart of applications in Science. This is in probability theory and therefore in statistics and quantum mechanics. The probability of an event P(E) is defined as the limit of the relative frequency of that event as the number of trials tends to infinity. For instance consider rolling an n sided die. As the number of sides increases the number of different possible outcomes increases. As the number of possible outcomes increases so the probability of any given outcome (ie an event) decreases. So as n tends to infinity P(E) tends to zero. So we have the apparent paradox to resolve of how can we have a probability when we know that the die must end up showing one face or another, yet the probability of showing any one face is zero. In QM we resolve this by taking the probability between x and (x + δx) and taking a limit as δx tends to zero. In 'shut up and calculate ' mode we don't think about this we just do it and get 'the right answer'

This Zeno paradox is deeper than any of the others and was not properly answered for 150+ years after the others. The other Zeno paradoxes rely on sequences of integers and their reciprocals. This one relies on something deeper. The solution came after it became necessary to integrate many functions that could not be integrated by the Riemann integral, commonly taught in high school today. As you likely know, the Riemann integral is the sum of lots of small rectangles that make up the area under a curve. In fact it is the limit as the width of these rectangles ten to zero. But Zeno's question is what happens when that limit is reached ie the width is zero? The generalisation the the Riemann integral was introduced by Lebesgue (1875 - 1941) adn this ushered in what today is known as measure theory. https://en.wikipedia.org/wiki/Henri_Lebesgue The other approach to this issue was also developed in the first half of the 29th century by Paul Dirac and is known as the Dirac Delta function.

No, an engine will not run without it. An assembly as described without friction or any load will need at least an initial input of work (energy) to start. Thereafter it will continue in its state of motion as you describe.

I don't quite agree. Things are slightly more complicated than this. An ideal flywheel, crank and piston assembly by itself is a closed system. Yes. So it will continue its state of motion or rest indefinitely. But if you want to supply shaft work you require to input that energy somehow. And since some of the shaft work output of an IC engine goes to run absolutely necessary auxiliary devices, continuous energy input is required.

Another well balanced post. +1

You are mixing up thermodynamics and mechanics. No you do not need to put energy into a mass to start it moving. Stand under my window where the flower pots are and let me push one off the ledge. When it hits your head tell me how much energy I put into it. No the engine is not a closed system. Mass in the form of air/fuel mixture enters and echaust exists. It is known as a constant flow system or pseudo-closed since the same amount of mass exits as enters. But that entering mass brings (chemical) energy with it. So it is not an isolated system.The rising piston does work compressing the gas. The expanding gas then does work on the piston. Although work and energy have the same units and are different aspects of the same phenomen, there are subtle differences I suggest you look up. https://www.google.co.uk/search?q=difference+between+work+and+energy&source=hp&ei=3YPVYdboC43KgQbT-6qYCw&iflsig=ALs-wAMAAAAAYdWR7R2QBD6hUnxptAl9631h-LuTuAZn&ved=0ahUKEwiWy9faw5r1AhUNZcAKHdO9CrMQ4dUDCAg&uact=5&oq=difference+between+work+and+energy&gs_lcp=Cgdnd3Mtd2l6EAMyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEOgsIABCABBCxAxCDAToOCC4QgAQQsQMQxwEQowI6CAgAEIAEELEDOg4ILhCABBCxAxDHARDRAzoFCC4QgAQ6CAguELEDEIMBOgUIABCxAzoICC4QgAQQsQNQAFj8LmCSMmgAcAB4AYAB2ASIAdI6kgELNi45LjguMy41LjGYAQCgAQE&sclient=gws-wiz But +1 for accepting that you were not exactly correct before.

Yes that is true. So 1) There are numbers of no special consequence in Physics. That is there are parts of Mathematics that have no special meaning in Physics. 2) There are facts (numbers) in Physics which have special meaning that have no special meaning in Mathematics. Both leading to the conclusion that there is incomplete overlap between Mathematics and Physics. Is that not rational thinking ? OK I consider myself driven off the forum.

So What ?

What behaviour ? I said there are mathematically definable consequences. Would these consequences not be different if the value was ten times different ? Put into what ? Does the 'standard model ' predict the values of such numbers ? If so why bother to have them ? Why not just use the numbers themselves ?

+1 Where do you think this supposedly lost energy goes when the piston crown stops and then changes direction. Hint in order to stop it there must be a force and therefore there must be an equal and opposite reaction force on something else.

It is often forgotten that Physics abounds with data for which there is no theoretical basis or Law which states such and such 'must' have this or that value. A large amount of Professor Millikan's highly successful and readable book discusses the decades of impediment cause by a lack of knowledge of the value of e/m. Although we have now measured it and moved on, to this day we still can't demonstrate why it has this value and no other. Of course there is plenty of theory as to the consequences of this value. In fact pretty well every scientific equation and formula in existence contains such values ( mostly constants) which just are what they are and we have to measure them empirically. Physics, of course, is not the only Science where rational thinking holds sway. The description of crystal forms in granite given in Professor Swinnerton's delightful book is a masterpiece of rational thinking, without any Mathematics whatsoever in evidence.

It is worth noting that there are four pairs of North-South poles involved. 1) The N-S poles used for or coordinate systems eg Latitude and Longitude. 2) The N-S poles at the surface ends of the mechanical spin axis. 3) The geomagnetic N and S poles at the surface surface ends of the axis of an equivalent bar magnet, centred at the Earth's centre. 4) The magnetic N and S poles at the surface where the field lines are vertical. https://en.wikipedia.org/wiki/Geomagnetic_pole For most geological purposes, which is N and which is S make no difference. But for some including the weather and the aurora there will be differences. Life in general and particularly creatures however, will experience greater effects. Many creatures use some form of magnetic navigationand I believe even some plant life has magnetic orientation. Humans may experience some unexpected disruptions in addition. For instance the ground of electric power grids will be partially disrupted and may result in blackouts.

Thank you. That actually was a reference to a TV programme I saw about industrialised methods of growing tomatoes (and other veg), where they actually wish to exclude all creatures, other than human. So it was a reference to a Vegan world without any other creatures whatsoever.

A discussion with rancour. +1 If you are asking a question then clearly it is in your own interests to provide extra detail to those prepared to answer but needing to know more. Often their gift in knowing the subject better is knowing what questions to ask. If you are presenting a report on something eg in the scientific news section then the onus is on you to add sufficient summary to allow others to evaluate the subject presented. If you are presenting a hypothesis or conjecture, it is up to you to introduce such supporting material as may be needed, including answering questions or objections from the membership on the presented material. Material to introduce general discussion can be presented as a question or statement, either way, supporting background and explanation aids the discussion. Taking (or agreeing to take) one point at a time can be very productive.

Yes welcome, you have shown yourself to be a cogent thinker in whatever is your discipline. +1

+1 for a detailed explanation. I would like to add the following. Momentum will be accompanied by moment of momentum and momentum changes by (unwanted) torques. That is why, in the many arrangements that have been used including the one you proposed, the pistons are aranged to reciprocate about the driveshaft axis. Auto engines configurations and mountings have included the upright inline and transverse, the angled (between horizontal and vertical) inline and transverse, and the horizontally mounted 'flat' engines. Transverse mounting adds the requirements of changing the drive direction. Older aero piston engines went the whole hog with radially mounted multicylinder engines.